Crystal Structure and Selected Physical Properties of Ago, Agf2 and Agclx Phases Under High Pressure

University of Warsaw Faculty of Chemistry

Crystal structure and selected physical properties of AgO, AgF2 and AgClx phases under high pressure

Adam Grzelak

Doctoral dissertation developed in 2014 – 2018 at Laboratory of Technology of Novel Functional Materials under the supervision of Prof. Wojciech Grochala

Warsaw, June 2018

Acknowledgments First of all, I would like to thank my thesis supervisor Prof. Wojciech Grochala for assigning me an interesting and challenging topic of research, for valuable discussions, which allowed me to gain a deeper understanding of chemistry and physics, and for constantly presenting me with numerous opportunities, which enabled me to learn new skills that I hope to use in my future scientific endeavors. I am very grateful to Dr Viktor Struzhkin from Carnegie Insitution of Washington, who taught me the essential principles of high-pressure experiments, including preparation of DAC systems, sample loading and X-ray diffraction measurements using synchrotron sources. I would also like to thank Dr Maddury Somayazulu for his help with preparation of Ag/Cl systems under high pressure. In addition, I would like to thank Jakub Gawraczyński, with whom I performed and later analyzed results of many of those experiments. I would like to thank Dr Mariana Derzsi for performing theoretical calculations, which proved indispensable for understanding experimental results and provided insight into physical properties of materials studied in this work, as well as for teaching me the technicalities of density functional theory calculations. I would like to express my gratitude to all members of Laboratory of Technology of Novel Functional Materials for creating a positive and encouraging working environment. I would especially like to acknowledge contributions from the following members of LTNFM: - Dr Tomasz Jaroń for his guidance through experimental details of high-pressure electrical resistance measurements; - Dr Dominik Kurzydłowski for valuable discussions, helpful comments and sharing resources and knowledge about chemistry of transition metal compounds; - Dr Piotr Leszczyński for the help with finding essential literature; - Fellow PhD students Jakub Gawraczyński, Agnieszka Starobrat, Rafał Owarzany, Wojciech Wegner and Piotr Orłowski for the shared experience of becoming a scientist and for their friendship extending well beyond work hours.

I would like to thank my Mother for her continued support during my doctoral studies, without which I would not have been able to finish this work. I am also grateful to all my friends and family for supporting and motivating me throughout the writing process.

Financial contributions Studies presented in this work were funded by the following sources:

 “HP” project from Polish National Science Center (NCN), grant no. 2012/06/M/ ST5/00344, led by Prof. Wojciech Grochala

 Research program no. P1-0045 Inorganic Chemistry and Technology from Slovenian Research Agency (ARRS), led by Dr Zoran Mazej

 Calculations performed by Dr Mariana Derzsi were carried out using ADVANCE-PLUS supercomputer under grant no. GA67-13 at Interdisciplinary Center for Mathematical and Computational Modelling (ICM), led by Prof. Wojciech Grochala

 X-ray diffraction studies were performed using two Advanced Photon Source facilities (a U.S. Department of Energy (DOE) Office of Science User Facility, operated for the DOE Office of Science by ANL under Contract DE-AC02-06CH11357) at Argonne National Laboratory: o GSECARS (sector 13), supported by the National Science Foundation (NSF), Earth Sciences (Grant EAR-1128799), and Department of Energy (DOE), GeoSciences (Grant DE-FG02-94ER14466) o HPCAT (sector 16), supported by DOE-NNSA under Award DE-NA0001974 and DOE-BES under Award No. DE- FG02-99ER45775, with partial instrumentation funding by the NSF

 Electrical resistance measurements of compressed samples of AgF2 were carried out as part of a DSM project funded by the Polish Ministry of Science, grant no. 501-D112-86- DSM-115100, led by myself

Contents

(EN) Abstract ...... 1 (PL) Streszczenie pracy ...... 3 (EN) Introduction ...... 5 (PL) Wprowadzenie ...... 7 (EN) Goals of this work ...... 9 (PL) Cele pracy ...... 11 Literature review...... 13 1. Introductory notes on several physical phenomena in solids ...... 13 1.1. Types of magnetic ordering...... 13 1.2. Jahn-Teller effect...... 15 1.3. Mott and charge-transfer insulators...... 17 2. High pressure science ...... 18 2.1. Historical notes ...... 18 2.2. Physical chemistry at high pressures ...... 20 2.3. Jahn-Teller effect at high pressure ...... 23 3. Chemistry of silver and its compounds ...... 25 3.1. Silver ...... 25 3.2. Chemical properties of silver ...... 26 3.3. Chemistry of silver(II) ...... 27 3.3.1. Silver(II) fluorides ...... 28 3.3.2. Other silver-fluorine systems ...... 34 3.3.3. Silver(II) compounds – beyond fluorides ...... 36 3.4. Silver-oxygen systems ...... 40

3.5. Hypothetical AgClx compounds ...... 47 4. Overview of relevant analogous compounds and their high pressure behavior ...... 49 4.1. High-pressure behavior of transition metal monoxides ...... 49 4.2. High-pressure behavior of mixed-valence compounds ...... 58 4.3. High-pressure behavior of transition metal difluorides ...... 65 4.4. High-pressure behavior of silver compounds...... 71 5. Overview of experimental methods ...... 74 5.1. The diamond anvil cell ...... 74 5.2. X-ray diffraction ...... 77 5.3. Electron transport properties ...... 83 Experimental results ...... 87 6. Silver(I,III) oxide AgO ...... 87 6.1. Powder X-ray diffraction studies of compressed AgO ...... 87 6.1.1. Experimental procedures ...... 87 6.1.2. Preliminary analysis of powder XRD patterns ...... 88 6.1.3. High pressure behavior of LP-AgO ...... 91 iii

6.2. Pressure-induced phase transitions of AgO as determined by powder XRD and theoretical methods ...... 95 6.2.1. LP to HP transition ...... 95 6.2.2. Crystal structure and high pressure behavior of HP-AgO ...... 97 6.2.3. HP1 to HP2 transition ...... 102 6.2.4. Local coordination of Ag atoms in LP and HP phases ...... 104 6.3. Properties of high-pressure polymorphic forms of AgO – insight from theoretical calculations ...... 106 6.3.1. Details of DFT calculations ...... 106 6.3.2. Dynamic instability of LP-AgO at high pressures ...... 106 6.3.3. Electronic structure of AgO at high pressures ...... 108

7. Silver(II) fluoride AgF2 ...... 110

7.1. Powder X-ray diffraction of compressed AgF2 and reference AgF ...... 110 7.1.1. Experimental methods ...... 110

7.1.2. Powder XRD patterns of AgF2 at high pressure ...... 112

7.2. High pressure polymorphism of AgF2 and relations to common structural polytypes ...... 114 7.2.1. HP1 form: a unique example of non-centrosymmetric layered structure of a transition metal compound ...... 114 7.2.2. HP2 form: a unique example of nanotubular structure of a binary transition metal compound ...... 119

7.2.3. Structural relationship between AgF2 polymorphs and comparison to known MX2 polytypes ...... 124

7.2.4. Compressibility of AgF2 polymorphs and pressure dependence of their crystal parameters ...... 127

7.3. Magnetic and electric properties of compressed AgF2 ...... 134 7.3.1. Theoretical description of magnetic and electronic properties of compressed AgF2 ...... 134

8. Higher chlorides of silver - AgClx ...... 136 8.1. Preliminary Raman spectroscopy studies on compressed Ag/Cl systems ...... 136 (EN) Summary of experimental findings ...... 141 (PL) Podsumowanie uzyskanych wyników ...... 144 (EN) Prospects of future research ...... 147 (PL) Perspektywy dalszych badań ...... 149 Appendices ...... 151 Appendix A: Gold equation of state parameters and pressure dependence of lattice constants of neon and tungsten in AgO XRD studies ...... 151 Appendix B: Equation of state parameters of AgO phases – experiment and theory ...... 153 Appendix C: Equation of state parameters of AgF ...... 154

Appendix D: High-pressure resistance measurements of AgF2 ...... 155 List of research papers with results from this work ...... 158 References ...... 159

(EN) Abstract

In this work, high-pressure studies on three silver-containing chemical systems – silver(I,III) oxide AgO, silver(II) fluoride AgF2 and Ag-Cl2 system – are reported. AgO is an important constituent of silver oxide batteries and an example of a relatively small class of mixed- valence binary compounds. AgF2 is a prototypical compound of silver(II) and a parent compound of fluoroargentates(II), which have for some time been investigated as a possible precursor towards a novel class of high-temperature superconductors. Both AgO and AgF2 were studied by means of X-ray diffraction under high pressure, and the discussion of experimental results is complemented by theoretical calculations performed by Dr hab. Mariana Derzsi, which proved crucial in determining their crystal structures and have provided insight into their physical properties at those conditions. Compressed AgO and AgF2 were also investigated by Jakub Gawraczyński using Raman spectroscopy, and his results corroborated the findings of this work, as discussed in his doctoral thesis. In addition, electrical resistance of AgF2 was measured as a function of pressure and temperature. The Ag-Cl2 system was studied mostly by means of Raman spectroscopy.

The first five chapters provide a theoretical background for understanding experimental results described in chapters 6-8. Chapter 1 introduces several important concepts of solid state physics. Chapter 2 is an overview of high pressure science, including historical developments, and with particular focus on physical chemistry and Jahn-Teller effect under high pressure. The next chapter deals with chemistry of silver, focusing especially on compounds containing silver at oxidation state +2 and on binary silver oxides. Chapter 4 summarizes the current state of knowledge on high-pressure behavior of several classes of compounds relevant for this work: monoxides and difluorides of transition metals, mixed-valence compounds, and silver compounds in general. Chapter 5 describes principles of operation and practical aspects of experimental methods and tools used in this work: the diamond anvil cell, X-ray diffraction, and four-probe electrical resistance measurements.

Chapter 6 reports two new high-pressure structures of AgO. A first-order phase transition between 16.1 and 19.7 GPa leads to a structure with increased coordination number of Ag(I) compared to that found at ambient pressure, i.e. from 2 to 8. Another, second-order phase transition at ca. 40 GPa is associated with an increase of symmetry, but without any major structural change. A non-trivial pressure dependence of band gap of AgO hints at a complex interplay of several factors which determine the energy barrier for inter-valence charge transfer.

In chapter 7, crystal structures of AgF2 in the pressure range up to ca. 40 GPa are described. At ca. 7 GPa, AgF2 transforms into a non-centrosymmetric structure via a slight rearrangement of metal sublattice. The new polymorph retains the layered structure of ambient- pressure AgF2, but the slight displacement of Ag atoms and concomitant disappearance of inversion center can be expected to lead to very different (and desirable) physical properties, such as multiferroicity. At ca. 15 GPa, a first-order phase transition leads to a unique nanotubular polymorph, which exhibits strongly anisotropic compressibility and unusually short Ag-Ag distances. This is the first instance of a nanotubular structure reported for a metal fluoride.

Though structures of both high-pressure polymorphs of AgF2 are unprecedented, it can be shown that they are in fact related to known polytypes of transition metal difluorides via Jahn-Teller effect-driven distortions of anionic sublattice. In addition, an unsuccessful attempt at measuring electrical resistance of AgF2 as a function of pressure is described in appendix D.

Chapter 8 reports preliminary attempts at synthesizing new chlorides of silver at high pressure. Samples of Ag+Cl2 and AgCl+Cl2 were compressed and heated with infrared laser, and the resulting systems were studied using Raman spectroscopy. Though the results of these experiments do not allow drawing any definite conclusions, appearance of new Raman bands and a change of color induced by heating the sample at high pressure suggests possible formation of new, hitherto unknown compounds of silver and chlorine.

(PL) Streszczenie pracy

Niniejsza praca opisuje wysokociśnieniowe badania trzech układów zawierających srebro: tlenku srebra(I,III) AgO, fluorku srebra(II) AgF2 oraz układu srebro-chlor Ag-Cl2. AgO wchodzi w skład ogniw srebrowo-cynkowych i jest ważnym przedstawicielem stosunkowo wąskiej grupy związków dwuskładnikowych o mieszanej walencyjności. AgF2 jest z kolei prototypowym związkiem srebra(II), zaś jego pochodne – fluorosrebrzany(II) – są obecnie badane jako potencjalne prekursory nowego typu nadprzewodników wysokotemperaturowych.

Zarówno AgO, jak i AgF2 zanalizowano w niniejszej pracy za pomocą dyfrakcji rentgenowskiej pod wysokim ciśnieniem. Interpretacja danych eksperymentalnych została uzupełniona wynikami obliczeń teoretycznych wykonanych przez dr hab. Marianę Derzsi. Obliczenia te okazały się kluczowe dla rozwiązania wysokociśnieniowych struktur krystalicznych obu związków i umożliwiły zrozumienie ich właściwości fizycznych w tych warunkach. Poddane działaniu wysokiego ciśnienia AgO i AgF2 były również przedmiotem badań z użyciem spektroskopii ramanowskiej, a wyniki tych eksperymentów, przedstawione w rozprawie doktorskiej Jakuba Gawraczyńskiego, stanowią potwierdzenie wniosków zaprezentowanych w niniejszej pracy. Ponadto podjęto próby pomiarów oporności AgF2 w funkcji ciśnienia i temperatury. Układ Ag-Cl2 zbadano z użyciem spektroskopii ramanowskiej.

Pierwsze pięć rozdziałów stanowi teoretyczny wstęp umożliwiający lepsze zrozumienie i zapewniający kontekst dla wyników eksperymentów opisanych w rozdziałach 6-8. Rozdział 1 pokrótce wprowadza kilka niezbędnych pojęć z zakresu fizyki ciała stałego. Rozdział 2 to ogólny przegląd różnych gałęzi nauki związanych z wysokim ciśnieniem, z uwzględnieniem ich historii i ze szczególnym naciskiem na chemię fizyczną oraz efekt Jahna-Tellera pod wysokim ciśnieniem. Kolejny rozdział opisuje wybrane zagadnienia z zakresu chemii srebra, w szczególności związki zawierające srebro na stopniu utlenienia +2 oraz dwuskładnikowe związki srebra i tlenu. Rozdział 4 podsumowuje obecny stan wiedzy na temat wysokociśnieniowych właściwości kilku grup związków, istotnych z punktu widzenia niniejszej pracy: tlenków i difluorków metali przejściowych, związków o mieszanej walencyjności oraz związków srebra. Rozdział 5 skupia się na podstawach działania oraz praktycznych aspektach zastosowania aparatury i metod eksperymentalnych użytych w niniejszej pracy: kowadeł diamentowych, dyfrakcji rentgenowskiej oraz czteroelektrodowych pomiarów oporności.

Rozdział 6 opisuje dwie nowe struktury wysokociśnieniowe AgO. W zakresie ciśnienia 16,1-19,7 GPa zachodzi przejście fazowe pierwszego rodzaju, które prowadzi do struktury o liczbie koordynacyjnej atomów srebra(I) zwiększonej do 8, w stosunku do 2 pod ciśnieniem

3 atmosferycznym. Kolejne przejście fazowe, tym razem drugiego rodzaju, wykryto ok. 40 GPa – wiąże się ono ze zwiększeniem symetrii, ale bez zasadniczych zmian strukturalnych. Nietrywialna zależność przerwy energetycznej AgO od ciśnienia wskazuje na stosunkowo złożone oddziaływanie wielu czynników wpływających na barierę energetyczną przeniesienia ładunku między stanami walencyjnymi srebra.

W rozdziale 7 opisano struktury krystaliczne AgF2 w zakresie ciśnienia od 5 do ok. 40 GPa. W wyniku stosunkowo niewielkiej reorganizacji atomów w podsieci metalu pod ciśnieniem ok. 7 GPa AgF2 przyjmuje strukturę pozbawioną środka symetrii. Struktura tak powstałej odmiany polimorficznej jest bardzo podobna do warstwowej struktury AgF2 pod ciśnieniem atmosferycznym, ale przemieszczenie atomów Ag prowadzi do zaniku środka symetrii, co najprawdopodobniej wiąże się z nowymi (i poszukiwanymi współcześnie) właściwościami fizycznymi, takimi jak multiferroizm. Pod ciśnieniem ok. 15 GPa kolejne przejście fazowe (pierwszego rodzaju) prowadzi do odmiany polimorficznej o unikatowej, nanorurkowej strukturze, która charakteryzuje się silnie anizotropową ściśliwością oraz wyjątkowo krótkimi odległościami między atomami srebra. Jest to pierwszy przypadek struktury typu nanorurki w układzie fluorku metalu. Chociaż struktury obu wysokociśnieniowych odmian AgF2 nie zostały dotychczas zaobserwowane w innych związkach, można dowieść, że są one de facto związane ze znanymi typami strukturalnymi fluorków metali przejściowych poprzez deformację podsieci anionów wywołaną działaniem efektu Jahna-Tellera. Dodatkowo, aneks D opisuje nieudaną próbę pomiaru oporności AgF2 w funkcji ciśnienia i temperatury.

Rozdział 8 przedstawia wstępne próby syntezy nowych chlorków srebra pod wysokim ciśnieniem. Próbki Ag+Cl2 oraz AgCl+Cl2 zostały skompresowane i ogrzane z użyciem lasera podczerwonego, a otrzymane układy zbadane za pomocą spektroskopii ramanowskiej. Chociaż wyniki tych eksperymentów nie pozwalają na wyciągnięcie definitywnych wniosków, pojawienie się nowych pasm w widmach ramanowskich oraz zmiana koloru próbki wywołana ogrzewaniem laserowym pod wysokim ciśnieniem sugerują powstawanie nowych, nieznanych dotychczas związków srebra i chloru.

(EN) Introduction

Silver is one of only several elements known to humanity since ancient times. This availability is largely due to its high resistance to oxidation, which means it can be found in native form, i.e. as a pure metal – contrary to most other metals, which have to be extracted from their ores. Despite this relative chemical inertness, a plethora of compounds of silver are known. Most of them feature silver(I) cations, and some of those have found applications in diverse fields, e.g. in photography as photosensitive materials, in medicine as antiseptic agents and, more recently, as superionic conductors – new solid materials that resemble liquid electrolytes in terms of electrical conductivity.

In recent years, the attention of chemists and physicists has shifted more towards higher oxidation states of silver, particularly +2. While silver(I) cation, with its closed-subshell d10 configuration, resembles to some extent cations of main group metals, compounds of silver(II) can exhibit properties more characteristic to other transition metal compounds, such as magnetic ordering of unpaired electron spins, Jahn-Teller effect, which lowers the symmetry of complexes and crystal structures, and many other. Specifically, silver is analogous to copper in terms of electron configuration and thus Ag(II) cations have the same d9 valence electron count as Cu(II). This is important, because copper(II) oxides (oxocuprates) are precursor compounds to an extremely important class of materials: high-temperature superconductors. Currently, they are the only group of compounds that exhibit superconductivity above the boiling point of nitrogen at ambient pressure.

Finding new high-Tc superconductors is one of the most important goals of modern materials science; however, there is no unified theory describing their properties, which would allow predicting new compounds of this type. It is widely believed that strong vibronic coupling and strong antiferromagnetic interactions are crucial to the emergence of superconductivity. As it turns out, silver(II) fluorides are similar to copper(II) oxides in those respects, because both are characterized by a relatively small energy difference between valence orbital levels of respective metal and ligand atoms. This leads to largely covalent character of chemical bonding and strong magnetic interactions via a mechanism referred to as superexchange. Therefore, silver(II) fluorides constitute a very promising area of study. Silver oxides, due to their analogy to aforementioned copper oxides, are also worth investigating. However, the compound of silver directly analogous to CuO – AgO – is not a genuine silver(II) oxide, but a disproportionated (mixed-valent) silver(I,III) oxide. Consequently, crystal structures of the two compounds are completely different. Also, contrary to

5 oxocuprates(II), where the valence band of Cu(II) lies slightly higher in energy than the valence band of oxygen anion, the analogous bands of Ag(II) and (even more so) Ag(III) lie below the oxygen band, which leads to the formation of holes in the oxide band. Because of that, higher oxides of silver are thermally unstable to varying extent.

In this work, two known compounds of silver – silver(I,III) oxide AgO and silver(II) fluoride AgF2 – have been subjected to pressure of tens of gigapascals (hundreds of thousands of atmospheres). Studies of high-pressure behavior of elements and compounds can provide a better understanding of factors determining their crystal structures and properties. High pressure science has been developing rapidly over the past several decades, and many substances have already been surveyed in a wide range of pressure (often exceeding millions of atmospheres). The field has arguably been dominated by geologists and physicists, who have been interested in learning the structure of matter in deeper parts of planets or stars, or to explore how increasing pressure affects properties such as electrical conductivity, magnetism, mechanical strength and many others. However, information on crystal structure and physical properties of materials under high pressure can also provide insight into the nature of chemical bonding in studied substances, which can be extremely useful to a chemist, and also from the point of view of designing new functional materials. In addition, applying high pressure can lead to formation of new materials with interesting properties, some of which could, in principle, be “quenched”, i.e. decompressed to ambient conditions while retaining their high pressure form.

In a way, research described in this work has been done at a crossroads of two branches of science that are seemingly unrelated: chemistry of silver and high pressures. However, relatively few high-pressure studies with very reactive chemical compounds – such as those of silver(II) – have been carried out to this day. Therefore, the relevance of this work is twofold: gaining new insight about crystal structures and physical properties of silver compounds at elevated pressures, and application of high-pressure experimental techniques for studying substances of exceptional chemical reactivity under such conditions.

(PL) Wprowadzenie

Srebro jest jednym z zaledwie kilku pierwiastków znanych ludzkości od czasów starożytnych. Jego dostępność w formie pierwiastkowej jest głównie związana z wysoką odpornością na utlenianie, dzięki czemu może ono występować w formie rodzimej, tj. jako metal – w przeciwieństwie do większości innych metali, które otrzymuje się z rud. Pomimo tej stosunkowej obojętności chemicznej srebra, znanych jest bardzo wiele jego związków. Większość z nich zawiera kation srebra(I); niektóre z nich znalazły zastosowanie w różnorodnych dziedzinach, takich jak fotografia analogowa (materiały światłoczułe), w medycynie (środki antyseptyczne) oraz, w ostatnim czasie, jako elektrolity stałe – nowe materiały przypominające swoim stosunkowo wysokim przewodnictwem elektrycznym roztwory elektrolitów.

Coraz większym zainteresowaniem naukowców w ostatnich latach cieszą się jednak wyższe stopnie utlenienia srebra, w szczególności +2. Podczas gdy kation srebra(I), o konfiguracji elektronowej d10 (całkowicie wypełniona podpowłoka d), w pewnym stopniu przypomina kationy metali grup głównych, związki srebra(II) mogą wykazywać właściwości typowe dla związków innych metali przejściowych, takie jak porządkowanie magnetyczne niesparowanych spinów elektronowych, efekt Jahna-Tellera obniżający symetrię układów kompleksowych, i wiele innych. Konfiguracja elektronowa srebra jest analogiczna do miedzi, a zatem kationy Ag(II) mają tyle samo elektronów walencyjnych (d9), co Cu(II). Jest to o tyle istotne, że tlenki miedzi(II) są prekursorami niezwykle ważnej grupy materiałów: nadprzewodników wysokotemperaturowych. Pochodne tlenków miedzi to obecnie jedyna znana grupa związków wykazujących nadprzewodnictwo w zakresie powyżej temperatury wrzenia azotu pod ciśnieniem atmosferycznym.

Poszukiwanie nowych nadprzewodników o wysokiej temperaturze krytycznej to jedno z najistotniejszych zadań współczesnej chemii i fizyki materiałów. Nie istnieje jednak obecnie żaden ogólny model opisujący ich właściwości, co utrudnia przewidywanie istnienia nowych związków tego typu. Uważa się jednak, że silne sprzężenie wibronowe oraz silne oddziaływania antyferromagnetyczne są niezbędne dla zaistnienia nadprzewodnictwa. W tym sensie fluorki srebra(II) są podobne do tlenków miedzi(II), gdyż obie grupy związków charakteryzują się niewielką różnicą energii między poziomami walencyjnymi metalu oraz ligandów wchodzących w ich skład. W rezultacie charakter wiązania chemicznego w tych związkach jest w dużej mierze kowalencyjny, co z kolei prowadzi do silnych oddziaływań magnetycznych poprzez mechanizm nadwymiany. Z tego powodu fluorki srebra(II) są obiecującym obiektem badań.

Tlenki srebra, z powodu wspomnianej analogii srebra i miedzi, również stanowią istotną grupę związków. Bezpośredni analog CuO – AgO – w istocie nie jest jednak tlenkiem srebra(II), lecz zdysproporcjonowanym tlenkiem srebra(I,III), a zatem związkiem o mieszanej walencyjności. Z tego powodu struktury krystaliczne obu związków są zupełnie różne. Ponadto, w przeciwieństwie do tlenków miedzi, w których pasmo przewodnictwa znajduje się nieco powyżej pasma walencyjnego anionu tlenkowego na skali energii, analogiczne pasmo dla Ag(II) oraz (tym bardziej) Ag(III) leży poniżej pasma tlenu, co prowadzi do powstania dziur w paśmie tlenkowym. Na skutek tego wyższe tlenki srebra są – w mniejszym lub większym stopniu – niestabilne termicznie.

W niniejszej pracy poddano analizie dwa związki srebra – tlenek srebra(I,III) AgO oraz fluorek srebra(II) AgF2 – w warunkach ciśnienia rzędu dziesiątek gigapaskali (setek tysięcy atmosfer). Wysokociśnieniowe badania pierwiastków i związków chemicznych umożliwiają lepsze zrozumienie czynników decydujących o ich strukturach krystalicznych oraz właściwościach. Gałęzie nauki związane z wysokim ciśnieniem znacząco rozwinęły się w ciągu ostatnich dziesięcioleci, a wiele znanych substancji zbadano już w szerokim zakresie ciśnienia (nierzadko przekraczającym milion atmosfer). Jest to głównie przedmiot zainteresowania takich dziedzin nauki jak geologia czy fizyka, których celem jest m.in. poznanie struktury materii w głębi planet czy gwiazd lub badania nad wpływem ciśnienia na właściwości fizyczne takie jak przewodnictwo elektryczne, magnetyzm, odporność mechaniczna itp. Warto jednak zauważyć, że informacje na temat struktury krystalicznej i właściwości fizycznych pod wysokim ciśnieniem mogą także ułatwić zrozumienie charakteru wiązań chemicznych w badanych substancjach, co jest interesujące z chemicznego punktu widzenia, jak również cenne dla projektowania nowych materiałów. Wysokie ciśnienie można również stosować do otrzymywania materiałów o nowych, interesujących właściwościach. Niektóre z tak otrzymanych substancji można, przynajmniej w teorii, zdekompresować do warunków atmosferycznych z zachowaniem ich wysokociśnieniowej formy i właściwości (ang. „quenching”).

Wyniki przedstawione w niniejszej pracy są owocem badań na pograniczu dwóch pozornie niezwiązanych ze sobą gałęzi nauki: chemii srebra oraz wysokiego ciśnienia. Dotychczas stosunkowo niewiele reaktywnych chemicznie substancji – których przykładem są związki srebra(II) – przeanalizowano w warunkach wysokiego ciśnienia. Naukowa wartość tej pracy jest zatem dwojaka: poznanie struktur krystalicznych i właściwości fizycznych związków srebra pod wysokim ciśnieniem, oraz zastosowanie wysokociśnieniowych technik eksperymentalnych do analizy wyjątkowo reaktywnych chemicznie próbek w tych warunkach.

(EN) Goals of this work

This work is part of a broader investigation of silver compounds as potential precursors for novel high-temperature superconductors, motivated by several crucial similarities they share with compounds of copper. In particular, there have been certain promising theoretical 1–3 4,5 predictions in the literature regarding high-pressure behavior of AgO and AgF2, as well as 6 the existence of hypothetical silver(II) chloride AgCl2. The main goal of research reported here was experimental verification of those predictions.

AgF2 is a parent compound of fluoroargentates(II), which are considered to be analogous to oxocuprates(II):7 a pronounced Jahn-Teller effect, leading to elongation of axial metal-ligand bonds, strong antiferromagnetic interactions realized through covalent bonds via a superexchange mechanism, and a layered structure make the two groups of compounds somewhat similar.

However, layers in the crystal structure of AgF2 are puckered and the Ag-F-Ag bonds connecting silver atoms are bent, which leads to a weaker magnetic coupling than in oxocuprates(II), where the analogous Cu-O-Cu bonds are linear. A theoretical study exploring alternative crystal structures of AgF2 has suggested that an system of flat layers may be stabilized under high pressure.4 In such arrangement, antiferromagnetic interaction would also be greatly enhanced.5 5 Ultimately, at 38 GPa AgF2 has been predicted to become metallic. This work has attempted to verify whether compression of AgF2 would indeed lead to such changes in its crystal structure and properties. In addition, high-pressure resistance measurements will help determine how pressure-induced phase transitions in AgF2 – whatever they may be – affect the electronic band gap of this compound.

AgO, though nominally a compound of silver(II), is in fact disproportionated and contains Ag(I) and Ag(III) cations in 1:1 ratio. The mixed-valent nature of this compound can be traced back to a pronounced Jahn-Teller distortion characteristic of a system containing d9 Ag(II) cations, which coupled to a charge-density wave leads to the presence of two distinct valence states of silver instead of one.8 There have been several contradictory predictions regarding its high pressure behavior. One of those works has concluded that AgO should become a low- density-of-states metal above 45 GPa and undergo a phase transition into a less symmetrical polymorph.1 Other authors have predicted a transition at 75 GPa leading to a comproportionated state – a genuine silver(II) oxide,2 although these results were later shown to be based on flawed calculation methods.3 Experimental data collected and analyzed during preparation of this thesis should provide information about the influence of pressure on crystal structure of AgO and valence state of silver in this compound.

Lastly, mixtures of silver and chlorine were investigated in the hope of synthesizing new, hitherto unknown AgClx compounds. Only one – silver(I) chloride AgCl – is currently known, but earlier theoretical analyses have suggested that a hypothetical silver(II) chloride AgCl2 could 6 also be stable at temperatures below 286 K or, alternatively, at high pressures. If obtained, AgCl2 would very likely be characterized by strongly covalent Ag-Cl bonding, which could in turn, under proper structural geometry, lead to very strong antiferromagnetic interactions, which are thought to be one of the prerequisites for high-Tc superconductivity. There are several other, no less interesting, possible outcomes of reaction between Ag and Cl2 at extreme conditions, such 9 as formation of polychlorides, analogous to e.g. NaCl3. Experiments reported in this work were meant to explore the possibility of formation of new silver chlorides.

(PL) Cele pracy

Niniejsza praca jest częścią zakrojonych na szeroką skalę badań związków srebra jako potencjalnych prekursorów nowych nadprzewodników wysokotemperaturowych. Badania te są uzasadnione kilkoma istotnymi podobieństwami między związkami srebra i miedzi. W szczególności, w dotychczas opublikowanej literaturze istnieje kilka bardzo obiecujących 1–3 4,5 przewidywań teoretycznych na temat wysokociśnieniowych właściwości AgO oraz AgF2, a 6 także na temat istnienia hipotetycznego chlorku srebra(II) AgCl2. Głównym celem przedstawionych w niniejszej pracy eksperymentów była weryfikacja tych przewidywań.

AgF2 oraz jego pochodne – fluorosrebrzany(II) – są uznawane za analogiczne do tlenków miedzi(II).7 Obie grupy związków charakteryzują się wyraźnym efektem Jahna-Tellera prowadzącym do wydłużenia aksjalnych wiązań metal-ligand, silnymi oddziaływaniami antyferromagnetycznymi poprzez mechanizm nadwymiany za pośrednictwem wiązań kowalencyjnych, oraz warstwową strukturą krystaliczną. Warstwy występujące w strukturze

AgF2 są jednak pofałdowane, a wiązania Ag-F-Ag łączące atomy srebra są zorientowane pod kątem, co prowadzi do słabszego sprzężenia magnetycznego niż w warstwowych tlenkach miedzi(II), w których analogiczne wiązania Cu-O-Cu są zorientowane często w linii prostej.

Teoretyczna analiza alternatywnych struktur krystalicznych AgF2 sugeruje stabilizację układu płaskich warstw w warunkach wysokiego ciśnienia.4 W takim ułożeniu struktury oddziaływania antyferromagnetyczne byłyby najprawdopodobniej dużo silniejsze.5 Obliczenia teoretyczne 5 przewidują również metalizację AgF2 pod ciśnieniem 38 GPa. W niniejszej pracy podjęto próbę sprawdzenia, czy kompresja istotnie prowadzi do takich zmian w strukturze krystalicznej i właściwościach AgF2. Ponadto, wysokociśnieniowe pomiary oporu elektrycznego pozwolą ustalić, w jaki sposób wywołane wysokim ciśnieniem przejścia fazowe AgF2 wpływają na przerwę energetyczną w tym związku.

Mimo że wzór sumaryczny AgO sugeruje, że jest on tlenkiem srebra(II), w rzeczywistości jest zdysproporcjonowanym związkiem zawierającym kationy Ag(I) i Ag(III) w stosunku 1:1. Mieszana walencyjność AgO może być traktowana jako efekt silnej deformacji Jahna-Tellera, typowej dla układu zawierającego kationy Ag(II) o konfiguracji d9.8 Deformacja ta, sprzężona dodatkowo z falą gęstości ładunku (ang. “charge density wave”, CDW), prowadzi do powstania dwóch różnych stanów walencyjnych Ag zamiast jednego.8 W dotychczas opublikowanej literaturze można znaleźć kilka sprzecznych ze sobą przewidywań na temat wysokociśnieniowych właściwości AgO. Według jednej ze wspomnianych prac, związek ten pod ciśnieniem 45 GPa powinien ulec przejściu fazowemu do struktury o niskiej (trójskośnej)

11 symetrii i stać się metalem o małej gęstości stanów elektronowych na poziomie Fermiego.1 Inna grupa badawcza przewiduje przejście fazowe w 75 GPa, prowadzące do zsynproporcjonowanego tlenku srebra(II);2 wykazano jednak, że wyniki tej pracy wynikają z błędnej metodologii obliczeń.3 Dane eksperymentalne zebrane i przeanalizowane w niniejszej pracy powinny dostarczyć informacji na temat wpływu ciśnienia na strukturę krystaliczną AgO oraz stan walencyjny srebra w tym związku.

Z kolei mieszaniny srebra i chloru zostały zanalizowane pod kątem otrzymania nowych, nieznanych dotychczas związków o stechiometrii AgClx. Znany jest obecnie tylko jeden tego typu związek – chlorek srebra(I) AgCl – jednakże wcześniejsze badania teoretyczne sugerują, że hipotetyczny chlorek srebra(II) AgCl2 może być trwały w temperaturze poniżej 286 K lub, 6 alternatywnie, pod wysokim ciśnieniem. Gdyby AgCl2 istotnie udało się otrzymać, najprawdopodobniej cechowałby się silnie kowalencyjnym charakterem wiązań Ag-Cl, co z kolei, przy zachowaniu odpowiedniej geometrii struktury, mogłoby prowadzić do silnych oddziaływań antyferromagnetycznych, które uznaje się za jeden z istotnych warunków dla zaistnienia wysokotemperaturowego nadprzewodnictwa. Istnieją również alternatywne, nie mniej interesujące, przewidywania dotyczące produktów reakcji między Ag i Cl2 w 9 ekstremalnych warunkach, takie jak powstawanie polichlorków analogicznych do np. NaCl3. Opisane w niniejszej pracy eksperymenty miały na celu zbadanie możliwości powstawania nowych chlorków srebra.

Literature review 1. Introductory notes on several physical phenomena in solids

There are several important types of physical properties that are frequently discussed throughout this work. Here, I will focus on the basic concepts pertaining to them, to the extent necessary for understanding subsequent parts of the text. Delving into more intricate physical details of these phenomena lies beyond the scope of this thesis; instead, I will introduce and clarify the vocabulary that will be used in the chapters that follow.

1.1. Types of magnetic ordering

In a solid which contains atoms with unpaired electrons, interaction between these electrons can result in some type of macroscopic ordering of spins. Two basic types of magnetic ordering can be distinguished: ferromagnetic (FM) and antiferromagnetic (AFM). The former occurs when neighboring spins point in the same direction, i.e. are aligned parallel to each other, resulting in a non-zero net magnetization of a system, even in the absence of external magnetic field (remnant magnetism). Conversely, antiparallel orientation of neighboring spins leads to AFM ordering, cancellation of their magnetic moments and consequently null net magnetization. A simplified illustration of FM and AFM ordering is shown in fig. 1.1.

Fig. 1.1. Two basic types of magnetic ordering: ferromagnetic (FM) and antiferromagnetic (AFM). Arrows indicate direction of magnetic moments. Ordering can occur in one dimension (chains, as in fig. 1.1), as well as two (layers) or three. More than one type of magnetic interactions can be present in a given solid. For example, in some transition metal monoxides, ferromagnetically ordered planes can be distinguished, which are in turn arranged antiferromagnetically with respect to one another, i.e. with all spins parallel within one plane and antiparallel to those in neighboring layers. In such a system, net magnetic moment is ideally zero. The two aforementioned effects and different combinations thereof, as well as many more complex, secondary effects lead to a variety of magnetic structures seen in the solid state. For example, when two different kinds of magnetically active atoms are present in a system (either two different elements or two different oxidation states of the same element), their magnetic moments will in principle have different values. Even if these spins couple in such a way that the 13 total number of both up and down orientation will be equal, the result will be a non-zero net magnetic moment. Materials which host such interactions are ferrimagnetic. The best-known and historically important example is Fe3O4, which contains Fe(II) and Fe(III) cations, both carrying magnetic moments (its structure, magnetic properties and high-pressure behavior are summarized in section 4.2). In general, magnetic coupling of neighboring spins arises as a quantum phenomenon and can be properly described using quantum-mechanical models. In the simplest approach, it can be described using the Heisenberg Hamiltonian:

퐻푎푏 = −퐽푎푏푆푎푆푏 where Sa and Sb are spins and J is the magnetic coupling constant or exchange constant. The latter is measured in units of energy (e.g. electron-volts) and can be used to quantify the magnitude of magnetic interactions. One convention is that for FM interactions, J is positive; for AFM – negative.

At sufficiently high temperatures (which are determined by the strength of interactions), magnetic ordering is destroyed, leading to a paramagnetic state, with randomly oriented spins and null net magnetization in the absence of external magnetic field. These threshold temperatures for ferromagnetic and antiferromagnetic three-dimensional ordering are referred to as Curie and Néel temperatures, respectively.10,11

The exact nature of magnetic exchange depends on the composition, as well as type and geometry of chemical bonding of a given solid. Direct exchange between neighboring spins occurs e.g. in elemental metals such as iron (a ferromagnet below ca. 1040 K) or manganese (antiferromagnet below ca. 100 K). In transition metal compounds, exchange between magnetically active cations can be realized via bridging non-magnetic anions such as oxygen. Goodenough-Kanamori-Anderson (GKA) rules can qualitatively predict the type of magnetic ordering based on electron occupancy of atomic orbitals participating in bonding, as well as geometry of this bonding.12 For example, systems with linearly arranged M–O–M bonds give rise to very strong antiferromagnetic interactions. This phenomenon is referred to as superexchange. It is considered to be one of important prerequisites for high-temperature superconductivity, exhibited by oxocuprates.13

1.2. Jahn-Teller effect

When a transition metal cation is placed in an octahedral ligand field, its (n-1)d orbitals (n – principal quantum number of its valence shell) are split into two sublevels (fig. 1.2). The lower lying, threefold degenerate t2g level corresponds to dxy, dxz and dyz orbitals, which lie along diagonals between axes on which ligands are positioned. They experience relatively weak

Coulombic repulsion from ligand electrons. On the other hand, dz2 and dx2-y2 orbitals are most affected by the ligand field, due to position of their orbital lobes along the axes. They constitute the higher, twofold degenerate eg level.

9 Fig. 1.2. Splitting of d energy levels of a d metal cation in perfectly octahedral (Oh) and tetragonally

distorted due to Jahn-Teller effect (D4h) ligand field. The above splitting scenario corresponds to elongation of metal-ligand distances along the z axis. Now let us consider a vibrational mode of tetragonal symmetry, which alternately stretches and contracts the octahedron along the z axis, with simultaneous contraction and elongation, respectively, of the remaining four contacts in the xy plane. Such normal mode is intrinsically coupled to electrons. For example, elongation of metal-ligand distances along the z axis and concomitant contraction of the other four contacts leads to further splitting of the eg level: electrons on dz2 orbital now experience weaker repulsion that those occupying dx2-y2 orbital, which is now energetically less favored. The t2g level also becomes split for the same reasons, albeit to a lesser extent. In systems with both t2g and eg levels (i.e. all d orbitals) unoccupied, singly occupied or fully occupied, this mode will have no effect on the total electronic energy. However, in atoms which have partially filled orbitals, it can lead to an overall decrease of electronic energy, as exemplified by d9 cations Cu(II) or Ag(II) and illustrated in fig. 1.2. This tetragonal distortion and subsequent removal of orbital degeneracy is referred to as Jahn-Teller 14 (JT) effect. Its occurrence depends on the electron count on t2g and eg levels in a given atom, which in turn depends on the strength of the ligand field, as well as other factors. In both Cu(II) and Ag(II) cations in a ligand field, the Jahn-Teller effect is often substantial and has a great influence over structure and properties of their compounds. The magnitude of JT effect is often 15 measured as a percentage of elongation or contraction of apical contacts relative to the four in- plane metal-ligand bonds. It has recently been shown that the splitting of eg levels due to the aforementioned tetragonal distortion of [MX6] octahedra in systems containing JT-active Cu(II) or Mn(III) cations depends linearly on the normal coordinate of that distortion.15 In crystals, tetragonally distorted octahedra of local ligand environment can be oriented relative to each other in a few different ways, a process known as collective Jahn-Teller effect. This can be realized in one of two basic patterns, which are referred to as ferrodistortive and antiferrodistortive ordering of octahedra. Ferrodistortive alignment means that neighboring octahedra are distorted along the same (parallel) axis, whereas antiferrodistortive ordering implies different axes of elongation for neighboring sites. In other words, metal-ligand contacts are alternately elongated and contracted in the direction of antiferrodistortive ordering, whereas in ferrodistortive pattern the length of M∙∙∙X contacts is constant along the ordering direction. Often both patterns are present in a given compound, working in different crystallographic directions. This is schematically illustrated in fig. 1.3. Such ordering is seen in e.g. KAgF3, albeit with some distortions.16 In fact, crystal chemistry of fluoroargentates(II) exhibits a variety of collective JT patterns – they are discussed in more detail in section 3.3.1.

Fig. 1.3. An example of elongated octahedra ordering in collective JT effect. Grey spheres – metal, yellow spheres – ligand. Red lines indicate elongated metal-ligand contacts, while contracted contacts are not shown. The ordering is antiferrodistortive in xz plane and ferrodistortive in the y direction. Collective JT effect is associated with orbital ordering – a regular pattern of spatial orientation of occupied orbitals, analogous to ordering of spins in magnetic structures. Orbital ordering and magnetic properties are closely linked in compounds containing JT-active cations. The relationship between JT effect and magnetism was thoroughly explored theoretically by Kugel and Khomskii.17 Some recent studies have begun to recognize other factors leading to the breaking of local Oh symmetry of [MX6] octahedra in solids and influencing the orbital ordering, such as electric field from the surrounding lattice ions.18 16

1.3. Mott and charge-transfer insulators

One of the limitations of conventional band theory involves description of strongly correlated systems. This is particularly evident in compounds of transition metals, whose electrical and magnetic properties are largely governed by strong electron correlation. Groundbreaking theoretical work in this field, which provided the first suitable description of such systems, was done in the 1930s by N. F. Mott.19 He received a Nobel Prize in Physics (shared with P. W. Anderson and J. H. Van Vleck) in 1977 for “[…] fundamental theoretical investigations of the electronic structure of magnetic and disordered systems”.20 This and more detailed formulations which followed (such as the commonly used Hubbard model21) explain high electrical resistivity of e.g. certain transition metal oxides in terms of on-site Coulomb repulsion between electrons (U). In the simplest approach, if this repulsion is sufficiently strong, it prevents electrons from “hopping” between neighboring metal atoms in the crystal lattice (this would imply metallic behavior). As a result, a band gap arises at the Fermi level between filled and empty valence states of the metal. Materials whose properties are described by such mechanism are referred to as Mott insulators. However, if the occupied nonmetal valence states lie higher in energy than the filled valence band of the metal, then the band gap is determined by the energy difference (Δ) between nonmetal valence states and empty conduction band of the metal. Such systems are known as charge-transfer (CT) insulators. Both cases are schematically illustrated in fig. 1.4. The distinction between Mott and charge-transfer insulators was introduced by Zaanen, Sawatzky and Allen in their seminal 1985 work on electronic structure of transition metal oxides and related compounds.22 This model gained more significance after the 1986 discovery of high-temperature superconductivity in doped copper(II) oxides.

Fig. 1.4. Two types of insulators described in text. Shaded bands are filled, unshaded – empty. 17

2. High pressure science

2.1. Historical notes

Temperature and pressure are probably the two thermodynamic quantities that are most easily understood intuitively – by scientists and non-scientists alike. While temperature has been extensively used as a variable in manufacturing of various goods and materials, and later in experimental sciences throughout their history, the influence of pressure is not nearly as thoroughly studied. Theoretical interest in this field dates back to the beginnings of modern science – Robert Boyle famously wrote in 1660 that “perhaps the pressure of the air might have an interest in more phenomena than men have hitherto thought."23 However, the progress of HP research as it is known today took place predominantly in the last 100 years. Late 19th century saw the development of first HP instruments for scientific purposes. The original type of HP apparatus – the piston-cylinder system – was introduced by Charles Parsons24, who is otherwise best known for the invention of steam turbine. In this setting, a sample was placed inside a hollow steel cylinder, sealed at one end and compressed with a steel piston from the other end. It also featured an electrical heating system. Parsons’ original design was capable of producing pressures up to 1.5 GPa (150,000 atm.) and temperatures up to 3000°C.25 One of the main objectives for first HP researchers like Parsons and his contemporaries was to synthesize diamond. Even though quite a few scientists between 1870s and 1950s claimed to have obtained synthetic diamonds, it was unequivocally achieved in a reproducible manner only in 1954 by H. T. Hall at General Electric Research Laboratory in New York state.26 Over the decades following Parsons’ invention, different designs of HP instruments have been developed and improved upon in order to reach ever higher pressures. Of all these contributions, the most significant is probably that of Percy Williams Bridgman, who invented the opposed anvil device.27–30 It consisted of two centrally aligned cylinders (originally made of tungsten carbide) with small circular faces raised on one end, pressed against each other. The sample was placed between the faces of cylinders and enclosed on the sides by an O-ring made of pipestone. Silver chloride was used as sample matrix to provide hydrostatic pressure within the entire sample.25 As is known from basic physics, pressure can be defined as a ratio of force acting on a surface to the area of that surface: p = F/A. In order to increase pressure, one can either increase the force or decrease the surface area upon which the given force is applied. It is the latter idea that is the basic principle of operation of opposed anvil devices. Pressures of tens of hundreds of gigapascals (100,000-1,000,000 atm.) can be easily reached in modern systems using a relatively

18 small axial thrust applied to the anvils. This force is spread out across the entire surface of the back (larger) face, which provides appropriate support. P. W. Bridgman was awarded the Nobel Prize in Physics in 1946 “for the invention of an apparatus to produce extremely high pressures, and for the discoveries he made there within the field of high pressure physics”.31 Systems using opposing anvils are capable of achieving the highest pressures produced in static experiments.25 The basic design described above has been developed into more sophisticated devices that continue to be used today. The most important of these systems is the diamond-anvil cell (DAC), widely utilized in high pressure physics, chemistry and related fields. The DAC was also used in experiments described in this thesis. Structure, principles of operation and techniques associated with DACs will be further elaborated upon in the description of experimental methods (chapter 5). The invention of opposed anvil devices opened up a whole new area of research, enabling scientists to achieve pressures hitherto known only in theory. A plethora of experiments probing properties of elements and compounds at extreme conditions followed, with much of the early work having been done by Bridgman himself (for example ref. [32]).

In general, modern high pressure experiments can be divided into two types: static compression and shock (dynamic) compression. The former includes the aforementioned anvil devices, while shock methods involve rapid compression of samples with e.g. explosions, projectiles or laser pulses. Though the highest pressures are by far those generated in shock experiments, these techniques also allow much less control over the exact experimental conditions. For example, significant temperature rise inevitably occurs during shock compression due to adiabatic heating of the sample.

Contemporary applications of high pressure techniques can be found in all areas of natural sciences. In biology, investigating properties of certain biomolecules under strong compression can give a better understanding of marine organisms living in deeper parts of the Earth’s oceans. Elevated pressures are also sometimes used in food industry as an alternative to thermal processing in order to better preserve their nutritional properties; however, such treatment is much more expensive and is therefore not as widespread as e.g. pasteurization. Perhaps most prominently, high pressures (often coupled with high temperatures) are used to simulate conditions in planetary interiors. It is estimated that over 90% of matter (by mass) in solar system is at pressures beyond 10 GPa.33 Information about structural properties of matter at those conditions is essential for proper modelling of e.g. seismic processes on Earth, as well as a range of phenomena in other celestial objects.

2.2. Physical chemistry at high pressures

The branch of high pressure science that is most relevant for the topic of this thesis is the one dealing with synthesis of new materials and fine-tuning of their physical properties by means of manipulating pressure. Therefore, I will present here a brief overview of high pressure physical chemistry, e.g. general trends in pressure-induced behavior of chemical compounds and important achievements in this field. Some of those trends are also exemplified and highlighted in chapter 4, which reviews compounds analogous to AgF2 and AgO under pressure.

High pressure behavior of a given substance is closely linked to the nature of its chemical bonding. Compressibility is largely determined by the structure of valence shell of constituent elements, because it directly participates in bond formation. Thus, for example, K, Rb and Cs exhibit relatively large initial compressibility at ambient pressure and an easy electron transfer from ns orbital to the deeper-lying and empty (n-1)d subshell.34 The latter means that at higher pressures they become somewhat more similar to transition metals.35 On the other hand, diamond, with its covalently bonded three-dimensional lattice, is the least compressible of all elements. Maxima of compressibility are also seen for heavier group 14 elements (silicon, germanium, tin and lead) in their respective periods, which shows that their electronic configuration is indeed a crucial contribution to low compressibility.25 Changes in free energy of a system induced by pressures that are nowadays feasible can be in the range of 10 eV or more. This value is higher than the energy of most chemical bonds at ambient conditions; therefore, strong compression can introduce dramatic changes in electronic density distribution in a system, leading to materials with completely different chemical and 36 physical properties. Even nitrogen, whose N2 molecules host an extremely strong covalent bond, polymerizes at pressure above 110 GPa (and at temperatures above 2000 K) and adopts a cubic three-dimensional structure, in which N atoms exhibit tetrahedral coordination: three covalent bonds with neighboring nitrogen atoms and one lone pair of each N atom.37 A general tendency in electronic structure upon compression is increasing electron delocalization and band overlap. Because of this, all elements are predicted to become metallic at sufficiently high pressures.38 This process has already been observed in many nonmetals, such as sulfur (95 GPa),39 iodine (17 GP)40 and oxygen (ca. 100 GPa).41 It is thought that liquid metallic hydrogen exists on Jupiter (and possibly other gas giants) as a layer between rocky core and outer gaseous layers. Obtaining metallic H2 would provide a better understanding of the inner structure of those planets. The most recent experimental reports claim that metallization of H2 occurs at ca. 495 GPa.42 However, these results have been questioned by the high pressure community due

20 to scarcity of presented data and unjustified extrapolations.43,44 Thus, metallization of hydrogen continues to be one of the most important experimental goals in high pressure research. A much less common scenario involves a transition from metallic to insulating state upon compression due to formation of electrides, i.e. compounds in which valence electrons are localized in interstitial voids and behave in a manner similar to anions. Thus, these electrons do not give rise to metallic conductivity. Such behavior is seen e.g. in compressed Li and Na.45 It should be noted, however, that this phenomenon does not preclude re-metallization at still higher pressures.

The aforementioned changes in free energy will often lead to a pressure-induced phase transition: i.e. a rearrangement of atoms into a structure that is more favorable at higher pressure conditions.36 Phase transitions can be divided according to behavior of Gibbs free energy derivative with respect to pressure during the process. If the first derivative δG/δp shows a discontinuity, the transition is said to be of first order. Such phase transitions entail an abrupt volume change between the two phases, which is usually associated with a pronounced structural rearrangement. Conversely, second-order phase transitions are characterized by a discontinuity of second derivative (δ2G/δp2) and a sudden drop in compressibility upon transition, but a continuous volume decrease. The two types of transitions may not necessarily be easy to distinguish based on experimental data alone. Another way to classify these processes is by a more direct comparison of crystal structures of the two phases.36 A reconstructive transition involves breaking and formation of chemical bonds and a significant change of the coordination environment of at least one element in the structure. A displacive transition occurs via a relatively small and cooperative movement of atoms; none or relatively few bonds are broken and the two structures are related by symmetry (e.g. group-subgroup relationship). One example of the latter is a pressure-induced martensitic phase transition in solid xenon.46 A transition from fcc to hcp structure occurs continuously over a wide pressure range (3-70 GPa) and involves formation of hcp domains within the fcc structure of Xe due to gradual introduction of stacking faults.46 First- order phase transitions are usually reconstructive, while displacive transitions are most often of second-order. Reconstructive transitions have a larger activation barrier and are accompanied by hysteresis upon decompression. This is especially true in covalently bonded materials such as carbon allotropes. A prevalent trend in phase transitions at high pressure is an increase of coordination number.35,47 In ionic solids, stability of a given structure at ambient pressure can be inferred from the first Pauling rule, which relates the ratio between radii of cations and anions r+/r- to the preferred coordination number.48 The higher the ratio (closer to unity, as cations are usually

21 smaller than anions), the higher the coordination number. These rules are also applicable at higher pressures, but because anions are much more compressible than cations, the ratio r+/r- will usually increase with pressure, which in turn will make higher coordination numbers more preferred. And indeed, for example NaCl with CN = 6 undergoes a phase transition at 29 GPa to a structure with CN = 8.49 Such structure is adopted by CsCl at ambient conditions. This hints at another common tendency. Elements of a given group will often adopt the structure of their heavier counterparts upon compression, or will require higher pressures to achieve the same structure.34 The simplest example is that of silicon and carbon. At ambient pressure, silicon adopts a diamond-type structure, which in carbon is (thermodynamically) stable only at high pressure.50 The same trend is often seen in binary compounds for a series of cations from a given group, as already exemplified by NaCl and CsCl. However, in a series of anions from the same group in combination with a given cation, an opposite tendency – lower CN in compounds with heavier anions – is observed. Since electronegativity decreases with increasing atomic number within a group, bonding with a heavier nonmetal will be more covalent in nature. This in turns means larger electron density between atoms and stronger repulsion between bonds, which favors lower coordination number compared to ionic bonding. Also, the r+/r- ratio decreases in such sequence, which further stabilizes lower CN.

A very promising use of high pressure techniques in chemical sciences is the search for new materials under pressure.36 They can be obtained by several different mechanisms: (a) transitions to new phases with different structure, (b) stabilization of exotic stoichiometries, (c) new chemical reactions enabled by altered reactivity at high pressures and (d) tuning electronic properties of materials through compression.51 However, novel compounds (or phases) synthesized at extreme conditions will rarely be stable at ambient pressure. Eventually, they should decompose (or transition) into species that are thermodynamically favored at atmospheric conditions. If this reverse process is sluggish, the high-pressure phase or compound may be quenched, i.e. brought back to ambient pressure, for example through decompression at low temperatures. The most prominent example of such kinetically stabilized material is diamond: graphite is thermodynamically more stable at atmospheric conditions, but the transition is impeded by a large kinetic barrier. Thus, for all practical purposes, diamond can be considered stable at room temperature and pressure. Other examples of compounds that have been synthesized at high pressures and turned out to be metastable at ambient conditions include exotic 52 iron sulfides Fe2S and Fe3S.

2.3. Jahn-Teller effect at high pressure

Compounds which contain cations with an odd number of electrons at eg level usually exhibit the Jahn-Teller effect.* It is often a crucial factor determining their overall crystal structure. This is evident for a d9 Ag(II) cation, as will be shown in chapter 3. Other important examples include Mn(III) (d4), Ni(III) (d7) or Cu(II) (d9 – thus, analogous to Ag(II)). In order to understand pressure-induced structural transition in compounds of Ag(II), it is interesting to see how JT-induced distortions in related systems withstand extreme compression. In the most basic approach, pressure should eventually lead to quenching of JT effect due to (a) increasing delocalization of electrons with concomitant weakening of electron-lattice coupling and (b) stiffening of the vibrational mode associated with the JT distortion.53 However, in some compounds the situation is much more complex, as will be exemplified below.

In compounds of Mn(III), there is an interplay between Jahn-Teller effect and spin state. Generally, relative stability of high- and low-spin states (HS and LS, respectively) depends on the energy of crystal field splitting (Δ) and the energy of repulsion between two electrons occupying the same atomic orbital (U). If U > Δ, HS state is energetically favored; otherwise, LS state is optimal. In particular, the JT splitting of eg level stabilizes HS configuration of Mn(III) in 54 compounds such as CsMnF4.

Fig. 2.1. Electronic structure of Mn(III) cation in octahedral ligand field without (left) and with (right) Jahn-Teller distortion (specifically, stretching along z axis). Δ is the crystal field splitting energy.

CsMnF4, which contains in its crystal structure elongated [MnF]6 octahedra, undergoes a first-order structural phase transition at 37 GPa and a simultaneous transition from HS to LS state.54 The latter transition is usually expected at high pressures, as the reduction in metal-ligand distances leads to stronger crystal field splitting; eventually, Δ becomes greater than U. However,

* This is of course true also for cations with degenerate, unevenly occupied t2g orbitals, but the splitting of t2g level due to a tetragonal distortion is generally weaker than that of eg level due to geometry of constituent d orbitals. 23

JT-induced distortion of [MnF]6 octahedra effectively reduces Δ and stabilizes the HS state, as shown in fig. 2.1. The JT effect persists at high pressures – more efficient packing (and subsequent reduction of unit cell volume in response to pressure increase) is instead achieved 54 through tilting of [MnF]6 octahedra. Above a certain pressure threshold (in this case 37 GPa), JT effect abruptly disappears, which is manifested as a first-order phase transition. At the same time, HS-to-LS transition occurs. JT effect also has a significant influence on the pressure-induced insulator to metal 55 transition in LaMnO3. At ambient pressure, all [MnO6] octahedra in the crystal structure of this compound are elongated. At 3 GPa, a new band appears in Raman spectra, which is attributed to the presence of undistorted octahedra. Intensity of this band increases with pressure, indicating that domains of undistorted octahedra are forming in LaMnO3 upon further compression. Transition to a metallic state occurs at ca. 30-32 GPa, and it appears that it is driven by the fraction 55 of undistorted octahedra reaching a certain critical threshold. Such behavior of LaMnO3 is peculiar also because of the persistence of JT effect up to pressure-induced metallization.55

In Cu(II) compounds, JT effect has been found to be particularly robust.53,56,57 As already shown in the case of Mn(III), tilting of octahedra is a good way to reduce the overall volume while retaining the JT-induced elongation. In copper chlorides, e.g. Rb2CuCl4, this scenario is well illustrated with local compressibility parameter – [CuCl6] octahedra turn out to be an order of magnitude less compressible than the unit cell.57 JT effect also accounts for the divergence of high-pressure behavior of CuF2 from that of other difluorides (see section 4.3). The strength of JT effect in compounds of divalent copper is especially evident in the case 53 of CuWO4. Although the magnitude of elongation of [CuO6] octahedra initially decreases with pressure, a first-order phase transition at 9.9 GPa abruptly reverses this trend and leads to a lower- symmetry polymorph, in which the JT-induced elongation again becomes more pronounced. In the high-pressure structure, [CuO6] octahedra become reoriented in a way which more easily accommodates their elongation compared to the ambient pressure polymorph. This suggests that the transition is accompanied by the robustness of JT effect: reorientation of the octahedra is energetically favored over further suppression of JT effect in response to external pressure.53

Based on the above considerations, it can be expected that the Jahn-Teller effect will also have a significant influence on the crystal structure of compounds containing JT-active Ag(II) cations (d9), even at elevated pressures, and may lead to uniquely structured polymorphs.

3. Chemistry of silver and its compounds

In this section, I will review selected aspects of the rich chemistry of silver compounds, with a particular focus on silver(II). Compounds of divalent silver have arguably attracted the most attention in recent decades, for reasons which will be explained below. I will also summarize the current knowledge about the two silver compounds which I have investigated in my experimental work: silver(I,III) oxide AgO and silver(II) fluoride AgF2. By extension, a stronger focus will be placed on combinations of silver with oxygen and fluorine.

3.1. Silver

Silver is one of the few elements known since antiquity. Its chemical symbol Ag and Latin name “argentum” are derived from the Greek word “argos” meaning “shiny” or “white”. Silver is primarily obtained as a by-product from ores of other metals – such as copper, lead, nickel or zinc – but it also occurs in its own minerals such as acanthite (Ag2S), chlorargyrite (AgCl) and pyrargyrite (Ag3SbS3), or in native (elemental) form. It is a period 5 element with atomic number 47, positioned between copper and gold in group 11 of the periodic table. The two known stable isotopes 107Ag and 109Ag are found in nature in almost equal abundance. At ambient conditions, silver is chemically inert and does not react with oxygen or water vapor in the atmosphere. However, it does react with even trace amounts of hydrogen sulfide, which results in a tarnished surface due to formation of Ag2S. Silver can be dissolved in nitric acid, forming silver nitrate AgNO3 and nitrogen (II) or (IV) oxide (depending on the concentration of the acid). At elevated temperatures, it reacts with oxygen and halogens, yielding silver oxides and halides, respectively. Reaction with F2 leads to Ag(II)F2. Physical properties of silver make it stand out among other elements. It has the lowest electrical resistivity, as well as the highest thermal conductivity and optical reflectivity of all metals. Silver is also very malleable and ductile to the extent that makes it possible to produce extremely thin, even monoatomic wires.58 Such properties have been attributed to the electronic configuration of its valence shell: [Kr]4d105s1. Large mobility of the single s electron, whose interaction with the filled d subshell is very weak, accounts for low electrical resistivity, while the low hardness of silver can be explained by relatively weak intermetallic bonding. The aforementioned properties are shared to varying extent with copper and gold, which have analogous electronic configuration; in fact, gold is even more ductile and malleable than silver. Throughout the ages, silver has been used as currency, jewelry, tableware, reflective surface of mirrors and as electrical conductor, to name just a few examples. For the latter purpose,

25 however, copper is usually chosen over silver due to its much lower price and only slightly higher resistivity (by ca. 6%).59 In chemical sciences and industry, arguably the most important application of metallic silver is in catalytic processes. For example, silver-catalyzed epoxidation of ethylene is used to produce about 15 million tons of ethylene oxide annually.60 The mechanism of this reaction involves adsorption of oxygen on Ag surface and subsequent oxidation of ethylene.61 This sequence is unlike that seen in many other surface-catalyzed processes, in which usually both substrates have to be adsorbed in order to initiate the reaction. The crucial role of chemisorbed oxygen on silver surface in catalysis has motivated many studies on the nature of Ag-O bonding in these systems.62,63 (and references therein)

3.2. Chemical properties of silver

Chemical properties of silver are governed by its electron configuration: [Kr]4d105s1. By far, the most stable and most commonly found oxidation state of silver is +1, with a stable, closed- subshell d10 configuration. As many as 16,000 silver(I) compounds are known,64 and they have found diverse applications. AgNO3, which is obtained by dissolving metallic silver in nitric acid, is the most common commercially available source of Ag(I) ions for chemical purposes. Silver(I) halides (except AgF) have been used in classical photography: when exposed to light, they decompose to metallic silver and respective dihalogen molecule. The remainder of the photosensitive material can then be washed away using a solution of sodium thiosulfate:

2− 3− − 퐴푔퐶푙 + 2푆2푂3 → 퐴푔(푆2푂3)2 + 퐶푙

Ag(I) ions in aqueous solutions have been shown to exhibit antibacterial properties and are sometimes used in medicine as a disinfecting agent.65

Compounds of silver at oxidation states +2, +3 and even +4 and +5 have also been synthesized, although the latter two are extremely reactive and difficult to characterize in detail.66 Additionally, a few molecular complexes of silver at the formal oxidation state of 0 are known, with both organic and inorganic ligands. Examples include ethylene,67 acetylene,68 propylene,69 70 71 72 73 74 75 benzene and allene (propadiene), as well as molecular oxygen O2, CO, HCN and PF3. These complexes are only formed at very low (liquid helium or liquid nitrogen) temperatures, are mononuclear (i.e. with one metal center) and can feature up to three ligands.75

3.3. Chemistry of silver(II)

Compounds of silver at oxidation state +2 are remarkable in many ways. Unlike copper, for which +2 is the most stable and common state, silver(II) compounds are very strong oxidizers. It should come as no surprise that divalent cations of group 11 metals, with their d9 electron configuration, would be easily reduced to +1 oxidation state. In the case of copper, this tendency is largely counteracted by a substantial solvation energy of the relatively small Cu(II) cation. On the other hand, gold is most commonly found at oxidation state +3, largely due to strong relativistic effects, which cause the expansion of 5d and contraction of 6s orbitals and subsequent decrease of the energy gap between them.76 From this perspective, the preference of silver for oxidation state +1 can be viewed as “normal” behavior for group 11 element, as opposed to the “exceptions” that are copper and gold (for reasons just mentioned).64 Even so, oxidizing properties of Ag(II) species are almost unparalleled. The value of second ionization energy of silver – 21.45 eV – is extremely large. Not only is it the highest among all divalent metals, it also surpasses second ionization energy of many nonmetals and is comparable to that of bromine (21.80 eV).64 Standard redox potential of the Ag(II)/Ag(I) pair against normal hydrogen electrode is equal to 1.98 V,77 but the formal potential can be as high as 2.9 eV in acidic solutions (see section 3.3.3).78 Because of these properties, preparation and characterization of silver(II) compounds is a challenging subject of experimental research. Until recent decades, knowledge of silver(II) chemistry was mostly limited to combinations with fluorine ligands.79 (and references therein) Relative stability of fluorine-coordinated Ag(II) systems stems from the fact that Fˉ is the most resistant to oxidation among all simple inorganic anions. After all, fluorine is the most electronegative among reactive elements and the standard redox potential of the F2/2Fˉ pair is 2.87 V.77

3.3.1. Silver(II) fluorides

Silver(II) fluorides have recently attracted attention due to the fact that they share some features with copper(II) oxides (oxocuprates), which constitute the most important family of 13 high-temperature superconductors. Crystal structure of a prototypical oxocuprate La2CuO4 – an important precursor for a number of superconducting materials – is shown in fig. 3.1.

Fig. 3.1. Crystal structure of La2CuO4 (Cmca space group). Cu – blue spheres, O – red spheres, La – green spheres. Cu-O contacts in y direction are about 27% longer than contacts within layers (xz plane, blue squares). A coherent model explaining high temperature superconductivity (the way BCS theory explains classic superconductivity) has not yet been formulated; however, strong vibronic coupling and strong antiferromagnetic interactions are considered crucial for the occurrence of this phenomenon.13 Fluorides of silver at oxidation states +2 and +3 exhibit an unusually large degree of covalency in chemical bonding between Ag and F,80 which is surprising given that metal fluorides are – due to record high electronegativity of fluorine – most often ionic. Moreover, this admixing of electronic states of Ag and F increases with oxidation state of silver, as evidenced by X-ray photoelectron spectroscopy.80 Strongly covalent bonds can give rise to antiferromagnetic superexchange and are therefore an important prerequisite for a potential superconductor.12,81 A strong Jahn-Teller effect is seen in both copper(II) oxides and silver(II) fluorides, most often leading to elongation of axial Cu-O or Ag-F bonds, respectively. In oxocuprates, this results in a

28 structure made up of flat [CuO2]n layers (fig. 3.1). Cu-O-Cu bridges within these layers are almost perfectly linear, which contributes to the strong AFM interaction. Obtaining silver fluorides with flat layers is therefore an objective worthy of pursuit; however, this has not yet been achieved.

Meissner-Ochsenfeld effect has been observed in BeF2/AgF2 phases, which indicates that silver(II) fluorides can indeed be a good candidate for this type of materials.82 Below, I will describe several Ag(II)-F systems, including their potential similarities to their Cu(II)-O counterparts and important differences.

The simplest example of an Ag(II)-F system – and, in fact, the earliest known Ag(II) compound in general – is the binary silver(II) fluoride AgF2. AgF2 is in turn the parent compound of fluoroargentates(II), most of which can be described with the general formula

[MF]xAgF2 – M being a monovalent group 1 metal cation and x being equal to either 1 or 2. Fluoroargentates(II) containing strontium and barium are also known.83

AgF2 is a dark brown solid, which can be prepared by fluorinating silver(I) compounds, 84 85 such as Ag2O, AgNO3 or AgF. AgF2 is extremely reactive and is one of the most potent known fluorinating agents. For example, it reacts with many metal oxides, forming fluorides or 84 86 sometimes peroxides; it can even react with xenon in the presence of BF3, yielding XeF2. When exposed to atmospheric conditions, it rapidly reacts with even trace amounts of moisture and decomposes into a greasy black mass.85 In general, high reactivity of silver(II) fluoride is also shared by fluoroargentates(II). Silver(II) fluoride crystallizes in an orthorhombic structure (Pbca space group), in which

[AgF4] squares are linked diagonally by their vertices into a two-dimensional arrangement of puckered layers (fig. 3.2 left).87,88

Fig. 3.2. Left: crystal structure of AgF2; right: coordination environment of Ag(II) cation. Grey spheres – Ag, yellow spheres – F.

The structure of AgF2, though unique among metal difluorides, can actually be characterized as a distorted fluorite (CaF2). In compounds with fluorite structure, fluorine atoms occupy tetrahedral voids within an fcc metal sublattice. This results in eightfold coordination of metal atoms and fourfold coordination of fluorine atoms. In the case of AgF2, the Ag(II) cation 6 3 with the (t2geg) electronic configuration in the ligand field experiences a strong Jahn-Teller effect, which causes elongation of some Ag-F contacts. This in turn leads to a layered structure.

Coordination environment of Ag(II) cation in AgF2 is shown in fig. 3.2 (right). The axial F ligands are 25% farther than the four F atoms in an [AgF4] square unit due to Jahn-Teller distortion. The structural relationship between AgF2 and other compounds of this type is discussed in more detail in section 4.3 in the context of transition metal difluorides and their high pressure behavior.

In terms of magnetic properties, AgF2 is often described as a “weak ferromagnet” below 163 K.87 Strong antiferromagnetic superexchange through shorter Ag-F-Ag bonds within each layer leads to antiparallel ordering of neighboring spins, which are aligned along the x direction. An estimated coupling constant J of −62 meV for these AFM interactions can be derived from early experiments.87,89 The most recent work by Gawraczyński et al. reports J = −74 meV based on two-magnon Raman scattering, while HSE06 calculations from the same work have found a value of −52 meV.90 In addition, the angle between Ag-F bonds is ca. 130°, which leads to a 87 complex magnetic exchange in AgF2, also known as Dzyaloshinskii-Moriya interaction. Consequently, the spins are slightly canted with respect to the xy plane, leading to a non-zero net magnetic moment in the z direction. Magnetic interactions between layers are much weaker and their magnetic moments are aligned parallel to each other, resulting in an overall (weakly) 91 ferromagnetic state. AgF2 is a charge-transfer insulator. 92 Another polymorph of AgF2 – known as β-AgF2 – has also been synthesized. It is a red- brown solid with diamagnetic properties, which indicates that it is disproportionated and contains II Ag(I) and Ag(III) cations – essentially a valence isomer of Ag F2. It is only stable at low temperatures and transforms into silver(II) fluoride above 0°C.

Ternary derivatives of AgF2 – collectively known as fluoroargentates(II) – constitute an important extension of its chemistry. Of these, fluoroargentates of alkali (group 1) metals have been most thoroughly characterized. Compounds with the general formula MAgF3 (M = Na, K,

Rb, Cs) are all dark brown solids, similarly to AgF2. Their analogs with higher alkali metal content – M2AgF4 – have also been synthesized; in contrast to MAgF3, they are usually violet or purple, which indicates different electronic properties. Structural and magnetic properties of fluoroargentates(II) were recently investigated in detail by Kurzydłowski in his doctoral thesis.93

Structures of all aforementioned [MF]xAgF2 compounds are made up of [AgF6] octahedra. These octahedra experience a pronounced Jahn-Teller distortion and are ordered in several different ways, which appear to be largely determined by the size of alkali metal cation.

MAgF3 derivatives crystallize in perovskite-like structures: M(I) cations are located in voids within a 3D framework of [AgF6] octahedra. In RbAgF3 and CsAgF3, which adopt a tetragonal (I4/mcm) KCuF3-type structure, [AgF6] octahedra are elongated within the xy plane arranged in an antiferrodistortive manner in all three crystallographic directions (fig. 3.3, right).94

In KAgF3, octahedra are ordered antiferrodistortively within each plane and ferrodistortively between planes. They are additionally tilted with respect to xy plane (see note to fig. 3.3), which results in a lower, orthorhombic Pnma symmetry (fig. 3.3, left).16 Also, Rb and Cs atoms occupy special positions (0,0,¼) in their respective analogs, whereas K atoms are shifted from these positions. At temperatures above 230 K, KAgF3 experiences a further disorder: variable tilting of

[AgF6] octahedra relative to the xy plane. This polymorph is better described with Pcma space 95 group (not shown). NaAgF3 crystallizes in a monoclinic system, but the exact structure has not yet been elucidated.96

Fig 3.3. Crystal structures of KAgF3 (left) and (Rb/Cs)AgF3 (right). Grey spheres – Ag, yellow spheres

– F, purple spheres – alkali metal (not to scale). Elongated Ag-F bonds are shown in green. Note: KAgF3 is shown in a non-standard representations for better comparison; additionally, the z direction is arbitrarily chosen as the direction perpendicular to the plane of elongated octahedra.

16,83,91 KAgF3 is a one-dimensional antiferromagnet below 64 K. Magnetic ordering is realized via the short Ag–F–Ag bonds on the diagonal of [AgF4] square units (grey squares); that is, along the z direction indicated in fig. 3.3. The magnetic superexchange constant is equal to ca. −100 meV, which is a relatively large value – comparable to non-doped oxocuprates.95 Between the AFM-ordered [AgF] chains there are relatively weak FM interactions. Interestingly, 31

LSDA+U calculations of spin density indicate that there is an uncompensated spin on F atoms which interconnect [AgF] chains within the xy plane, with ca. ⅙ of the overall magnetic moment residing on these inter-chain F atoms.16

In terms of electrical properties, a microwave cavity perturbation study has found KAgF3 to be a metallic conductor above 50 K,91 although this has not yet been confirmed by actual dc conductivity studies, as they are difficult to carry out due to strongly oxidizing properties of 83 fluoroargentates(II). CsAgF3 is also an antiferromagnet, and though not experimentally tested, its superexchange constant has been theoretically predicted to be −145 meV – an even larger 89,97 value than that measured for KAgF3.

In M2AgF4 (M = K, Rb, Cs), [AgF6] octahedra are connected into layers interspersed with 98 M(I) cations, a structure referred to as layered perovskite. Cs2AgF4 crystallizes in an orthorhombic (Bbcm) structure of K2CuF4 type (fig. 3.4, left) with antiferrodistortive ordering of 99 octahedra within layers. Most recent experiments concluded that Rb2AgF4 also adopts this structure.100

Fig 3.4. Crystal structures of (Rb/Cs)2AgF4 (left) and Na2AgF4 (right). Grey spheres – Ag, yellow spheres – F, purple spheres – alkali metal (not to scale). Elongated Ag-F bonds are shown in green.

The case of K2AgF4 has been more ambiguous. Two polymorphs are known, referred to in literature as “α” or high-temperature (HT) and “β” or low-temperature (LT), respectively.101 94 HT-K2AgF4 has been known for several decades, but only recently has it been confirmed that its structure is very similar to those of cesium and rubidium analogs. Like the latter two, it consists of antiferrodistortively arranged [AgF6] octahedra, but in K2AgF4, these octahedra are additional tilted and disordered100 – a result corroborated by detailed theoretical models.98 Similar distortions are seen in previously mentioned KAgF3 as compared to Rb/Cs analogs. In fact, 32 layered perovskite (HT) phase of K2AgF4 has been found to be metastable with respect to the LT phase.101 This is attributed to the smaller radius of K(I) cation compared to Rb(I) and Cs(I), which turns out to be insufficient to stabilize the layered perovskite system. Na2AgF4, which hosts an even smaller cation, does not adopt such structure at all. Instead, it is monoclinic (P21/c) and 102 consists of [AgF6] octahedra linked into chains via vertices (fig. 3.4, right). This structure is labelled as post-perovskite. Interestingly, the Ag∙∙∙Ag distance of 3.342 Å in Na2AgF4 is the shortest ever encountered in an Ag(II) compound. LT-K2AgF4 adopts a post-perovskite Na2CuF4- type structure very similar to Na2AgF4, but with a different relative arrangement of octahedra chains and, consequently, different coordination environment of K(I) cations.101

In contrast to MAgF3, M2AgF4 compounds with layered perovskite structures are ferromagnets, with Curie temperatures of 14, 17.5 and 13.4 K for Cs, Rb and K analogs, 100 respectively. (and references therein) Due to antiferrodistortive ordering of [AgF6] octahedra, Ag-F contacts within layers are alternately long and short, which reduces orbital overlap and weakens magnetic superexchange. This is evidenced by coupling constants, which are in the order 16,99,100 of 4-5 meV. Na2AgF4, the lightest member of this family with a different crystal structure, is a weak antiferromagnet (J = −0.6 meV): magnetic coupling is realized both through space 102 between neighboring Ag atoms, and by weak superexchange via F atoms. M2AgF4 are electrical insulators, as exemplified by Cs2AgF4, in which optical measurements have determined a band gap of 2.17 eV.103

Overall, silver(II) fluorides are a promising area of study. A substantial overlap of electronic states between Ag(II) and fluorine gives rise to magnetic superexchange and strong AFM coupling, provided suitable geometry of Ag-F bonding. Relatively high J values have already been observed in these compounds, and even higher have been predicted, e.g. in 89 89,97 [AgF][BF4] or the aforementioned CsAgF3. Based on HSE06 calculations, a hypothetical flat-layered polymorph of AgF2 would likely also host extremely strong AFM interactions, with superexchange constant in the range of −140-200 meV.5,104 Stabilizing a layered perovskite structure with ferrodistortive ordering of elongated [AgF6] octahedra and strong 2D AFM interactions appears to be a crucial step towards potential silver-based high-temperature superconductors, and it is the main driving force behind high-pressure studies on AgF2 described in experimental section of this work.

3.3.2. Other silver-fluorine systems

Silver(I) fluoride AgF is a brown solid which adopts a rocksalt-type structure.105 It is largely ionic, as evidenced by X-ray photoelectron spectroscopy.80 It is an electrical insulator, although interestingly, hybrid DFT calculations are not capable of reproducing the experimentally determined band gap of this compound (2.8 eV, indirect).106 AgF differs from other silver(I) halides in that it is soluble in water and is much less photosensitive. High reactivity of Ag(II)-F compounds often leads to their reaction with even traces of water vapor or with parts of the experimental setup; these reactions predominantly yield AgF as a by-product, so it is important to take into account its presence in those systems.

A somewhat special case is the silver subfluoride, Ag2F. It is a brown, metallic solid, which crystallizes in an anti-CdI2 structure (P3̅m1). It can be visualized as a face-centered cubic Ag sublattice, in which every one in three Ag layers has been substituted with F atoms (fig. 3.5, 107 left). The formal oxidation of silver in Ag2F is +½. It is a metallic conductor at room temperatures and a superconductor below 0.06 K.108

AgF3 – silver (III) fluoride – is a red, diamagnetic solid. Its structure is identical to that of AuF3 (P6122 space group): [AgF4] squares are connected via vertices into a helical structure 109 (fig. 3.5, right). AgF3 is highly unstable at room temperature and decomposes within hours, 109 releasing F2 gas and yielding Ag3F8, a mixed-valent silver fluoride.

Fig. 3.5. Silver subfluoride Ag2F (left) and silver(III) fluoride AgF3 (right). Grey spheres – Ag, yellow spheres – F. Ternary compounds containing Ag(III) – fluoroargentates(III) – are also known. These compounds are more stable than AgF3, but are still very strong oxidizers. NMR spectra indicate 109 that the chemical shift of Ag in [AgF4]ˉ anions takes a record-high value due to de-shielding – decrease of electronic density at Ag nuclei – which occurs at such relatively high oxidation state.110 Fluoroargentates(III) of lithium,111 sodium,112 potassium113,114 and cesium,113 as well as 34

+ 115 + of Xe(VI) (with [XeF5] cations) and O2 have been synthesized. Their high reactivity has made structural characterization a difficult task, but XRD data for both KAgF4 and (XeF5)AgF4 indicate that they crystallize in tetragonal structures containing square-planar [AgF4] units.

Three mixed-valent fluorides of silver have been characterized: the already described β-

AgF2, as well as two mixed Ag(II)/Ag(III) fluorides Ag3F8 and Ag2F5. Ag3F8 is better described II III as Ag Ag 2F8; its structure contains both cations in elongated octahedral coordination, 116 III connected into a ribbon-like pattern. Ag2F5 contains square planar [Ag F4]ˉ units and infinite [AgF]+ chains.117 Mixed-valent Ag(II)/Ag(III) and Ag(I)/Ag(II) fluorides have been suggested as potential superconductors, although compounds of the latter type have not yet been obtained.118

In addition to the already described binary fluorides and ternary fluoroargentates, there are numerous other ternary and quaternary compounds containing Ag(II) species. For example,

Ag(SbF6)2 is frequently used in syntheses, as will be seen in the next section. The diversity of crystal and electronic structures of silver-fluorine systems was reviewed in a 2001 work by Grochala and Hoffmann.118

3.3.3. Silver(II) compounds – beyond fluorides

Though silver(II) chemistry is by far dominated by fluorides, many other combinations are known. Organic ligands such as pyrazine,119 cyclam120 and tetraphenylporphyrine121 have been used to stabilize Ag(II) cations in solutions and in solids.

An interesting type of Ag(II) compounds consists of sulfates and their fluoro-substituted derivatives. The structure of Ag(SO3F)2 is somewhat reminiscent of AgF2: it consists of layers of 122 [AgO4] squares connected diagonally via fluorosulfate anions. Again, the coordination environment of Ag(II) is in fact an elongated octahedron due to JT effect. The two longer (axial) 123 Ag∙∙∙O contacts separate the layers. Ag(SO3F)2 is a semiconductor and a weak ferromagnet. A I II 124 mixed-valent Ag 2Ag (SO3F)4 is also known and exhibits 1D antiferromagnetic coupling.

Other substances of this type include trifluoromethanesulfonate (triflate) Ag(SO3CF3)2 and II II IV 122 several mixed fluorosulfates such as K2Ag (SO3F)4 and Ag Pt (SO3F)6.

Perhaps the most interesting member of this family is silver(II) sulfate AgSO4. It is the first known inorganic, ternary compound of silver(II) without fluorine. Its synthesis was carried out independently by both Malinowski and Mazej and using two different reactions:125 a metathesis of silver(II) hexafluoroantimonate Ag(SbF6)2 and K2SO4 in anhydrous HF as solvent:

퐴푔(푆푏퐹6)2 + 퐾2푆푂4 → 퐴푔푆푂4 ↓ +2퐾푆푏퐹6 or from AgF2 and sulfuric acid:

퐴푔퐹2 + 퐻2푆푂4 → 퐴푔푆푂4 ↓ +2퐻퐹 ↑

AgSO4 is a black solid with strong oxidizing properties. It readily reacts with water vapor when exposed to atmosphere. At temperatures above 120°C, it decomposes according to the following equation:126

4퐴푔푆푂4 → 2퐴푔2푆2푂7 + 푂2 ↑

This process is highly atypical for several reasons. First, 120°C as the onset temperature 127 of decomposition is by far the lowest among known metal sulfates. The analogous CuSO4 is 127 far more thermally stable and decomposes above 300°C. Additionally, CuSO4 and other metal 127 sulfates typically yield metal oxide and SO3 upon heating. Disulfate Ag2S2O7 and oxygen as 128 decomposition products make AgSO4 more similar to peroxodisulfates such as K2S2O8. Indeed, it has been theorized that such thermal behavior of AgSO4 is due to the hole transfer from Ag(II) 9 2– 79,126 cation (d ) to the SO4 anion.

129 AgSO4 is a semiconductor with a band gap of ca. 1 eV. It adopts a monoclinic (C2/c) 2– structure consisting of Ag(II) cations squarely coordinated by four oxygen atoms from SO4 129 anions. These anions connect the [AgO4] squares into a 3-dimensional network (fig. 3.6).

Fig. 3.6. Crystal structure of AgSO4 viewed along the c direction. Grey spheres – Ag, yellow spheres – S, red spheres – O. O atoms have been shrunk relative to other atoms for clarity. Silver(II) sulfate exhibits interesting magnetic properties. Along the a direction of the unit cell, close to linear [–Ag–O–O–]n chains can be distinguished. The angle between these contacts is ca. 166 degrees (fig. 3.7). Within the chains, spins on Ag(II) cations are ordered antiferromagnetically. Interestingly, magnetic superexchange occurs via a diatomic O∙∙∙O bridge between two silver cations and omits sulfur atoms.129,130

Fig. 3.7. Antiferromagnetically ordered [-Ag-O-O-] chains in AgSO4. O atoms not participating in magnetic superexchange are not shown. Note the close to linear arrangement of Ag and O atoms. Green arrows indicate relative (and not actual) spin orientation.

The antiferromagnetic interaction in AgSO4 is quite strong: superexchange constant is equal to −18.7 meV129,130 – comparable to NiO (−19 meV).64 However, in the latter, there is only one intermediary O atom between magnetic Ni(II) centers. Therefore, the absolute value of superexchange constant observed in AgSO4 should be seen as unusually high; in fact, it is the highest among all known metal sulfates. The strength of AFM interaction in AgSO4 is further evidenced by that fact that magnetic ordering is retained up to 100°C – virtually in the entire 125 thermal stability range of the compound. Ag(II) cations in AgSO4 exhibit the highest chemical shift of binding energy ever observed in X-ray electron spectroscopy for silver(II) compounds.131 37

It is important to point out that another compound with empirical formula AgSO4 is 132 known – silver(I) peroxodisulfate Ag2S2O8. The AgSO4/Ag2S2O8 pair is a rare example of electromerism (valence isomerism): a phenomenon in which two compounds with the exact same elemental composition differ in terms of oxidation states of constituent atoms. The only other

known inorganic system which exhibits valence isomerism is PbS2. Its two electromers can 2– 2– 133 contain either Pb(IV) cations and S anions or Pb(II) and disulfide (S2 ) species. Silver(I) peroxodisulfate was first synthesized by Gilewski.132 It contains Ag(I) cations 2– and peroxodisulfate S2O8 anions; the latter can be thought of as two sulfate anions linked together via a peroxide (-O-O-) group. Consequently, the formal oxidation state of bridging O

atoms is −1. Ag2S2O8 is obtained as an off-white, microcrystalline powder in the following reaction:

2퐴푔[퐴푙(푂-푡-퐶4퐹9)4] + [(푛-퐶4퐻9)4푁]2푆2푂8 → 퐴푔2푆2푂8 ↓ +2[(푛-퐶4퐻9)4푁][퐴푙(푂-푡-퐶4퐹9)4] It is an insulator with a band gap of ca. 3 eV.132 It crystallizes in a monoclinic Cc space group, which lacks an inversion center; as a result, the unit cell of this compound exhibits an

uncompensated dipole moment. Because of that, grains of Ag2S2O8 can easily accumulate static charge, which combined with very fine crystallinity can make handling of samples very difficult.

Due to the closed-subshell configuration of the Ag(I) cation, Ag2S2O8 has no unpaired electrons

and is diamagnetic. A comparison of properties of AgSO4 and Ag2S2O8 is shown in the table 3.1.

Ag oxidation state Electrical properties Appearance Magnetic properties

AgSO4 Ag(II) semiconductor (1 eV) black powder antiferromagnetic

Ag2S2O8 Ag(I) insulator (3 eV) white powder diamagnetic

Table 3.1. Comparison of AgSO4 and Ag2S2O8.

The case of AgSO4/Ag2S2O8 clearly illustrates that valence isomerism, a phenomenon which can basically be described as different distribution of electrons between atoms within a compound, greatly affects chemical and physical properties.

Ag(II)-S-O systems have also been studied in solutions as a powerful oxidizing agent.78 (and references therein) A recent work by Połczyński and co-workers reported a system with 78 Ag(II) cations solvated by hydrogen sulfate (HSO4ˉ) anions. It was obtained by means of electrochemical oxidation of Ag(I) species on fluorine-doped tin oxide electrodes in 33% oleum.134 Formal redox potential of Ag(II)/Ag(I) pair in this system reaches 2.9 V, which is the highest value ever observed for a fluorine-free oxidizer. Studies of potential applications of the II [Ag (HSO4)2] system (as well as AgSO4) as reagents for oxidative C–C coupling of organic

38 compounds are currently underway.135 The process of electrochemical oxidation of Ag(I) in oleum can also be utilized as a more efficient method of AgSO4 synthesis, compared to the two reactions presented above.136 Interestingly, samples of silver(II) sulfate generated through electrochemical process differ slightly from those obtained via chemical synthesis. They form shiny black crystals, which are relatively stable at atmospheric conditions and less susceptible to moisture-induced decomposition. Exposure to atmosphere on the timescale of tens of hours yields a different black solid, distinguished by the loss of quasi-metallic luster seen in electrochemically prepared AgSO4. The black product was identified as a hydrate of silver(II) sulfate, 137 AgSO4∙H2O. It adopts a triclinic (P1̅) crystal structure, in which two distinct sites of Ag(II) cations can be differentiated. Both feature four O atoms in their nearest coordination environment, but in one type of sites, two of these O atoms are from H2O molecules; the rest are 2– part of SO4 anions. Therefore, a formula [Ag(OH2)2][Ag(SO4)2] can also be used to more accurately describe this compound. Given that Ag(II) compounds are usually very reactive towards water and readily oxidize it to elemental oxygen, the presence of H2O ligands in Ag(II) coordination environment is unprecedented. The hydrate of AgSO4 also exhibits one-dimensional antiferromagnetic ordering, with an exchange constant estimated at −10 meV, based on similarity 137 to Ag(SO3CF3)2.

At the time this thesis is submitted (June 2018), AgSO4, its hydrate and a mixed-valent oxide described in the next section remain the only known inorganic compounds of silver(II) in a homoleptic ligand environment of O atoms.

To sum up, unique electronic properties of Ag(II) give rise to such phenomena as very strong magnetic superexchange, pronounced Jahn-Teller effect and unparalleled oxidizing power. Deliberate fine-tuning of these properties through synthesis of new Ag(II) compounds may in the future produce new materials with useful properties. Therefore, chemistry of silver(II) constitutes an important and promising area of chemistry and warrants further studies.

3.4. Silver-oxygen systems

As previously mentioned, silver oxides and in general Ag-O systems are important from the point of view of industrial processes. Some of them are also used in various power sources. This section will focus on the five known binary silver oxides and selected more complex derivatives.

Silver(I) oxide Ag2O is a black solid. It is isostructural with Cu2O (space group Pn3̅m): silver atoms are coordinated linearly by two O atoms, whereas the latter are surrounded by four Ag atoms in a tetrahedron (fig. 3.8).138 It can also be described as an intergrowth of bcc sublattice of O atoms and fcc sublattice of Ag atoms.

Fig. 3.8. Crystal structure of Ag2O. Grey spheres – Ag, red spheres – O.

139 Ag2O is an insulator with a band gap of ca. 1.3 eV. It can be most easily obtained in a reaction between a silver(I) salt and hydroxide ions in solution:

+ − 2퐴푔 + 2푂퐻 → 퐴푔2푂 + 퐻2푂

AgOH is thermodynamically unstable at ambient conditions and the reaction leads straight to Ag2O. Though Ag2O is not soluble in water, it reacts with acids, yielding soluble or insoluble silver(I) salts, or with ammonia solutions, forming soluble ammine complexes. Silver(I) oxide is used in one type of silver oxide batteries as a cathode (with zinc as an anode). It is based on the following process:

퐴푔2푂 + 푍푛 → 2퐴푔 + 푍푛푂

Antimicrobial properties of Ag(I) species present in Ag2O have found application in 140 medicine, for example in Ag2O-doped bioactive glass materials. Mixed Ag2O/TiO2 materials with photocatalytic activity have also been synthesized.141

Ag2O undergoes facile decomposition at higher temperatures, beginning at ca. 190°C and yielding silver metal and oxygen:

2퐴푔2푂 → 4퐴푔 + 푂2 ↑

Ternary derivatives of Ag2O – oxoargentates(I) – are also known and can be classified 142 into three families: MAgO (M4Ag4O4), MAg3O2 and M3AgO2 (where M is an alkali metal). (and references therein) Their crystal structures feature Ag(I) cations in linear coordination, as in

Ag2O.

143 Although initially reported as a polymorph of Ag2O with Ag2F-type structure, a silver 144 oxide with the formula Ag6O2 is a compound distinct from Ag2O. It adopts a trigonal (P3̅1m) structure of anti-BiI3 type (fig. 3.9). This structure is in fact related to Ag2F, but in Ag6O2, O atoms occupy ⅔ of the positions occupied by F in Ag2F, which is reflected in different stoichiometry and doubled length of a and b lattice constants. Alternatively, both structures can be visualized as a hexagonal close-packed lattice of Ag atoms, with nonmetal atoms sitting in ⅔

(Ag6O2) or all (Ag2F) octahedral voids at z = ½. Like silver subfluoride, Ag6O2 features partly filled 5s-5p states of Ag and is a metallic conductor.

Fig. 3.9. Crystal structure of Ag6O2. Grey spheres – Ag, red spheres – O. In general, electrolytic oxidation of solutions of Ag(I) salts or suspended powders of silver or its compounds can yield higher silver oxides, which exhibit a variety of Ag oxidation states and structures. Some of these products are described below.

Silver(III) oxide Ag2O3 can be obtained by anodic oxidation of solutions of certain 145 silver(I) salts, e.g. AgPF6, AgClO4 or AgBF4, at 0°C. It is a black solid with metallic luster, which crystallizes in an orthorhombic, non-centrosymmetric (Fdd2) structure – identical to that of Au2O3 (fig. 3.10). The structure consists of [AgO4] square units connected via oxygen atoms into a three-dimensional network. Coordination number of O atoms is either 2 or 3. Additionally, Ag atoms are slightly displaced from the plane of Ag-O bonds (by ca. 0.09 Å).

Ag2O3 is stable at temperatures below -20°C. At room temperature, it easily decomposes, releasing oxygen.146 Its electrical properties have not been determined experimentally, but it is theoretically predicted to be an insulator with an indirect band gap of 1.9 eV.147

Fig. 3.10. Crystal structure of Ag2O3. Grey spheres – Ag, red spheres – O.

A controlled thermal decomposition of Ag2O3 leads to a mixed-valent silver(II,III) oxide 146 Ag3O4. This compound can also be obtained via electrochemical processes like those used for synthesis of Ag2O3, albeit at lower potentials. Its structure is somewhat similar to Ag2O3 in that it is a three-dimensional network of [AgO4] square units (fig. 3.11). However, all O atoms are surrounded by 3 Ag atoms and the structure is monoclinic (P21/c).

Fig. 3.11. Crystal structure of Ag3O4. Grey spheres – Ag(II), blue sphere – Ag(III) , red spheres – O.

III XRD data indicates that [Ag O4] squares are distorted (out-of-plane shift of Ag(III) II cation) as in Ag2O3, while [Ag O4] units are not distorted, and that the average Ag∙∙∙O distance is 2.03 Å and 2.07 Å for Ag(II) and Ag(III), respectively. However, 109Ag NMR spectroscopy data suggest that only one oxidation state of silver is present.148 Given that the coordination environment is essentially the same for all Ag atoms (the differences outlined above are slight), 149 it is assumed that they exhibit an intermediate valence state of +2.67. Above 63°C, Ag3O4 undergoes a rapid decomposition to AgO (described below), although this process has been found to occur even at room temperatures in a matter of hours.149

In case of some anions and under proper conditions, anodic oxidation or ozonation of Ag(I) species in solution can result in more complex products: silver clathrate salts. For 150,151 example, oxidizing a solution of AgNO3 can lead to the formation of Ag7O8NO3. Several other compounds of this type have been synthesized, which can be described with a general +2.67 + 149 formula (Ag )6Ag O8X (X = NO3ˉ, ClO4ˉ, HSO4ˉ¸HCO3ˉ, HF2ˉ). (and references therein). Their cubic (Fm3̅m) crystal structure consist of Ag cations of intermediate +2.67 valence coordinated with four O atoms in square planar units and arranged into rhombicuboctahedra (fig. 3.12). Each of these cubo-octahedra hosts an inorganic anion X within, and they are separated by Ag(I) cations cubically coordinated with eight O atoms.

Fig. 3.12. Selected part of the crystal structure of Ag7O8X compounds. Grey spheres – Ag(I), blue spheres – Ag(II/III), red spheres – O, green spheres – inorganic anion X. Note: there are additional contacts between O atoms in anion X and Ag(II/III) atoms, but the structure of anion X is not shown for the sake of clarity.

Due to intermediate valence state of silver, both Ag3O4 and Ag7O8X compounds exhibit metallic properties, as evidenced by conductivity measurements152 and vibrational spectroscopy.149 (Properties of mixed-valence compounds are described in more details in section 4.2) Silver clathrate salts are also superconductors at temperatures ca. 1 K or lower.152,153 In general, they are more thermally stable than Ag3O4 – for example, Ag7O8NO3 begins to decompose only above 100°C.149

In addition, depending on preparation conditions, oxides with stoichiometry intermediate 154 between Ag2O3 and Ag3O4 may be obtained. Their structure has not yet been elucidated.

One particular silver oxide warrants a broader description, as it has been the subject of experimental work described in this thesis: silver(I,III) oxide AgO. It is a dark grey solid, and although its stoichiometric formula may suggest the presence of Ag(II), it is in fact a mixed- valent compound, containing Ag(I) and Ag(III) cations in equal number.155 Silver atoms of the two oxidation states can be distinguished by their different coordination environment,156 and the mixed-valence nature of AgO has been confirmed by several different instrumental methods. X- ray photoelectron spectroscopy (XPS) studies have shown that the Ag 3d band of AgO is broader than in the case of both metallic silver and Ag2O, indicating the presence of more than one Ag oxidation state in this compound.157,158 Early theoretical studies predicted silver in AgO to be at +1 and +2 oxidation states, with holes on oxygen anions surrounding Ag(II).159 Although this would explain the relatively broad O 1s band in XPS spectra, the broadening can also be attributed to carbonate impurities, which are almost inevitable in AgO samples.160 On the other hand, diamagnetic properties of AgO effectively rule out the presence of Ag(II) species, which would feature an unpaired electron in its d subshell (d9).156 Additionally, XPS and X-ray absorption spectroscopy have found that Ag(III) cations are in fact present in AgO.161,162

In terms of crystal structure, two different polymorphs of silver(I,III) oxide are known to exist at ambient pressure and temperature. Both of them feature Ag(III) ions coordinated by four oxygen atoms in a square planar pattern, while Ag(I) ions are coordinated linearly by two oxygen atoms. The more common polymorph of AgO (and the one that is commercially available) can be obtained by anodic oxidation of AgNO3 solution in water. It adopts a monoclinic P21/c III structure, in which [Ag O4] squares are connected into corrugated layers, separated by linearly coordinated Ag(I) ions. The crystal structure of monoclinic AgO (fig. 3.13) was determined by MacMillan in 1960.156 AgO can also be obtained by means of ozonation of a stirred suspension of Ag2O or Ag in water. This reaction yields another polymorph, which crystallizes in a tetragonal 163 (I41/a) structure (fig. 3.14). The main difference between the two crystal structures lies in the

III arrangement of [Ag O4] square units. In the monoclinic form, these squares form separate layers, while in the tetragonal form they are arranged into a three-dimensional network. The two structures are a result of two different charge ordering patterns coupled to Jahn-Teller distortion of a hypothetical silver(II) oxide in NaCl-type structure.8 This mechanism is explained in more detail within the framework of other transition metal monoxides (section 4.1).

Fig. 3.13. Structure of monoclinic (P21/c) polymorph of AgO. Grey spheres – Ag(I), blue spheres – Ag(III), red spheres – O.

Fig. 3.14. Structure of tetragonal (I41/a) polymorph of AgO. Grey spheres – Ag(I), blue spheres – Ag(III), red spheres – O. AgO is a semiconductor with a band gap of ca. 1 eV at ambient conditions.155 It is insoluble in water, but can be dissolved in acids, releasing oxygen. The latter process is evidence of its oxidizing properties, due to the presence of Ag(III) cations:

+ + 4퐴푔푂 + 4퐻 → 4퐴푔 + 2퐻2푂 + 푂2 ↑

Silver(I,III) oxide undergoes decomposition at temperatures above 120°C.160 The reaction yields oxygen and Ag2O, and further heating leads to metallic silver, as in the case of Ag2O. AgO is used as a cathode in silver-oxide-zinc batteries, similarly to the aforementioned Ag2O.

Clearly, all binary silver oxides discussed above (except for Ag6O2) are thermodynamically unstable with respect to oxygen and silver at temperatures which decrease with increasing oxidation state of silver. This sequence can be written as follows:

120°퐶 190°퐶 퐴푔2푂3 → 퐴푔3푂4 → 퐴푔푂 → 퐴푔2푂 → 퐴푔

The exact onset temperatures of the first two decomposition reactions are not known.

Overall, silver oxides are less thermodynamically stable than corresponding fluorides at a given oxidation state. This is not surprising, since O2– anions are less resistant to oxidation than Fˉ. Interestingly, in contrast to fluorides, Ag(II) species is virtually nonexistent in silver-oxygen systems. AgO is actually a mixed-valent (I,III) oxide, and Ag3O4, though technically a (II,III) oxide, exhibits intermediate valence due to facile electron transfer between almost equivalent Ag crystallographic sites.

3.5. Hypothetical AgClx compounds

Although the hitherto described chemistry of silver at oxidation states higher than +1 features quite a few compounds with interesting properties, the overall number of stable combinations is quite limited – increasingly so with the increasing oxidation state of silver. Due to extremely strong oxidizing properties of Ag(II), only the most electronegative elements like fluorine and oxygen can withstand its presence in their local coordination environment. This is reflected in the fact that the majority of known compounds of silver(II) are fluorides, or contain fluorine atoms in the first coordination sphere of Ag(II) in their crystal structures. Chlorine is ranked third among elements (behind fluorine and oxygen) in terms of electronegativity (3.16 on the Pauling scale) and thus, Clˉ anions can be expected to be less resistant to oxidation by Ag(II) species than Fˉ or O2–. If standard redox potentials are compared, 2– 2– the Cl2/2Clˉ pair (+1.36 V) is also ranked third after F2/2Fˉ (+2.87 V) and O2 /2O (+1.76 V for 77 H2O2 in acidic solutions). Given these considerations, it is not surprising that the set of currently known compounds of silver and chlorine only contains silver(I) chloride AgCl and its several 164 ternary derivatives – chloroargentates(I) e.g. CsAgCl2 and Cs2AgCl3. The observed instability

(i.e. absence) of silver(II) halides other than AgF2 can also be explained in terms of the second ionization potential of Ag and polarizability of halide anions.165 As previously mentioned in section 3.3, this potential is very high in the case of silver, and even fluoride anions (which normally exhibit relatively low polarizability) are strongly polarized by Ag(II) cations, which 80 ultimately leads to a considerably covalent character of Ag-F bonding in AgF2. The other – larger, more polarizable and more easily oxidized – halide anions do not seem to be able to withstand the presence of Ag(II) species, at least at ambient conditions.

Fig. 3.15. Three most stable structures predicted for the hypothetical compound of AgCl2 stoichiometry.

Grey spheres – Ag atoms; Cl atoms are located at vertices of green squares. AgF2-like and CuCl2-like structures contain Ag(II), while Au4Cl8-like structure is made up of Ag(I) and Ag(III). Reproduced with permission from ref. [6]

Nevertheless, thermodynamic and dynamic stability of hypothetical structures of AgCl2 has been theoretically investigated in the past by Dr Mariana Derzsi.6 Three most likely candidate

47 structures have emerged from this search (fig. 3.15). Two of them contain Ag(II) cations and 87 resemble the layered structure of AgF2 or the structure made up of chains characteristic of 166 CuCl2, respectively. The third candidate is a disproportionated polymorph featuring Ag(I) and

Ag(III) cations arranged into clusters analogous to those seen in the structure of AuCl2 167 (Au4Cl8).

Based on thermodynamic considerations, AgCl2 should be stable at 0 K, given that the free enthalpy of its formation at these conditions (∆G0K) in the following reaction: 1 퐴푔퐶푙 + 퐶푙 → 퐴푔퐶푙 2 2 2 is calculated to be equal to −31.8 kJ/mol (−0.33 eV).6 The value of ∆G is much more positive at higher temperatures due to relatively high entropy of chlorine gas, but it can be estimated that it should be negative below 286 K (just below room temperature), thus favoring the formation of

AgCl2. Shifting the equilibrium of the reaction towards AgCl2 formation could also be achieved by means of high pressures.

Alternatively, higher chlorides of silver could also contain complex polychloride anions

(Clxˉ, where x is an odd number between 3 and 9). Several compounds of this type are known, e.g. tetraalkylammonium trichlorides.168 More recently, trichlorides of alkali metals have been 9,169 170 synthesized under high pressure, and the existence of HCl3 has been predicted theoretically.

To our knowledge, there have been no attempts at synthesizing higher chlorides of silver at high pressure, so predictions described in this section remain to be verified experimentally. Among these scenarios, formation of genuine silver(II) chlorides would likely be the most interesting. Compared to fluorine 2p orbitals, 3p orbitals of chlorine are more diffuse, which would result in a better overlap with 4d orbitals of silver(II), and consequently Ag-Cl bonding 80 with a higher degree of covalency, as compared to already quite covalent Ag-F bonding in AgF2. Indeed, EPR and optical spectroscopy studies of Ag(II) states produced by γ-irradiation of Ag(I)- doped KCl have hinted at a very strong covalency of Ag(II)-Cl bonds in those systems.171 This could give rise to a very strong magnetic superexchange (see section 1.1) – likely even stronger than that seen in silver(II) fluorides. Therefore, synthesis of silver(II) chlorides is certainly a goal worth pursuing, especially given the predicted thermodynamic stability of AgCl2 at temperatures below 286 K.6 The alternative scenario – formation of silver polychlorides – has not been investigated theoretically, but nevertheless, it should be taken into account as one of possible outcomes of experiments involving silver and chlorine at high pressure.

Preliminary results of experiments aimed at obtaining novel AgClx compounds are described in chapter 8 of this thesis. 48

4. Overview of relevant analogous compounds and their high pressure behavior

When dealing with a particular chemical system, one can often place it in a broader framework of other compounds, based on similarity of composition, structure or properties.

Therefore, in the case of AgO and AgF2, which are studied here, it is useful to review how compounds similar or analogous to them behave under high pressure. Such treatment and comparison will enable us to better understand the processes occurring in these two systems when they are subjected to compression. In this section I will summarize the current state of knowledge on high pressure behavior of (a) transition metal monoxides, (b) mixed-valence compounds, (c) transition metal difluorides and (d) compounds of silver. Through these particular examples, this chapter will also highlight the more general trends and rules governing high pressure behavior of chemical compounds already outlined in section 2.2.

4.1. High-pressure behavior of transition metal monoxides

Based on its chemical formula, AgO can be considered a metal monoxide – a member of a class of compounds with the general formula MO. However, unlike most monoxides, AgO does not feature divalent metal cation in its structure. Instead, it hosts Ag(I) and Ag(III) ions, which makes it a mixed-valence compound. It is the only known example of mixed-valence among transition metal monoxides. Consequently, crystal structure of AgO is also unique. Chemistry and physics of transition metal monoxides (TMOs) is indeed very rich and has been extensively studied, including in the high pressure regime.

Fig. 4.1. Prevalence of different structural types in monoxides of d-block elements. Fig. 4.1 presents the occurrence of different crystal structures in TMOs at ambient pressure. The majority of them crystallize in the cubic rocksalt (NaCl) structure (fig. 4.2, top right), although some of them are distorted. Specifically, monoxides of Mn, Fe, Co and Ni exhibit

AFM ordering, which gives rise to a rhombohedral or monoclinic distortion of the otherwise cubic NaCl lattice.172 Their respective Néel temperature increases in the series Mn → Ni. For

MnO and FeO, those temperatures lie below 200 K, but for CoO, TN is equal to 291 K and it reaches 523 K in the case of NiO.172 This means that AFM-ordered polymorphs of the latter two compounds can be observed at or near ambient conditions. AFM ordering occurs in the [111] direction of the unit cell: magnetic moments are parallel within a given (111) plane and antiparallel to moments in neighboring layers.

Fig. 4.2. Structural types seen in transition metal monoxides discussed in text. Grey spheres – metal; red spheres – nonmetal. The other known TMOs feature a variety of unique structures. NbO adopts a cubic structure similar to rocksalt, but with regular vacancies resulting in 4-fold square planar (instead of 6-fold) coordination of both Nb and O atoms.173 PdO and PtO crystallize in a tetragonal 174 175 P42/mmc structure. CuO adopts a monoclinic C2/c structure. PdO, PtO and CuO all feature square planar coordination of metal atoms and tetrahedral coordination of O atoms. ZnO is known to exist in two different polymorphs at ambient conditions: hexagonal wurtzite-type176 and cubic sphalerite-type;177 both host tetrahedrally coordinated Zn and O atoms. Three polymorphs of HgO are known at ambient pressure: orthorhombic Pnma (CN = 5),178 a related triclinic P1̅179 or a hexagonal cinnabar-type (HgS) structure.180,181

Relationship between late TMOs (groups 10-12) and their rocksalt-structured counterparts (groups 4-9) has been carefully analyzed by Derzsi and co-workers.8,182 The seemingly unrelated structures of PdO & PtO, CuO, AgO and HgO (Pnma) can in fact all be traced back to Jahn-Teller distortion of the cubic rocksalt lattice typical of other monoxides (fig. 4.3).182 The JT effect, as explained in section 1.2, causes elongation or contraction along the z axis of the octahedron. This distortion coupled to other vibrational or electronic degrees of freedom is responsible for the variety of structures in late TMOs. The ordering of the JT-distorted orbitals in these compounds has been shown to be coupled to the L3 acoustic mode at the L point 8 of the Brillouin zone of their respective undistorted rocksalt lattice. The fact that the L3 mode – which affects primarily the oxygen sublattice – is imaginary in PdO, PtO, CuO, AgO and HgO forced into an NaCl-type lattice is evidence of dynamic instability of such high-symmetry arrangement (fig. 4.4). In the case of AgO, the JT distortion is also coupled to charge transfer Ag2+ (d9) → Ag1+ (d10) / Ag3+ (d8), which results in opening of the band gap (~1 eV) at Fermi level. The two known structures of AgO are the result of two different charge ordering patterns.8 The fact that HgO experiences distortions due to JT effect is an interesting phenomenon in itself; after all, Hg(II) ion has a closed-subshell electronic configuration analogous to that of Zn(II) and Cd(II). However, due to the large size and, consequently, pronounced relativistic effects, a significant mixing of 5d and 6s states occurs in Hg(II) ion, which results in partial depopulation of the 5d level and makes JT effect possible.8 As a side note, the hypothetical gold monoxide AuO has been predicted to also be disproportionated at ambient pressure, much like AgO, albeit with an entirely different structure.183

Fig. 4.3. Crystal structures of selected late transition metal monoxides in rocksalt representation. Reproduced with permission from ref. [182] 51

Fig. 4.4. Phonon dispersion curves of selected late transition metal monoxides forced into rocksalt structure, calculated with PBEsol method. Note the imaginary mode at L point in all four compounds. Reproduced with permission from ref. [8] As explained in section 2.2, the influence of pressure typically increases the coordination number of atoms in a given compound.36 For example, wurtzite polymorph of ZnO has been found to transform to a rocksalt structure at 9 GPa184 – a transition that corresponds to an increase of CN from 4 to 6. A further increase is seen in CdO, which transforms into CsCl-type (CN = 8) structure at 90 GPa.185 Further compression of NaCl-type HP polymorph of ZnO is also predicted to induce this type of transition at ca. 260 GPa.186 However, two observations should be made here. First, eight-fold coordination characteristic of CsCl-type structure can only be achieved with a sufficiently large cation-to-anion radius ratio; otherwise, such transition requires a really large pressure (hence the 260 GPa predicted for ZnO). Second, ZnO and CdO are different from other TMOs because of closed-subshell electronic configuration of their metal cations (d10). Consequently, their high pressure behavior is more similar to heavier alkali earth metal monoxides. Indeed, the NaCl to CsCl transition is typical of the latter class, as exemplified by CaO.187 On the other hand, the CsCl-type structure among TMOs has only been observed in the aforementioned HP polymorph of CdO. The analogous compound of mercury does not follow this simple trend. Orthorhombic polymorph of HgO has been shown to transform at 14 GPa to a tetragonal structure, most probably tetragonally distorted rocksalt type.188 Upon further compression to 31.5 GPa, HgO adopts the proper cubic NaCl-type structure.189 Both phase transitions are associated with a relatively small volume drop, and the second transition (at 31.5 GPa) is very likely second-order,

52 based on the structural similarity of consecutive HP polymorphs and the fact that there is no hysteresis upon decompression. It should be pointed out that the pressure of transition into rocksalt structure in HgO is higher than in ZnO (9 GPa) and CdO (NaCl-type at ambient pressure), which is an exception from a more general trend. In this case, the discrepancy is attributed to relativistic effects in the heavy Hg atom and, consequently, increased covalency of Hg-O bonding in HgO, which makes it more resistant to compression.189

Monoxides of metals in the middle of the 3d transition series – MnO, FeO, CoO and NiO – are perhaps the most interesting from the point of view of solid state physics for being some of the most strongly correlated systems. The former three monoxides are all typical examples of Mott insulators, while NiO is considered a prototypical charge-transfer (CT) insulator. In NiO, Ni d valence bands lie lower in energy than O p valence band.190 The opposite is true for MnO, FeO and CoO. In all these compounds, however, the conduction band is made up of empty d states of the metal (as shown in fig. 1.4). All four compounds have been predicted to become metallic under sufficiently high pressures – a process known as the Mott transition.191 However, these transitions do not necessarily follow one simple scenario and are often preceded, accompanied or followed by other processes.192 Among these four monoxides, FeO has probably attracted the most attention, especially in geosciences. Numerous studies on iron(II) oxide have been carried out in the wide range of pressure and temperature in order to simulate core and mantle conditions.193,194 (and references therein) That is because FeO is likely present in Earth’s outer core as the mineral wüstite and is the end-member component of mangesiowüstite (Mg,Fe)O (also called ferropericlase), which in turn is an important mineral in Earth’s mantle.195 Details of phase diagram of FeO and geophysical implications thereof are beyond the scope of this work; I will only summarize here the most important phenomena that occur upon compression at ambient temperature from the point of view of solid state chemistry and physics. At around 17 GPa, FeO undergoes a rhombohedral (i.e. along the [111] body diagonal) 196 elongation of the cubic unit cell. The same distortion is seen in FeO below TN due to AFM ordering; thus, increasing pressure shifts the Néel temperature to higher values. The exact pressure boundary of this transition has varied in different reports, depending on the pressure medium (and consequent non-hydrostatic conditions) or exact composition (FeO is often non- stoichiometric).197 Additionally, the transition from rocksalt to distorted rocksalt structure does not exactly coincide with the onset of AFM ordering, which can be observed by means of Mössbauer spectroscopy already at 5 GPa.198 A further transition from the rhombohedrally distorted rocksalt structure to NiAs-type polymorph has been observed at high pressures and

53 temperatures (e.g. at 74 GPa and 900 K).199 As can be inferred from extrapolation of the phase boundary, at room temperature this transition should occur at ca. 100 GPa, but this has never been achieved without heating. Ozawa et al. reported that in the HP NiAs-type phase, a transition to a metallic state occurs at ca. 120 GPa.200 At the same time, a spin crossover from high-spin to low- spin state is observed in X-ray emission spectra (XES), and coincides with a volume drop of 2.5% which corresponds to a transition from inverse to normal NiAs structure.† These findings are corroborated by resistance measurements.201 It is important to stress that this summary of HP behavior of FeO is necessarily selective: for example, the most recent study on magnetic transition using Mössbauer spectroscopy have found that the spin crossover is not complete until 200 GPa,202 but this has been attributed partly to possible differences in composition between

Fe1-xO samples. Research in this area is still ongoing and is expected to bring more precise information on the exact nature of HP phases of FeO. However, the transition from NaCl-type to NiAs-type via a rhombohedrally distorted polymorph and subsequent metallization and magnetic collapse can be considered well documented, based on the above considerations. MnO also experiences a pressure-induced rhombohedral distortion: a contraction along the [111] direction, starting at ca. 37 GPa.203 Two further structural phase transitions have been observed at 90 GPa and at ca. 120 GPa, as indicated by XRD data.204–207 Metallic luster of compressed MnO samples suggests a transition to metallic state with an onset at ca. 90 GPa, which was further evidenced by IR reflectivity and absorption,208 as well as resistivity measurements.209 More detailed studies have shown that the rhombohedral phase transforms into NiAs-type at 90 GPa and becomes paramagnetic.210 The Mott transition occurs at 105 GPa as a first-order isostructural phase transition (i.e. within the same NiAs-type phase). It is associated with a 6.6% volume drop and is driven by magnetic moment collapse, leading to a diamagnetic metallic state.210,211 Compressed CoO experiences stretching along the [111] direction, starting from ca. 43 GPa. However, the extent of this distortion is relatively small: it is seen as a decrease of symmetry in XRD patterns and there is no associated sharp volume drop.212 It undergoes two further phase transitions at ca. 90 and 120 GPa. At 90 GPa, the rhombohedrally distorted NaCl-type phase transforms into a higher-density phase of the same symmetry, with a volume drop of 2.7%.213 Above 120 GPa, the high-density rhombohedral polymorph again adopts undistorted, cubic NaCl-type structure.212 Importantly, the sequence of transitions: LP(NaCl) → HP1(r-NaCl) → HP2(r-NaCl) → HP3(NaCl) preserves the basic rocksalt-type arrangement of atoms; it is only

† In normal NiAs-type arrangement, metal atoms are coordinated in an octahedral pattern, whereas the arrangement around nonmetal/semimetal atoms forms a trigonal prism. In inverse (anti-) NiAs, the situation is reversed. 54 more or less distorted. This sequence stands in contrast to those seen in FeO and MnO, which at largest achieved pressures transform into NiAs-type structure. Electrical resistivity measurements indicate a decrease of resistivity of about 8 orders of magnitude between 43 and 60 GPa – after the onset of rhombohedral distortion.214 Another, although much smaller drop in resistivity begins at the transition point between two rhombohedral phases. No significant resistivity change accompanies the transition into HP cubic polymorph. Theoretical studies (DFT and dynamic mean-field theory, DMFT) suggest that high pressure behavior of CoO is an example of orbitally- selective Mott transition. During the first transition to HP1(r-NaCl), only the t2g bands of Co(II) attain metallic character, while the eg levels are predicted to remain insulating up to 170 GPa.215,216 The volume drop between the two rhombohedral phases at 90 GPa is associated with a transition to a fully metallic state driven by high-spin to low-spin magnetic transition.191,215,216 CoO is therefore an interesting system in which large changes in electronic and magnetic properties occur separately – at 43 and 90 GPa, respectively. NiO, as already mentioned, is different from MnO, FeO and CoO in that it is a charge- transfer insulator. At ambient pressure, the cubic NaCl-type structure is already rhombohedrally distorted due to AFM ordering – even at room temperature. Upon compression, it does not appear to undergo any structural phase transition up to 240 GPa, at which point a transition to metallic state is observed.217,218 This is indicated by UV and optical reflectivity measurements, as well as a change in resistivity, which shows a three orders of magnitude drop at 240 GPa.218 However, XRD data do not indicate any structural changes up to 280 GPa apart from a gradual increase of the rhombohedral distortion.219 In the same pressure range, Mössbauer spectroscopy studies have failed to find evidence of magnetic collapse usually associated with a Mott transition.219 AFM ordering is retained up to 280 GPa – the highest pressure at which magnetism has been observed in any material.219

There have been several studies on high pressure behavior of CuO, the two most recent of which focused on the relationship between pressure-induced structural changes and magnetic and electric properties of this compound.220,221 CuO is known to behave as a type-II multiferroic between 213 and 230 K at ambient pressure.222 Upon compression, a ferroelectric transition is observed between 3.4 and 4.4 GPa, and Raman spectra indicate a change in magnetic ordering in the same pressure range. Based on this data, Jana et al. concluded that the influence of pressure shifts the temperature of multiferroic ordering to ambient values.220 However, a more recent study by Kozlenko et al.,221 employing neutron and X-ray diffraction as well as hybrid-DFT calculations, failed to find evidence of that and instead found that CuO undergoes a phase transition at 13 GPa, in which the coordination number of Cu atoms changes from 4 (square-

55 planar) to 6 (octahedral). The pressure dependence of volume does not show any discontinuity at transition, which suggests that it is of second-order. Indeed, the extent of elongation of [CuO6] octahedra gradually decreases with pressure – from ca. 42% at ambient conditions to ca. 18% at 38 GPa.221 Therefore, the influence of pressure appears to diminish the magnitude of Jahn-Teller effect in CuO to some extent. AuO, the hypothetical gold monoxide, is predicted to undergo comproportionation above 80 GPa and metallization at an impressively high pressure of over 300 GPa.183 PdO, which features low-spin Pd(II) (d8) centers, undergoes a first-order phase transition at 12 GPa, as evidenced by a sharp volume drop seen in energy-dispersive XRD data.223 The unit cell of the high pressure polymorph is also tetragonal, although the exact structure has not yet been determined. The authors of the cited high-pressure study conclude that it is probably a tetragonally elongated modification of rocksalt structure. No data on compression of the isostructural PtO appears to exist in literature. No sources with high pressure data on VO, CrO, ZrO, NbO and TaO have been found. TiO has only been studied theoretically – it is predicted to transform into CsCl-type structure in the pressure range between 60 and 100 GPa.224–226

Clearly, there is a great diversity among TMOs in terms of high-pressure behavior and it is therefore difficult to summarize their structural behavior by any general statement that would apply to all of them. In late TMOs, this stems partly from their already diverse electronic and crystal structures at ambient pressure. On the other hand, monoxides in the middle of the transition series, although similar in terms of crystal structure and magnetic ordering, exhibit a complex interplay of structural, electronic and magnetic transitions that is largely dependent on electronic configuration (i.e. d-electron count) of the given metal cation. In general, significant discrepancies between experimental results and theoretical predictions for TMOs have been observed, which has in turn stimulated numerous studies aimed at improving theoretical models describing such strongly correlated systems. Given that TMOs constitute prototypical examples of Mott and charge-transfer insulators, proper understanding of their high-pressure behavior is an important goal for solid state chemistry and physics. Because of that, pressure-induced processes in TMOs continue to be among the most intensely studied areas of contemporary physics.227 A graph in the next page summarizes experimental information about structural phase transitions and metallization pressures of selected TMOs. As already mentioned, the ambient- pressure structures of HgO and PdO indicated in red can be traced back to NaCl-type structure via a JT distortion, coupled with lattice instabilities.

4.2. High-pressure behavior of mixed-valence compounds

Silver(I,III) oxide is different from most metal monoxides in that it features silver at two different oxidation states – Ag(I) (CN = 2) and Ag(III) (CN = 4). This property makes it a member of another class: mixed valence compounds – systems in which one of the constituent elements exists at multiple oxidation states. Most known mixed valence compounds are formed by transition or post-transition metals. In the former group, the d subshell often allows more than one stable electronic configuration of the cation, e.g. Fe(II) (d6) and Fe(III) (d5). Similar considerations can be applied to lanthanides (f-block). In the case of p-block elements, different oxidation states arise depending on whether the s subshell in the cation is filled or empty, for example Pb(II) ([Xe]6s25d10) and Pb(IV) ([Xe]5d10). Several compounds of this type are found in nature. The best-known among them is 228 229 probably magnetite Fe3O4. Other mixed-valent minerals include minium Pb3O4, 230 231 232 233,234 hausmannite Mn3O4, pitchblende U3O8, cervantite Sb2O4, covellite CuS and greigite 235 Fe3S4. Among synthetic compounds of this class are halogenoaurates M2Au2X6 (M – group 1 236–239 metal; X – Cl, Br, I), several mixed-valent compounds of silver: AgO, Ag3O4, Ag3(SbF6)4; 240 241 242 Ga2Cl4, Tl4O3, Co3O4 and dyes such as Prussian blue Fe4[Fe(CN)6]3, to name just a few. Mixed valence compounds as a unified class with common characteristics were first thoroughly described in a 1968 review by Robin and Day.243 They proposed a classification based predominantly on their electron transport properties. In class I, atoms of different oxidation states exist in two distinct crystallographic sites with different coordination environment; consequently, electrons do not move freely between the two sites and the material exhibits insulating or semiconducting properties. AgO is an example of class I compound. Class II features the two oxidation states in distinct sites, but with a very similar coordination pattern; this results in a slight charge delocalization and at least one electronic transition in the visible range spectrum. Prussian blue with its deep blue color is a representative example of this. Finally, in class III compounds, atoms of different oxidation states are indistinguishable due to rapid exchange of electric charge between them. Class III can be further divided into III-A and III-B. In the former, charge delocalization is limited to isolated, polynuclear clusters. In the latter, it occurs within the entire cationic sublattice. Consequently, III-A compounds are insulators, while III-B are characterized by metallic properties, such as relatively high conductivity and reflectivity in the visible range.243 Below, I review several important mixed valence compounds and their high pressure properties.

Fe3O4, Co3O4 and Mn3O4 are mixed-valent oxides of transition metals, which feature divalent and trivalent metal cations in 1:2 ratio. All three adopt a spinel structure or a slight modification thereof (fig. 4.5). The ideal spinel structure (Fd3̅m space group) consists of a face- centered cubic sublattice of oxygen anions, in which ⅛ of tetrahedral voids and ½ of octahedral voids are occupied by metal cations. In a so-called normal spinel, tetrahedral sites host M2+ cations and octahedral – M3+ cations. Tetrahedral and octahedral sites are often referred to as A 2+ 3+ 3+ and B sites, respectively. In general, a normal spinel can be described as [M ]A[M M ]BO4. In the inverse spinel, half of the B sites are occupied by divalent cations, while half of trivalent 3+ 2+ 3+ cations sit at A sites instead – this can be written as [M ]A[M M ]BO4.

Fig. 4.5. Crystal structure of spinels. Grey spheres – metal; red spheres – oxygen.

Fe3O4 occurs in nature as a mineral magnetite and crystallizes in an inverse spinel structure.228 Fe(II) and Fe(III) oxidation states are indistinguishable within the sublattice of cations at B sites – electrons can move freely between them and the formal oxidation state of iron is equal to 2.5. As a result, magnetite exhibits almost metallic (102-103 Ω-1cm-1) electrical 244 conductivity. No charge transfer occurs between A and B sites. Consequently, Fe3O4 can be thought of as a class I mixed valence compound with respect to the relationship between A and 243 B sites, but a class III-B compound because of charge delocalization within B sites. Fe3O4 is ferrimagnetic: ferromagnetic ordering of spins within B-site sublattice and their antiferromagnetic coupling with spins at A sites results in a non-zero net magnetization. Because iron(II,III) oxide, like FeO, is an important part of Fe/O phase diagram (crucial from geological perspective), it has also been extensively studied within a large range of pressures and temperatures. One of its best known features is that at temperature of ca. 120 K and ambient pressure it undergoes a structural and electronic transition, known as Verwey transition.245 This

59 process is a complex interplay of lattice dynamics and electronic degrees of freedom,246 which results in a sharp rise of electrical resistivity by two orders of magnitude and a distortion of the cubic spinel structure into a monoclinic phase. Many questions regarding this transition remain unanswered and it continues to be studied.247 Upon compression, the temperature of the Verwey 248 transition (TV) steadily decreases and it disappears altogether (i.e. reaches 0 K) at about 8 GPa.

In terms of crystal structure, Fe3O4 transforms into a high-pressure polymorph (designated 249 250 as h-Fe3O4) at ~25 GPa. The new structure is orthorhombic, either of CaMn2O4 (Pbcm) or 251,252 CaTi2O4 (Bbmm) type. The ambiguity arises from several factors: both structures are very similar and fit the XRD data very well; at the same time, this transition is very sluggish and although reflections from the h-Fe3O4 phase appear spontaneously above the transition pressure, heating has been employed to speed up and facilitate complete transformation. The structure of h-Fe3O4 consists of Fe(III) ions coordinated in distorted octahedra (CN=6) and Fe(II) sitting in bicapped trigonal prisms. In the isostructural CaTi2O4, Ca(II) ions are eightfold coordinated, but in high pressure magnetite, the effective coordination number of Fe(II) ions at these sites is 6, 252 253 due to their smaller size. The h-Fe3O4 polymorph is paramagnetic. Its resistivity decreases with increasing pressure, but even at 140 GPa the relatively high values of ρ suggest that a genuine metallic state is not yet achieved.254

Fe3O4 has been predicted to become thermodynamically unstable at higher pressures, 255 which would favor its decomposition into FeO and Fe2O3. However, this has not been seen in experiments; instead, a further phase transition into another orthorhombic (Pnma) structure has recently been observed at ~70 GPa, without any indication of decomposition.256 There has also been much discussion regarding the electronic and magnetic properties of 257 Fe3O4 below 25 GPa. (and references therein) It appears that no transition from inverse to normal spinel is taking place, according to most recent neutron diffraction data and contrary to previous suggestions.258 (and references therein) Other properties, such as decreasing resistivity below the first phase transition and decreasing bulk magnetization between 15 and 25 GPa can be explained by the increasing delocalization of 3d electrons of Fe.257 Though recent conductivity measurements have also found that Fe3O4 at certain, non-hydrostatic conditions behaves more like a semiconductor above ca. 25 GPa, the existing body of research concludes that the ground state of magnetite at pressures above the suppression of Verwey transitions is indeed metallic.259

Analogous to Fe3O4 in terms of stoichiometry, cobalt(II,III) oxide is different from magnetite for several reasons. At ambient conditions, it adopts a normal spinel structure.242 The octahedra are somewhat distorted – all six Co-O bonds are equal in length, but the angles between them deviate from 90° seen in ideal spinels. Above 17.7 GPa, an abrupt change in O atom

60 coordinates is observed in XRD data, but the pressure dependence of unit cell volume does not indicate any phase transition.260 This is attributed to a change from normal to partially inverse spinel structure: increased pressure facilitates charge transfer between A and B sites, which in turn strongly influences Co-O bond lengths. The charge transfer scenario is further supported by 260 X-ray absorption spectroscopy. Above 30 GPa, Co3O4 has been found to transform to a monoclinic P21/c polymorph, which features two distinct Co octahedral coordination sites corresponding to two Co valence states.261 It is suggested that the phase transition is driven by the previously mentioned charge transfer: the Co(II) ion, which at higher pressure finds itself in 6 1 the strong octahedral ligand field and, consequently, low spin state (t2geg), becomes Jahn-Teller- active and induces a deformation of the octahedral coordination environment. This effect competes with compression, which reduces the angle variance in the [CoO6] octahedra. Overall, the cubic structure becomes increasingly unstable at higher pressures and the transition to the 261 monoclinic structure becomes favorable. Upon decompression, the P21/c polymorph transforms into another monoclinic phase (space group C2/m) between 28 and 19 GPa. The new monoclinic phase is quenchable down to 2 GPa.261 In both high-pressure monoclinic structures, II [Co O6] octahedra experience a significant Jahn-Teller distortion.

Manganese(II,III) oxide Mn3O4 also crystallizes in a structure of normal spinel, but it is 230 III even more distorted than Co3O4. The [Mn O6] octahedra are elongated along their z axis due 3 1 to Jahn-Teller effect – electron configuration of Mn(III) cations in octahedral ligand field is t2geg. These octahedra are slightly tilted with respect to the c direction. Consequently, the structure of

Mn3O4 is tetragonal (I41/amd). Applying pressure of 10-20 GPa induces a transition to an 262–264 orthorhombic phase of CaMn2O4 type (Pbcm space group), which is essentially very similar III to the HP structure of magnetite discussed above, but the [Mn O6] octahedra are more distorted III than analogous [Fe O6] ones. Below the phase transition, increasing pressure suppresses the deformation caused by JT effect; it is suggested that this is one of the driving forces for the transition under high pressure.264 This could also be one of the reasons why this transition occurs at a significantly lower pressure than in analogous Fe3O4.

Overall, the three mixed-valent spinels discussed above illustrate how in seemingly very similar compounds, electronic configuration can have a very strong influence on crystal structures under high pressure. Additionally, pressure-induced increase in band overlap and facilitated charge transfer can lead to distortions that would not occur at ambient conditions.

An interesting example of a subtle change in electronic structure is seen the case of lead(II,IV) oxide. Pb3O4, which is found in nature as mineral minium, hosts Pb(II) and Pb(IV) 61 ions in its crystal structure. At ambient conditions, it crystallizes in a tetragonal P42/mbc space group, in which Pb(IV) cations are six-fold coordinated in slightly twisted [PbO6] octahedra, whereas Pb(II) and four O atoms form an irregular pyramid with O atoms at the base and Pb atom at the vertex.229 Such structure of Pb(II) coordination environment is determined by the fact that the lone pair in Pb(II) ion acts as if it were a fifth ligand. At a relatively low pressure of 0.1-0.3

GPa, Pb3O4 transforms into an orthorhombic (Pbam) polymorph, which is very similar to the 265 ambient pressure phase – only the [PbO6] octahedra and [PbO4] pyramids are more regular. At 5.4-6.6 GPa, a transition to another orthorhombic phase with the same symmetry is observed. In that structure, Pb(II) ions are coordinated in a pattern of capped trigonal prism; effectively, coordination number increases from 4 to 7. It appears that under pressure, the character of the lone pair on Pb(II) changes to a predominantly s-type during the second phase transition, which greatly reduces its stereochemical activity with respect to the ambient pressure polymorph, enabling a more symmetrical coordination environment.265

From the point of view of this work, which is focused on chemistry of silver, an important and perhaps the most relevant case of mixed valence are halogenoaurates: compounds with the I III general formula M2Au Au X6¸where M is a group 1 metal (most often cesium) and X is Cl, Br or I. All three cesium halogenoaurates have very similar properties under ambient conditions; I 236,237 will describe Cs2Au2Cl6 as an example. It crystallizes in a structure similar to perovskite, but there are differences in coordination of Au(I) and Au(III) ions. Along the z direction, the

[AuCl6] octahedra are alternately elongated and contracted. At the same time, in the xy plane, they experience alternate tetragonal elongation and contraction of Au-Cl bonds. These distortions from the ideal perovskite structure result in linear 2-fold coordination of Au(I) (along the z direction) and square planar, 4-fold coordination of Au(III) (in the xy plane). Overall, the structure is tetragonal with a I4/mmm symmetry. The absorption spectrum features two intense inter- valence charge transfer bands between the two Au sites (Au(I) → Au(III)) at 16,500 and 21,500 cm–1.266 The number of CT bands reflects the splitting of Au(I) d levels in the ligand field. These 243 properties make Cs2Au2X6 typical members of class II of mixed valence compounds.

Upon compression, Cs2Au2Cl6 experiences a drop in resistivity by nine orders of magnitude at ca. 6 GPa and a transition from semiconducting to metallic state, based on temperature dependence of resistivity below and above that pressure, respectively.267 This is associated with a gradual displacement of Cl atoms, which at 5.2 GPa reach the midpoint between two adjacent Au atoms.268 Above 5.2 GPa, all Au crystallographic sites are equivalent; however,

[AuCl6] octahedra remain elongated in the z direction. At the same time, Mössbauer spectra indicate that Au remains disproportionated even above that pressure.269,270 Based on most recent

62 single crystal XRD data, transition to an ideal cubic perovskite structure and comproportionation to Au(II) valence state is realized at 12.5 GPa.271 Although Au(II) should experience a strong

Jahn-Teller distortion of its coordination octahedra, this is not the case in HP Cs2Au2Cl6.

Regularity of [AuCl6] octahedra in the HP structure is attributed to a second-order Jahn-Teller effect – a result of competition between elongation and contraction at neighboring sites.271

Structures of ambient pressure and HP polymorphs of Cs2Au2Cl6 are shown in fig. 4.6.

Fig. 4.6. Crystal structures of Cs2Au2Cl6: left – ambient pressure; right – 15 GPa. Green spheres – Cl atoms. Au atoms are located within octahedra.

In Cs2Au2Br6, a structural phase transition to a different tetragonal polymorph and metallization are seen at about 9 GPa.272 The position of Br atoms indicate comproportionation and equivalence of all Au atoms, but the [AuBr6] remain elongated along the z direction, presumably due to Jahn-Teller effect. Heating the sample to ca. 120°C above 9 GPa results in a further transition into a cubic polymorph, which is metastable upon decompression.272

Interestingly, the transition to single-valence state in Cs2Au2Br6 has also been achieved by irradiating a compressed sample (6.4-6.8 GPa) with a 1.9 eV excimer laser.273 This creates stable single-valence clusters within the sample, which accumulate through further irradiation. The resulting single-valence state reverts to mixed valence upon decompression below 5.5 GPa.273

The iodine-containing analog – Cs2Au2I6 – exhibits a somewhat more complex high pressure behavior. It was initially reported to undergo a semiconductor to metal transition at ca. 6 GPa, while retaining the tetragonal symmetry (i.e. distorted octahedra) – similarly to 274,275 Cs2Au2Br6. The drop in resistivity of 7 orders of magnitude up to 6 GPa is followed by a 274 subsequent increase. However, most recent XRD data indicate that in Cs2Au2I6, the transition at ca. 5.5 GPa breaks the tetragonal symmetry and leads to an orthorhombic polymorph.276 Two structures have been proposed which fit the XRD data equally well, but spectroscopic studies277 appear to favor one of them, in which all [AuI6] octahedra are equivalent and feature divalent 63 silver cations. They are elongated along their z axis due to Jahn-Teller effect and tilted relative to the c direction of the unit cell, resulting in Ibmm symmetry. IR spectroscopy measurements indicate that the orthorhombic polymorph is an insulator. It appears that charge density wave (CDW)-induced band gap gradually closes with compression as a result of I atoms approaching midpoint positions between Au atoms, but the subsequent phase transition into the comproportionated orthorhombic polymorph – in which the strong Jahn-Teller effect causes significant distortions – reopens the band gap. The exact origin of this gap is as yet unknown.277 276 Upon further compression to 12-14 GPa, Cs2Au2I6 undergoes reversible amorphization. Differences in high pressure behavior between halogenoaurates discussed above are attributed to increasing covalence of Au-X bonds and, consequently, Jahn-Teller effect becoming 272,277 more pronounced in the sequence Cs2Au2Cl6 → Cs2Au2Br6 → Cs2Au2I6.

When discussing pressure-induced comproportionation, as seen in Cs2Au2X6 compounds, an opposite scenario – disproportionation – is also worth mentioning. For example, nitrogen monoxide NO has been found to produce N2O4, N2O and trace amounts of N2O3 when cooled to 278 175 K and compressed to 1.5 GPa. On the other hand, N2O upon laser heating to 2000-3400 K III + V – 0 279 and compression to 10-55 GPa yields a mixture of (N O )(N O3 ) and N 2. But perhaps the most interesting example of disproportionation under high pressure was recently observed in hydrogen sulfide, which exhibits conventional superconductivity at 90 GPa and 203 K.280 XRD measurements confirmed that the superconducting sample consists of a higher hydride HxS (where x ≈ 3) and elemental sulfur.281 That disproportionation is sometimes favored under pressure can be explained by the fact that spheres of different radii (e.g. atoms at different oxidation states) can be more tightly packed than uniform spheres.35

4.3. High-pressure behavior of transition metal difluorides

AgF2 is one of many transition metal difluorides (TMF2) – compounds with the general formula MF2. The majority of compounds in this class adopt a structure of either rutile (TiO2,

P42/mnm) or fluorite (CaF2, Fm3̅m). The former consists of metal atoms coordinated by six ligands in an octahedron, while in the latter, metal coordination number is equal to 8. The occurrence of these two structural types among TMF2 is shown in fig. 4.7, and the two structures 282 are shown in fig. 4.8. It should be pointed out that TiF2 was only synthesized at high pressures; this – together with relatively large size of Ti(II) cation compared to other 3d metals – may explain the fact that it was observed in fluorite structure, in contrast to other difluorides of period 3 transition metals.

Fig. 4.7. Prevalence of different structural types in difluorides of period 3 and 4 d-block elements.

Fig. 4.8. Common structural types in transition metal difluorides at ambient pressure. Grey spheres – metal, yellow spheres – nonmetal.

Two polymorphs of PdF2 are known at ambient pressure. Apart from the rutile polytype, it can also crystallize in a cubic structure often referred to as HP-PdF2, because it was first obtained through compression to 1.5 GPa.283–285 Later, it was also synthesized at ambient 286 pressure. HP-PdF2 (space group Pa3̅) consists of a face-centered cubic metal sublattice, very much like CaF2, but the anions do not sit exactly at tetrahedral voids as in ideal fluorite. This results in a six-fold coordination of metal atoms in a distorted octahedron. The structure of this 65 polymorph is also somewhat similar to pyrite (FeS2): fractional coordinates of nonmetal atoms in

HP-PdF2 (ca. 0.34) can be thought of as intermediate between fluorite (0.25) and pyrite (ca. 0.38).284 In fact, this number has far-reaching consequences for coordination chemistry of the three structures. A change from 0.25 (CaF2) to 0.34 (HP-PdF2) reduces the CN of metal atom from 8 to 6. FeS2, with an even larger fractional coordinate of nonmetal atom (at ca. 0.38), hosts genuine S-S bonds. All three structures are shown in fig. 4.9.

Fig. 4.9. Comparison of CaF2, HP-PdF2 and FeS2 structures. Grey spheres – metal, green – nonmetal.

Three TMF2’s show deviations from ideal rutile or fluorite structure at ambient conditions. CrF2 exhibits a significant elongation of [CrF6] octahedra (~22%) due to Jahn-Teller 287 effect, which leads to an overall monoclinic instead of tetragonal symmetry. In CuF2, Jahn-

Teller distortion results in a structure consisting of [CuF4] square planar units connected into 288 corrugated layers. As described in section 3.3.1, AgF2 also adopts a layered structure, but the structure of CuF2 is monoclinic (P21/c), while AgF2 is orthorhombic (Pbca). In fact, although the

Jahn-Teller effect leads to a system of layers in both compounds, AgF2 is better described as a distorted fluorite because of a different arrangement of atoms in its metal sublattice.289 This is illustrated in fig. 4.10.

Fig. 4.10. Pattern of nearest contacts in metal sublattice of TiO2, CaF2 and AgF2.

Many TMF2 exhibit magnetic ordering at lower temperatures. Most of them are antiferromagnets: the highest Néel temperature observed in this class is 180 K of rutile polymorph 13 of PdF2. Ferromagnetic ordering is seen in cubic (HP) polymorph of PdF2 below ca. 220 K. 66

(and references therein) AgF2 is also effectively ferromagnetic below 163 K, although due to slightly more complex interactions already described in section 3.3.1.

Compared to monoxides, relatively few studies on high pressure behavior of TMF2 have been carried out. Most reliable data exists for group 12 metal difluorides. For example, ZnF2 290 transforms into a CaCl2-type phase at ca. 5 GPa and into HP-PdF2 type at ca. 10 GPa. CaCl2 (Pnnm) structure is very similar to that of rutile, but when viewed along the z direction, nonmetal atoms deviate from their positons on xy diagonal of the unit cell. Consequently, [MX6] octahedra are also rotated with respect to those diagonals and the structure is orthorhombic. The rutile →

CaCl2 transition is of second order, as it does not involve a significant volume drop.

Upon decompression, ZnF2 reverts to a mixture of two phases: one with fluorite structure and another with α-PbO2 structure (Pbcn space group). This polytype consists of a distorted fcc metal sublattice – every other layer of metal atoms perpendicular to the c axis is slightly shifted in the [010] direction – while oxygen atoms occupy quasi-tetrahedral sites. Metal atoms are thus six-fold coordinated in distorted octahedra.291 Virtually the same series of transitions is seen in 292 MgF2 in the 0-20 GPa pressure range. This should come as no surprise, since ionic radii of Mg(II) and Zn(II) are almost identical (86 and 88 pm, respectively).293

A heavier analog of zinc fluoride – CdF2 – undergoes a transition to an orthorhombic phase at 7 GPa.294 The resulting HP polymorph is isostructural with cotunnite – mineral with the 295 chemical formula PbCl2. In this structure, metal atoms are coordinated by 9 nonmetal atoms

(fig. 4.11, left). Cotunnite (space group Pnma) is an important polytype among MF2 compounds at high pressures. HgF2 has been theoretically predicted to undergo an analogous transition at 4.7 GPa.296 Heavier group 2 metal fluorides have also been observed to transform into this structure: 297 CaF2, SrF2 and BaF2 at 9, 5 and 3 GPa, respectively. (and references therein)

Fig. 4.11. Structural types with CN > 8 found in metal difluorides at high pressure.

The highest-density phase achieved in metal difluorides is that of anti-Ni2In type (CN =

11, space group P63/mmc) (fig. 4.11, right). CaF2, SrF2 and BaF2 adopt this structure above 72, 67

29 and 14 GPa, respectively.297 Although it is reasonable to predict that some TM difluorides would also transform into anti-Ni2In structure at sufficiently high pressures, this has not yet been observed.

No data on VF2 under elevated pressures has been found in literature. TiF2 is stable in the fluorite crystal structure up to at least 6.5 GPa.282 No phase transitions have been observed for 298 CrF2 up to 9 GPa.

CuF2 transforms at 9 GPa to a polymorph isostructural with AgF2 at ambient conditions (Pbca space group), as indicated by Raman scattering and theoretical calculations performed 299 recently by Kurzydłowski in our laboratory. This process occurs at a pressure similar to CaCl2

 HP-PdF2 transition in ZnF2 (10 GPa). This is an expected result, since both processes can be understood as a transition from rutile to fluorite polytype, and cationic radii of Cu(II) and Zn(II) 293 are very similar. However, in case of CuF2, both the low-pressure P21/c structure and high- pressure Pbca structure are strongly distorted with respect to regular rutile and fluorite structures, respectively, due to a strong Jahn-Teller effect in the coordination environment of Cu(II) cations. Additionally, DFT+U calculations reported in the same work indicate that the fluorite-like structures of CuF2 remain stable up to ca. 70 GPa, while ZnF2 transforms into cotunnite already 299 at 29 GPa. Therefore, it appears that JT effect in CuF2 makes the transition to more highly coordinated cotunnite-like polytype less favored and shifts it to higher pressures.

High pressure behavior of mid-transition metal difluorides – MnF2, FeF2, CoF2 and NiF2

– has been studied in greater detail. Among these, MnF2 has attracted the most attention, although it has arguably been the most elusive. Most recent data by Stavrou et al.300 – a combined XRD,

Raman and theoretical (DFT) study – indicate that MnF2 transforms into a structure similar to

SrI2 (orthorhombic, Pbca, 7-fold coordination of metal cations) at 3 GPa. A further transition to cotunnite structure occurs at 13 GPa. However, earlier studies have suggested that a transition to 301 the CaCl2 structure occurs at still lower pressures – ca. 1.5 GPa. Also, α-PbO2 phase of MnF2 was observed upon decompression.302 That the more detailed, recent study failed to observe those transitions does not necessarily disprove their existence. First, the rutile → CaCl2 transition is often second-order and could have been easily missed, especially if it is very closely followed by another transition. Second, those discrepancies can be explained by different pressure media used in experiments and, consequently, different degree of hydrostaticity, which could alter the observed sequence of transitions to some extent.300 The influence of deviations from perfectly hydrostatic conditions is evident in the case of

CoF2. It has been shown to undergo a series of transitions: rutile → CaCl2 → HP-PdF2 → CaF2

→ cotunnite, with the onset at 3.6, 8, 15 and 44 GPa, respectively.303 However, the ideal cubic

HP-PdF2 coexists with its orthorhombically distorted (Pbca) polymorph and even with the CaCl2 phase up to 15 GPa – that is, until the transition to fluorite polymorph. Additionally, while the theoretical (PBEsol) calculations are in quite good agreement with the experimental findings, they predict the HP CaF2-type phase to be distorted (tetragonal, I4/mmm) under ideally hydrostatic conditions and undistorted at non-hydrostatic conditions. Also, the energy difference between distorted and undistorted HP-PdF2 phase is calculated to be only 0.3 meV/FU, which may explain their coexistence in the entire pressure range of their stability.

Data on FeF2 and NiF2 under high pressure is very scarce. NiF2 transforms into CaCl2 structure at 1.5 GPa304 and to a cubic polymorph described as distorted fluorite at 8.5 GPa,301 but the exact structure of the latter has not been determined. A recent theoretical study predicts a transition to a monoclinic phase at 30 GPa,305 but the aforementioned experimental data – 301 collected up to 29.3 GPa – found no indication of this. FeF2 undergoes a transition to a distorted fluorite at 4.5 GPa and to an unknown hexagonal phase at 22 GPa, with no further transitions up to 40 GPa.301,306 This stands in contrast to theoretical calculations, which indicate that a following series: rutile → CaCl2 → distorted HP-PdF2 → CaF2 → PbCl2 should occur in FeF2, at 307 corresponding pressures of 5.3, 8.2, 20.4 and 25.3. Given that (a) MnF2 and CoF2 both transform to cotunnite phase at 13 and 44 GPa, respectively, and (b) theory predicts a transition to cotunnite at 25.3 GPa in FeF2, it is possible that the transition in FeF2 at 22 GPa reported by Ming et al. has been incorrectly described as leading to a hexagonal polymorph and yields, in fact, cotunnite phase. However, this is impossible to determine based on such limited data.

To sum up, the science on high pressure behavior of transition metal difluorides is still far from settled. Only a few of these compounds have been studied in greater detail. It appears that the size of metal cation – largely determined by the number of d electrons – plays a crucial role in structural transformations of TMF2. Pressure-induced metallization has not yet been observed in these compounds and indeed, it is expected to occur at much higher pressures compared to TMOs. As pointed out in section 2.2, increasing pressure leads to broadening of and stronger interactions between bands. However, since Fˉ bands lie lower in energy and are narrower than O2– bands, their interaction with valence d states of transition metal cations is almost nonexistent at ambient pressure. Therefore, much stronger compression is required in order for TMF2 to attain 35 metallic state. Experimentally determined structural behavior of TMF2 up to 30 GPa is graphically summarized on the next page.

4.4. High-pressure behavior of silver compounds

Studies of silver compounds under high pressure have not been nearly as extensive as those of other transition metals. In fact, the existing body of research deals predominantly with halides and chalcogenides (i.e. sulfides, selenides and tellurides) of monovalent silver.

Among binary silver(I) halides, the iodide AgI has been especially well studied. It has attracted attention due to its superionic conductivity at certain conditions. This phenomenon is characterized by mobility of ions much larger than normally seen in ionic solids, which in turn gives rise to electrical conductivity in the order of 0.1 to 1 Ω-1 cm-1 – comparable to that of molten salts. For this reason, those materials are sometimes referred to as solid electrolytes. Superionic conductivity has allowed using solid instead of liquid electrolytes in certain electrical devices such as batteries or capacitors.308 At ambient pressure and temperature, AgI adopts either wurtzite or sphalerite structure, much like ZnO (see section 4.1).309 (and references therein) Above 150°C, it transforms into a structure consisting of a body-centered cubic sublattice of iodide anions, within which Ag(I) cations occupy ⅙ of tetrahedral interstices. The facile diffusion of cations between neighboring tetrahedral sites is responsible for superionic conductivity of the high-temperature phase.309 However, in order for superionic conductivity to have practical applications, it should preferably be achieved at or close to room temperature. In AgI, this has been successfully realized under high pressure. Above 11.3 GPa, it transforms into a monoclinic (P21/m) KOH-type structure, which is essentially a distorted rocksalt lattice.310 This phase has been found to exhibit fast ion -1 -1 311 conductivity in the order of 0.1 Ω cm . In AgCl, electronic conductivity coexists with ionic conductivity in the high-pressure KOH-type phase (above 6.6 GPa).312 Diffusion of Ag(I) cations in AgCl follows a different mechanism that in AgI, and the ionic bonding is much stronger in the former compound, which explains the difference in magnitude of ionic conductivity between the 106 two compounds. Mixed Ag(F1-xClx) phases have also been obtained. However, despite a large disorder of their anionic sublattice, they exhibit a higher activation energy for ionic conductivity than both AgF and AgCl. High pressure behavior of these mixed phases has not been investigated. As previously outlined, the nature of chemical bonding also determines crystal structures of halides at ambient conditions, as well as the onset of pressure-induced transitions. The predominantly ionic AgF adopts a NaCl-type structure at ambient pressure and transforms into a more closely packed CsCl-type at 2.7 GPa.313 On the other side of this spectrum, the much more covalent AgI preferably adopts one of already mentioned ZnS-type structures (CN = 4) at ambient pressure and only transforms into rocksalt-type upon compression.310 Further pressure increase

71 leads to the KOH-type structure, and subsequent transitions to TlI-type (CN = 7) and CsCl-type (CN = 8) structures have been predicted theoretically.314,315 Such series of transitions has been observed experimentally in AgCl and AgBr, although at ambient pressure they already adopt the NaCl-type structure.316 The high-pressure CsCl-type phases of AgCl and AgBr achieve superconducting state above 289 and 276 GPa, respectively.317

Binary silver(I) chalcogenides also exhibit a range of interesting electrical and magnetic properties, which has motivated several studies under high pressure. Ag2S, Ag2Se and Ag2Te are all semiconductors (with band gaps at ambient pressure of 1.0, 0.3 and 0.2 eV, respectively).318 319 Like AgI, they transform to superionic phases at high temperatures. In addition, Ag2Te is a topological insulator, i.e. an insulator or semiconductor in bulk, but with metallic states on the surface.320 The latter property is somewhat enhanced under high pressure, because compression 321 of Ag2Te up to 1.8 GPa (after which a phase transition occurs) reduces bulk conductivity. Such behavior is relatively uncommon, since in most compounds the band gap decreases with pressure, leading to higher conductivity. High pressure studies of Ag2Se and Ag2S have suggested that these two compounds may also become topological insulators, but this has not yet been 322,323 unequivocally confirmed. Ag2Te and Ag2Se become metallic at 3 and 8 GPa, 322,324 respectively. Ag2S, on the other hand, undergoes an inversion of majority charge carriers from n- to p-type at 13.5 GPa and subsequent metallization at 22 GPa.323,325

Silver oxides have also been investigated under high pressure. Silver(I) oxide Ag2O undergoes a structural transition to a hexagonal phase at 0.4 GPa, as does the isostructural Cu2O at 10 GPa studied in the same report.326 The exact structure has not been determined, but it is related to the CdCl2-type structure adopted by Cu2O at still higher pressure of 18 GPa.

Fig. 4.12. Theoretically predicted high pressure structures of AgO. Red spheres represent O atoms in both structures. Left: triclinic polymorph at 45 GPa (ref. [1]). Grey spheres – Ag(I), blue spheres – Ag(III). Right: trigonal polymorph at 75 GPa (ref. [2]). Grey spheres – Ag(II). Silver(I,III) oxide AgO under pressure was studied computationally in two independent works. Włodarska and co-workers have theoretically predicted a transition to a triclinic 72 polymorph (P1̅), which retains the mixed-valent electronic state of silver and coordination pattern of Ag(I) and Ag(III) cations (fig. 4.12, left).1 This polymorph should also exhibit metallic conductivity, albeit with a very low density of states at the Fermi level. An unrelated work by Hou and collaborators in turn predicted comproportionation and metallization at 75 GPa, accompanied by a phase transition to a trigonal (R3̅m) structure (fig. 4.12, right).2 However, authors of the latter study did not take into account magnetic interactions and Jahn-Teller effect, both of which are expected in a system containing Ag(II) cations with d9 configuration.3

A relatively rare phenomenon of negative linear compressibility (NLC) has been observed 327 328 in several compounds of silver, e.g. Ag3[Co(CN)6] and [Ag(ethylenediamine)]NO3. In both these systems, the overall decrease of volume at increasing pressures is achieved through contraction of two unit cell dimensions and (in spite of) simultaneous expansion in the third direction. In the latter compound, NO3ˉ anions are located within 1D channels formed by the metal-organic framework. The orientation of hydrogen bonds between anions and ethylenediamine molecules within that framework is responsible for the anisotropy of 328 compressibility. The magnitude of NLC in [Ag(en)]NO3 is the strongest ever observed in a metal-organic framework.328

Excluding research described in the experimental section of this thesis, the only known 129 instance of high pressure experiments on silver(II) compounds is the sulfate AgSO4. At 14 GPa, a disproportionate reduction of two crystallographic directions leads to a quasi-cubic unit cell, but the overall structure retains its ambient-pressure features. The AFM-ordered 1D chains of Ag(II) cations connected via sulfate anions appear to be much less compressible than the distances between chains, which is reflected in the anisotropic compression of the unit cell. Additionally, DFT calculations indicate that Jahn-Teller effect remains an important factor in

AgSO4 at elevated pressure. Though the axial Ag∙∙∙O contacts are much more compressible than square planar ones, the former are still on average 14% longer than the latter at 30 GPa. Above 129 23 GPa, AgSO4 decomposes to a HP form of Ag2S2O7 and O2.

The very promising physical properties of silver(II) fluorides (section 3.3.1) have motivated several theoretical studies into their high pressure behavior. AgF2 has been predicted to adopt a structure of flat layers above 15 GPa4 – as opposed to corrugated layers at ambient pressure. This polymorph would likely host much stronger antiferromagnetic interactions and could perhaps exhibit superconductivity at 40 GPa.5 Verification of these predictions was one of the objectives of this thesis. High pressure has also been suggested as a means of synthesizing 329 mixed-valent silver fluorides, i.e. AgF2 doped with either Ag(I) or Ag(III) cations.

5. Overview of experimental methods

5.1. The diamond anvil cell

Among different static compression techniques and devices which have been developed over the years, by far the most widely used is the diamond anvil cell (DAC). A typical DAC consists of two brilliant-cut diamonds attached to supports (seats), which are in turn brought together within a mechanical setup, usually with a set of screws. The sample is compressed between the smaller faces of diamonds (called culets) and separated from the external environment by a gasket. Depending on the sample and the type of experiment, the gasket can be made of stainless steel, harder and more noble metals such as rhenium, or other materials. Fig. 5.1 shows a cross section of the interior of a DAC. The diameter of culets is in the order of 0.1 mm.

Fig. 5.1. Basic components of a diamond anvil cell (cross section). Green coloring represents pressure- transferring medium, which fills up the chamber. Diamond is an excellent material for anvils for several reasons. First, it is arguably the hardest known substance, which makes it possible to compress virtually any sample without damaging the anvils. Second, diamond is quite transparent to a wide range of electromagnetic radiation, which enables probing the sample within DAC with many different spectral techniques.330 As shown in fig. 5.1, seats have a hole in the center and the diamond anvils act as a window through which the sample within the DAC can be examined by either reflected or transmitted radiation.

First DACs were developed independently at the U.S. National Bureau of Standards (now National Institute and Standards and Technology) and University of Chicago towards the end of

74 the 1950s.331 These early designs (NBS-type cell) used a lever, which was attached to a piston at one end and to a screw at the other end. By tightening the nut on the screw, the piston with one of the diamond anvils would be moved towards the other, stationary diamond, and the sample between them would be compressed. Mao and Bell later improved on that design by introducing a system which ensured better alignment of diamonds.330 In addition, a modified cut of diamonds (with bevels) allowed them to reach megabar pressures for the first time (in 1978).330 A triangular Merrill-Bassett-type DAC, developed specifically for X-ray diffraction, used two platens on which the diamonds were mounted and which were compressed together using three screws located on the vertices.332 In this setup, the force acting on diamonds is (in principle) exactly perpendicular to culets, as opposed to earlier DACs with levers. Beryllium seats were used to widen the opening angle for X-rays. Since then, symmetrical DACs consisting of a steel body and set screws like the Almax-Boehler or Mao design have become a widely used tool in high pressure studies.330,332 An example of such cell, utilized in this work, is shown in fig. 5.2.

Fig. 5.2. A symmetrical (Mao-type) DAC used in experiments reported in this work. Due to the small overall size of DAC, the amount of sample is relatively minuscule, which entails both advantages and drawbacks. On the one hand, with sample grains of several microns in diameter, the hazards associated with potential toxicity or explosiveness are effectively marginalized. Even in the event of unexpected decompression due to breaking of diamond or gasket, the release of contents of the pressure chamber hardly poses any risk.331 On the other hand, a particular grain selected from the batch of sample obtained e.g. in a preceding synthesis may not necessarily be representative of the compound that we intend to study. This can also happen in the case of highly reactive compounds, which can yield unintended contaminants in reaction with parts of the equipment (needles, gaskets or even diamonds) or simply through decomposition. Furthermore, the quality of data from such small samples is often comparatively lower, which requires developing special techniques adapted for DAC (such as use of synchrotron radiation for XRD, section 5.2). 75

Apart from the sample, usually two other substances are loaded into the high-pressure chamber. In order to provide a uniform pressure distribution, a pressure-transmitting medium is used. Most often it is a noble gas such as helium or neon. They are chemically inert and thus do not interact with other components of the system. Additionally, they produce very weak signal or none at all in common methods such as vibrational spectroscopy or X-ray diffraction – He is very light and Ne has a very simple XRD pattern when solidified at high pressure. Other materials used as pressure-transmitting media include simple ionic salts such as NaCl, liquids such as ethyl alcohol, and polymers.332

Another essential part of the HP setup is pressure gauge – a substance which gives a reliable indication of pressure inside the DAC. For example, a small ruby crystal is often placed inside the pressure chamber – measuring the position of its fluorescence band by means of Raman spectroscopy is a quick and simple way to determine pressure conditions.333,334 The high-edge frequency of the first order Raman band of diamond is also a good indicator, though it works reliably only in the middle of the culet.335 A common and reliable method involves measuring X-ray diffraction of a substance for which the pressure dependence of lattice constants is well studied. This dependence is known as equation of state (EoS). Many different formulations of EoS have been developed, and their applicability depends on several factors, such as the type of crystal structure or bonding.34 Two such formulations are mostly used in this work:

3 3 Birch-Murnaghan EoS336 푝 = 퐵 (휂−7 − 휂−5)[1 + (퐵′ − 4)(휂−2 − 1)] (Eq. 5.1) 2 0 4 0

3 ′ 337 −2 (퐵0−1)(1−휂) Vinet EoS 푝 = 3퐵0휂 (1 − 휂)푒2 (Eq. 5.2)

3 푉 where 휂 = √ , V is volume at a given pressure and V0 is volume at ambient pressure. B0 is the 푉0

푑푝 bulk modulus, formally defined as 퐵 = −푉 , and characterizes compressibility of a given 0 푑푉 substance at ambient pressure. B0’ is the pressure derivative of bulk modulus. Of course, such simple relationship between pressure and volume will not be valid during and in the vicinity of a phase transition. Additionally, goodness of EoS fit decreases with increasing pressure range, because any EoS formulation is only an approximation of the actual V vs. p relationship of a given substance.34 Finding the most suitable pressure gauge depends on the particular experimental conditions. Transition metals such as gold or silver are often used due to both low chemical reactivity and a wide range of stability of their simple fcc crystal structure.338

5.2. X-ray diffraction

Determination of crystal structure is very often carried out using X-ray diffraction (XRD) techniques. Wavelength of hard X-rays is in the same order of magnitude (~1 Å) as interatomic spacing in solids; thus, the periodic lattice of atoms in a crystal can act as a diffraction grating. When X-rays pass through a crystal, some of the radiation becomes scattered on electron clouds of constituent atoms – the heavier the element (i.e. higher atomic number Z), the higher the intensity of scattered X-rays. Scattering on each atom occurs spherically in all directions, but the resulting waves will constructively interfere and produce a diffraction peak only at specific angles for a given crystal orientation. These angles are determined by distances between lattice planes within the crystal structure (fig. 5.3). Lattice planes are defined by Miller indices h, k and l, corresponding to a, b and c crystallographic directions, respectively. In general, a set of planes labelled as (hkl) is orthogonal to the vector [h, k, l] in direct space. Inter-planar spacing d in a given set is related to unit cell dimensions and Miller indices in the following way:

1 ℎ2 푘2 푙2 = + + (Eq. 5.3) 푑2 푎2 푏2 푐2 Constructive interference of X-rays – scattered on electron density periodically distributed in the crystal lattice – has to occur in order for diffraction peaks to be observed. For that, the following relation (first formulated by William Bragg in 1912) has to be fulfilled: 푛휆 = 2푑푠푖푛휃 (Eq. 5.4) where n is a positive integer, λ is the wavelength of incident X-rays and θ is half the angle between incident and scattered rays (fig. 5.3). Based on eq. 5.4 and measured diffraction angles, XRD techniques can provide information about the unit cell dimensions and arrangement of atoms within it.

Fig. 5.3. Scattering of X-rays (green lines) on a periodic lattice of atoms.

In the description of x-ray diffraction‡ on a periodic crystal lattice, reciprocal space is often used as a convenient mathematical construct. A set of lattice planes in direct space defined as (hkl) corresponds to a point (h, k, l) in reciprocal space. If we denote k0 and k1 as wave vectors of incident and scattered radiation, respectively (both with a length of 1/λ), then diffraction will occur if: ∗ 푘1 − 푘0 = 푑ℎ푘푙 (Eq. 5.5) * where d hkl is a vector from the origin of reciprocal space to the point (h, k, l); thus, it too corresponds to the (hkl) set of lattice planes. Eq. 5.5 is in fact a different formulation of the Bragg relation. The end points of all possible orientations of k1 vector form a surface called the Ewald sphere. Diffraction peaks are produced in directions at which a point from the reciprocal space coincides with the Ewald sphere.

Two basic types of XRD techniques can be distinguished, depending on macroscopic form of the sample. Single-crystal XRD uses a monocrystalline sample placed on a goniometer head and rotated around an axis perpendicular to incident X-rays. Depending on the orientation of the crystal (i.e. the rotation angle), different reciprocal space points will intersect the Ewald sphere and produce diffraction peaks. Powder diffraction (PXRD), on the other hand, uses a polycrystalline sample. Due to the sheer number of millimeter-sized crystallites, virtually all possible orientations of the reciprocal space can be probed at the same time in such samples. This can also be visualized as a set of diffraction cones, in which points in reciprocal space form rings around the center, at specific angles determined by the Bragg relation (fig. 5.4).

Fig. 5.4. Right: a hk0 layer of points in reciprocal space. Left: superimposition of different orientations of reciprocal space from many different crystallites – the origin of diffraction cones.

‡ The same considerations apply to neutron diffraction, which is not discussed here. 78

A PXRD pattern can be obtained in two ways. A capillary with polycrystalline sample can be rotated so that diffraction peaks are collected as a function of rotation angle. This effectively probes only a linear cross section of diffraction cones. Alternatively, a photographic plate or other similar detector can be used to register a two-dimensional pattern, which contains the entire circumference of cones. The more randomly oriented crystallites are present in the sample, the more averaged out a PXRD pattern will be.

Both single-crystal and powder diffraction techniques are employed in high pressure research. However, single crystals are sometimes difficult to come by, especially in cases of highly reactive samples such as AgF2 studied here. Additionally, compression in DAC can lead to fragmentation, and any single crystal left in the pressure chamber after initial compression often does not survive a structural phase transition that may occur at higher pressures.34 Also, the structure of a typical DAC only enables a narrow angular range of transmitted radiation; effectively, it cannot be rotated other than around the axis perpendicular to culets, which is also the axis of incident radiation in most cases. In experiments reported in this thesis, only powder diffraction was used.

There are other limitations associated with high pressure crystallography in general and have to be taken into account in both single-crystal and powder methods.339,340 As already mentioned, the amount of sample is usually very small, since the pressure chamber in DAC is approximately 100-200 μm in diameter and tens of μm high. Therefore, the intensity of diffracted X-rays is relatively low. The already mentioned narrow angular size of transmitted X-rays is also problematic, as it limits the number of registered diffraction cones. In modern XRD at high pressures, synchrotrons are a preferred source of X-rays for multiple reasons. Their brightness is several orders of magnitude larger than that of conventional X-ray tubes, which not only provides a reasonable intensity of diffracted X-rays, but also reduces the time needed to collect a single pattern from several hours in classic powder XRD to several minutes or even seconds. The wavelength of synchrotron X-rays is also much shorter than those produced by metal cathodes, usually well below 1 Å. This reduces the angular size of an XRD pattern (as per eq. 5.4) and makes it possible to collect a sufficient data set even through a narrow DAC opening. In addition, diamonds exhibit strong absorption of X-rays in energy range below ca. 12 keV (i.e. λ > 1 Å); thus, synchrotron radiation is more suitable for such systems.338 Synchrotron X-rays can also be collimated into beams several microns in diameter, which allows obtaining data selectively from different spots of the sample and to avoid signal from the gasket surrounding the pressure chamber.339

Fig. 5.5. Left: 2D PXRD image. Right: 1D PXRD pattern. The transmitted X-rays produce a pattern of concentric rings and are registered using a 2D image plate. This image can then be integrated to obtain a familiar 1D graph (fig. 5.5), which can be further refined to elucidate crystal structure (more on that below). Such integration also improves signal to noise ratio and enables averaging of signal from many different crystallites. In ambient-pressure powder XRD, this is additionally achieved by rotating the container (e.g. capillary) with polycrystalline sample. In a DAC, such rotation is impossible, but some oscillation around the main axis (parallel to incident X-rays) can still improve averaging.340 Even so, relative intensities of reflections will often vary, and preferred orientation will have to be taken into account during structure refinement.

The hitherto described procedure of XRD data acquisition is referred to as angle- dispersive X-ray diffraction (ADXRD), because the intensity of diffracted radiation is collected as a function of angle relative to the incident, monochromatic X-ray beam. Alternatively, energy- dispersive XRD (EDXRD) has also been extensively used in high-pressure crystallography, especially during the early years of its development.340 In this method, a polychromatic X-ray beam is passed through the sample and into an energy-resolving detector. The main advantage of using EDXRD with DACs is that the detector is placed at one particular diffraction angle during the measurement, which means that the typically narrow opening of DACs is sufficient for data collection. However, resolution of energy-dispersive diffraction is generally inferior to that of angle-dispersive methods, and interpretation of EDXRD patterns is further made problematic by the presence of strong background and fluorescence peaks.341 Relative intensity of peaks is also less reliable, given the strong collimation of X-rays used in EDXRD and consequently, small angular beam size and poor averaging. Nevertheless, this method remains a widely used tool for determination of crystal structures under high pressure, e.g. in studies of metal hydrides.342,343

The first step in analysis of a pattern such as that in fig. 5.5 on the right is indexing. Based on the number of peaks and their positions, this procedure calculates a likely crystal system and unit cell dimensions. Most often, it yields several possible results, which can be evaluated using a parameter referred to as “figure of merit” (FoM).344 Comparison with analogous compounds (if they are known) can provide additional information about the probable space group. Indexing is followed by determination of relative intensities through mathematical modelling of the experimental pattern. Background can be described either manually or using Legendre or Chebyshev polynomials. Diffraction peaks are modelled using Gauss or Lorentz functions (or a combination of both, e.g. Voigt). In principle, a given diffraction peak in PXRD can consist of several components, either due to multiplicity (i.e. both (020) and (02̅0) lattice planes give rise to a reflection at the same angle) or coincidence (e.g. in an orthorhombic structure where a = 2b, reflections originating from (200) and (010) planes will overlap). LeBail refinement is the most often used method for deconvolution of peaks.345 Once the intensities of all reflections are known, the exact space group and positions of atoms in the unit cell can be determined. After that, the proposed structural model can be more accurately refined using the Rietveld method.346,347 The Rietveld method is the most commonly used approach, which apart from structural details (unit cell dimensions and atomic coordinates), also takes into account other factors, such as peak asymmetry, preferred orientation of crystallites, X-ray absorption etc. in order to accurately model the entire diffraction pattern. The mathematical procedure behind Rietveld method consists of finding the minimal value (using the nonlinear least-squares method) of the M parameter, which is defined as a sum: ∑ 표( ) 푐 2 푀 = 휃푖 푤(휃𝑖)(푌 휃𝑖 − 푌 (휃𝑖)) (Eq. 5.6) o c where Y and Y are observed and calculated intensities at each θi data point and w is the weight function sum element, calculated from the variance (square of standard deviation) of Yo. Theoretical intensity at each point (Yc) is in turn calculated from the following: 표 푐 2 푌 (휃𝑖) = 푏(휃𝑖) + 푠 ∑ℎ푘푙 푇ℎ푘푙 ∙ 퐴(휃𝑖) ∙ |퐹ℎ푘푙| ∙ 푃(휃𝑖 − 휃ℎ푘푙) (Eq. 5.7) where b is the background function, s is a scale factor, T is a function describing preferred orientation of crystallites, A is absorption correction, F is the structure factor for a given reflection calculated from the structural model and P is a profile function (Gaussian, Lorentzian, Voigt or other). In this work, March-Dollase formulation for preferred orientation was used.348 Computer software with built-in tools for all the aforementioned procedures is widely available. Jana2006 was used for Rietveld refinement of XRD patterns in this work.349

The overall quality of Rietveld fit can be evaluated using several parameters. Profile R- factor Rp, weighted profile R-factor Rwp, experimental R-factor Rexp and goodness of fit GOF are used by Jana2006349 and consequently in this work:

∑ |푌표(휃 )−푌푐(휃 )| 푅 = 휃푖 푖 푖 ∗ 100% (Eq. 5.8) 푝 ∑ 푌표(휃 ) 휃푖 푖

표 푐 2 ∑휃 푤(휃푖)(푌 (휃푖)−푌 (휃푖)) 푅 = √ 푖 ∗ 100% (Eq. 5.9) 푤푝 ∑ 푤푌표(휃 )2 휃푖 푖

∑ 푤푌표(휃 )2 푅 = √ 휃푖 푖 ∗ 100% (Eq. 5.10) 푒푥푝 푛−푝 푅 퐺푂퐹 = 푤푝 (Eq. 5.11) 푅푒푥푝 where n is the number of profile points and p is the number of refined parameters.

In the practice of high-pressure X-ray crystallography, there are several factors which sometimes limit the application of a step-by-step structure solution procedure. An important phenomenon to consider in structural studies in DACs is pressure distribution, which more often than not deviates from perfect uniformity in the entire sample. Usually a pressure gradient arises across the anvil face, with the highest pressure in the center.338 Non-uniform strain experienced by sample crystallites leads to broadening of reflections, which makes precise refinement much more difficult and often even impossible.350 For this reason, theoretical calculations are an extremely important tool in high-pressure structure elucidation, especially the density functional theory (DFT).351,352 Not only do they allow reliable predictions of structures of high-pressure phases, but can also help determine positions of lighter atoms, whose contribution to diffraction pattern is relatively small and whose atomic positions may not be reasonably refined. This approach is different from determination of crystal structure via indexing, because it provides ready structural models that can be tested against and then refined based on experimental data. Such approach has been an essential part of research reported in this work.

Another limitation of XRD methods inherent to high pressures is the quality of data. In order to produce ever increasing pressures, culets have to be ever smaller, which in turn means that the amount of sample will also decrease, leading to poorer quality of XRD patterns obtained with a given radiation source. Therefore, the continuing development of ever brighter X-ray sources is closely tied to the increasing experimental pressure threshold.33

Crystal structures appearing throughout this work were drawn using VESTA software.353 X-ray diffraction patterns were drawn using Fityk software.354 82

5.3. Electron transport properties

Pressure has a great influence on electronic structure of matter. Thus, compression often leads to increased electrical conductivity, which in many cases occurs as an abrupt insulator-to- metal transition around a particular pressure point. During such transition, conductivity can increase by several orders of magnitude. Metallization of a sample under high pressure can also be observed by other means, such as reflectivity in IR, visual or UV range, but direct electrical measurements are the best way to verify its occurrence. One of the most commonly used techniques involves connecting four electrical contacts to the sample. These contacts are used either to apply current or to measure voltage. Fig. 5.6 shows an example of such setup adapted for high pressure, with contacts labelled as A, B, C and D.

Fig. 5.6. An example setup of a DAC chamber for resistivity measurements at high pressure. If a DC current of known value (I) is applied between contacts A and B, and the voltage (U) is measured between contacts C and D, then resistance (R) of sample can be obtained using Ohm’s law:

푈퐶,퐷 푅퐴퐵,퐶퐷 = (Eq. 5.12) 퐼퐴,퐵 The value of resistance can then be used to calculate resistivity (ρ): 퐴 휌 = 푅 (Eq. 5.13) 푙 where A and l are cross section and length of the sample, respectively, relative to the direction of electric current. Resistivity is given in Ω∙m (ohm meters) and characterizes a substance at given conditions. In the most basic approach, finding resistivity from resistance requires knowledge of

83 dimensions of the sample, as shown in eq. 5.13. However, an alternative method has been developed by van der Pauw.355 It can be shown that: 푑 푑 exp (−휋푅 ) + exp (−휋푅 ) = 1 (Eq. 5.14) 퐴퐵,퐶퐷 휌 퐵퐶,퐷퐴 휌 where d is the thickness of the sample, and the two R expressions refer to resistance values measured for two different connection settings defined by their subscripts as per eq. 5.12 and fig. 5.6. This relation is fulfilled if contacts are (a) placed at the circumference of the sample and (b) sufficiently small, and the sample (c) is homogenous in thickness and (d) does not contain holes in its macroscopic structure. Thus, using van der Pauw method it is possible to find resistivity by measuring only resistance in two different connection settings and thickness of the sample. Eq. 5.14 is usually solved in the following way: 휋푑 푅 +푅 휌 = 퐴퐵,퐶퐷 퐵퐶,퐷퐴 푓(푟) (Eq. 5.15) ln(2) 2 where f is a function of r (defined as the ratio of resistances RAB,CD/RBC,AD) and is sometimes referred to as geometric factor.355,356 Several algorithms for calculating the value of f for a given r have been developed.356,357 Electrical conductivity (σ) can then be found as the inverse of resistivity (σ = 1/ρ) and is expressed in S/m (siemens per meter). Van der Pauw method partially eliminates the need to measure sample dimensions, but at high pressure, finding the thickness can be challenging. It can be estimated within an order of magnitude e.g. based on thickness of the pre-indented gasket, but it usually changes during experiment with every compression step. However, in the practice of high pressure electrical measurements, finding the exact value of resistivity/conductivity is often not even necessary. Instead, pressure dependence of resistance (or resistivity estimated using d) can provide sufficient evidence for the occurrence of insulator-to-metal transition. As already mentioned, such transition usually involves a resistivity change of several orders of magnitude. In addition, temperature dependence of these quantities at a given pressure can give insight into whether the sample behaves as an insulator, semiconductor or a metal. In other words, unless there is a need to compare exact values of resistivity of different materials at the same conditions, order of magnitude of ρ or simply the value of R and their pressure and temperature dependences already allow one to draw meaningful, qualitative conclusions about electron transport properties of a studied substance.

There are a few difficulties inevitably associated with resistivity measurements at high pressures.332 The entire system – electrodes, leads and sample on the diamond culet – is very small and the experiment has to be prepared with great precision. Electrodes can be prepared e.g. by cutting out of a thin metal foil. Electrodes can also be deposited as thin metallic films on the

84 surface of diamond anvils. Nowadays, diamonds with deposited electrodes are available commercially. In general, metallic gaskets are not suitable for electrical transport measurements due to their high conductivity. In some cases, they can be replaced with insulating materials. For example, in the first high-pressure, four-probe resistivity study, Mao and Bell used a pre-pressed disc made of MgO both as a gasket and as support for electrodes.358 However, it has been shown that most insulating gaskets fail at supporting the electrodes and at preventing diamond anvils from breaking at pressures higher than 25 GPa.359 The underlying reason is that malleability of metals is much better than that of any known insulator. Thus, the latter are much less suitable as gasket material. Alternatively, a classic metallic gasket can be used, provided proper insulation from leads and electrodes (as in the example shown in fig. 5.6). This can be achieved by coating the gasket with e.g. ceramic paint.332 (and references therein) Another possible technique involves pre-pressing the wires into the gasket and then coating the resulting grooves with insulating material before putting the wires in place for the experiment.360 More recently, Gao and co- workers have developed a system with molybdenum electrodes deposited on diamond surface 361 and further coated with a thin film of Al2O3. Both layers were appropriately etched into shapes of suitable geometry for measurements. Cubic boron nitride (c-BN) can also serve as a gasket- coating material; such procedure was used in experiments reported in this thesis.

Experimental results 6. Silver(I,III) oxide AgO

The following chapter reports structural studies of silver(I,III) oxide under high pressure. Using powder XRD, as well as structures derived from DFT calculations performed by Dr Mariana Derzsi, I was able to characterize two novel high-pressure phases of AgO.

6.1. Powder X-ray diffraction studies of compressed AgO

6.1.1. Experimental procedures

Silver(I,III) oxide was purchased from Alfa Aesar in the form of black grains (ca. 50 μm) of 99.9% purity. A symmetrical Mao-type diamond anvil cell was used (as shown in fig. 5.2), with culets 250 μm in diameter. Rhenium was used as gasket material and gold was used as pressure gauge.362 Sample preparation for HP XRD measurements consisted of the following steps: (a) Pre-indentation of Re gasket; (b) Laser-cutting of a hole (ca. 150 μm in diameter) in the gasket; (c) Placing several grains of AgO and a grain of Au on the diamond culet using a tungsten needle; (d) Closing and calibration of the diamond anvil cell; (e) High-pressure (170 MPa) loading of pressure medium (Ne).

X-ray diffraction data was collected using synchrotron radiation at Advanced Photon Source in Argonne National Laboratory, Illinois, United States. The wavelength of X-rays was equal to 0.406626 Å, which corresponds to an energy of 30.491 keV. X-ray beam was focused into a spot 5.9 μm x 8.0 μm. CeO2 powder at ambient pressure was used for detector calibration. Diffraction patterns were obtained in the form of 2D images and later converted into spectra (intensity vs 2θ) using DIOPTAS software.363 Subsequent analysis and structural refinement was carried out using Jana2006.349 Legendre polynomials were used for background and pseudo- Voigt functions were used for peak profiles. Preferred orientation (March-Dollase) was used for gold, neon and AgO whenever necessary. During the experiment, the sample was compressed up to ca. 56 GPa and then decompressed down to ca. 21 GPa, which was followed by complete depressurization after the last decompression step. Several XRD patterns were collected at each pressure point: they differed only in relative intensities of reflections from constituent phases. One pattern from each pressure was selected for analysis, based on relative intensity of reflections from AgO.

6.1.2. Preliminary analysis of powder XRD patterns

Fig. 6.1. Powder XRD patterns of AgO collected during compression. Most prominent reflections from Au, Ne and W are indicated on top. Red asterisks indicate selected reflections characteristic of the HP1 phase of AgO.

Fig. 6.1 shows patterns selected for analysis from the compression run. The lowest pressure point studied here was 4.9 GPa. Reflections from gold can be easily discerned throughout the entire pressure range. Additionally, the sample turned out to be contaminated with tungsten from the needle used for loading AgO and Au. Though this contamination only amounted to a few percent by volume, tungsten is one of the heaviest element in this system (much heavier than Ag, O and Ne) and thus readily visible in XRD. Luckily, its bcc crystal structure produces a simple diffraction pattern, and its high-pressure behavior has been thoroughly investigated – it does not undergo any phase transition in the pressure range that was studied here.362 Because of that, I could actually use W as a secondary pressure gauge: lattice constants of W plotted against pressure as determined from Au EoS show a good agreement with previously reported values.362 Technical details of pressure scale used here can be found in appendix A. Reflections originating from solid neon (fcc) only appear after compression to 8.2 GPa, the strongest one at ca. 11° being clearly visible in fig. 6.1. Since neon has been reported to solidify above 4.7 GPa at 293 K,364 it is reasonable to suggest that it was still just below freezing point at 4.9 GPa in my experiment (which was performed at room temperature) and only solidified during the second compression step. There are some discrepancies in terms of relative intensities of reflections from neon, especially at lower pressures, but this phenomenon has also been observed in the past and has been ascribed to partial recrystallization of neon microcrystals with increasing pressure.365 Preferred orientation was used during Rietveld refinement to make up for these discrepancies.

At 4.9 GPa, reflections originating from the ambient-pressure monoclinic polymorph of AgO can be readily identified. Thus, in order to gain insight into the crystal structure of AgO at elevated pressures, XRD patterns were initially modelled using the structure of ambient-pressure monoclinic (P21/c) polymorph, which will be henceforth referred to as LP-AgO or LP. This produced satisfactory results up to 16.1 GPa. Behavior of the LP phase is described in section 6.1.3. At 19.7 GPa, as seen in fig. 6.1, the diffraction pattern changes noticeably. A set of new reflections appears, which suggests that a different unit cell is required to properly describe the pattern. This is an indication of a phase transition occurring between 16.1 and 19.7 GPa. The inverse process was not observed due to the decompression being abruptly discontinued after 20.8 GPa. Sequence of XRD patterns from decompression is shown in fig. 6.2. The pressure dependence of reflection positions very much resembles that seen in the compression sequence. One may notice that the first pressure point shown in decompression sequence is actually higher

89 than the last one in compression. Both values fall within each other’s uncertainty range at these pressures (0.7-0.8 GPa) and thus can be considered practically equal. That the pressure did not noticeably decrease after the first decompression step can be explained either by deformation of the gasket which initially prevented relaxation of the pressure chamber, or simply by a relatively small unwinding of DAC set screws.

Fig. 6.2. Powder XRD patterns of AgO collected during decompression.

6.1.3. High pressure behavior of LP-AgO

Fig. 6.3. Pressure dependence of volume per formula unit of the LP (P21/c) phase. Ambient pressure data (hollow marker) was taken from ref. [366] Dashed line shows the EoS fit (table 6.1).

Fig. 6.4. Pressure dependence of lattice constants of the LP (P21/c) phase. Lattice constant b is multiplied by 2 for clarity of presentation. Ambient pressure data (hollow markers) is from ref. [366] PXRD data from 4.9-16.1 GPa range provides information about the high pressure behavior of LP-AgO; that is, before the phase transition. Figs. 6.3 and 6.4 show the pressure dependence of crystallographic parameters in this pressure range. Values for 0 GPa are taken from neutron diffraction study by Scatturin et al.366 Unit cell volume at 16.1 GPa decreases to 87.9% of the ambient pressure value. Lattice constant b proves to be the most compressible,

91 showing a 7.3% decrease, while a and c only decrease by 3.0% and 2.6%, respectively. The result III of this slightly anisotropic compression is that the puckered layers of [Ag O4] squares parallel to the yz plane become increasingly corrugated. Lattice constant b corresponds to the shortest distance between Ag(III) cations within layers. The relatively large decrease of b is somewhat surprising, given a strong repulsion that can be expected in interactions between these strongly positive cations. However, there is a strong mixing of Ag(III) d states with O 2p states, resulting III in a partial depopulation of the latter and more diffuse charge distribution over the entire [Ag O4] square. Indeed, Allen et al. have calculated (by means of hybrid-DFT HSE06 functional) that the charge on Ag(III) atoms is equal to +1.17155 – thus, much less than the nominal +3. β angle shows only a slight decrease throughout compression of LP-AgO – from 107.5° to 106.6° – and its pressure dependence is not plotted here. Distances between Ag and O atoms also decrease continuously with pressure and nearly to the same relative extent for both Ag oxidation states: by 3.6% and 3.7% for Ag(I)-O and Ag(III)-O, respectively (fig. 6.5). There are in fact two different Ag(III)-O bond lengths in the LP-AgO structure. The difference between the two values is a measure of deformation of III [Ag O4] units from a perfect square. In this pressure range, this value does not exceed 0.3% and does not change monotonically with pressure. An initial decrease to virtually zero (within the uncertainty margin) after the first compression step to 4.9 GPa is followed by a steady increase back up to the ambient-pressure value at 16.1 GPa. In fig. 6.5, the average Ag(III)-O distance at each pressure is plotted.

Fig. 6.5. Pressure dependence of Ag-O distances in the LP (P21/c) phase. Ambient pressure data (hollow markers) is from ref. [366]

Compressibility of the LP phase was modelled using the Vinet formulation of EoS (eq. 5.2). Parameters thus obtained are presented in table 6.1. As can be seen in fig. 6.3, they provide a very good approximation of V(p) dependence of the LP phase in the entire range of its stability.

The ambient-pressure volume of LP-AgO was used as reference volume (V0) and it was kept fixed for the EoS fitting. The unit cell of LP-AgO contains 4 AgO formula units (Z = 4).

3 V0/Z [Å ] B0 [GPa] B0’ LP-AgO 26.7 82.8 6.5 CuO 20.3 88 7.5

Table 6.1. Comparison of Vinet EoS parameters of LP-AgO and CuO. Compressibility data on CuO is taken from ref. [221] High pressure behavior of LP-AgO can be compared with that of CuO – its lighter analog, which was most recently studied with XRD up to 38 GPa by Kozlenko et al.221 As it turns out, bulk modulus (B0) of LP-AgO is comparable, though slightly lower (by 6%) than that of CuO. Both compounds crystallize in the monoclinic system and are (at least partially) made up of

[MO4] square units. However, the structure of CuO is a three-dimensional network of such units, III while in AgO, two-dimensional corrugated layers of [Ag O4] units are linked together with linearly coordinated Ag(I) atoms. Structures of the two oxides are compared in fig. 6.6.

Fig. 6.6. Comparison of ambient-pressure crystal structures of AgO (P21/c, left) and CuO (C2/c, right). Red spheres – O. In AgO: grey spheres – Ag(I), blue spheres – Ag(III). In CuO: blue spheres – Cu(II). Slightly different compressibility values for LP-AgO and CuO can therefore be attributed to two factors. Two distinct coordination patterns of Ag atoms in LP-AgO result in a lower overall symmetry compared to CuO (P21/c vs. C2/c). Consequently, the former is a little less closely packed and allows more structural flexibility. Furthermore, Ag atoms are larger and softer than Cu atoms, which also contributes to higher compressibility of LP-AgO.

Fig. 6.7 on the next page shows two selected Rietveld fits from the range of stability of LP-AgO. Precise values of lattice constants, as well as fit parameters are listed in table 6.2.

Fig. 6.7. Rietveld fits of the LP-AgO phase at 4.9 GPa (top) and 16.1 GPa (bottom). Black pattern – experimental data, red pattern – Rietveld model.

3 3 p(Au) [GPa] a [Å] b [Å] c [Å] β [°] V [Å ] V/Z [Å ] GOF Rwp Rp 0 5.852 3.478 5.495 107.50 106.66 26.666 n/a n/a n/a 4.9(1) 5.791(2) 3.378(1) 5.438(2) 107.32(2) 101.53(2) 25.384 0.42 1.42 2.32 8.2(1) 5.749(2) 3.324(1) 5.406(1) 107.04(1) 98.79(1) 24.698 0.34 1.07 1.78 11.3(2) 5.717(3) 3.279(1) 5.378(2) 106.86(2) 96.48(2) 24.120 0.45 1.21 1.85 16.1(3) 5.674(4) 3.223(2) 5.352(3) 106.56(4) 93.81(3) 23.452 0.49 1.46 2.06 Table 6.2. Results of Rietveld refinement of XRD data in the 4.9-16.1 GPa range (green rows): pressure values, lattice constants of LP-AgO and fit parameters. Uncertainties are given in brackets. Values for 0 GPa (top row, grey) are from ref. [366]

6.2. Pressure-induced phase transitions of AgO as determined by powder XRD and theoretical methods

6.2.1. LP to HP transition

Compression of AgO from 16.1 to 19.7 GPa brings about a noticeable, qualitative change in the diffraction pattern. This is especially well illustrated by reflections in the low-angle range below the Au(111) reflection (the strongest one in the pattern). Two new reflections appear in that region, and relative positions of reflections also change. Pressure dependence of interplanar distances corresponding to those reflections is plotted in fig. 6.8.

Fig. 6.8. Pressure dependence of d-spacings of AgO in the range below Au(111) reflection. Red squares correspond to two of the reflections marked with red asterisks in fig. 6.1. Dotted line indicates the phase transition. Such behavior is indicative of a significant structural change. Previous theoretical studies summarized in section 4.4 have suggested candidates for the high-pressure structure of AgO. However, both Włodarska et al.1 and Hou et al.2 predicted the phase transition to occur at much higher pressures – at 45 and 75 GPa, respectively. Bearing in mind these large discrepancies between theoretical calculations from those works and preliminary analysis of experimental results, I have nevertheless tested the XRD pattern obtained at 19.7 GPa for a possible transition of AgO to the triclinic (P1̅) polymorph.1 The possibility of transition to the trigonal (R3̅m) polymorph2 was tested in the context of still higher pressures in section 6.2.3. Importantly, attempts at indexing the patterns obtained above 19.7 GPa have failed insofar as the results of indexing did not provide a reasonable model for experimental data. In addition to the two previously published theoretical structures, more recent calculations performed by Dr Mariana Derzsi resulted in yet another model for the high-pressure polymorph

95 of AgO – a monoclinic structure with the same space group as LP-AgO (P21/c), but with an entirely different coordination environment of Ag(I) atoms, as well as several other differences. This model was also fitted to the experimental XRD patterns. Its theoretical origin will be explained in section 6.3. Both the triclinic polymorph and the newly predicted monoclinic polymorph produce, at the first glance, very good Rietveld fits at 19.7 GPa (fig. 6.9). However, closer scrutiny reveals that the P1̅ structure does not properly account for all experimental reflections. This is particularly evident in the case of reflection at ca. 8°: its calculated intensity is almost negligible in the triclinic structure and the Rietveld model only makes up for that by fitting it with the background. On the other hand, the monoclinic structure satisfactorily describes the entire experimental pattern. We tentatively label this new polymorph as HP-AgO or HP. It is discussed in the next section. Detailed fit parameters for the ca. 20-56 GPa range can be found in table 6.4 at the end of section 6.2.

Fig. 6.9. Rietveld fits of two theoretically predicted polymorphs: triclinic (top) and the new high- pressure monoclinic (bottom) at 19.7 GPa. Black pattern – experimental data, red pattern – Rietveld fit. 96

6.2.2. Crystal structure and high pressure behavior of HP-AgO

Fig. 6.10. Crystal structure of HP polymorph of AgO. Grey spheres – Ag(I), blue spheres – Ag(III), red spheres – O.

Although coincidentally both LP and HP polymorphs are characterized by the same P21/c space group, there are two main differences between their crystal structures. In HP, O atoms are located at vertices of Ag(I)-centered parallelepipeds; consequently, the coordination number of III Ag(I) is increased from 2 to 8. Relative orientation of [Ag O2] layers is also different, which leads to a doubled length of the unit cell in the x direction. Consequently, the unit cell of HP- AgO contains 8 AgO formula units (Z = 8). The transition from LP to HP can be visualized as a combination of (i) relative shift of III every other [Ag O2] layer by b/2 and (ii) movement of Ag(I) cations into the resulting quasi- cubic voids. This scenario is illustrated in fig. 6.11.

Fig. 6.11. Relationship between crystal structures of AgO: LP (top) and HP (bottom) viewed along the z direction. Black arrows indicate relative movement of structural elements.

Fig. 6.12. Pressure dependence of volume per formula unit of AgO in the entire studied pressure range. Solid markers – compression, hollow markers – decompression. Dashed lines are EoS fits (table 6.3), extrapolated for better comparison. Dotted line indicates approximate LP/HP phase boundary. Values for 0 GPa are from ref. [366] The LP → HP phase transition is associated with a 4.9% volume drop, which can be noticed in fig. 6.12. Due to the aforementioned structural differences between LP and HP, the latter is more closely packed and thus energetically favored above a certain pressure threshold (which lies somewhere between 16.1 and 19.7 GPa). All this indicates that it is a first-order phase transition. Volumetric data obtained for the HP phase was fitted – as in the case of LP-AgO – with Vinet equation of state. The calculated EoS parameters are compared in table 6.3. As can be expected for a high-pressure polymorph, the reference volume (i.e. unit cell volume extrapolated to 0 GPa) of HP-AgO is lower than ambient-pressure volume of LP-AgO, which is a consequence of its more closely packed structure. At the same time, bulk modulus B0 of HP-AgO is larger by 31%, which indicates lower compressibility of the HP phase. Pressure derivative of bulk modulus

(B0’) is lower than for LP, which is manifested in a less pronounced curvature of volume/pressure dependence. In other words, compressibility of HP phase decreases with pressure at a relatively slower rate than that of LP and thus its EoS fit more closely resembles a straight line.

3 V0/Z [Å ] B0 [GPa] B0’ LP-AgO 26.7 82.8 6.5 HP-AgO 25.6 108.2 3.9

Table 6.3. Comparison of Vinet EoS parameters of LP and HP polymorphs of AgO.

Fig. 6.13. Pressure dependence of lattice constants of AgO in the entire studied pressure range. Solid markers – compression, hollow markers – decompression. Dotted line in each graph indicates approximate LP/HP phase boundary. Values for 0 GPa are from ref. [366] Let us now turn to a more detailed analysis of structural behavior of the new AgO polymorph with increasing pressure. Fig. 6.13 presents pressure dependence of lattice constants of both polymorphs. All three dimensions of the unit cell, as well as the beta angle, show a discontinuity at the LP/HP phase boundary. As previously noted, unit cell length becomes doubled in the x direction. Nevertheless, both a in LP and a/2 in HP correspond to the same III parameter: distance between [Ag O]2 layers, which exhibits a sharp, 4.1% decrease between 16.1 and 19.7 GPa. A comparable drop (by 4.5%) is seen in pressure dependence of b. On the other hand, while lattice constant c steadily decreases during compression of LP-AgO, it then increases at the phase transition by 1.7%. This increase can be attributed to a relative reorientation of III [Ag O4] units: though in both structures Ag(III) atoms form straight lines along the z direction, III [Ag O4] rectangles centered on them lie in the same plane in HP-AgO, while in the LP phase they are slightly tilted relative to one another, although still parallel. This is illustrated in fig. 6.14.

III Fig. 6.14. View of [Ag O2] layers along the x direction. Left – LP (16.1 GPa), right – HP (19.7 GPa). Blue spheres – Ag(III), red spheres – O. In the pressure dependence of beta angle, a relatively slight decrease in the LP phase region is followed by a sharp drop at the phase transition (by 5° or 4.6 %) and a further, continuous decrease in the HP phase region down to exactly 90° above 40 GPa. This requires an explanation. Finding the value of β at 41.4 GPa turned out to be somewhat problematic. If we fit the data with monoclinic HP-AgO and let the Rietveld refinement program run its course, it does not converge to any reasonable result: the β angle either increases again or drops a few degrees below 90°. Alternatively, b increases by almost 0.1 Å, which is inconsistent with the trend it exhibits up to that pressure. None of these scenarios are supported by DFT calculations, as will be shown in section 6.3. However, upon further compression to 44.8 GPa, β takes the value of 90.3° and the fit is practically indistinguishable from one with β fixed at 90°. All this suggests that a transition to a higher-symmetry structure is taking place above 40 GPa. Therefore, experimental XRD data collected above 40 GPa was modelled using a new orthorhombic structure (Imma space group), which is obtained by setting β in HP-AgO at exactly 90° (fig. 6.15). Because of that, β(p) dependence in fig. 6.13 is flat above 40 GPa.

Fig. 6.15. Crystal structure of HP2-AgO (in Imam setting). Grey spheres – Ag(I), blue spheres – Ag(III), red spheres – O.

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The pattern of local coordination of constituent atoms in the new crystal structure is the same as in the hitherto discussed HP-P21/c polymorph. We label this orthorhombic polymorph as HP2, in order to distinguish it from the monoclinic HP polymorph, which we will henceforth refer to as HP1. Since the default setting of Imma space group of HP2 leads to different labelling of directions compared to HP1, unit cell dimensions of HP2 in text, figures, graphs and tables are given in Imam setting. Incidentally, the structure of HP2 is somewhat similar to the structure of 367 PbPdO2 (with the same Imma space group). However, in the latter compound, Pb(II) atoms (which correspond structurally to Ag(I) atoms in HP2-AgO) are coordinated by 4 O atoms in a tetragonal pyramid, with Pb(II) atom at the apex and O atoms at vertices of the base.367 At 41.4 GPa, HP2 polymorph turns out to provide a better model for experimental data than HP1: specifically, though the quality of both fits is visually and numerically quite similar (fig. 6.16), HP2 fit yields more reasonable unit cell dimensions.

Fig. 6.16. Rietveld fits of HP1 (top) and HP2 (bottom) AgO at 41.4 GPa. Black pattern – experimental data, red pattern – Rietveld fit. 101

6.2.3. HP1 to HP2 transition

As seen in fig. 6.12, pressure dependence of volume does not exhibit any discontinuity at HP1/HP2 boundary. Therefore, fitting the entire HP range with one EoS (with parameters given in table 6.3) is justified. Upon decompression, both HP1 and HP2 were tested as a model for data in the 35-45 GPa range. As it turns out, β angle again increases and an inverse, albeit smooth transition to HP1 structure is observed between 44.3 and 37.4 GPa. Based on these findings, it can be concluded that a second-order HP1 → HP2 phase transition occurs between 37.4 and 41.4 GPa.

The HSE06 calculations – described in more detail in section 6.3 – also predict a decrease of β angle with pressure (fig. 6.17). The proposed HP1 → HP2 transition is merely an increase of symmetry from monoclinic to orthorhombic, without any major structural change. Though the calculations suggest that β remains slightly larger than 90° up to 80 GPa, it is already below 91° at 50 GPa, which, as previously noted, cannot be distinguished from a perfectly orthorhombic cell based on our experimental data. Moreover, calculations indicate that structures of monoclinic

P21/c HP1 and orthorhombic Imma HP2 are degenerate in terms of volume and enthalpy in the 40-80 GPa range (fig. 6.17) – both models lead to the same theoretical solution. Therefore, the HP1 → HP2 indeed appears to be of second order.

Fig. 6.17. Left – pressure dependence of β angle in HP1 and HP2. Right – pressure dependence of volume per formula unit of HP1 and HP2 polymorph. Results from HSE06 calculations.

Importantly, the comproportionated AgO polymorph with trigonal (R3̅m) structure, which Hou et al.2 have predicted to form above 75 GPa, does not fit experimental data even at 55.7 GPa (fig. 6.18) – the highest pressure studied here – and indeed at any point within the studied range.

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However, the authors of that study failed to account for magnetic interactions and JT effect, both of which are indispensable for a proper description of this d9 system.3

Fig. 6.18. Rietveld fits of HP2 (top) and trigonal (bottom) AgO at 55.7 GPa. Black pattern – experimental data, red pattern – Rietveld fit.

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6.2.4. Local coordination of Ag atoms in LP and HP phases

Fig. 6.19. Pressure dependence of Ag-O distances for Ag(I) (left) and Ag(III) (right) cations. Solid markers – compression, hollow markers – decompression. Dotted lines indicate approximate phase boundaries. Values for 0 GPa (triangles) are from ref. [366] Since the main structural difference between LP and HP phases lies in local coordination environment of Ag(I) atoms, it is important to examine how Ag(I)-O distances change with pressure in both phases. These changes are plotted in fig. 6.19 (left). A large increase – between 10 and 32% – is seen upon the LP → HP1 phase transition. Such increase is necessary to I accommodate 8 O atoms in the vicinity of Ag(I), instead of 2 O atoms in the [Ag O2] dumbbell. Nevertheless, as could be observed from V(p) dependence (fig. 6.12), this local expansion of Ag(I)-O distances is part of an overall decrease of unit cell volume, which makes this transition I energetically favored. Upon transition to HP2, the [Ag O8] parallelepipeds become more symmetrical, but still not perfectly cubic. III Although [Ag O4] square units are essentially conserved within the entire studied pressure range, noticeable changes occur at both phase transitions (fig. 6.19, right). As previously demonstrated, deformation of these squares amounts to only a fraction of a percent in LP-AgO, which cannot even be seen at the scale used in fig. 6.19. However, after the LP → HP1 transition, Ag(III)-O distances diverge by as much as 16.7% (relative to the shorter one). This process is accompanied by an increase of the average distance by ca. 3% compared to right before the first transition (at 16.1 GPa), which in turn is associated with the aforementioned slight reorientation III of [Ag O4] units and is also manifested in the slight increase of c lattice constant. Deformation III of [Ag O4] rectangles then decreases with pressure in HP1 and upon transition to HP2, they become perfect squares. Interestingly, the Ag(III)-O distance at the highest studied pressure (55.7 GPa) is only 0.3% shorter than at 16.6 GPa and 4% shorter than at ambient pressure. This shows III that [Ag O4] rectangular units constitute the most rigid element of the crystal structure of AgO.

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To summarize, two pressure-induced phase transition of AgO were detected in XRD data up to ca. 56 GPa: a first-order LP → HP1 transition, accompanied by an increase of Ag(I) coordination number from 2 to 8, and a subsequent HP1 → HP2 second-order transition, resulting in an increase of symmetry: appearance of 2-fold rotation axes in all three directions and mirror planes orthogonal to x and z (in Imam setting). In all three structures of AgO, there are two distinct Ag crystallographic sites with very different local coordination, which suggests that the mixed- valent nature of AgO is retained in the entire studied pressure range. In the next section, it will be shown how these structures originated and what their properties may be, as predicted by DFT calculations.

Table 6.4 below lists results of Rietveld fits for both HP phases of AgO obtained within the entire studied range of their stability.

3 3 p(Au) [GPa] a [Å] b [Å] c [Å] β [°] V [Å ] V/Z [Å ] GOF Rwp Rp compression 19.7(3) 10.89(2) 3.077(3) 5.440(10) 101.62(8) 178.50(2) 22.312 0.68 1.35 2.03 22.0(3) 10.86(2) 3.039(2) 5.437(8) 100.00(7) 176.67(2) 22.083 0.44 0.89 1.30 23.8(2) 10.87(2) 2.977(2) 5.431(12) 97.88(7) 174.09(2) 21.762 0.43 0.83 1.28 24.9(3) 10.86(3) 2.952(3) 5.420(13) 96.75(8) 172.51(2) 21.563 0.48 0.84 1.46 27.2(5) 10.82(2) 2.934(5) 5.447(9) 94.55(11) 172.34(3) 21.542 0.46 0.86 1.40 31.9(4) 10.70(1) 2.892(4) 5.437(6) 93.63(12) 167.94(2) 20.993 0.53 1.12 1.74 37.0(4) 10.68(1) 2.825(2) 5.429(4) 93.24(7) 163.61(2) 20.451 0.42 0.97 1.39 41.4(6) 10.60(6) 2.802(22) 5.399(5) 90 160.29(3) 20.036 0.48 0.96 1.59 44.8(6) 10.55(2) 2.771(2) 5.393(9) 90 157.71(2) 19.713 0.49 1.02 1.74 48.8(7) 10.51(1) 2.762(6) 5.371(4) 90 155.98(3) 19.497 0.40 0.85 1.41 50.8(9) 10.51(1) 2.748(5) 5.361(5) 90 154.76(4) 19.345 0.40 0.86 1.33 54.5(7) 10.47(2) 2.746(11) 5.347(5) 90 153.70(3) 19.212 0.56 1.14 1.99 55.6(8) 10.45(1) 2.746(6) 5.346(4) 90 153.44(3) 19.180 0.36 0.83 1.32 decompression 56.1(7) 10.47(7) 2.732(30) 5.347(6) 90 152.90(3) 19.112 0.69 1.47 2.62 51.1(7) 10.52(28) 2.73(12) 5.368(7) 90 154.19(3) 19.274 0.76 1.63 2.88 46.3(7) 10.54(1) 2.761(6) 5.385(4) 90 156.77(3) 19.597 0.32 0.73 1.18 44.3(7) 10.56(1) 2.768(4) 5.397(4) 90 157.76(4) 19.720 0.30 0.72 1.08 37.4(9) 10.62(2) 2.799(8) 5.427(6) 90.47(22) 161.36(5) 20.170 0.29 0.70 1.06 34.1(4) 10.61(2) 2.882(6) 5.446(5) 94.03(14) 166.09(3) 20.761 0.60 1.47 2.30 32.0(7) 10.62(2) 2.875(6) 5.450(5) 94.37(11) 165.90(4) 20.738 0.27 0.78 1.02 20.8(4) 10.94(2) 2.989(2) 5.476(9) 98.54(6) 177.16(3) 22.145 0.20 0.57 0.77 Table 6.4. Results of Rietveld refinement of XRD data in the ca. 20-56 GPa range: pressure values, lattice constants of HP-AgO and fit parameters. Yellow rows – HP1, red rows – HP2 (Imam setting) Uncertainties are given in brackets.

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6.3. Properties of high-pressure polymorphic forms of AgO – insight from theoretical calculations

The two aforementioned theoretical works on AgO at high pressures1,2 failed to predict the outcome of experiment described in this work. In terms of crystal structure, neither the triclinic (P1̅) nor the trigonal (R3̅m) polymorph provide a satisfactory model for XRD data. The onset pressure of phase transition – between 16.1 and 19.7 GPa – is also much lower than 45 and 75 GPa suggested by Włodarska et al.1 and by Hou et al.,2 respectively. Thus, in order to find the structure of HP polymorph of AgO, more precise calculations than those reported in previous studies were performed. All theoretical calculations discussed in this section were carried out by Dr hab. Mariana Derzsi. However, they are described here in order to provide a conceptual link between experimental and theoretical data, as well as to give proper credit to theoretical methods, which played a key role in determination of crystal structures of AgO under high pressure. Results of these calculations were published together with the analysis of experimental XRD data in one paper,368 which is listed at the end of this work.

6.3.1. Details of DFT calculations

Density functional theory calculations were performed using a hybrid HSE06 functional as implemented in the VASP package,369–373 with the Hartree-Fock/DFT mixing parameter equal to 0.25 and plane-wave cutoff set at 520 eV. Structural optimization was performed with a k- spacing of 0.3 Å-1, while electronic structure and total energy were calculated using a denser, 0.2 Å-1 k-spacing. Phonon dispersion curves were calculated using the direct method developed by Parliński, Li and Kawazoe374 and implemented in PHONOPY software.375 A larger supercell (2x4x2) of ambient-pressure AgO structure was used in order to explore more degrees of freedom than the previous work.1

6.3.2. Dynamic instability of LP-AgO at high pressures

Phonon dispersion curves of monoclinic (P21/c) AgO supercell were calculated at 40 GPa – a pressure point chosen for being well beyond the range of stability of the ambient-pressure structure of AgO based on the appearance of new reflections (fig. 6.8). Imaginary frequencies at B and C points of the Brillouin zone (fig. 6.20, left) suggest that LP-AgO is indeed no longer stable at such conditions for reasons of lattice dynamics. Włodarska et al. actually reached a very similar conclusion, having predicted a phonon instability above 45 GPa.1 However, in their work, imaginary features in the calculated phonon dispersion curves were also present at A and E points.

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In general, relaxing the structure along the normal coordinate of an imaginary mode can produce a new, dynamically stable structure.375 Thus, for example, the aforementioned triclinic (P1̅) polymorph was found by following the mode at E point.1 The calculations described here used a larger, 2x4x2 supercell instead of 1x3x1 used by Włodarska et al. This more detailed treatment turned out to be crucial, as it revealed a more complex lattice movement than the previous work. Since the new calculations did not indicate an instability at E point, we followed instead the mode at B point (½,0,0). This way, the P21/c structure of HP1-AgO was found. The structure of HP1 polymorph of AgO turns out to fit the experimental data very well, which has been demonstrated in section 6.2.

Fig. 6.20. Left – phonon dispersion curves of LP-AgO at 40 GPa. Right – pressure dependence of relative enthalpy of the three structures discussed in text. Reproduced from ref. [368] As previously shown in fig. 6.11, LP and HP1 structures are related via motion of Ag(I) III cations and [Ag O2] layers. Such rearrangement of atoms leads to a lowering of enthalpy by 0.88 meV per formula unit at 40 GPa. The HP1 structure actually becomes thermodynamically more stable already at 20 GPa (fig. 6.20, right). This prediction is in very good agreement with experimental XRD data, in which the LP → HP1 transition is seen between 16.1 and 19.7 GPa. According to these findings, the triclinic (P1̅) polymorph becomes more stable than LP above 45 GPa, but is still less stable than HP1 in the probed range of pressure.

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6.3.3. Electronic structure of AgO at high pressures

Theoretically predicted structures of HP-AgO, verified experimentally with XRD data, indicate that AgO remains disproportionated up to at least 56 GPa. The very different coordination environment of Ag(I) and Ag(III) atoms prevents facile charge transfer between the two sites. This is characteristic of class I of mixed valence and gives rise to semiconducting properties of AgO at ambient conditions.243 On the other hand, the influence of high pressure can be expected to overcome this effect at least to some extent due to increasing band overlap.35 Results of HSE06 calculations, which provide some insight into the electronic structure of AgO at high pressure, are shown in fig. 6.21. In terms of density of states, it can be noticed that the conduction band is composed predominantly of Ag(III) states, while the top of the valence band consists mostly of Ag(I) states.

Fig. 6.21. Top: electronic density of states calculated for high-pressure AgO structures. Bottom: pressure dependence of the calculated bandgap of AgO. Reproduced from ref. [368] Red arrow indicates the band gap drop at LP → HP1 transition. The band gap of LP-AgO decreases steadily with pressure, and in the hypothetical absence of phase transitions, LP-AgO should, according to calculations, become metallic at 50 GPa. This I decrease of band gap can be attributed to a decrease of Ag-O distances, both in [Ag O2] dumbbells III and [Ag O4] rectangles. In the former, this leads to a stronger repulsion between O p(z) and Ag(I) d(z2) electrons, which shifts the d(z2)-p(z) antibonding levels up in energy; simultaneously, due to larger dispersion of the valence (d(z2)-p(z) of Ag(I)) and conducting bands (empty d(x2- y2) orbital of Ag(III)), the band gap progressively narrows down. Overall, increasing pressure

108 brings the energy levels of electron donors (Ag(I)) and acceptors (Ag(III)) closer together, thus closing the inter-valence charge-transfer band gap. However, metallization is precluded by a dramatic structural change. Upon LP → HP1 phase transition, the band gap drops from ca. 0.6 to ca. 0.4 eV, after which it slightly increases in the 20-40 GPa range, and then again decreases down to ca. 0.3 eV at 100 GPa. Since at such high pressures even oxygen has been reported to become metallic,41 persistence of a non-zero band gap is somewhat intriguing. On the other hand, Ag(I)-O distances experience a substantial elongation upon transition from linear (LP) to quasi-cubic (HP1) coordination, which should decrease repulsion between fully occupied Ag(I) d and O p orbitals and stabilize the donor Ag(I) level, thus leading to an increase of band gap. This kind of behavior was reported for the hypothetical gold oxide AuO, which is predicted to undergo a series of pressure-induced structural transitions which preserve the band gap against increasing pressure and concomitant band overlap.183 The non-trivial pressure dependence of band gap in AgO is likely a result of several counteracting factors (such as the aforementioned increasing band overlap and changes in local coordination, among others), and it is difficult to determine which one is dominant.

At ambient pressure, local coordination of Ag(I) in LP-AgO is a result of a second-order 10 JT effect: although the eg states in the d Ag(I) cation are fully occupied, there is a significant admixing of 5s states. This results in a partial depopulation of the d(z2) orbital, which lies on the axis of Ag(I)-O bonds, and the electron density becomes partly redistributed into the plane I perpendicular to the [Ag O2] dumbbell. On the other hand, the pressure-induced transition to a quasi-cubic symmetry of local coordination of Ag(I) in HP1 and HP2 structures suggests a change to a more spherical distribution of electron density around the Ag(I) cation. Therefore, from the point of view of chemical bonding, the increase of coordination number of Ag(I) from 2 to 8 is associated with a change towards a less directional and more ionic Ag(I)-O bonding character.

Pressure-induced changes in electronic structure of AgO stand in contrast to e.g. halogenoaurates discussed in section 4.2, which become metallic at relatively modest pressures of several GPa. Arguably, the difference between AgO and Cs2Au2X6 can be traced back to a different magnitude of the JT effect. The latter belong to class II of mixed valence already at ambient conditions, because the local coordination of Au atoms is relatively similar for both oxidation states. In fact, since the structures of both AgO and halogenoaurates are a result of a JT distortion coupled to a charge density wave, one could argue that the strong JT effect characteristic of Ag(II) in a ligand field is indirectly responsible for a much stronger resistance to metallization compared to halogenoaurates.

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7. Silver(II) fluoride AgF2

In this chapter I describe the discovery of two high-pressure polymorphs of AgF2 and some of their properties, based on powder X-ray diffraction data and theoretical calculations, as well as attempts at performing electrical resistivity measurements for some of them. Both of these new polymorphs have some characteristics which make them unique among transition metal compounds. At the same time, their structures can be derived from the well-known polytypes of other transition metal difluorides through distortions induced by Jahn-Teller effect, as will also be demonstrated here.

7.1. Powder X-ray diffraction of compressed AgF2 and reference AgF

7.1.1. Experimental methods

Silver(II) fluoride was synthesized by Dr Zoran Mazej (Jožef Stefan Institute, Slovenia) through fluorination of AgNO3 dissolved in anhydrous HF. A symmetrical Mao-type diamond anvil cell was used (fig. 5.2), with culets 200 μm in diameter. Rhenium gaskets were prepared in the same way as that described in section 6.1.1. AgF2 samples were loaded using a tungsten needle. X-ray diffraction data was collected using synchrotron radiation at Advanced Photon Source in Argonne National Laboratory, Illinois, United States. Raman signal from the diamond anvil was used for preliminary pressure determination during the experiment.335 Two HP experiments with AgF2 – labelled as “A” and “B” – are described here, which differed in terms of X-ray wavelength and pressure medium (table 7.1). FEP stands for perfluorinated polyethylene, a polymer chosen for its resistance to fluorination.

Dataset: Wavelength (energy) Pressure medium Pressure range (in GPa) A 0.3344 Å (37.08 keV) Neon 5 ↗ 26 B 0.4113 Å (30.14 keV) FEP slivers 12 ↗ 36 ↘ 17

Table 7.1. Experimental details for A and B PXRD datasets. “↗” indicates compression and „↘” – decompression.

CeO2 powder at ambient pressure was used for detector calibration. Diffraction patterns were obtained in the form of 2D images and later converted into spectra (intensity vs 2θ) using DIOPTAS software.363 Subsequent analysis and structural refinement was carried out using Jana2006.349 Legendre polynomials were used for background and pseudo-Voigt functions were used for peak profiles. Preferred orientation (March-Dollase) was used for neon and AgF2 whenever required.

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There are several difficulties in high-pressure experiments involving AgF2, most of which stem from very high chemical reactivity of this compound. AgF2 is far more reactive than AgO described in the previous chapter. It can react with parts of the experimental setup: gasket (rhenium), seat (tungsten carbide), needle used for loading (tungsten) or even diamond (carbon). In these reactions, AgF is always one of the expected products, but it can also form at any preparation step if insufficient care is taken and AgF2 is accidentally exposed to even traces of atmosphere. Consequently, at least some contamination with AgF is almost inevitable, and as is evident from the obtained XRD patterns, it was present in both A and B samples. The exact amount – as measured by mass fraction of AgF relative to the amount of both AgF and AgF2 – varied between 0.12 and 0.47, only in one case reaching 0.66, and with the mean value of 0.28 over the entire range of A and B datasets. Presence of AgHF2 can also be anticipated in AgF2 samples if traces of moisture are present, but this compound has not been detected.

There have been several earlier attempts at compression of AgF2 carried out by other members of our laboratory, and in one such experiment, the sample turned out to consist almost entirely of AgF. Compression and PXRD measurements of this system in the 3-39 GPa range allowed us to obtain pressure dependence of lattice constant of AgF. Though AgF crystallizes in NaCl-type structure at ambient conditions, it transforms into CsCl-type structure at a relatively modest pressure of 2.7 GPa,313 which is below the studied range. Therefore, I was able to fit the data thus obtained with Birch-Murnaghan equation of state (eq. 5.1). AgF in samples A and B is also exclusively within the range of stability of CsCl-type structure, and thus I was able to use it as internal pressure gauge common for both samples. All pressure values describing the A and B systems given in text, graphs and figures are derived from the AgF pressure scale. Pressure dependence of AgF volume in 3-39 GPa range and EoS fit parameters are given in appendix C.

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7.1.2. Powder XRD patterns of AgF2 at high pressure

PXRD patterns from experiments A and B are shown on the next page in figs. 7.1 and 7.2, respectively. The differences in angular positions (2θ) of reflections between the two sets are due to different wavelengths used for each experiment (see table 7.1). The first two pressure points in experiment A – at 4.9 and 8.5 GPa – can be satisfactorily described with the ambient-pressure polymorph of AgF2, which will be henceforth referred to as

LP-AgF2 or LP. Upon further compression of sample A to 10.0 GPa, a new, low-angle reflection appears at 2θ ≈ 5.4° (d ≈ 3.57 Å). This reflection, albeit initially small, can be clearly discerned at still higher pressures and also in XRD patterns of sample B, all of which were collected above 10 GPa. This kind of change in XRD pattern may indicate a slight decrease of symmetry. Subjecting sample B to still higher compression of 14.8 GPa leads to the appearance of yet another low-angle reflection at 2θ ≈ 5.2° (d ≈ 4.58 Å). This reflection is much less prominent than the one previously mentioned, but is visible in XRD patterns of sample B at pressures 14.8 GPa and higher, and in sample A above 21 GPa. Neither of the two new reflections can be accounted for by the LP structure. Therefore, the next section will describe two new high-pressure polymorphs of AgF2 which fit the experimental data, as well as details of their origin, derived from DFT calculations and structural analysis. Similarly as in the case of AgO, numerous attempts at indexing high-pressure diffraction patterns failed at finding reasonable models for the experimental data.

In addition to reflections from ambient- and high-pressure polymorphs of AgF2 and AgF contaminant, additional reflections at ca. 8° and ca. 13° were present in several diffraction patterns from dataset “A”. They do not appear systematically throughout the entire dataset (i.e. can only be found at particular spots of the sample), and are entirely absent from dataset “B”. Therefore, they most probably originate from local impurities which may have formed as a reaction product between AgF2 and parts of the experimental setup. Due to scarcity and relatively low intensity of these reflections, their origin could not be precisely determined. However, based on that scarcity it can also be inferred that they do not arise from either AgF2 or AgF (which do appear consistently in all studied XRD patterns) and thus do not impact the general considerations regarding crystal structures of high-pressure polymorphs of AgF2.

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Fig. 7.1. PXRD patterns from experiment A – compression only. Red squares and stars indicate new

reflections characteristic of HP1 and HP2 phases of AgF2, respectively.

Fig. 7.2. PXRD patterns from experiment B. Left panel – compression, right panel - decompression. Red

squares and stars indicate new reflections characteristic of HP1 and HP2 phases of AgF2, respectively.

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7.2. High pressure polymorphism of AgF2 and relations to common structural polytypes

In order to elucidate the structure of silver(II) fluoride under high pressure, we used the dynamical instability approach, which proved to be effective in the case of silver(I,III) oxide. 376 Structural models of AgF2 were optimized using hybrid PBEsol functional implemented in VASP.369–373 A plane-wave cutoff of 520 eV and k-spacing of 0.2 Å-1 were used. Total energy (enthalpy) calculations, results of which are presented in subsequent parts of the text, were -1 performed using a k-spacing of 0.11 Å . Magnetic interactions in AgF2 were accounted for with an AFM model constructed according to Goodenough-Kanamori-Anderson rules.12,81,377 Electronic bandgap calculations were performed using a spin-polarized GGA+U functional, modelling the on-site Coulomb repulsion between Ag 3d electrons with Coulomb integral U set at 5 eV and Hund’s exchange J set at 1 eV. Phonon dispersion curves were calculated with the aforementioned PHONOPY software.374,375 Again, all calculations were performed by Dr Mariana Derzsi from our laboratory.

As a result of this theoretical approach, two new structures of AgF2 were found. One of them is a non-centrosymmetric layered polymorph (orthorhombic, Pca21 space group, labelled as HP1): very similar to LP-AgF2, but with important differences. The other is a unique system consisting of nanowires (also orthorhombic, Pbcn space group, labelled as HP2). In order to facilitate subsequent discussion, all crystallographic data regarding the three polymorphs will be given in representations that allow continuity of axes labelling. Unit cell dimensions of LP-AgF2 at ambient conditions are taken from a neutron study by Fischer et al.87 and the same Pbca representation as used in their work will be adopted here. HP1 and HP2 structures will be presented in Pbc21 and Pbna representations, respectively.

7.2.1. HP1 form: a unique example of non-centrosymmetric layered structure of a transition metal compound

Using a 2x2x2 supercell of LP-AgF2, phonon dispersion curves were calculated at several pressure points. According to the obtained results, the ambient-pressure structure becomes dynamically unstable at 6 GPa, as evidenced by an imaginary feature at Γ point of the Brillouin zone (fig. 7.3, left), which corresponds to an optical mode of B2u symmetry. Relaxing the structure along the normal coordinate of this imaginary mode leads to the new, Pca21 structure of HP1 (fig.

7.3, right). Like LP-AgF2, HP1 consists of layers of interconnected [AgF4] quasi-square units. However, Ag atoms in HP1 do not lie in the same plane as their four nearest F atoms, and the layers are slightly shifted relative to one another, compared to LP.

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Fig. 7.3. Left – superimposed phonon dispersion curves of LP-AgF2 at 0 and 6 GPa. Note the imaginary

frequency at Γ point at 6 GPa. Reproduced from ref. [289] Right – the structure of HP1-AgF2 in Pbc21 representation. Grey spheres – Ag, yellow spheres – F. More precise calculations of relative enthalpies of LP and HP1 structures indicate that the latter should become energetically favored above 8 GPa. This is very close to the pressure range above which a new reflection appears in experimental XRD patterns (between 8.5 and 10 GPa).

Indeed, the structure of HP1 does provide a better model than LP-AgF2 for XRD data above 10 GPa, as exemplified by fits at 11.7 GPa shown in fig. 7.4.

Fig. 7.4. Comparison of Rietveld fits to the XRD pattern at 11.7 GPa (sample B). Note the reflection at ca. 6.7°, which is not accounted for by the LP model.

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Table 7.3, containing crystallographic parameters of LP and HP1 phases derived from

Rietveld fits, can be found in section 7.2.4 in the context of compressibility of all three AgF2 phases. HP1 phase was only found at three experimental pressure points: 10.0 and 13.5 GPa in sample A, and 11.7 GPa in sample B. This relative scarcity of data limits the discussion regarding high pressure behavior and structural properties of that phase, but several well-grounded conclusions can still be made, as will be shown below. The same is true for the LP phase, for which only two high-pressure data points were collected.

Fig. 7.5. Structural relationship between LP and HP1 structures of AgF2. View along the x axis. Red arrows indicate relative movement of layers along the y axis. Green dotted lines indicate closest inter- layer Ag-F constants. Blue dashed lines are drawn to illustrate magnitude of displacement (see text).

The movement along the normal coordinate of B2u mode and thus the proposed mechanism of LP → HP1 phase transition is shown in fig. 7.5. The two structures are related via an antiphase shift of neighboring layers along the y direction. Magnitude of this shift, as measured by displacement of the middle sheet relative to two neighboring sheets during the phase transition, amounts to 14% of the distance between blue dashed lines in fig. 7.5. In addition to the movement of layers, Ag atoms become displaced from the plane formed by the four F atoms which form the square [AgF4] units. Consequently, the structure of HP1 lacks a center of inversion, as well as glide plane and screw axes lying in the xy plane, compared to LP. It is this lowering of symmetry that leads to the appearance of the new low-angle reflections (at 2θ ≈ 6.7° in fig. 7.4), corresponding to the set of [110] crystallographic planes. A closer look at local coordination of Ag atoms reveals more changes relative to the LP structure (fig. 7.6). As has been pointed out in section 4.3, the ambient-pressure structure of AgF2 can be traced back to the fluorite polytype via a deformation caused by Jahn-Teller effect. Heavily distorted [AgF8] parallelepipeds can actually be discerned in LP-AgF2¸ although the two longest

116

Ag-F contacts are over 50% longer than the four shortest bonds that make up the [AgF4] square unit. In HP1, on the other hand, the out-of-plane displacement of Ag atoms brings them closer to one of the neighboring sheets than to the other. Consequently, there are three inter-layer Ag-F contacts on one side of the square unit and one on the other (fig. 7.6, right), and the structure of

HP1-AgF2 departs even further from the CaF2 type. In LP-AgF2, the fcc cationic sublattice characteristic of fluorite is retained (albeit orthorhombically distorted), and the difference between LP-AgF2 and CaF2 is mostly due to a displacement of F atoms from tetrahedral voids, caused by Jahn-Teller effect. On the other hand, the relative movement of sheets, which leads to the HP1 structure, is actually a distortion of the entire cationic sublattice, shifting every other [001] plane of Ag atoms along the y direction.

Fig. 7.6. Coordination environment of Ag atoms in LP (left) and HP1 (right) structures. Ag-F distances are given in angstroms and are derived from ref. [87] for 0 GPa and from experimental XRD data at 10.0 GPa (sample A). The change in Ag coordination environment brought about by the LP → HP1 phase transition can also be discussed within the context of Jahn-Teller effect. At 0 GPa, the magnitude of Jahn-Teller distortion, measured by the elongation of axial Ag-F contacts relative to the average length of Ag-F bond in the square unit, is equal to 24.8%. Compression to 8.5 GPa – still within the LP phase – reduces this elongation only slightly, i.e. to 23.6%. Upon the phase transition, these two axial contacts diverge in length by ca. 0.05 Å, and their elongation is further reduced to on average ca. 17.6% (both values averaged over all three HP1 data points). As can be seen in fig. 7.7, the pressure dependence of this elongation does not appear monotonic either in LP or in HP1 stability range – perhaps only due to scarcity of data. Even so, a drop by ca. 6 percentage points between the two phases is clearly visible. 117

Fig. 7.7. Pressure dependence of the magnitude of JT effect in LP and HP1 phases of AgF2, as measured by the elongation of the average apical Ag-F distance relative to the average in-plane Ag-F distance. As already mentioned, the relative orientation of apical Ag-F contacts is different between phases LP and HP1. In LP, the inclination of apical Ag-F contacts relative to the [AgF4] plane is ca. 13° within the entire pressure range of stability. This is not very far from 0° degrees expected 2 for a perfect D4h system and indicates that a lone d(z ) pair only moderately repels with the p(z) orbitals at F atoms. On the other hand, in HP1 at 10 GPa, the longer of those bonds is inclined at 24°, while the shorter one only at ca. 5°. This change affects the interaction between electrons on 2 d(z ) orbital of Ag(II) – which is orthogonal to the [AgF4] plane – and fluorine ligands. While increased inclination of the top bond (as shown in fig. 7.6) decreases that repulsion on one side, shortening and smaller angle of the other axial bond must lead to a slightly stronger repulsion on the other side. However, it appears that overall, such arrangement is favored over the more symmetrical coordination pattern of LP-AgF2. This can be understood if a significant admixture of unoccupied 5p orbital is considered: one of the d(z2)p orbitals hosts the lone electron pair and is oriented towards the three farther F ligands (above the [AgF4] unit as drawn in fig. 7.6), while the unoccupied hybrid sticks out roughly in the direction of the shorter Ag-F axial contact. Therefore, the increased inclination of apical Ag-F contacts and d/p hybridization minimizes the repulsion between F and Ag d(z2) lone pair while still allowing for volume reduction induced by increasing pressure. It should also be pointed out that in this arrangement, the ratio of axial and equatorial Ag-F distances is not a meaningful determinant of the magnitude of JT effect anymore, as there are no longer any clearly discernible axial contacts.

Such deformation of [AgF6] octahedra is somewhat different than what is seen Cu(II) compounds under pressure, i.e. tilting of entire octahedra which allows for better packing without suppression of JT effect (examples of this have been discussed in section 2.3). 118

The LP → HP1 phase transition may at the first glance appear only as a minor structural change. However, the disappearance of inversion center and departure of Ag atoms from the [F4] plane in square units should lead to an uncompensated dipole moment and, consequently, ferroelectric properties. To our knowledge, HP1-AgF2 is the first known instance of a non- centrosymmetric layered structure among transition metal fluorides. Since AgF2, as a genuine compound of silver(II), also hosts relatively strong AFM interactions,87,89,90 the HP1 phase is a possible candidate for a multiferroic material, i.e. system exhibiting magnetic and ferroelectric properties in the same phase. Whether or not HP1-AgF2 can be obtained as a metastable phase at ambient pressure remains to be verified. Regardless, the aforementioned properties warrant more detailed studies of electrical and magnetic properties of this polymorph of AgF2.

7.2.2. HP2 form: a unique example of nanotubular structure of a binary transition metal compound

In a manner analogous to LP-AgF2, the structure of HP1-AgF2 was investigated theoretically in terms of dynamic stability, using both 2x2x2 and 2x4x2 supercells. Calculations were carried out at higher pressures than those achieved in XRD experiments reported here.

Results from both supercells led to the same conclusion: HP1-AgF2 structure becomes dynamically unstable at 70 GPa, as evidenced by the imaginary mode at Y (0,½,0) point of the Brillouin zone (fig. 7.8, left). Following the normal coordinate of this mode produces the Pbcn structure of HP2-AgF2 (fig. 7.8, right).

Fig. 7.8. Left – phonon dispersion curves of HP1-AgF2 at 70 GPa. Note the imaginary frequency at Y

point. Reproduced from ref. [289] Right – the structure of HP2-AgF2 in Pbna representation. Grey spheres – Ag, yellow spheres – F. The HP2 structure differs considerably from those of both LP and HP1 polymorphs of

AgF2. It is not composed of corrugated layers; instead, [AgF4] squares are arranged into channels propagating along the y direction. These channels, which we will refer to as nanotubes due to 119 their similarity to such systems, are arranged in the xz plane in a hexagonal (honeycomb-like) manner. The movement of atoms which leads from HP1 to HP2 structure is illustrated in fig. 7.9 and is somewhat more complex than the distortion which relates LP and HP1. When the structure of HP1 is viewed along the y axis, Ag atoms in each layer can be grouped into neighboring pairs along x. The mode at Y point shifts these pairs along the z axis. These shifts are coupled in-phase in y and anti-phase in x and z directions. Such pattern of atomic displacements destroys the layered arrangement and leads to the formation of channels along y. Although some of the short Ag-F bonds break upon this transition, the majority of them (75%) are retained – this suggests that the [AgF4] units are relatively robust and can withstand (to a large degree) this structural reorganization. The out-of-plane displacement of Ag atoms relative to the four nearest F atoms, which first appeared in HP1, is still present in HP2: Ag atoms are slightly shifted to the outside of each channel. However, the structure of HP2 is again centrosymmetric and is not expected to exhibit an uncompensated dipole moment. Also, the unit cell length is doubled in the x direction compared to LP and HP1.

Fig. 7.9. Structural relationship between structures HP1 (left) and HP2 (right) structures of AgF2. View along the y axis. Red arrows indicate movement of Ag atoms.

The nanotubular structure of HP2-AgF2 obtained through the aforementioned calculations turns out to fit the experimental data very well (fig. 7.10). In particular, it produces another low- angle reflection – one more than the HP1 structure – which is able to account for the previously discussed changes in XRD patterns of AgF2 above a certain pressure threshold in both samples.

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Fig. 7.10. Rietveld fit to the XRD pattern at 36.2 GPa (sample B). Note the new, low-angle reflection at ca. 5.5° characteristic to HP2. The transition from layered to nanotubular arrangement brings about further changes to local coordination of Ag atoms (fig. 7.11). As already mentioned, [AgF4] quasi-square units are still present in the HP2 polymorph. However, the (strongly distorted) [AgF6] octahedra can no longer be recognized. Instead, six secondary Ag-F contacts can be distinguished: four F atoms from neighboring nanotubes at distances between 2.4 and 2.6 Å, and two F atoms from the opposite side of the same nanotube at ca. 2.6-2.7 Å.

Fig. 7.11. Coordination environment of Ag atoms in HP2 structure. Ag-F distances are given in angstroms and are derived from XRD data at 36.2 GPa (sample B).

A further departure of F atoms from the axial position above and below [AgF4] units can again be explained on the grounds that it minimizes repulsion between 2p electrons of F and the 2 lone pair on d(z ) orbital of Ag(II) – the latter orbital being orthogonal to the [AgF4] plane. When viewed from this perspective, the 1D structure of HP2 is actually more closely packed than 2D structures of both LP and HP1. Although the choice of boundary of local coordination

121 environment may appear somewhat arbitrary in such structure, it can be argued that coordination number of Ag atoms does increase upon HP1 → HP2 transition from 8 to 10 (compare figs. 7.6 and 7.11). Similarly as in HP1-AgF2, Ag atoms are displaced from the F4 plane and consequently,

[AgF4] units are locally non-centrosymmetric, but globally, the structure of HP2-AgF2 does have an inversion center.

Fig. 7.12. Pressure dependence of the shortest distances between Ag atoms in polymorphs of AgF2. Dotted lines indicate approximate phase boundaries. The emergence of nanotubular polymorph at high pressure also strongly affects distances between silver atoms. Although both pressure-induced phase transitions in AgF2 are associated with a drop in the shortest Ag-Ag distance, the HP1 → HP2 transition decreases it by over 10% (fig. 7.12). In LP and HP1 polymorphs, this parameter corresponds to the distance between neighboring [AgF4] units within the same layer. In HP2, the nearest Ag-Ag contacts are between square units on the opposite sides of a nanotube. However, since [AgF4] units are not in fact located exactly opposite each other within each tube (which can be seen in fig. 7.13), an appropriate determinant of the nanotube width is the average distance between Ag and F atoms on its opposite sides. At 36.2 GPa, this distance is equal to ca. 2.68 Å, which is much shorter than the sum of van der Waals radii of Ag and F atoms (3.19 Å). This means that there is no room left inside the nanotube even for a smallest single atom; therefore, the structural constituent of HP2-

AgF2 can be more accurately described as a nanowire.

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Fig. 7.13. Side view of a single nanowire in HP2-AgF2, with relevant interatomic distances in angstroms (at 36.2 GPa, sample B) indicated by dotted lines. The Ag-F distance across the wire width is an average of two values shown also in fig. 7.11. The nanowire structure of HP2 is unprecedented in many ways, especially among transition metal halides. First of all, it is the first known example of a tubular structure made up of square units, instead of e.g. hexagonal ones, which are much more common. Nanotubular structures are not themselves rare: carbon nanotubes alone have been one of the most intensely studied systems since the 1991§ publication by Iijima,378 and a plethora of other similar systems have also been reported. They range from elements (including nonmetals, metals and metalloids) to a variety of binary compounds: carbides, nitrides, oxides, sulfides and others; sometimes even more complex stoichiometries. However, the only known example of a halide nanotube is 379 NiCl2. This has to do mostly with the character of chemical bonding required for the formation of such low-dimensional arrangement of atoms. In general, nanotubes and related structures are characterized by low coordination number of constituent atoms (e.g. 3 in carbon nanotubes), which can only be achieved if the chemical bond is rigid and directional. Covalent bonds are thus much better suited for that purpose. In contrast, low-dimensional assembly of ions cannot withstand structural collapse due to electrostatic forces which bind ionic solids. Since metal halides are predominantly ionic, the extreme scarcity of nanotubular structures among them should – in light of these considerations – come as no surprise. Especially fluorides, of all binary metal-nonmetal compounds, are then the least likely candidates for such systems. However, AgF2 can be considered a special case: X-ray photoelectron spectroscopy studies of silver fluorides have revealed that Ag-F bonding in AgF2 is in fact largely covalent, as measured by the ratio of contribution from Ag(4d) states to the metal band and the ligand band (58:42).80 Given the aforementioned considerations, and when compared to other metal difluorides, the structure of HP2 polymorph of AgF2 may appear somewhat exotic and indeed, unlikely.

§It should be noted, however, that Iijima was almost certainly not the first to synthesize carbon nanotubes. Most probably, the first confirmed instance of their formation is from a 1952 Soviet publication by Radushkevich, which did not become immediately available worldwide, both for political and linguistic reasons. See also ref. [392]. 123

Therefore, in the next section I will present how HP2-AgF2 is in fact closely related to other known MX2 polytypes and can be derived from already known crystal structures via relatively simple distortions.

7.2.3. Structural relationship between AgF2 polymorphs and comparison to known MX2 polytypes

It has already been stated that the ambient-pressure structure of AgF2 is closely related to the fluorite (CaF2) polytype: specifically, this relation manifests itself in the similarity of sublattice of metal atoms between the two compounds. Patterns of collective movement of atoms within that sublattice, associated with LP/HP1 and HP1/HP2 transitions described here, have also been presented. Here, I will more closely examine Ag and F sublattices in all three relevant polymorphs of AgF2 and how they change upon both phase transitions.

Fig. 7.14. Arrangement of metal sublattice in the three structures of AgF2 and compared to fluorite

(CaF2) and cotunnite (PbCl2). A simple way to visualize the metal sublattice in fluorite-related structures is with a triangular bicupola centered on one Ag atom surrounded by 12 other Ag atoms (fig. 7.14 A). It consists of 6 square and 8 triangle faces. In the cubic structure of CaF2, it is in fact a regular cuboctahedron, whose opposite triangular faces are aligned in the (111) or other symmetry- equivalent direction (i.e. body diagonal of the unit cell). A nearly identical pattern is present in

LP-AgF2 (fig. 7.14 B); it is only slightly distorted, leading to an orthorhombic (Pbca) instead of cubic (Fm3̅m) symmetry. The transition to HP1, as previously described, involves a slight motion of half of Ag atoms in the y direction relative to the other half and an additional displacement of all Ag atoms from their positions in their respective [AgF4] units. This deformation and the resulting 124 disappearance of inversion center is noticeable in fig. 7.14 C. Despite these changes, the quasi- cuboctahedron, although distorted with respect to CaF2, remains clearly recognizable. A more drastic change is associated with the second, HP1 → HP2 phase transition. The pattern of 12 Ag atoms around the central one in HP2 structure also resembles a cuboctahedron (fig. 7.14 D), but with one half rotated by 180° relative to the other. In this polyhedron (which in a regular, undistorted form is referred to as triangular orthobicupola), only two of the 8 triangular faces are positioned opposite each other, and they are oriented differently that in a cuboctahedron. As it turns out, this arrangement of metal atoms is very similar to the one characteristic of cotunnite (PbCl2) polytype (fig. 7.14 E). Therefore, even though both HP1 and HP2 structures are strongly distorted with respect to CaF2 and PbCl2, respectively, the transition between the two high-pressure phases of AgF2 can, in fact, be considered analogous to the fluorite → cotunnite transition that has been reported in several other difluorides under high pressure (section 4.3).

Fig. 7.15. Arrangement of anions in the three structures of AgF2 and compared to fluorite (CaF2) and

cotunnite (PbCl2). Grey spheres – Ag, yellow spheres – F/Cl. Only selected F/Cl atoms are drawn.

The series of pressure-induced transitions in AgF2 can also be examined from the point of view of anionic sublattice (fig. 7.15). While in the structure of fluorite F atoms are located in tetrahedral voids between metal atoms (fig. 7.15 A), they are pushed away from these positions 9 in LP-AgF2 due to collective Jahn-Teller effect, which acts on the local environment of d Ag(II) cations. In the latter structure, they are located on opposite triangular faces of octahedra, which can be discerned in cationic sublattice (fig. 7.15 B). Upon transition to HP1 polymorph, one of these anions (i.e. half in total) becomes slightly shifted towards the center of the aforementioned octahedron (fig. 7.15 C). This relative movement again reflects the departure of [AgF4] units from planarity that is characteristic of the first pressure-induced phase transition in AgF2. 125

The HP1 → HP2 transition further shifts one of the F atoms into the octahedron, while the other F atom also moves from its position on the triangular face and into the tetrahedral void (fig. 7.15 D). It can again be noticed that the metal sublattice is now heavily deformed compared to CaF2, LP-AgF2 and HP1-AgF2. In fact, if we expand the view around the central octahedron (fig. 7.15 E), the same fragment of HP2 crystal structure is clearly much more similar to cotunnite (fig. 7.15 F). In place of half of the previously shown tetrahedral voids, one can distinguish two new octahedral voids, rotated by 60° relative to the central octahedron (their vertices are not drawn in fig. 7.15 for better transparency). The entire sequence of anion displacement from LP to HP2 structure is therefore associated with increasing occupancy of octahedral voids within the cationic sublattice: from null

(in LP-AgF2, which in this sense is the same as CaF2) via partial in HP1 to full occupancy in HP2

– characteristic of PbCl2.

Fig. 7.16. Comparison of hypothetical PbCl2-type structure of AgF2 with only selected Ag-F contacts drawn (left), and nanotubular structure of HP2-AgF2 (right). The circle in the middle of a central pair of chains in PbCl2-type AgF2 marks the axis of rotation that relates both structures (see text). Grey spheres – Ag, yellow spheres – F.

Incidentally, if we consider AgF2 in the cotunnite-type structure and draw only selected

Ag-F contacts, a pattern of edge-sharing [AgF4] quasi-square units can be discerned (fig. 7.16, left). These units are connected into chains (similar to those seen in the structure of CuCl2), which in turn are additionally aligned into parallel pairs. The nanotubular structure of HP2-AgF2 (fig.

7.16, right) can then be derived from this PbCl2-type structure if half of Ag atoms in parallel pairs of chains are rotated around an axis that runs along and between chains of each pair (marked in fig. 7.16 as a circle with a dot).

This point of view provides further understanding of pressure-induced phase transitions of AgF2 within the well-known framework of CaF2 → PbCl2 transitions. Of course, it should be noted that crystal structures of HP1 and HP2 polymorphs of AgF2 are quite different from their 126 respective fluorite and cotunnite parent structures. These divergences can ultimately be traced back to the Jahn-Teller distortion, which again proves to be a significant factor in determining crystal structures of compounds containing d9 and thus JT-active transition metal cations. However, within this framework, it is easier to understand how both unprecedented structures, HP1 and HP2, can arise in such system.

7.2.4. Compressibility of AgF2 polymorphs and pressure dependence of their crystal parameters

Thus far, we have mostly considered qualitative relationship between AgF2 phases and not the exact extent to which lattice constants and interatomic distances (with a few exceptions) change upon phase transitions, and within each phase, as a result of compression. Let us now examine compressibility of all three hitherto discussed AgF2 phases. Pressure dependence of volume per formula unit is plotted in fig. 7.17. A noticeable volume drop occurs at both phase transitions. The one at HP1/HP2 boundary is larger and amounts to 5%. This transition is clearly first-order: a considerable volume reduction and very different crystal structures both strongly support that conclusion. The LP → HP1 transition is more ambiguous. On the one hand, the two structures are very similar and are related via a comparatively slight, collective movement of half of metal sublattice, with no breaking or formation of chemical bonds taking place. Moreover, theoretical calculations suggest that the volume drop at LP/HP1 boundary should only be ca. 1%. On the other hand, experimental data shows a volume reduction of 3.2% between 8.5 GPa (LP) and 10.0 GPa (HP1).

Fig. 7.17. Pressure dependence of unit cell volume per formula unit of AgF2 phases. Solid markers – compression, hollow markers – decompression. Dotted lines indicate approximate phase boundaries. Colored dashed lines indicate EoS fits. Version “A” of EoS for HP1 is plotted here (see also table 7.2). It should again be noted that there are relatively few data points pertaining to LP and HP1 phases. A closer look at fig. 7.17 reveals that without the data point at 10.0 GPa, the remaining 127 two points in HP1 range connected with three points in LP range would together show a steady, continuous decrease, characteristic of a second-order transition. However, there is no reason to discard this particular pressure point and not any of the other two. For now, we leave the order of the LP → HP1 transition unassigned.

Modelling of AgF2 compressibility is a little more challenging than in the case of AgO. Most known formulations of equation of state work best when applied to relatively simple solids such as elemental metals, ionic compounds or solidified noble gases.34 Directional chemical bonding can introduce some degree of anisotropy, which is particularly evident in layered structures of LP and HP1, and nanotubular structure of HP2. Nevertheless, I fitted the compression data of LP and HP1 phases with the Birch-Murnaghan EoS (eq. 5.2). For the nanotubular HP2 polymorph, I used a formulation developed by Kholiya specifically to describe high pressure behavior of carbon nanotubes:380 −1 −2 퐵0 ′ ′ 푉 ′ 푉 푝 = [(퐵0 − 3) − 2(퐵0 − 2) ( ) + (퐵0 − 1) ( ) ] (Eq. 7.1) 2 푉0 푉0

EoS parameters for all three phases of AgF2 are listed in table 7.2. The corresponding curves are plotted in fig. 7.17 together with experimental data. For the LP phase, volume at ambient pressure from Fischer et al.87 was used as reference volume.

3 V0/Z [Å ] B0 [GPa] B0’

LP-AgF2 (B-M) 40.76 (fixed) 81.6 1.8

HP1-AgF2 (B-M) [A] 39.9 81.6 (fixed) 2.6

HP1-AgF2 (B-M) [B] 39.6 92.9 1.8 (fixed)

HP2-AgF2 (Kholiya) 37.9 71.5 5.7

Table 7.2. Comparison of EoS parameters of AgF2. “B-M” and “Kholiya” indicate Birch-Murnaghan and Kholiya EoS, respectively. [A] and [B] indicate different fit constraints for HP1 phase (see text). Compressibility of HP1 turns out to be more problematic to model. If the LP → HP1 transition were of second-order, fitting both phases with one EoS should produce a reasonable result. However, such treatment (with the volume of AgF2 at 0 GPa again fixed as V0) yields a value of B0’ below 1. This implies an increasing compressibility with pressure and increasingly downwards slope of EoS fit in V(p) plot, which is a physically dubious conclusion. Unfortunately, this also occurs if the data for HP1 is fitted separately (with all three parameters released for optimization). Therefore, I decided to fix either B0 or B0’ as equal to the corresponding value for LP phase, which can be justified on the grounds of their structural similarity. Both fits give sensible results, and it is difficult to determine which one makes more physical sense based on such limited data. In fact, it is this scarcity of data that likely gives rise to the aforementioned

128 problems in the first place. In fig. 7.17, the result from fit “A” is plotted. Importantly, both fits yield a reference volume on average 2.5% lower than the volume of LP-AgF2, which – given their better quality compared to joint LP+HP1 fits – would further hint at a first-order character of LP → HP1 transition.

Using the EoS developed for nanotubes to describe compressibility of HP2-AgF2 produces a reasonable result. It may appear counter-intuitive that a high-pressure polymorph has a lower bulk modulus than the ambient-pressure phase of the same compound. However, a combination of relatively low bulk modulus and high value of its derivative is consistent with what has been previously reported for bundles of single-walled carbon nanotubes,380 and such systems can be considered a good approximation to the structure of HP2-AgF2.

Fig. 7.18. Pressure dependence of lattice constants of AgF2. Solid markers – compression, hollow markers – decompression. Dotted lines indicate approximate phase boundaries. 129

High-pressure behavior of lattice constants of AgF2 reveals a substantial anisotropy in compressibility of all three polymorphs (fig. 7.18). The ambient-pressure polymorph experiences reduction of all three unit cell dimensions upon compression from 0 to 8.5 GPa. Lattice constant a proves to be the most compressible, with a 4.8% volume reduction in that range, while b is only reduced by 0.9%. Both a and b are parallel to corrugated [AgF2] sheets: a runs along the direction of their puckering, while b is more or less parallel to “ridges” and “valleys”. A larger reduction of a means that these layers become increasingly corrugated with pressure. This is not surprising: from a purely mechanical perspective, it should be easier to compress a harmonica-like structure in the direction in which it is already folded. The distance between layers – c – is reduced in that pressure range by 3.7%.

Pressure dependence of lattice constants in high-pressure phases of AgF2 is even more anisotropic. Though the data for HP1 appears a little contradictory depending on the pressure point, it can be inferred, in part based on pressure dependence in neighboring phases, that a and c continue to decrease, indicating further puckering of and reduced distance between sheets, respectively. Interestingly, lattice constant b increases with pressure after the LP → HP1 transition, and especially upon the HP1 → HP2 transition, after which its pressure dependence flattens out above 30 GPa. Since a and c still decrease with pressure, the overall effect is a reduction of volume, which is an expected response to stronger compression. In the nanotubular structure of HP2, such behavior of lattice constants would indicate that nanotubes become more densely packed in the plane parallel to their cross section, but at the expense of slight elongation. In other words, they become thinner as a result of increased external pressure. This anisotropic trend in compression can actually be seen as further evidence for low dimensionality of the HP2 structure. Negative linear compressibility (NLC) – which in HP phases of AgF2 is manifested as the increase of lattice constant b with pressure – is a rare phenomenon, although not unprecedented: as already pointed out in section 4.4, several other compounds of silver with low- dimensional structures have been shown to exhibit strong anisotropy in their high-pressure behavior.327,328

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Fig. 7.19. Pressure dependence of the average Ag-F distance in [AgF4] units in all three polymorphs of

AgF2. Solid markers – compression, hollow markers- decompression. Dotted lines indicate approximate phase boundaries. Due to substantial differences in local coordination between layered LP/HP1 and nanotubular HP2 phases, it is difficult to establish a parameter that would measure the extent of

JT distortion in all three structures. On the other hand, the quasi-square [AgF4] units are retained in AgF2 structure in the entire studied pressure range. Fig. 7.19 shows pressure dependence of the average Ag-F distance in these units. Notably, this value increases upon both phase transitions, and while it shows a downward trend with pressure in all three phases, the overall reduction at the highest studied pressure, compared to ambient conditions, only amounts to 1.3%

(ca. 0.03 Å). This testifies to an unprecedented rigidity of [AgF4] units. From this perspective, their substantial increase occurring at phase transitions can indicate a release of stress accumulated during compression, which explains why both transitions are favored once a corresponding pressure threshold is reached. Indeed, one of the main changes during the LP → HP1 transition is the out-of-plane shift of Ag atoms, which – even with positions of F atoms unchanged – leads to an increase of Ag-F bond lengths in [AgF4] units. During the HP1 → HP2 transition, the rearrangement from layered to nanotubular structure is in part achieved by breaking of ¼ of short Ag-F bonds and formation of new bonds in their place (differently oriented). The increased length of these short bonds after the second phase transition may be viewed as a consequence of the increased coordination number of Ag(II) – from 4+3+1 in HP1 to 4+4+2 in HP2 (compare fig. 7.6 and fig. 7.11). The four nearest F atoms move away slightly – from 2.04 Å at 13.5 GPa to 2.10 Å at 14.8 GPa – in order to accommodate the larger number of longer Ag-

F contacts on both sides of [AgF4] quasi-square units.

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In summary, two new high-pressure phases of AgF2 have been identified and their crystal structure characterized based on theoretical calculations and two independent sets of X-ray diffraction data. The HP1 polymorph emerges above 8.5-10 GPa as a slight distortion of the ambient-pressure structure, but this distortion – concomitant with the disappearance of inversion center – is uncommon in transition metal compounds and probably has important consequences for physical properties of HP1-AgF2. Above ca. 15 GPa, AgF2 transforms into a nanotubular structure, unique among transition metal compounds and especially among fluorides. Although structures of HP1 and HP2 may seem unlikely at first, a more detailed analysis of Ag and F sublattices provides an explanation for their formation within the framework of phase transitions known to occur in other metal difluorides under high pressure. Uniqueness of these crystal structures can be justified on the grounds of very strong Jahn-Teller effect experienced by the local coordination environment of Ag(II) cations. The structure of LP-AgF2 can be thought of as a result of JT-induced displacement of F atoms from their positions in tetrahedral voids in the otherwise only slightly distorted metal sublattice of fluorite. An increase of pressure introduces further changes into that structure, driven both by increasing spatial confinement and the JT effect. In general, the persistent JT effect enforces structural patterns which minimize repulsion between F ligands and the lone d(z2) pair on Ag(II) cations, which – at 0 GPa – is oriented nearly orthogonally to the [AgF4] square units. In the increasing pressure sequence, this repulsion is avoided by tilting of some of the longer Ag-F contacts and pushing them away from axial positions and, presumably, by increased hybridization between occupied d(z2) orbital and unoccupied p orbitals in order to redistribute electron density. Local coordination of Ag atoms thus changes from 4+2+2 in LP via 4+3+1 in HP1 to 4+4+2 in HP2.

Of other transition metal difluorides, AgF2 can be most easily compared to CdF2, since both compounds host metal cations of virtually equal radius (Cd(II) – 109 ppm, Ag(II) – 108 ppm). As has been demonstrated, the HP1 → HP2 transition in AgF2 is in many ways equivalent to the fluorite → cotunnite transition in other MF2. The former transition occurs at ca. 15 GPa, 294 while the latter occurs at 7 GPa in CdF2. Furthermore, the fluorite → cotunnite transition in 297 CaF2 (Ca(II) radius – 114 ppm) occurs at 9 GPa. On the one hand, this is a similar order of magnitude. On the other hand, the two times higher transition pressure of AgF2 compared to CdF2 and over 1.5 times higher compared to CaF2 is probably a consequence of persistent Jahn-Teller effect, which is absent in the local coordination environment of closed-subshell Cd(II) and Ca(II) cations. Therefore, the JT effect appears to be an important factor which prevents – at least at lower pressures – a major structural rearrangement in AgF2, and shifts it to higher pressures.

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3 3 p(AgF) [GPa] a [Å] b [Å] c [Å] V [Å ] GOF Rp Rwp V/Z [Å ] 0 5.073 5.529 5.813 163.05 n/a n/a n/a 40.76 sample A - compression 4.9(1) 5.485(1) 5.656(1) 4.965(2) 154.03(10) 0.26 0.38 0.56 38.51 8.5(2) 5.477(3) 5.598(3) 4.828(3) 148.01(3) 0.59 0.88 1.37 37.00 10.0(5) 5.475(7) 4.704(6) 5.564(6) 143.32(10) 0.52 0.85 1.27 35.83 13.5(6) 5.572(8) 4.513(7) 5.523(7) 138.88(9) 0.39 0.70 0.96 34.72 16.9(6) 5.475(13) 8.350(22) 5.693(15) 260.2(1.3) 0.35 0.57 0.86 32.53 21.8(1.0) 5.300(16) 8.234(18) 5.714(17) 249.4(1.7) 0.47 0.86 1.31 31.17 25.9(1.8) 5.198(23) 8.137(31) 5.716(17) 241.8(2.4) 0.41 0.73 1.03 30.22 sample B - compression 11.7(5) 5.585(7) 4.500(8) 5.634(7) 141.58(8) 0.13 0.51 0.70 35.39 14.8(6) 5.475(10) 8.331(15) 5.787(7) 264.0(1.1) 0.50 0.50 0.71 33.00 25.3(8) 5.301(10) 8.100(16) 5.777(9) 248.1(1.2) 0.45 0.39 0.60 31.01 32.7(1.2) 5.197(17) 7.947(19) 5.821(10) 240.4(1.4) 0.43 0.41 0.61 30.05 36.2(8) 5.129(10) 7.849(11) 5.803(7) 233.6(8) 0.30 0.29 0.44 29.20 sample B - decompression 34.4(6) 5.141(7) 7.905(11) 5.802(6) 235.8(8) 0.23 0.24 0.32 29.47 32.8(1.1) 5.173(15) 7.920(20) 5.810(10) 238.1(1.4) 0.38 0.39 0.53 29.76 28.5(7) 5.198(10) 7.951(13) 5.833(7) 241.1(9) 0.26 0.28 0.37 30.14 24.6(9) 5.250(15) 8.010(20) 5.858(10) 246.4(1.5) 0.30 0.33 0.43 30.80 20.1(4) 5.322(12) 8.128(15) 5.851(5) 253.1(4) 0.33 0.34 0.51 31.64 16.5(3) 5.355(9) 8.305(13) 5.836(10) 259.5(4) 0.33 0.34 0.54 32.44

Table 7.3. Results of Rietveld refinement of XRD data from samples A and B of AgF2: pressure values, lattice constants and fit parameters. Grey row – ambient-pressure data from ref. [87], magenta rows – LP

(in Pbca setting), green rows – HP1 (in Pbc21 setting), yellow rows - HP2 (in Pbna setting) Uncertainties are given in brackets.

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7.3. Magnetic and electric properties of compressed AgF2

7.3.1. Theoretical description of magnetic and electronic properties of compressed AgF2

Experimental determination of magnetic properties of strongly compressed matter is one the most challenging tasks in high pressure science. This is due to the inherent design features of experimental tools used for compression: the volume of sample is necessarily small and very often insufficient to detect any magnetic interactions beyond the diamagnetic background of the DAC apparatus. In practice, high pressure magnetic measurements are limited to detecting ferromagnetism and Meissner-Ochsenfeld effect in superconductors, and even in those systems the signal is often buried in the background and requires a careful compensation. Antiferromagnetic interactions can only be detected indirectly – like paramagnets, AFM-ordered materials exhibit zero magnetization in the absence of external field, but the temperature dependence of their magnetic susceptibility exhibits a maximum at Néel temperature.

In the particular case of AgF2¸ magnetic measurements are further complicated by the high chemical reactivity of this compound. Therefore, magnetic properties of AgF2 were instead investigated theoretically by Dr Dominik Kurzydłowski and Dr Mariana Derzsi, taking structural models derived from X-ray diffraction results (hitherto discussed in this chapter) as a starting point. These calculations are not technically part of this work – their results and computational details can be found in a separate contribution.381 However, selected findings are summarized here in order to illustrate the influence of pressure-induced structural changes on magnetic interactions and electronic properties in AgF2.

Fig. 7.20. Magnetic superexchange pathways (red lines) in three polymorphs of AgF2: LP (top left), HP1 (top right) and HP2 (bottom).

134

Fig. 7.20 shows magnetic coupling pathways in all three structures of AgF2. The lowering of symmetry upon the LP → HP1 transition leads to two non-equivalent intra-layer coupling constants (J2D’ and J2D’’), compared to only one in LP-AgF2 (J2D). The angle between Ag-F-Ag bonds in LP is ca. 130°, whereas in HP1, the angle corresponding to J2D’ pathway is equal to ca.

129°, and the one corresponding to J2D’’ – 117° (at 10.0 GPa). Consequently, the value of J2D’’ decreases compared to J2D in LP, in accordance with Goodenough-Kanamori-Anderson rules.

The situation is even more complex in nanotubular HP2-AgF2, where three different intra-tubular coupling constants can be discerned. The pathway corresponding to Jt’ is almost linear (172° at 36.2 GPa), which leads to very strong AFM interactions (ca. −250 meV). A similar system of 382 [Ag2F7] dimers has been previously observed in Ag2ZnZr4F14. The coupling pathway in that compound is perfectly linear, which – according to most recent calculations – leads to an even 381 stronger AFM coupling (J = −313 meV). On the other hand, interactions described by Jt’’’, realized at an almost right angle of 97°, are weakly ferromagnetic (4-30 meV). Jt’’ corresponds to AFM coupling of moderate strength (ca. −25 meV), mediated through Ag-F-Ag bonds oriented at 120°.

Theoretical calculations of electronic band gap of AgF2 show that it is only weakly pressure-dependent (fig. 7.21). In the studied pressure range (0-40 GPa), it shows only a relatively slight variation between 2.40 and 2.55 eV. This behavior can be attributed to the presence of

AFM interactions and to the rigidity of Ag-F bonds in [AgF4] square units, which, according to experimental XRD data, are mostly retained in the entire studied range of pressure.

High-pressure resistivity measurements of AgF2 have been attempted as part of this work. Results of those attempts are summarized in appendix D.

Fig. 7.21. Pressure dependence of electronic band gap of AgF2 derived from HSE06 calculations. Reproduced from ref. [381] 135

8. Higher chlorides of silver - AgClx

In addition to the XRD structural studies of AgO and AgF2, I have also performed preliminary experiments involving silver and chlorine under high pressure. As outlined in section 3.5, only silver(I) chloride and its ternary derivatives – chloroargentates – are known.

8.1. Preliminary Raman spectroscopy studies on compressed Ag/Cl systems

Two types of systems were studied: mixtures of Cl2 with either Ag or AgCl. Experiments were carried out using the same type of symmetrical DAC as in XRD studies of AgO and AgF2 described in two previous chapters. Chlorine was loaded in a cryogenic procedure, which required additional preparation steps. A hole was cut in a pre-indented rhenium gasket, and a cylinder of slightly smaller diameter was cut out of Hastelloy foil and placed inside the hole. The system was again compressed to join the gasket materials together. The hole for sample was then cut within the inner, Hastelloy part of the gasket. Such prepared gasket was placed on one of the diamonds and pressed against it using a metal ring, in order to prevent chlorine from leaking through the bottom. The parts of gasket surrounding the hole were covered with Al2O3 powder to prevent the gasket from sliding against the diamond. Both bases of the DAC were then placed in liquid nitrogen bath. Chlorine gas was passed through a capillary and into the hole of the gasket placed on the diamond. A speck of Ag or AgCl was placed on the other diamond. The DAC was then closed without the addition of any pressure medium or gauge. Due to toxicity of chlorine, loading was carried out in a glove bag. Pressure at any given point was determined by the first-order Raman band of diamond.335 Compressed Ag/Cl systems were heated with an infrared laser (1064 nm) at selected pressure points. Raman spectra were collected using a setup with 532 nm laser.

Fig. 8.1. Raman spectrum of AgCl+Cl2 sample collected at 42 GPa without prior laser heating. 136

If no reaction were to take place in the system, the only prominent Raman signals would be expected to originate from solid Cl2. Pressure dependence of Raman spectra of solid chlorine has been previously studied by Johannsen et al.383 AgCl, as an ionic solid with NaCl-type structure of cubic (Oh) symmetry, should not in principle exhibit any Raman-active modes (since each atom sits at a center of inversion), although the first overtone of an IR-active transverse optic mode384 in the range below 400 cm-1 can be expected; at any rate, this band should be very weak compared to those originating from Cl2. Ag, as a metal, should not give rise to any Raman signal at all. Indeed, most of the obtained spectra of Ag/Cl systems are dominated by an intense band originating from the stretching mode of Cl2 molecules (fig. 8.1); at lower pressures, this band is additionally split due to isotopic effects.383

Fig. 8.2. Left: diamond anvil cell with compressed Ag/Cl system during laser heating. Right: the sample

of Ag+Cl2 after laser heating. Red circle indicates the laser-heated spot, which exhibits a color change.

Laser heating of Ag+Cl2 and AgCl+Cl2 samples induced a change in the appearance of the sample, which turned reddish-brown around the spot at which it was heated (fig. 8.2). This change was accompanied by emergence of new bands in Raman spectra, most prominently in the -1 400-550 cm range (fig. 8.3). Interestingly, in one Ag+Cl2 sample, new bands appeared even without laser heating and at pressures as low as ca. 3 GPa. The fact that no such process was observed for samples containing AgCl could be explained by a relatively higher activation energy for reaction between AgCl and Cl2 than between Ag and Cl2 – that is, if any of the new bands originate from a novel AgClx compound.

137

Fig. 8.3. Raman spectrum of Ag+Cl2 sample collected at 6.4 GPa without prior laser heating. There are several scenarios that would explain the appearance of new bands. Perhaps the least desirable outcome would be the reaction between diamond and chlorine, leading to carbon tetrachloride CCl4. Fortunately, high-pressure behavior of CCl4 in terms of Raman spectra has been reported in a study by Chen et al.,385 which allows us to compare positions of known bands of CCl4 with our results (fig. 8.4).

Fig. 8.4. Pressure dependence of Raman shift of selected bands from compressed Ag/Cl samples (black

circles), compared with bands of CCl4 (colored diamonds) as reported in ref. [385]. Some of the bands, particularly the two marked with red diamond, appear to overlap in a limited pressure range. On the other hand, the band marked in green, reported as the second most 138 prominent by Chen et al., is completely absent in our data, which strongly undermines the 385 hypothesis of CCl4 formation. This does not, however, rule out the presence of other compounds which could be formed in a reaction between carbon and chlorine.

Based on considerations in section 3.5, polychlorides of silver could also be anticipated among reaction products in compressed Ag/Cl systems. There have been several studies which examined polychlorides with anions of different stoichiometry and geometry, ranging from Cl3ˉ 386–389 to Cl9ˉ, by means of Raman spectroscopy and theoretical calculations. Unfortunately, none of those compounds have been studied spectroscopically at elevated pressures, which limits the possibility of comparison with our data. Nevertheless, Raman shifts of bands of different polychloride anions from the aforementioned works are shown in fig. 8.5 together with our results.

Fig. 8.5. Pressure dependence of Raman shift of selected bands from compressed Ag/Cl samples (black circles), compared with positions of bands from various polychloride anions at ambient pressure (color markers). “exp” indicates experimental values and “theor” – theoretically calculated values. Data for polychlorides is taken from: “Haller” – ref. [386], “Bruckner” – ref. [387], “Hu” – ref. [388], “Taraba” – ref. [389]. Dashed lines are not fits to data – they are drawn to guide the eye. Without the knowledge of pressure-induced changes in polychloride anions, it is difficult to compare their Raman shifts with high pressure data. However, the length of Cl-Cl bonds can be expected to decrease with increasing pressure, which would shift the corresponding bands to 383 higher frequencies, as is the case in Cl2 molecule. An approximate extrapolation of pressure dependence of our data to 0 GPa suggests Cl3ˉ, Cl7ˉ and Cl9ˉ as possible candidates for the origin

139 of new bands observed in spectra of compressed Ag/Cl samples. Regardless of the exact results of these extrapolations, most of the previously reported vibrational frequencies of polychloride anions lie in the same spectral range as the new bands arising from our samples (i.e. below the

Cl2 vibron), which strengthens the case for the presence of such species. Of course, such inference requires further corroboration, which cannot be provided by the presented Raman spectra alone. Nevertheless, vibrational spectroscopy data will certainly prove useful in studies of those systems, since polychloride anions are predicted to occur in a variety of isomeric forms (fig. 8.6) and may be most easily distinguished by their spectral signatures.387

Fig. 8.6. Possible geometries of polychloride anions. Top: Cl5ˉ, middle: Cl7ˉ, bottom: Cl9ˉ. Reproduced with permission from ref. [387]. It should also be noted that the intensity of the experimental bands in question (i.e. those of uncertain origin) is very low in most spectra, which makes the determination of their Raman shift less precise. The spectrum in fig. 8.3 is therefore not representative of relative intensities, but it was chosen to highlight the processes occurring in studied Ag/Cl samples. At any rate, this low intensity of new bands and low precision of their Raman shift determination further contributes to the difficulty of assigning them to any possible products.

As it stands, the identity of the dark-colored reaction products in the studied silver/chlorine systems remains unknown. Given the marked change in color of the sample and appearance of new Raman bands, it is reasonable to suggest that some reaction does take place in this system, especially upon laser heating. However, other analytical methods, such as X-ray diffraction, will have to be employed in order to elucidate the exact nature of compounds present in compressed Ag/Cl systems. Future interpretation of experimental data (both Raman and XRD) will also have to be supplemented by more detailed theoretical calculations, as in the case of analyses of high-pressure behavior of AgO and AgF2. Such studies will be undertaken in the near future.

140

(EN) Summary of experimental findings

Based on X-ray diffraction data and supplemented by theoretical calculations (the latter performed by Dr Mariana Derzsi), this work has succeeded at elucidating crystal structures of high-pressure polymorphs of two silver compounds – silver(I,III) oxide AgO and silver(II) fluoride AgF2. In addition, preliminary experiments with compressed samples of Ag/AgCl and chlorine have to some extent given credibility to previous theoretical predictions that new compounds of silver and chlorine may form at elevated pressures.

AgO undergoes two phase transitions in the pressure range up to 58 GPa. Its ambient- pressure structure (LP, P21/c space group) can be thought of a result of Jahn-Teller instability of a hypothetical AgIIO in an idealized NaCl-type lattice, coupled to charge-density wave, which leads to the presence of two different valence states of silver (+1 and +3) instead of one (+2). Between 16.1 and 19.7 GPa, LP transforms into a structure described by the same monoclinic space group (HP1, P21/c), but with a very different local coordination pattern of Ag(I): coordination number of those atoms increases from 2 (dumbbell, linear) to 8 (quasi-cubic). This change can also be interpreted as a shift from covalent to more ionic bonding character between Ag(I) and O atoms. A second transition occurs at ca. 40 GPa and leads to HP2 polymorph, which differs from HP1 only in an increased symmetry (orthorhombic, Imma space group). The LP → HP1 transition is associated with a noticeable volume drop, reflecting the major structural rearrangement taking place, and is therefore of the first order. On the other hand, the transition from HP1 to HP2 is merely a consequence of a steady decrease of monoclinic β angle in LP and HP1 phases with increasing pressure – down to 90° at phase transition – and is of the second order, without any discontinuity in pressure dependence of volume. Overall, XRD data indicates that the mixed-valent character of AgO is retained up to at least 58 GPa. Raman spectroscopy data, which are not discussed in this work, further extend this range to ca. 80 GPa. The evolution of inter-valence charge-transfer band gap of AgO with increasing pressure – derived from DFT calculations – is not monotonic. Perhaps most surprisingly, according to

141 calculations AgO exhibits a non-zero gap of 0.3 eV even at pressures as high as 100 GPa – in contrast to oxygen, which is already metallic at such conditions. High-pressure behavior of AgO testifies to a particularly strong resistance of this transition metal oxide to undergo comproportionation and concomitant metallizaton – a property which could be of interest to solid state physics.

AgF2 was found to transform to a non-centrosymmetric polymorph (HP1) at ca. 9 GPa, which retains the layered structural arrangement of the ambient-pressure polymorph (LP), but the Ag atoms diverge from their positions in plane of four nearest F atoms. This relatively minor change should lead to an uncompensated dipole moment, which together with the canting of antiferromagnetically ordered spins suggests that HP1 is likely multiferroic, i.e. it could exhibit magnetic ordering and ferroelectric properties within the same phase. In such materials, magnetic properties can be tuned by external electric field and vice versa. At ca. 15 GPa, AgF2 further transforms into a nanotubular polymorph (HP2), which is the only instance of such 1D structure among fluorides. Both high-pressure polymorphs of AgF2 are unique among transition metal difluorides in terms of crystal structures. However, they are in fact closely related to more common structural polytypes of ionic AX2 compounds via a Jahn-Teller effect-driven distortions of anionic sublattice.

Although magnetic properties of AgF2 under high pressure were not studied experimentally, theoretical calculations – based on structural models derived from XRD data discussed in this work – suggest a very strong antiferromagnetic coupling in the nanotubular polymorph (J = −250 meV). Such high value of J is comparable to that seen in oxocuprates(II); 3- however, in nanotubular AgF2 the magnetic superexchange is 0D, i.e. it only occurs in [Ag2F7] dimers and does not extend in any dimension of the crystal structure.

There are also important differences between high-pressure behavior of AgF2 and CuF2 (both systems with prominent Jahn-Teller effect), the latter very recently studied by Dr Dominik Kurzydłowski by means of Raman spectroscopy and theoretical calculations.299 In particular,

142 computational results suggest that CuF2 does not adopt a nanotubular structure of HP2-AgF2 type and instead transforms to a PbCl2-type structure at ca. 70 GPa.

High-pressure behavior of AgF2 exemplifies the strong influence that a prominent Jahn- Teller effect – characteristic of d9 systems such as Ag(II) – exerts on crystal structures and physical properties of compounds containing JT-active cations. In AgF2, JT effect leads to structures that are strongly distorted in comparison to difluorides of closed-subshell cations with comparable radius – CaF2 and CdF2. It also causes the transition between layered and nanotubular polymorphs of AgF2 to occur at significantly higher pressure than the corresponding fluorite to cotunnite transition in CaF2 and CdF2. The differences between AgO and its closed-subshell analogs CdO and CaO in terms of crystal structures and pressure-induced phase transitions are even more pronounced: while the ambient-pressure monoclinic polymorph of AgO is related to the rocksalt structure of more typical metal monoxides, its crystal structures at higher pressures show no discernible correspondence either to NaCl or CsCl polytypes. This can be attributed to the mixed-valent character of AgO and, consequently, the presence of two different Ag crystallographic sites with very different local coordination.

In both AgF2 and AgO, the approximately square-planar [AgX4] structural units show a remarkable rigidity: they are retained in crystal structures of all studied polymorphs of these compounds, and the Ag-X bond lengths exhibit relatively little variability with pressure.

It is important to note that crystal structures of high pressure polymorphs of both AgO and AgF2 were initially derived from density functional theory computations. Remarkably, they turned out to fit the experimental XRD data very well, both in terms of quality of Rietveld fits and in terms of pressure range of their stability. This shows that the employed theoretical method – searching for lattice dynamic instabilities, distorting the initial structure along the normal coordinate of imaginary mode(s) arising at high pressures, and optimization of the obtained structure at given conditions – is a very useful tool for determination of very complex crystal structures of even such strongly correlated systems as compounds of silver(II).

Results obtained for Ag/Cl systems are less understood, but still very promising. Based on the appearance and Raman spectra of compressed and laser-heated samples of Ag/AgCl and chlorine, it is very likely that a reaction has taken place, leading to new, hitherto unknown AgClx compounds. Polychlorides containing complex Clxˉ anions appear to be the most likely candidates for those products, but the presence of some type of compounds of silver(II) cannot be ruled out. These results certainly justify further studies of Ag/Cl systems under high pressure.

143

(PL) Podsumowanie uzyskanych wyników

Na podstawie danych dyfrakcji rentgenowskiej, uzupełnionych obliczeniami teoretycznymi przeprowadzonymi przez dr hab. Marianę Derzsi, udało się w niniejszej pracy rozwiązać struktury krystaliczne wysokociśnieniowych odmian polimorficznych dwóch związków – tlenku srebra(I,III) AgO oraz fluorku srebra(II) AgF2. Ponadto, wstępne eksperymenty z użyciem skompresowanych próbek Ag/AgCl i chloru częściowo potwierdziły wcześniejsze przypuszczenia o możliwości powstawania nowych związków srebra i chloru pod wysokim ciśnieniem.

AgO ulega dwóch przejściom fazowym w zakresie ciśnienia do 58 GPa. Jego struktura pod ciśnieniem atmosferycznym (LP, grupa przestrzenna P21/c) może być rozumiana jako efekt deformacji hipotetycznego tlenku AgIIO w sieci typu NaCl pod wpływem działania efektu Jahna- Tellera sprzężonego z falą gęstości ładunku, co prowadzi do utworzenia dwóch stanów walencyjnych srebra (+1 i +3) zamiast jednego (+2). W zakresie 16,1-19,7 GPa, odmiana LP przekształca się w strukturę o tej samej grupie przestrzennej (HP1, P21/c), lecz o zupełnie innym otoczeniu jonów Ag(I): liczba koordynacyjna tych atomów zwiększa się z 2 (koordynacja liniowa) do 8 (quasi-kubiczna). Zmiana ta może być także interpretowana jako zmiana charakteru wiązania między Ag(I) i O z kowalencyjnego na bardziej jonowy. Drugie przejście fazowe zachodzi ok. 40 GPa i prowadzi do odmiany HP2, która od HP1 różni się tylko zwiększoną symetrią (rombowa, grupa Imma). Przejście LP → HP1 wiąże się z widocznym spadkiem objętości, który odzwierciedla zasadniczą reorganizację struktury; z tego powodu przejście to jest pierwszego rodzaju. Z drugiej strony, przejście z HP1 do HP2 jest jedynie konsekwencją stopniowego zmniejszania się kąta β w fazach LP i HP1 ze wzrostem ciśnienia – aż do 90° w punkcie przejścia fazowego – i jest drugiego rodzaju, bez nieciągłości w zależności objętości od ciśnienia. Sumarycznie, dane XRD wskazują, że mieszana walencyjność AgO jest zachowana co najmniej do 58 GPa. Dane spektroskopii ramanowskiej, niepokazane w tej pracy, zwiększają ten zakres do ok. 80 GPa. Przebieg zależności przerwy energetycznej przeniesienia ładunku między stanami Ag w AgO od ciśnienia – obliczony metodą DFT – nie jest monotoniczny. Co zaskakujące, według 144 tych obliczeń AgO wykazuje niezerową przerwę energetyczną (0,3 eV) nawet pod ciśnieniem 100 GPa – w przeciwieństwie do tlenu, który w takich warunkach jest metalem. Wysokociśnieniowe właściwości AgO wskazują na szczególnie wysoką odporność tego tlenku metalu przejściowego na komproporcjonację i metalizację. Własność ta jest bardzo interesująca z punktu widzenia fizyki ciała stałego.

AgF2 ulega przekształceniu ok. 9 GPa w pozbawioną środka symetrii odmianę HP1, która zachowuje warstwowy układ strukturalny odmiany niskociśnieniowej (LP), jednak atomy Ag odbiegają w niej ze swojego położenia w płaszczyźnie czterech najbliższych atomów F. Ta stosunkowo niewielka zmiana powinna skutkować nieskompensowanym momentem dipolowym. W połączeniu z odchyleniem uporządkowanych antyferromagnetycznie spinów sugeruje to, że HP1-AgF2 jest multiferroikiem, tj. może wykazywać porządkowanie magnetyczne i ferroelektryczne w ramach tej samej fazy. W tego typu materiałach, własności magnetyczne mogą być kontrolowane poprzez zewnętrze pole elektryczne i vice versa. Ok. 15 GPa, AgF2 ulega przemianie w odmianę nanorurkową (HP2) – jedyny przykład tego typu jednowymiarowej struktury spośród fluorków. Obie wysokociśnieniowe odmiany AgF2 są wyjątkowe wśród fluorków metali pod względem struktury krystalicznej. Mimo to, są one blisko spokrewnione z częściej występującymi typami strukturalnymi związków jonowych o stechiometrii AX2 za pośrednictwem efektu Jahna-Tellera, deformującego podsieć anionów.

Mimo że własności magnetyczne AgF2 pod ciśnieniem nie zostały zbadane eksperymentalnie, obliczenia teoretyczne – bazujące na modelach strukturalnych wyprowadzonych z danych XRD omawianych w niniejszej pracy – sugerują bardzo silne sprzężenie antyferromagnetyczne w odmianie nanorurkowej (J = −250 meV). Tak wysoka wartość J jest porównywalna z tą obserwowaną w tlenkach miedzi(II), jednak w nanorurkowym 3- AgF2 nadwymiana magnetyczna jest zero-wymiarowa, tj. zachodzi tylko w dimerach [Ag2F7] i nie rozciąga się w którymkolwiek wymiarze struktury krystalicznej.

Istnieją zasadnicze różnice między wysokociśnieniowymi właściwościami AgF2 i CuF2

(w obu układach występuje wyraźny efekt Jahna-Tellera). Przypadek CuF2 został niedawno przeanalizowany przez dr. Dominika Kurzydłowskiego z użyciem spektroskopii ramanowskiej i 145

299 obliczeń teoeretycznych. W szczególności, wyniki obliczeń sugerują, że CuF2 nie przyjmuje nanorurkowej struktury typu HP2-AgF2; zamiast tego przyjmuje strukturę typu PbCl2 pod ciśnieniem ok. 70 GPa.

Wysokociśnieniowe właściwości AgF2 są przykładem silnego wpływu efektu Jahna- Tellera – charakterystycznej cechy układów d9 takich jak Ag(II) – na struktury krystaliczne i właściwości fizyczne związków zawierających tego typu kationy. Wskutek zachodzenia efektu

JT struktury AgF2 są silnie zdeformowane w porównaniu do struktur difluorków zawierających kationy metali o porównywalnym promieniu, ale o zamkniętych podpowłokach elektronowych –

CaF2 i CdF2. Efekt JT powoduje także przesunięcie przejścia między warstwową a nanorurkową strukturą AgF2 do wyższego ciśnienia w porównaniu do analogicznego przejścia fluoryt → kotunnit w CaF2 i CdF2. Różnice między AgO a CdO i CaO – jego analogami o zamkniętopowłokowych kationach – są jeszcze wyraźniejsze. Chociaż niskociśnieniowa odmiana AgO jest spokrewniona ze strukturą typu NaCl, występującą w innych tlenkach metali, struktury wysokociśnieniowych odmian AgO nie wykazują tego typu relacji ani z typem NaCl, ani CsCl. Przyczyną takiego stanu rzeczy jest zdysproporcjonowany charakter AgO, w którego strukturze atomy Ag występują w dwóch różnych pozycjach krystalograficznych o zasadniczo odmiennej koordynacji.

Zarówno w AgF2, jak i w AgO, (w przybliżeniu) płaskie kwadratowe podjednostki

[AgX4] wykazują wyjątkową sztywność: są one zachowane w strukturach wszystkich badanych odmian obu związków, a długości wiązań Ag-X prawie nie zmieniają się pod wpływem ciśnienia.

Należy zauważyć, że struktury wysokociśnieniowych odmian AgO i AgF2 zostały początkowo znalezione z użyciem obliczeń DFT. Okazały się one wyjątkowo dobrze pasować do danych XRD, zarówno pod względem jakości modeli rietveldowskich, jak i ciśnieniowych zakresów stabilności. Dowodzi to, że zastosowana metoda – poszukiwanie niestabilności fononowych, deformacja wzdłuż współrzędnej urojonego modu i optymalizacja tak otrzymanej struktury – jest skutecznym sposobem rozwiązywania złożonych struktur krystalicznych występujących w układach o silnej korelacji elektronowej, takich jak związki srebra(II).

Wstępne wyniki otrzymane dla układów Ag/Cl są na razie mniej zrozumiałe, niemniej interesujące. W oparciu o wygląd próbki i widma ramanowskie skompresowanych i ogrzanych laserowo próbek Ag/AgCl i chloru, można z dużym prawdopodobieństwem stwierdzić, że zaszła reakcja prowadząca do nowych, nieznanych dotychczas związków AgClx. Polichlorki, zawierające kompleksowe aniony Clxˉ wydają się być najbardziej prawdopodobnymi produktami, ale nie można też wykluczyć obecności związków srebra(II). Wspomniane wyniki z całą pewnością uzasadniają dalsze badania nad układami Ag/Cl pod wysokim ciśnieniem.

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(EN) Prospects of future research

Pressure-induced structural transitions of AgO and AgF2 reported in this work have turned out to be quite different than those predicted in previously published theoretical papers. Though several promising predictions have been proven false, they have been replaced by new ones, which are based on experimentally verified structural models. The newly discovered high pressure polymorphs of both compounds can now be further investigated in order to determine their physical properties.

The strong resistance of AgO to pressure-induced metallization, suggested by most recent calculations, can be verified using direct resistivity measurements and by spectral methods, which enable optical determination of electronic band gap. Especially the latter method is relatively easy to employ, and such obtained data could have the potential of providing a better understanding of how the interplay between Jahn-Teller effect and mixed valence affects electric properties of transition metal compounds.

The first known oxocuprate precursor for high-temperature superconductors – La2CuO4 – can only achieve the desired superconducting properties when doped with holes on a fraction of

Cu(II) atoms, as in La2-xBaxCuO4 (which formally leads to the presence of Cu(III) states). AgO, due to its mixed-valent (Ag(I)/Ag(III)) character, is very different from CuO, for example in being diamagnetic. Nevertheless, it would be interesting to study doped AgO systems and see how doping affects their electric and magnetic properties.390

Compression of AgF2 does not lead to flattening of its layered structure, which would have been promising from the point of view of potential superconductivity. However, high pressure polymorphs of AgF2 exhibit very rare structural features which can lead to interesting physical properties. The potential multiferroicity of HP1 polymorph can in principle be tested using electric and magnetic measurements, especially since the pressure required to reach the HP1 phase is relatively modest (ca. 9 GPa). The very strong antiferromagnetic coupling predicted in the nanotubular HP2 polymorph also warrants experimental verification. Ternary fluoroargentates(II), which are in many ways analogous to oxocuprates(II), are yet to be studied at high pressures. In particular, it would be interesting to see how compression affects orbital ordering and arrangement of elongated octahedra – phenomena which are crucial determinants of magnetic interactions in compounds with layered perovskite structure, and those interactions are in turn thought to be an essential feature of copper-oxide-based high-temperature superconductors.

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Another promising pathway of research involves compression of AgF2 samples doped with Ag(I) species. Such samples have only recently been obtained in collaboration with Dr Zoran Mazej from Jožef Stefan Institute in Ljubljana, Slovenia. In principle, through analogy to doped oxocuprates(II), they could exhibit a much lower band gap than undoped AgF2 and become metallic at relatively low pressures. This is a subject of ongoing studies.

There are also quite a few compounds that are in one way or another analogous to AgO or AgF2 and which have not been studied in great detail under high pressure. This is especially 9 true for fluorides such as CuF2 (a d system like AgF2) or PdF2. Pressure-induced phase transitions of the former have only been studied with Raman spectroscopy and theoretical calculations,299 and it would be useful to corroborate findings of that study with structural (e.g. XRD) data.

Although the structure of high-pressure polymorph of PdF2 has been found in several other compounds with MX2 stoichiometry subjected to compression, PdF2 itself has only been investigated up to ca. 6 GPa,284 which is a relatively modest pressure.

Square-planar [AgX4] (X = O or F) units in crystal structures of both AgO and AgF2 have been shown to be quite rigid under high pressure. Several other transition metal compounds also feature such [MX4] units in their structures: monoxides CuO, PdO and (isostructural) PtO, as well as all known dihalides of Pd and Pt (except PdF2). Among those compounds, only CuO has been studied in more detail (X-ray and neutron diffraction, complemented by hybrid-DFT calculations), and the published data indicate that [CuO4] units experience very little pressure- induced deformation.221 It would be interesting to see how compression affects other structures made up of [MX4] units, such as those of the aforementioned compounds of Pd and Pt.

Analogous compounds of gold – AuO and AuF2 – are also worth investigating. Neither of the two is currently known, but possible crystal structures of AuO and their physical properties have been explored by means of theoretical calculations in a recent study by Hermann et al.183 Throughout most of the studied pressure range (0-400 GPa), AuO is thermodynamically unstable with respect to elemental Au and O2, but nevertheless, experimental probing of Au/O phase diagram at high pressures is still warranted.

Experimental data obtained from compressed Ag/Cl systems suggests formation of new, hitherto unknown compounds of silver and chlorine. In order to elucidate their identity and properties, X-ray diffraction should be employed in the next step of analysis, as it can provide insight into the crystal structure of those new products. In addition, detailed theoretical calculations will be indispensable for understanding experimental XRD data and physical properties of resulting compounds, such as AgCl2, AgCl3 etc.

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(PL) Perspektywy dalszych badań

Wysokociśnieniowe przemiany strukturalne AgO i AgF2 opisane w niniejszej pracy okazały się być różne od tych przewidzianych w opublikowanych dotychczas pracach. Chociaż niektóre z wcześniejszych, obiecujących przewidywań okazały się fałszywe, w ich miejsce pojawiły się nowe, tym razem oparte na zweryfikowanych eksperymentalnie modelach strukturalnych. Nowoodkryte wysokociśnieniowe odmiany polimorficzne obu związków mogą w dalszej kolejności zostać dokładniej zbadane pod kątem ich właściwości fizycznych.

Najnowsze obliczenia przewidują niezwykłą odporność AgO na metalizację wywołaną wysokim ciśnieniem. Twierdzenie to można zweryfikować za pomocą bezpośrednich pomiarów oporu lub z użyciem metod spektroskopowych, umożliwiających optyczne wyznaczanie przerwy energetycznej. Szczególnie ta druga metoda jest względnie łatwa w zastosowaniu, a otrzymane w ten sposób dane mogą pomóc w zrozumieniu zależności między efektem Jahna-Tellera a mieszaną walencyjnością oraz wpływu tych czynników na własności elektryczne związków metali przejściowych.

La2CuO4 – pierwszy prekursor wysokotemperaturowych nadprzewodników – wykazuje pożądane właściwości nadprzewodzące jedynie po domieszkowaniu dziurowym lub elektronowym, jak np. w La2-xBaxCuO4, co formalnie prowadzi do istnienia stanów Cu(III) na części atomów miedzi. AgO, ze względu na swój zdyspropocjonowany charakter (Ag(I)/Ag(III)), znacznie różni się od CuO (np. jest diamagnetykiem). Niemniej analiza wpływu domieszkowania na własności elektryczne i magnetyczne AgO może być ciekawą ścieżką badań.390

Kompresja AgF2 nie prowadzi do spłaszczenia warstw w jego strukturze, co byłoby obiecujące pod kątem potencjalnego nadprzewodnictwa. Tym niemniej wysokociśnieniowe odmiany AgF2 wykazują rzadkie cechy strukturalne, które mogą skutkować interesującymi właściwościami fizycznymi. Multiferroiczny charakter formy HP1 należałoby zweryfikować poprzez pomiary elektryczne i magnetyczne, szczególnie że ciśnienie potrzebne do otrzymania tej fazy jest stosunkowo niskie (ok. 9 GPa). Przewidywania bardzo silnego sprzężenia antyferromagnetycznego w odmianie HP2 również wymagają eksperymentalnego potwierdzenia. Potrójne fluorosrebrzany(II), analogiczne pod wieloma względami do tlenków miedzi(II), nie były jeszcze analizowane pod wysokim ciśnieniem. Szczególnie interesujące może być sprawdzenie wpływu ciśnienia na porządkowanie orbitali i ułożenie wydłużonych oktaedrów. Zjawiska te mają kluczowy wpływ na oddziaływania magnetyczne w związkach o strukturze warstwowego perowskitu, a z kolei te oddziaływania uznawane są za zasadniczy element wysokociśnieniowych nadprzewodników miedziowo-tlenowych.

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Kolejną obiecują ścieżką badań może być kompresja AgF2 domieszkowanego jonami Ag(I). Tego typu próbki zostały niedawno otrzymane we współpracy z dr. Zoranem Mazejem z Instytutu Jožefa Stefana w Lublanie (Słowenia). Przez analogię do domieszkowanych tlenków miedzi(II), związki te powinny cechować się mniejszą przerwą energetyczną i ulegać metalizacji pod niższym ciśnieniem. Obecnie prowadzone są w naszym zespole badania w tej tematyce.

Istnieje również szereg związków analogicznych do AgO lub AgF2 w ten lub inny sposób, a które nie były jeszcze szczegółowo analizowane pod wysokim ciśnieniem. W szczególności 9 dotyczy to fluorków takich jak CuF2 (układ d – jak AgF2) lub PdF2. Wysokociśnieniowe przemiany fazowe CuF2 zostały dotychczas zbadane jedynie z użycie spektroskopii ramanowskiej i obliczeń teoretycznych;299 uzupełnienie tych wyników danymi z dyfrakcji rentgenowskiej byłoby bardzo pomocne. Struktura wysokociśnieniowej odmiany PdF2 została zaobserwowana w kilku innych związkach o stechiometrii MX2 poddanych kompresji, jednakże 284 sam PdF2 przeanalizowano jedynie w zakresie do ok. 6 GPa.

Kwadratowe układy [AgX4] (X = O lub F) obecne w strukturach krystalicznych AgO i

AgF2 okazały się być bardzo sztywne pod wysokim ciśnieniem. Kilka innych związków metali przejściowych, np. CuO, PdO i (izostrukturalny) PtO, oraz wszystkie znane dihalogenki Pd i Pt

(oprócz PdF2), zawiera w swojej strukturze tego typu podjednostki [MX4]. Spośród tych związków, jedynie CuO poddano dokładnej analizie pod ciśnieniem (dyfrakcja rentgenowska i neutronowa oraz obliczenia hybrydowe DFT); otrzymane dane wskazują, że układy [CuO4] ulegają bardzo niewielkiej deformacji.221 W przyszłości warto byłoby zbadać wpływ ciśnienia na inne struktury złożone z podjednostek [MX4], np. wspomniane związki Pd i Pt.

Analogiczne związki złota – AuO oraz AuF2 – również są warte zbadania. Żaden z nich nie jest obecnie znany, jednakże możliwe struktury krystaliczne AuO oraz ich właściwości fizyczne zostały przeanalizowane w niedawnej pracy teoretycznej autorstwa Hermanna i in.183 W przeważającej części zbadanego zakresu ciśnienia (0-400 GPa), AuO jest termodynamicznie nietrwały w stosunku do pierwiastków, tym niemniej eksperymentalne zbadanie diagramu fazowego Au/O pod wysokim ciśnieniem może być interesujące.

Dane eksperymentalne dla skompresowanych układów Ag/Cl sugerują powstawanie nowych, nieznanych dotychczas związków srebra i chloru. W kolejnym etapie badań należy zastosować dyfrakcję rentgenowską w celu ustalenia ich struktury krystalicznej i składu. Eksperymenty te będą musiały być uzupełnione obliczeniami teoretycznymi, które powinny znacznie ułatwić interpretację danych XRD oraz zrozumienie właściwości fizycznych powstających związków, np. AgCl2, AgCl3 itp.

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Appendices Appendix A: Gold equation of state parameters and pressure dependence of lattice constants of neon and tungsten in AgO XRD studies

Pressure in AgO samples was calculated using the lattice constant of gold obtained from fit at each pressure point, and Vinet EoS parameters from the study by Dewaele et al.362 (table A.1). As can be seen in figs. A.1 and A.2, lattice constants of neon and tungsten extracted from the same fits and plotted against pressure (as determined with the aforementioned Au EoS) show a relatively good agreement with previous studies.362,391 There are some discrepancies at higher pressures, which can be explained by the fact that the studied AgO system actually consisted of four different phases. Consequently, some of the reflections overlapped, which in turn may have led to slight errors in determination of lattice constants. Nevertheless, the Au pressure scale has proved to be quite reliable in this case.

3 V0/Z [Å ] B0 [GPa] B0’ 16.962 167 6.0

Table A.1. Vinet EoS parameters of Au from Dewaele et al. (ref. [362])

Fig. A.1. Pressure dependence of lattice constant of neon. Points marked with hollow squares are from Dewaele et al. (ref. [391])

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Fig. A.2. Pressure dependence of lattice constant of tungsten. Points marked with hollow squares are from Dewaele et al. (ref. [362])

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Appendix B: Equation of state parameters of AgO phases – experiment and theory

Pressure dependence of unit cell volume of AgO derived from both experiment and theory can be compared in order to further verify theoretical predictions. It is plotted in fig. B.1. HP1 and HP2 phases are considered jointly due to second-order character of transition between them.

3 V0/Z [Å ] B0 [GPa] B0’ Experiment 26.7 82.8 6.5 Theory 26.8 77.5 6.0

Table B.1. Experimental and theoretical parameters of Vinet EoS of LP-AgO.

3 V0/Z [Å ] B0 [GPa] B0’ Experiment 25.6 108.2 3.9 Theory 25.1 102.8 5.7

Table B.2. Experimental and theoretical parameters of Vinet EoS of HP-AgO (HP1&HP2 jointly).

Fig. B.1. Pressure dependence of volume of LP-AgO and HP-AgO from both experiment and theory. In experimental data, solid markers indicate compression, hollow – decompression. Dashed line indicates LP/HP phase boundary. Comparison between theoretical and experimental Vinet EoS for LP and HP phases is shown in tables B.1 and B.2, respectively. In the case of LP-AgO, theoretical and experimental values are in very good agreement, especially given the narrow range of stability of LP-AgO and thus relatively scarce experimental data. For HP-AgO, values of reference volume V0 and bulk modulus B0 coincide very well, but a significant difference is seen between values of B0’. This discrepancy means that compressibility of HP-AgO is predicted to decrease to a larger extent than suggested by experimental data. This cannot be currently verified, as experimental data was collected only up to ca. 56 GPa.

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Appendix C: Equation of state parameters of AgF

AgF was previously studied at high pressure up to 7 GPa by Hull et al.313 A phase transition to CsCl-type structure was detected at 2.7 GPa. Results used in this work were collected in 3-39 GPa pressure range, i.e. above the aforementioned phase transition, and were fitted using the Birch-Murnaghan (B-M) equation of state. Its parameters are given in table C.1 and the pressure dependence of CsCl-type AgF unit cell volume is plotted in fig. C.1. Clearly, there is a large discrepancy between the bulk modulus obtained from our fit and the value reported by Hull et al. It can be ascribed to a relatively narrow pressure range of the earlier study, and does not invalidate our model, which – as can be seen in fig. C.1 – fits the experimental data very well. Therefore, the use of AgF as a pressure gauge is justified.

3 V0 [Å ] B0 [GPa] B0’ B0 [GPa] (ref. [313]) 26.673(9) 87.1(2) 5.26(3) 110

Table C.1. Parameters of B-M EoS of AgF in CsCl-type structure obtained from a least-square fit to experimental data. Uncertainties are given in brackets.

Fig. C.1. Pressure dependence of volume of AgF in CsCl-type structure. The dashed line represents B-M EoS fit with parameters from table C.1, extrapolated down to 0 GPa.

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Appendix D: High-pressure resistance measurements of AgF2

Resistance measurements presented here were the first such attempt by the author of this work. They were meant to complement a previous experiment by Dr T. Muramatsu, who measured the resistance of AgF2 in the 20-50 GPa pressure range (unpublished results). The experiment was carried out using a diamond anvil cell (fig. D.1) specially developed for use in a Quantum Design PPMS (Physical Property Measurement System) apparatus. This type of DAC is considerably smaller than the ones used for XRD measurements – 3 cm high and 2.3 cm in diameter at the base. The diamonds were 200 μm in diameter.

Fig. D.1. Diamond anvil cell (top) placed upside down on a PPMS sample puck (gold and green). Leads are soldered to electrodes in the DAC at one end and to the puck at the other. The system was prepared as follows. An initial rhenium gasket was pre-indented in a usual manner, but a hole slightly larger than the culet was cut in the middle using an EDM drill. This gasket was then glued to the bottom diamond and covered (including the cavity indented by the top diamond) with an insulating paste containing boron nitride. The system was again indented and additionally covered around the cavity with black epoxy glue. A space for sample (as seen in fig. D.2 right) was carved out with a needle. Four triangular electrodes were cut out from a 4 μm thick platinum foil and glued around the bottom diamond using black epoxy (fig. D.2 left). They were placed in a way which ensured that their tips would extend into the sample chamber (fig. D.2 right). The system was then gently compressed again and left for a day to fix the electrodes in place. Four wires made of copper, insulated with transparent coating, were soldered to the outer ends of electrodes. A few grains of

AgF2 were loaded into the sample space in an inert atmosphere (glove box). The system was closed and the wires extending from electrodes were soldered to contacts in the PPMS sample puck. 155

Fig. D.2. Left: the black-epoxy-covered bottom diamond with four platinum electrodes placed around the sample chamber (bright spot in the middle). A copper wire soldered to one of the electrodes is seen on the right hand side of the picture. Right: the magnified view of empty sample chamber through the top diamond pressed against the bottom part of the system. The four silvery triangles are tips of Pt electrodes.

Due to very high reactivity of AgF2, using a speck of ruby as pressure gauge was impractical. Instead, the pressure was determined using diamond Raman scale developed by Akahama et al.335 After the initial compression, the value of pressure was measured as equal to ca. 0.8 GPa, although it has to be stressed that this pressure scale was originally intended for pressures in the order of tens and hundreds of gigapascals.335

The sample puck with DAC was placed in the PPMS unit and electrical resistance of the sample was measured in the temperature range 300-2 K (cooling sequence). The results are plotted in fig. D.3.

Fig. D.3. Temperature dependence of resistance of AgF2 at ca. 0.8 GPa (cooling sequence). 156

In the range from 300 to ca. 298 K, the resistance of sample decreases considerably from initial 2.5 MΩ to 1 MΩ. It then remains relatively stable (ca. 0.5-1 MΩ) upon cooling down to 275 K. Below that temperature (not shown), the system returns alternately positive and negative values of resistance in the order of several megaohms or no values at all, which we interpret as an abrupt spike in resistivity of the sample below ca. 275 K. Such behavior does not agree with previously reported results of impedance spectroscopy measurements of AgF2 at ambient pressure.106 In that work, resistivity never showed a downward trend with decreasing temperature. However, as follows from my interpretation of the previously published data, a spike in resistivity occurs below ca. 275 K, which is similar to what has been observed here. After the next compression step, which increased the pressure up to ca. 2 GPa, a short circuit occurred, as evidenced by extremely low resistance values registered by PPMS (ca. 0.0001 Ω) and the appearance of sample space (fig. D.4). Therefore, the experiment was discontinued.

Fig. D.4. The inside of DAC sample space after the second compression step (ca. 2 GPa). The silvery shapes are Pt electrodes, which were joined together by compression, which in turn caused a short

circuit. One of the electrodes is dark instead of silvery, likely because it is covered with AgF2, some amount of which ended up around the sample space during loading. These preliminary results are unsatisfactory, as they provide no information on pressure dependence of resistivity of AgF2. They also largely contradict previously published results obtained at ambient pressure,106 as well as HP measurements previously conducted by Dr Muramatsu. The failure of the experiment could be attributed to insufficient care taken during loading of AgF2 in the glove box. Likely, the sample space (i.e. the hole in the insulating gasket material) was not properly filled with AgF2, which led to its collapse. The collapsing gasket material may have “dragged” the tips of electrodes into the center and towards each other, leading to short circuit. The fact that AgF2 had to be loaded in an inert atmosphere compromised the manual precision required for proper preparation of the system.

157

List of research papers with results from this work

Results described in chapter 6 – high pressure behavior of silver(I,III) oxide AgO – were published in: 1. A. Grzelak, J. Gawraczyński; T. Jaroń, M. Somayazulu, M. Derzsi, V. Struzhkin, W. Grochala, “Persistence of Mixed and Non-Intermediate Valence in the High-Pressure Structure of Silver(I,III) Oxide, AgO: A Combined Raman, X-Ray Diffraction (XRD), and Density Functional Theory (DFT) Study.” Inorg. Chem. 2017, 56, 5804–5812.

Results described in chapter 7 – high-pressure behavior of silver(II) fluoride AgF2 – were published in: 2. A. Grzelak, J. Gawraczyński, T. Jaroń, D. Kurzydłowski, Z. Mazej, P. J. Leszczyński, V. B. Prakapenka, M. Derzsi, V. Struzhkin, W. Grochala, “Metal Fluoride Nanotubes Featuring Square-Planar Building Blocks in a High-Pressure Polymorph of AgF2.” Dalton Trans. 2017, 46, 14742–14745. 3. A. Grzelak, J. Gawraczyński, T. Jaroń, D. Kurzydłowski, A. Budzianowski, Z. Mazej, P. J. Leszczyński, V. B. Prakapenka, M. Derzsi, V. Struzhkin, W. Grochala, “High-Pressure Behavior of Silver Fluorides up to 40 GPa.” Inorg. Chem. 2017, 56, 14651–14661. Theoretically calculated magnetic and electronic properties of high-pressure polymorphs of AgF2, based on structural models derived from this work, will be published in: 4. D. Kurzydłowski, M. Derzsi, P. Barone, A. Grzelak, V. Struzhkin, J. Lorenzana and W. Grochala, “Dramatic Enhancement of Spin-Spin Coupling and Quenching of Magnetic Dimensionality in Compressed Silver Difluoride”, submitted to Chem. Comm., 2018. The four papers listed above are attached at the end of this work. Other publications with contribution from the author of this thesis: 5. A. Grzelak, T. Jaroń, Z. Mazej, T. Michałowski, P. Szarek, W. Grochala, “Anomalous chemical shifts in X-ray photoelectron spectra of sulfur-containing compounds of silver (I) and (II).” J. Electron Spectrosc. Relat. Phenom. 2015, 202, 38–45. 6. T. Gilewski, P. J. Leszczyński, A. Budzianowski, Z. Mazej, A. Grzelak, T. Jaroń, W. Grochala, “Ag2S2O8 meets AgSO4: the second example of metal–ligand redox isomerism among inorganic systems.” Dalton Trans. 2017, 45, 18202–18207.

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References

1 I. Włodarska, M. Derzsi and W. Grochala, Phys. status solidi - Rapid Res. Lett., 2015, 9, 401–404. 2 C. J. Hou, J. Botana, X. Zhang, X. Wang and M.-S. Miao, Phys. Chem. Chem. Phys., 2016, 18, 15322–15326. 3 M. Derzsi and W. Grochala, Phys. Chem. Chem. Phys., 2016, 18, 31973–31974. 4 J. Romiszewski, W. Grochala and L. Z. Stolarczyk, J. Phys. Condens. Matter, 2007, 19, 116206. 5 T. Jaroń and W. Grochala, Phys. Status Solidi - Rapid Res. Lett., 2008, 2, 71–73. 6 M. Derzsi, "Theoretical search for AgCl2", in 18th International Conference on Solid Compounds of Transition Elements, Lisbon, 2012. 7 W. Grochala, J. Supercond. Nov. Magn., 2018, 31, 737–752. 8 M. Derzsi, P. Piekarz and W. Grochala, Phys. Rev. Lett., 2014, 113, 1–5. 9 W. Zhang, A. R. Oganov, A. F. Goncharov, Q. Zhu, S. E. Boulfelfel, A. O. Lyakhov, E. Stavrou, M. Somayazulu, V. B. Prakapenka and Z. Konopkova, Science, 2013, 342, 1502–1505. 10 P. Curie, "Propriétés magnétiques des corps a diverses températures", doctoral thesis, University of Paris, 1895. 11 The Nobel Prize in Physics 1970, https://www.nobelprize.org/nobel_prizes/physics/laureates/1970/, (accessed 5 April 2018). 12 J. B. Goodenough, Phys. Rev., 1955, 100, 564–573. 13 W. Grochala, J. Mater. Chem., 2009, 19, 6949. 14 H. A. Jahn and E. Teller, Proc. R. Soc. A Math. Phys. Eng. Sci., 1937, 161, 220–235. 15 F. Rodríguez, Inorg. Chem., 2017, 56, 2029–2036. 16 Z. Mazej, E. Goreshnik, Z. Jagličić, B. Gaweł, W. Łasocha, D. Grzybowska, T. Jaroń, D. Kurzydłowski, P. Malinowski, W. Koźminski, J. Szydłowska, P. Leszczyński and W. Grochala, CrystEngComm, 2009, 11, 1702–1710. 17 K. I. Kugel’ and D. I. Khomskiĭ, Sov. Phys. Uspekhi, 1982, 25, 231–256. 18 J. A. Aramburu, P. García-Fernández, N. R. Mathiesen, J. M. Garcia-Lastra and M. Moreno, J. Phys. Chem. C, 2018, 122, 5071–5082. 19 N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys, 1936. 20 The Nobel Prize in Physics 1977, https://www.nobelprize.org/nobel_prizes/physics/laureates/1977/, (accessed 13 March 2018). 21 J. Hubbard, Proc. R. Soc. A Math. Phys. Eng. Sci., 1963, 276, 238–257. 22 J. Zaanen, G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett., 1985, 55, 418–421. 23 R. J. Hemley and N. W. Ashcroft, Phys. Today, 1998, 51, 26–32. 24 C. Parsons, Proc. R. Soc. London, 1888, 44, 320–323. 25 H. T. Hall, "High-pressure inorganic chemistry", in Progress in Inorganic Chemistry, ed. F. A. Cotton, 1966. 26 H. T. Hall, Rev. Sci. Instrum., 1960, 31, 125–131. 27 P. W. Bridgman, Phys. Rev., 1935, 48, 825–847. 28 P. W. Bridgman, Proc. Am. Acad. Arts Sci., 1937, 71, 387. 29 P. W. Bridgman, J. Appl. Phys., 1941, 12, 461–469. 30 P. W. Bridgman, Proc. R. Soc. A Math. Phys. Eng. Sci., 1950, 203, 1–17. 31 The Nobel Prize in Physics 1946, https://www.nobelprize.org/nobel_prizes/physics/laureates/1946/, (accessed 30 November 2017). 32 P. W. Bridgman, Phys. Rev., 1941, 60, 351–354. 159

33 R. J. Nelmes and M. I. McMahon, J. Synchrotron Radiat., 1994, 1, 69–73. 34 W. B. Holzapfel, Rep. Prog. Phys., 1996, 59, 29–90. 35 W. Grochala, R. Hoffmann, J. Feng and N. W. Ashcroft, Angew. Chemie - Int. Ed., 2007, 46, 3620–3642. 36 F. J. Manjón and D. Errandonea, Phys. Status Solidi Basic Res., 2009, 246, 9–31. 37 M. I. Eremets, A. G. Gavriliuk, I. A. Trojan, D. A. Dzivenko and R. Boehler, Nat. Mater., 2004, 3, 558–563. 38 E. Wigner and H. B. Huntington, J. Chem. Phys., 1935, 3, 764–770. 39 H. Luo, S. Desgreniers, Y. K. Vohra and A. L. Ruoff, Phys. Rev. Lett., 1991, 67, 2998– 3001. 40 B. M. Riggleman and H. G. Drickamer, J. Chem. Phys., 1963, 38, 2721–2724. 41 S. Desgreniers, Y. K. Vohra and A. L. Ruoff, J. Phys. Chem., 1990, 94, 1117–1122. 42 R. P. Dias and I. F. Silvera, Science, 2017, 355, 715–718. 43 A. F. Goncharov and V. V. Struzhkin, arXiv:1702.04246. 44 I. Silvera and R. Dias, arXiv:1703.03064. 45 M.-S. Miao and R. Hoffmann, Acc. Chem. Res., 2014, 47, 1311–1317. 46 H. Cynn, C. S. Yoo, B. Baer, V. Iota-Herbei, A. K. McMahan, M. Nicol and S. Carlson, Phys. Rev. Lett., 2001, 86, 4552–4555. 47 C. T. Prewitt and R. T. Downs, Rev. Mineral. Geochemistry, 1998, 37, 283–317. 48 L. Pauling, J. Am. Chem. Soc., 1929, 51, 1010–1026. 49 Y. Sato-Sorensen, J. Geophys. Res., 1983, 88, 3543. 50 F. P. Bundy, J. Geophys. Res., 1980, 85, 6930. 51 L. Zhang, Y. Wang, J. Lv and Y. Ma, Nat. Rev. Mater., 2017, 2, 1–16. 52 Y. Fei, J. Li, C. M. Bertka and C. T. Prewitt, Am. Mineral., 2000, 85, 1830–1833. 53 J. Ruiz-Fuertes, A. Segura, F. Rodríguez, D. Errandonea and M. N. Sanz-Ortiz, Phys. Rev. Lett., 2012, 108, 23–26. 54 F. Aguado, F. Rodriguez and P. Núñez, Phys. Rev. B - Condens. Matter Mater. Phys., 2007, 76, 1–6. 55 M. Baldini, V. V. Struzhkin, A. F. Goncharov, P. Postorino and W. L. Mao, Phys. Rev. Lett., 2011, 106, 1–4. 56 F. Aguado and F. Rodriguez, in High Pressure Research, 2006, vol. 26, pp. 319–323. 57 F. Aguado, F. Rodríguez, R. Valiente, J. P. Itiè and M. Hanfland, Phys. Rev. B - Condens. Matter Mater. Phys., 2012, 85, 1–5. 58 H. Masuda, "Combined Transmission Electron Microscopy – In situ Observation of the Formation Process and Measurement of Physical Properties for Single Atomic-Sized Metallic Wires", in Modern Electron Microscopy in Physical and Life Sciences, InTech, 2016. 59 R. A. Matula, J. Phys. Chem. Ref. Data, 1979, 8, 1147–1298. 60 S. Rebsdat and D. Mayer, "Ethylene Oxide", in Ullmann’s Encyclopedia of Industrial Chemistry, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2001. 61 G. H. Twigg, Trans. Faraday Soc., 1946, 42, 284. 62 A. I. Boronin, S. V. Koscheev and G. M. Zhidomirov, J. Electron Spectros. Relat. Phenomena, 1998, 96, 43–51. 63 T. C. R. Rocha, A. Oestereich, D. V. Demidov, M. Hävecker, S. Zafeiratos, G. Weinberg, V. I. Bukhtiyarov, A. Knop-Gericke and R. Schlögl, Phys. Chem. Chem. Phys., 2012, 14, 4554. 64 W. Grochala and Z. Mazej, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 2015, 373, 20140179–20140179. 65 A. B. G. Lansdown, Curr. Probl. Dermatol., 2006, 33, 17–34. 66 W. Levason and M. D. Spicer, Coord. Chem. Rev., 1987, 76, 45–120. 67 P. H. Kasai and J. D Mcleod, J. Am. Chem. Soc., 1975, 97, 6602–6603.

160

68 P. H. Kasai, D. McLeod and T. Watanabe, J. Am. Chem. Soc., 1980, 102, 179–190. 69 P. H. Kasai, J. Am. Chem. Soc., 1984, 106, 3069–3075. 70 A. J. Buck, B. Mile and J. A. Howard, J. Am. Chem. Soc., 1983, 105, 3381–3387. 71 J. H. B. Chenier, J. A. Howard and B. Mile, J. Am. Chem. Soc., 1985, 107, 4190–4191. 72 J. A. Howard, R. Sutcliffe and B. Mile, J. Phys. Chem., 1984, 88, 4351–4354. 73 D. S. McIntosh and G. A. Ozin, J. Am. Chem. Soc., 1976, 98, 3167–3175. 74 J. A. Howard and R. Sutcliffe, J. Phys. Chem., 1984, 88, 5155–5157. 75 M. Histed, J. A. Howard, R. Jones, M. Tomietto and H. A. Joly, J. Phys. Chem., 1992, 96, 1144–1146. 76 H. Schmidbaur, S. Cronje, B. Djordjevic and O. Schuster, Chem. Phys., 2005, 311, 151– 161. 77 A. J. Bard, R. Parsons and J. Jordan, Standard potentials in aqueous solutions, Marcel Dekker, New York, NY, 1985. 78 P. Połczyński, R. Jurczakowski and W. Grochala, Chem. Commun., 2013, 49, 7480. 79 W. Grochala, Inorg. Chem. Commun., 2008, 11, 155–158. 80 W. Grochala, R. G. Egdell, P. P. Edwards, Z. Mazej and B. Žemva, ChemPhysChem, 2003, 4, 997–1001. 81 J. B. Goodenough, J. Phys. Chem. Solids, 1958, 6, 287–297. 82 W. Grochala, A. Porch and P. P. Edwards, Solid State Commun., 2004, 130, 137–142. 83 R.-H. Odenthal, D. Paus and R. Hoppe, Zeitschrift für Anorg. und Allg. Chemie, 1974, 407, 151–156. 84 P. Malinowski, Z. Mazej and W. Grochala, Zeitschrift fur Anorg. und Allg. Chemie, 2008, 634, 2608–2616. 85 H. F. Priest and C. F. Swinehert, "Anhydrous Metal Fluorides", in Inorganic Syntheses: Volume III, 1950, pp. 171–183. 86 P. Patnaik, Handbook of Inorganic Chemicals, McGraw-Hill, New York, NY, 2003. 87 P. Fischer, G. Roult and D. Schwarzenbach, J. Phys. Chem. Solids, 1971, 32, 1641–1647. 88 A. Jesih, K. Lutar, B. Žemva, B. Bachmann, S. Becker, B. G. Müller and R. Hoppe, ZAAC ‐ J. Inorg. Gen. Chem., 1990, 588, 77–83. 89 D. Kurzydłowski and W. Grochala, Angew. Chemie - Int. Ed., 2017, 56, 10114–10117. 90 J. Gawraczyński, D. Kurzydłowski, W. Gadomski, Z. Mazej, G. Ruani, I. Bergenti, T. Jaroń, A. Ozarowski, S. Hill, P. J. Leszczyński, K. Tokár, M. Derzsi, P. Barone, K. Wohlfeld, J. Lorenzana and W. Grochala, arXiv:1804.00329. 91 W. Grochala and P. P. Edwards, Phys. Status Solidi Basic Res., 2003, 240, 10–13. 92 C. Shen, B. Žemva, G. M. Lucier, O. Graudejus, J. A. Allman and N. Bartlett, Inorg. Chem., 1999, 38, 4570–4577. 93 D. Kurzydłowski, "Fluoroargentates(II) of alkali metals - synthesis, structure, phase transitions and magnetic properties", doctoral thesis, University of Warsaw, 2012. 94 R.-H. Odenthal and R. Hoppe, Monatshefte für Chemie, 1971, 102, 1340–1350. 95 D. Kurzydłowski, Z. Mazej, Z. Jagličić, Y. Filinchuk and W. Grochala, Chem. Commun., 2013, 49, 6262. 96 A. I. Popov, Zh. Neorg. Khim., 1987, 32, 2276–2280. 97 Z. Mazej, D. Kurzydłowski and W. Grochala, "Unique Silver(II) Fluorides: The Emerging Electronic and Magnetic Materials", in Photonic and Electronic Properties of Fluoride Materials: Progress in Fluorine Science Series, 2016, pp. 231–260. 98 D. Kurzydłowski, M. Derzsi, Z. Mazej and W. Grochala, Dalt. Trans., 2016, 45, 16255– 16261. 99 S. E. McLain, M. R. Dolgos, D. A. Tennant, J. F. C. Turner, T. Barnes, T. Proffen, B. C. Sales and R. I. Bewley, Nat. Mater., 2006, 5, 561–565. 100 D. Kurzydłowski, T. Jaroń, A. Ozarowski, S. Hill, Z. Jagličić, Y. Filinchuk, Z. Mazej and W. Grochala, Inorg. Chem., 2016, 55, 11479–11489.

161

101 D. Kurzydłowski, M. Derzsi, A. Budzianowski, Z. Jagličić, W. Koźmiński, Z. Mazej and W. Grochala, Eur. J. Inorg. Chem., 2010, 2919–2925. 102 D. Kurzydłowski, Z. Mazej and W. Grochala, Dalt. Trans., 2013, 42, 2167–2173. 103 J. Tong, J. Köhler, A. Simon, C. Lee and M.-H. Whangbo, Zeitschrift für Anorg. und Allg. Chemie, 2012, 638, 1792–1795. 104 D. Kurzydłowski and W. Grochala, unpublished HSE06 calculations. 105 G. L. Bottger and A. L. Geddes, J. Chem. Phys., 1972, 56, 3735–3739. 106 W. Adamczyk, P. Połczyński, A. Mika, T. Jaroń, Z. Mazej, K. J. Fijalkowski, R. Jurczakowski and W. Grochala, J. Fluor. Chem., 2015, 174, 22–29. 107 A. Williams, J. Phys. Condens. Matter, 1989, 1, 2569–2574. 108 K. Andres, N. A. Kuebler and M. B. Robin, J. Phys. Chem. Solids, 1966, 27, 1747–1748. 109 B. Žemva, K. Lutar, A. Jesih, W. J. Casteel, A. P. Wilkinson, D. E. Cox, B. Robert von Dreele, H. Borrmann and N. Bartlett, J. Am. Chem. Soc., 1991, 113, 4192–4198. 110 R. Eujen and B. Zemva, J. Fluor. Chem., 1999, 99, 139–140. 111 G. M. Lucier, J. M. Whalen and N. Bartlett, J. Fluor. Chem., 1998, 89, 101–104. 112 R. Hoppe and R. Homann, Zeitschrift für Anorg. und Allg. Chemie, 1970, 379, 193–198. 113 R. Hoppe, Zeitschrift für Anorg. und Allg. Chemie, 1957, 292, 28–33. 114 K. Lutar, S. Milicev, B. Zemva, B. G. Muller, B. Bachmann and R. Hoppe, Eur. J. Solid State Inorg. Chem., 1991, 28, 1335–1346. 115 K. Lutar, A. Jesih and B. Zemva, Rev. Chim. Miner., 1986, 23, 565–571. 116 O. Graudejus, A. P. Wilkinson and N. Bartlett, Inorg. Chem., 2000, 39, 1545–1548. 117 R. Fischer and B. G. Müller, Zeitschrift für Anorg. und Allg. Chemie, 2002, 628, 2592– 2596. 118 W. Grochala and R. Hoffmann, Angew. Chemie Int. Ed., 2001, 40, 2742–2781. 119 J. L. Manson, K. H. Stone, H. I. Southerland, T. Lancaster, A. J. Steele, S. J. Blundell, F. L. Pratt, P. J. Baker, R. D. McDonald, P. Sengupta, J. Singleton, P. a Goddard, C. Lee, M.-H. Whangbo, M. M. Warter, C. H. Mielke and P. W. Stephens, J. Am. Chem. Soc., 2009, 131, 4590–1. 120 E. K. Barefield and M. T. Mocella, Inorg. Chem., 1973, 12, 2829–2832. 121 C. E. Holloway, M. Melnik, W. A. Nevin and W. Liu, J. Coord. Chem., 1995, 35, 85– 178. 122 P. Leung and F. Aubke, Inorg. Chem., 1978, 17, 1765–1772. 123 P. J. Malinowski, M. Derzsi, Z. Mazej, Z. Jagličić, P. J. Leszczyński, T. Michałowski and W. Grochala, Eur. J. Inorg. Chem., 2011, 2011, 2499–2507. 124 T. Michałowski, P. J. Malinowski, M. Derzsi, Z. Mazej, Z. Jagličić, P. J. Leszczyński and W. Grochala, Eur. J. Inorg. Chem., 2011, 3, 2508–2516. 125 P. J. Malinowski, M. Derzsi, Z. Mazej, Z. Jagličić, B. Gaweł, W. Łasocha and W. Grochala, Angew. Chemie - Int. Ed., 2010, 49, 1683–1686. 126 P. J. Malinowski, M. Derzsi, A. Budzianowski, P. J. Leszczyński, B. Gaweł, Z. Mazej and W. Grochala, Chem. - A Eur. J., 2011, 17, 10524–10527. 127 J. Mu and D. D. Perlmutter, Ind. Eng. Chem. Process Des. Dev., 1981, 20, 640–646. 128 V. M. Gorbachev, F. R. Verzhbitsky, K. G. Myakishev and O. G. Potapova, J. Therm. Anal., 1984, 29, 19–27. 129 M. Derzsi, A. Budzianowski, V. V. Struzhkin, P. J. Malinowski, P. J. Leszczyński, Z. Mazej and W. Grochala, CrystEngComm, 2013, 15, 192–198. 130 J. Köhler, Angew. Chemie - Int. Ed., 2010, 49, 3114–3115. 131 A. Grzelak, T. Jaroń, Z. Mazej, T. Michałowski, P. Szarek and W. Grochala, J. Electron Spectros. Relat. Phenomena, 2015, 202, 38–45. 132 T. E. Gilewski, P. J. Leszczyński, A. Budzianowski, Z. Mazej, A. Grzelak, T. Jaroń and W. Grochala, Dalt. Trans., 2016, 45, 18202–18207. 133 M. S. Silverman, Inorg. Chem., 1966, 5, 2067–2069.

162

134 P. Połczyński, R. Jurczakowski and W. Grochala, J. Phys. Chem. C, 2013, 117, 20689– 20696. 135 A. K. Budniak, M. Masny, K. Prezelj, M. Grzeszkiewicz, J. Gawraczyński, Ł. Dobrzycki, M. K. Cyrański, W. Koźmiński, Z. Mazej, K. J. Fijałkowski, W. Grochala and P. J. Leszczyński, New J. Chem., 2017, 41, 10742–10749. 136 P. Połczyński, T. E. Gilewski, J. Gawraczyński, M. Derzsi, P. J. Leszczyński, W. Gadomski, Z. Mazej, R. Jurczakowski and W. Grochala, Eur. J. Inorg. Chem., 2016, 2016, 5401–5404. 137 T. E. Gilewski, J. Gawraczyński, M. Derzsi, Z. Jagličić, Z. Mazej, P. Połczyński, R. Jurczakowski, P. J. Leszczyński and W. Grochala, Chem. - A Eur. J., 2017, 23, 1805– 1813. 138 R. W. G. Wyckoff, Am. J. Sci., 1922, s5-3, 184–188. 139 L. H. Tjeng, M. B. Meinders, J. van Elp, J. Ghijsen, G. A. Sawatzky and R. L. Johnson, Phys. Rev. B, 1990, 41, 15–1990. 140 M. Bellantone, H. D. Williams and L. L. Hench, Antimicrob. Agents Chemother., 2002, 46, 1940–1945. 141 W. Zhou, H. Liu, J. Wang, D. Liu, G. Du and J. Cui, ACS Appl. Mater. Interfaces, 2010, 2, 2385–2392. 142 M. Sofin, K. Friese, J. Nuss, E. M. Peters and M. Jansen, Zeitschrift für Anorg. und Allg. Chemie, 2002, 628, 2500–2504. 143 S. S. Kabalkina, S. V. Popova and L. F. Serebrjanaja, N.R. Vereshchagin, Dokl. Akad. Nauk SSSR, 1963, 8, 853–855. 144 W. Beesk, P. G. Jones, H. Rumpel, E. Schwarzmann and G. M. Sheldrick, J. Chem. Soc. Chem. Commun., 1981, 8, 664. 145 B. Standke and M. Jansen, Angew. Chem. Intl. Ed. Engl., 1985, 1, 118–119. 146 B. Standke and M. Jansen, Angew. Chemie Int. Ed. English, 1986, 25, 77–78. 147 J. P. Allen, D. O. Scanlon and G. W. Watson, Phys. Rev. B - Condens. Matter Mater. Phys., 2011, 84, 1–14. 148 L. Van Wüllen, S. Vensky, W. Hoffbauer and M. Jansen, Solid State Sci., 2005, 7, 920– 924. 149 G. I. N. Waterhouse, J. B. Metson and G. A. Bowmaker, Polyhedron, 2007, 26, 3310– 3322. 150 I. Naray-Szabo and K. Popp, Zeitschrift für Anorg. und Allg. Chemie, 1963, 322, 286– 296. 151 I. Náray-Szabó, G. Argay and P. Szabó, Acta Crystallogr., 1965, 19, 180–184. 152 M. B. Robin, K. Andres, T. H. Geballe, N. A. Kuebler and D. B. McWhan, Phys. Rev. Lett., 1966, 17, 917–919. 153 A. C. Gossard, D. K. Hindermann, M. B. Robin, N. A. Kuebler and T. H. Geballe, J. Am. Chem. Soc., 1967, 89, 7121–7123. 154 P. Fischer, M. Jansen, H. V. Volden, R. A. Andersen, R. W. Berg, N. J. Bjerrum and A. E. Underhill, Acta Chem. Scand., 1991, 45, 816–819. 155 J. P. Allen, D. O. Scanlon and G. W. Watson, Phys. Rev. B - Condens. Matter Mater. Phys., 2010, 81, 1–4. 156 J. A. M. Millan, J. Inorg. Nucl. Chem., 1960, 13, 28–31. 157 G. B. Hoflund and Z. F. Hazos, Phys. Rev. B, 2000, 62, 126–133. 158 M. Bielmann, P. Schwaller, P. Ruffieux, O. Gröning, L. Schlapbach and P. Gröning, Phys. Rev. B, 2002, 65, 235431. 159 K.-T. Park, D. L. Novikov, V. A. Gubanov and A. J. Freeman, Phys. Rev. B, 1994, 49, 4425–4431. 160 G. I. N. Waterhouse, G. A. Bowmaker and J. B. Metson, Phys. Chem. Chem. Phys., 2001, 3, 3838–3845.

163

161 P. Behrens, S. Aßmann, U. Bilow, C. Linke and M. Jansen, Zeitschrift für Anorg. und Allg. Chemie, 1999, 625, 111–116. 162 D. Lützenkirchen-Hecht and H. H. Strehblow, Surf. Interface Anal., 2009, 41, 820–829. 163 K. Yvon, A. Bezinge, P. Tissot and P. Fischer, J. Solid State Chem., 1986, 65, 225–230. 164 S. Hull and P. Berastegui, J. Solid State Chem., 2004, 177, 3156–3173. 165 D. F. C. Morris, J. Phys. Chem. Solids, 1958, 7, 214–217. 166 A. F. Wells, J. Chem. Soc., 1947, 1670–1675. 167 D. B. Dell’Amico, F. Calderazzo, F. Marchetti and S. Merlino, J. Chem. Soc. Dalt. Trans., 1982, 1982, 2257. 168 J. Evans and G. Lo, J. Chem. Phys., 1966, 3638, 10–12. 169 W. Zhang, A. R. Oganov, Q. Zhu, S. S. Lobanov, E. Stavrou and A. F. Goncharov, Sci. Rep., 2016, 6, 26265. 170 Q. Zeng, S. Yu, D. Li, A. R. Oganov, G. Frapper, A. O. Lyakhov, B. Liu, W. Tian, T. Cui and T. Cui, Phys. Chem. Chem. Phys., 2017, 19, 8236–8242. 171 J. A. Aramburu and M. Moreno, Solid State Commun., 1986, 58, 305–309. 172 W. L. Roth, Phys. Rev., 1958, 110, 1333–1341. 173 G. Brauer, Zeitschrift für Anorg. und Allg. Chemie, 1941, 248, 1–31. 174 W. J. Moore and L. Pauling, J. Am. Chem. Soc., 1941, 63, 1392–1394. 175 G. Tunell, Ε. Posnjak and C. J. Ksanda, Zeitschrift für Krist. - Cryst. Mater., 1935, 90, 120–142. 176 R. B. Heller, J. McGannon and A. H. Weber, J. Appl. Phys., 1950, 21, 1283–1284. 177 W. L. Bragg and J. A. Darbyshire, Trans. Faraday Soc., 1932, 28, 522. 178 K. Aurivillius, B. N. Cyvin, S. Rodmar, B. Nihlgård and L. Nilsson, Acta Chem. Scand., 1964, 18, 1305–1306. 179 D. J. Benjamin, Mater. Res. Bull., 1982, 17, 179–189. 180 K. Aurivillius, I.-B. Carlsson, S. Gardell, A. Magnéli, A. Magnéli, H. Pestmalis and S. Åsbrink, Acta Chem. Scand., 1957, 11, 1069–1069. 181 K. Aurivillius, I.-B. Carlsson, C. Pedersen, K. Hartiala, S. Veige and E. Diczfalusy, Acta Chem. Scand., 1958, 12, 1297–1304. 182 M. Derzsi, A. Hermann, R. Hoffmann and W. Grochala, Eur. J. Inorg. Chem., 2013, 4, 5094–5102. 183 A. Hermann, M. Derzsi, W. Grochala and R. Hoffmann, Inorg. Chem., 2016, 55, 1278– 1286. 184 C. H. Bates, W. B. White and R. Roy, Science, 1962, 137, 993–993. 185 H. Liu, H. K. Mao, M. Somayazulu, Y. Ding, Y. Meng and D. Häusermann, Phys. Rev. B - Condens. Matter Mater. Phys., 2004, 70, 094114. 186 H. Liu, J. S. Tse and H. Mao, J. Appl. Phys., 2006, 100, 093509. 187 P. Richet, H.-K. Mao and P. M. Bell, J. Geophys. Res. Solid Earth, 1988, 93, 15279– 15288. 188 T. Zhou, U. Schwarz, M. Hanfland, Z. X. Liu, K. Syassen and M. Cardona, Phys. Rev. B, 1998, 57, 153–160. 189 J. Yan, B. Chen, S. V. Raju, B. K. Godwal, A. A. MacDowell, J. Knight, H. Ma and Q. Williams, Phys. Chem. Miner., 2012, 39, 269–275. 190 G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett., 1984, 53, 2339–2342. 191 R. E. Cohen, Science, 1997, 275, 654–657. 192 J. Kuneš and V. I. Anisimov, Ann. der Phys., 2011, 523, 682–688. 193 R. A. Fischer, A. J. Campbell, G. A. Shofner, O. T. Lord, P. Dera and V. B. Prakapenka, Earth Planet. Sci. Lett., 2011, 304, 496–502. 194 H. Ozawa, F. Takahashi, K. Hirose, Y. Ohishi and N. Hirao, Science, 2011, 334, 792– 794.

164

195 W. F. McDonough, "Compositional Model for the Earth's Core", in Treatise on Geochemistry, Elsevier, 2003, pp. 547–568. 196 T. Yagi, T. Suzuki and S.-I. Akimoto, J. Geophys. Res. Solid Earth, 1985, 90, 8784– 8788. 197 H. Mao, J. Shu, Y. Fei, J. Hu and R. J. Hemley, Phys. Earth Planet. Inter., 1996, 96, 135–145. 198 A. P. Kantor, S. D. Jacobsen, I. Y. Kantor, L. S. Dubrovinsky, C. A. McCammon, H. J. Reichmann and I. N. Goncharenko, Phys. Rev. Lett., 2004, 93, 19–22. 199 Y. Fei and H. -k. Mao, Science, 1994, 266, 1678–1680. 200 H. Ozawa, K. Hirose, K. Ohta, H. Ishii, N. Hiraoka, Y. Ohishi and Y. Seto, Phys. Rev. B - Condens. Matter Mater. Phys., 2011, 84, 1–6. 201 K. Ohta, K. Hirose, K. Shimizu and Y. Ohishi, Phys. Rev. B - Condens. Matter Mater. Phys., 2010, 82, 16–19. 202 M. Hamada, S. Kamada, E. Ohtani, T. Mitsui, R. Masuda, T. Sakamaki, N. Suzuki, F. Maeda and M. Akasaka, Phys. Rev. B, 2016, 93, 1–6. 203 E. Ito, D. Yamazaki, T. Yoshino, S. Shan, X. Guo, N. Tsujimo, T. Kunimoto, Y. Higo and K. Funakoshi, Phys. Earth Planet. Inter., 2014, 228, 170–175. 204 R. Jeanloz and A. Rudy, J. Geophys. Res. Solid Earth, 1987, 92, 11433–11436. 205 Y. Noguchi, K. Kusaba, K. Fukuoka and Y. Syono, Geophys. Res. Lett., 1996, 23, 1469– 1472. 206 T. Kondo, T. Yagi, Y. Syono, T. Kikegawa and O. Shimomura, Rev. High Press. Sci. Technol., 1998, 7, 148–150. 207 T. Kondo, T. Yagi, Y. Syono, Y. Noguchi, T. Atou, T. Kikegawa and O. Shimomura, J. Appl. Phys., 2000, 87, 4153. 208 Y. Mita, D. Izaki, M. Kobayashi and S. Endo, Phys. Rev. B - Condens. Matter Mater. Phys., 2005, 71, 1–3. 209 J. R. Patterson, C. M. Aracne, D. D. Jackson, V. Malba, S. T. Weir, P. A. Baker and Y. K. Vohra, Phys. Rev. B - Condens. Matter Mater. Phys., 2004, 69, 1–4. 210 C. S. Yoo, B. Maddox, J. H. P. Kiepeis, V. Iota, W. Evans, A. McMahan, M. Y. Hu, P. Chow, M. Somayazulu, D. Häusermann, R. T. Scalettar and W. E. Pickett, Phys. Rev. Lett., 2005, 94, 1–4. 211 J. Kuneš, A. V. Lukoyanov, V. I. Anisimov, R. T. Scalettar and W. E. Pickett, Nat. Mater., 2008, 7, 198–202. 212 Y. Noguchi, T. Atou, T. Kondo, T. Yagi and Y. Syono, Jpn. J. Appl. Phys., 1999, 38, L7–L9. 213 Q. Guo, H. K. Mao, J. Hu, J. Shu and R. J. Hemley, J. Phys. Condens. Matter, 2002, 14, 11369–11374. 214 T. Atou, M. Kawasaki and S. Nakajima, Jpn. J. Appl. Phys., 2004, 43, L1281–L1283. 215 L. Huang, Y. Wang and X. Dai, Phys. Rev. B - Condens. Matter Mater. Phys., 2012, 85, 1–5. 216 A. A. Dyachenko, A. O. Shorikov, A. V. Lukoyanov and V. I. Anisimov, JETP Lett., 2012, 96, 56–60. 217 T. Eto, S. Endo, M. Imai, Y. Katayama and T. Kikegawa, Phys. Rev. B, 2000, 61, 14984. 218 A. G. Gavriliuk, I. A. Trojan and V. V. Struzhkin, Phys. Rev. Lett., 2012, 109, 1–5. 219 V. Potapkin, L. Dubrovinsky, I. Sergueev, M. Ekholm, I. Kantor, D. Bessas, E. Bykova, V. Prakapenka, R. P. Hermann, R. Rüffer, V. Cerantola, H. J. M. Jönsson, W. Olovsson, S. Mankovsky, H. Ebert and I. A. Abrikosov, Phys. Rev. B, 2016, 93, 20–24. 220 R. Jana, P. Saha, V. Pareek, A. Basu, S. Kapri, S. Bhattacharyya and G. D. Mukherjee, Sci. Rep., 2016, 6, 31610. 221 D. P. Kozlenko, K. Druzbicki, S. E. Kichanov, E. V. Lukin, H. P. Liermann, K. V. Glazyrin and B. N. Savenko, Phys. Rev. B, 2017, 95, 1–9.

165

222 T. Kimura, Y. Sekio, H. Nakamura, T. Siegrist and A. P. Ramirez, Nat. Mater., 2008, 7, 291–294. 223 A. G. Christy and S. M. Clark, Phys. Rev. B, 1995, 52, 9259–9265. 224 R. Ahuja, O. Eriksson, J. M. Wills and B. Johansson, Phys. Rev. B, 1996, 53, 3072–3079. 225 R. Chauhan, S. Singh and R. K. Singh, Cent. Eur. J. Phys., 2008, 6, 277–282. 226 Y. O. Ciftci, Y. Ünlü, K. Colakoglu and E. Deligoz, Phys. Scr., 2009, 80, 025601. 227 I. Leonov, L. Pourovskii, A. Georges and I. A. Abrikosov, Phys. Rev. B, 2016, 94, 1–6. 228 M. E. Fleet, Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem., 1981, 37, 917– 920. 229 M. K. Fayek and J. Leciejewicz, Zeitschrift für Anorg. und Allg. Chemie, 1965, 336, 104–109. 230 D. Jarosch and U. Wien, Mineral. Petrol., 1987, 37, 15–23. 231 F. Gronvold, Nature, 1948, 162, 70. 232 J. Amador, E. Gutierrez Puebla, M. A. Monge, I. Rasines and C. Ruiz Valero, Inorg. Chem., 1988, 27, 1367–1370. 233 J. Howard T. Evans and J. A. Konnert, Am. Mineral., 1976, 61, 996–1000. 234 H. J. Gotsis, A. C. Barnes and P. Strange, J. Phys. Condens. Matter, 1992, 4, 10461– 10468. 235 B. J. Skinner, R. C. Erd and F. S. Grimaldi, Am. Mineral., 1964, 49, 543–555. 236 N. Elliott, J. Chem. Phys., 1934, 2, 419–420. 237 J. C. M. T. Eijndhoven and G. C. Verschoor, Mater. Res. Bull., 1974, 9, 1667–1670. 238 N. Matsushita, F. Fukuhara and N. Kojima, Acta Crystallogr. Sect. E Struct. Reports Online, 2006, 61, i123–i125. 239 N. Matsushita, H. Kitagawa and N. Kojima, Acta Crystallogr. Sect. C Cryst. Struct. Commun., 1997, 53, 663–666. 240 R. K. McMullan and J. D. Corbett, J. Am. Chem. Soc., 1958, 80, 4761–4764. 241 G. Chaudron, C. R. Acad. Sc. Paris Série C, 1973, 277, 863–865. 242 W. L. Smith and A. D. Hobson, Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem., 1973, 29, 362–363. 243 M. B. Robin and P. Day, Adv. Inorg. Chem. Radiochem., 1968, 10, 247–422. 244 R. M. Cornell and U. Schwertmann, The iron oxides—Structure, properties, reactions, occurrence and uses, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 1996. 245 E. J. W. Verwey, Nature, 1939, 144, 327–328. 246 P. Piekarz, K. Parlinski and A. M. Oleś, Phys. Rev. B, 2007, 76, 165124. 247 Walz F., J. Phys., 2002, 14, R285–R340. 248 S. Todo, N. Takeshita, T. Kanehara, T. Mori and N. Môri, J. Appl. Phys., 2001, 89, 7347–7349. 249 H.-K. Mao, T. Takahashi, W. A. Bassett, G. L. Kinsland and L. Merrill, J. Geophys. Res., 1974, 79, 1165–1170. 250 Y. Fei, D. J. Frost, H. Mao, C. T. Prewitt and D. Hausermann, Am. Mineral., 1999, 84, 203–206. 251 C. Haavik, S. Stølen, H. Fjellvåg, M. Hanfland and D. Häusermann, Am. Mineral., 2000, 85, 514–523. 252 L. S. Dubrovinsky, N. A. Dubrovinskaia, C. McCammon, G. K. Rozenberg, R. Ahuja, J. M. Osorio-Guillen, V. Dmitriev, H.-P. Weber, T. Le Bihan and B. Johansson, J. Phys. Condens. Matter, 2003, 15, 7697–7706. 253 M. P. Pasternak, S. Nasu, K. Wada and S. Endo, Phys. Rev. B, 1994, 50, 6446–6449. 254 W. M. Xu, G. Y. Machavariani, G. K. Rozenberg and M. P. Pasternak, Phys. Rev. B - Condens. Matter Mater. Phys., 2004, 70, 1–6.

166

255 P. Lazor, O. N. Shebanova and H. Annersten, J. Geophys. Res. Solid Earth, 2004, 109, 1–16. 256 A. Ricolleau and Y. Fei, Am. Mineral., 2016, 101, 719–725. 257 K. Glazyrin, C. McCammon, L. Dubrovinsky, M. Merlini, K. Schollenbruch, A. Woodland and M. Hanfland, Am. Mineral., 2012, 97, 128–133. 258 S. Klotz, Chinese Sci. Bull., 2014, 59, 5241–5250. 259 T. Muramatsu, L. V. Gasparov, H. Berger, R. J. Hemley and V. V. Struzhkin, J. Appl. Phys., 2016, 119, 135903. 260 L. Bai, M. Pravica, Y. Zhao, C. Park, Y. Meng, S. V Sinogeikin and G. Shen, J. Phys. Condens. Matter, 2012, 24, 435401. 261 S. Hirai and W. L. Mao, Appl. Phys. Lett., 2013, 102, 041912. 262 C. R. Ross II, D. C. Rubie and E. Paris, Am. Mineral., 1990, 75, 1249–1252. 263 E. Paris, C. R. Ross Il and H. Olijnyk, Eur. J. Mineral., 1992, 4, 87–94. 264 Y. Moritomo, Y. Ohishi, A. Kuriki, E. Nishibori, M. Takata and M. Sakata, J. Phys. Soc. Japan, 2003, 72, 765–766. 265 R. E. Dinnebier, S. Carlson, M. Hanfland and M. Jansen, Am. Mineral., 2003, 88, 996– 1002. 266 N. Kojima and H. Kitagawa, J. Chem. Soc. Dalt. Trans., 1994, 327. 267 R. Keller, J. Fenner and W. B. Holzapfel, Mater. Res. Bull., 1974, 9, 1363–1369. 268 W. Denner, H. Schulz and H. D’Amour, Acta Crystallogr. Sect. A, 1979, 35, 360–365. 269 J. Stanek, S. S. Hafner and H. Schulz, Phys. Lett. A, 1980, 76, 333–334. 270 J. Stanek, J. Chem. Phys., 1982, 76, 2315–2320. 271 N. Matsushita, H. Ahsbahs, S. S. Hafner and N. Kojima, J. Solid State Chem., 2007, 180, 1353–1364. 272 N. Kojima, M. Hasegawa, H. Kitagawa, T. Kikegawa and O. Shimomura, J. Am. Chem. Soc., 1994, 116, 11368–11374. 273 X. J. Liu, Y. Moritomo, A. Nakamura and N. Kojima, J. Lumin., 2001, 94–95, 541–544. 274 N. Kojima, H. Kitagawa, T. Ban, F. Amita and M. Nakahara, Solid State Commun., 1990, 73, 743–745. 275 H. Kitagawa, H. Sato, N. Kojima, T. Kikegawa and O. Shimomura, Solid State Commun., 1991, 78, 989–995. 276 S. Wang, S. Hirai, M. C. Shapiro, S. C. Riggs, T. H. Geballe, W. L. Mao and I. R. Fisher, Phys. Rev. B - Condens. Matter Mater. Phys., 2013, 87, 1–6. 277 S. Wang, A. F. Kemper, M. Baldini, M. C. Shapiro, S. C. Riggs, Z. Zhao, Z. Liu, T. P. Devereaux, T. H. Geballe, I. R. Fisher and W. L. Mao, Phys. Rev. B - Condens. Matter Mater. Phys., 2014, 89, 1–7. 278 S. F. Agnew, B. I. Swanson, L. H. Jones and R. L. Mills, J. Phys. Chem., 1985, 89, 1678–1682. 279 C. S. Yoo, V. Iota, H. Cynn, M. Nicol, J. H. Park, T. Le Bihan and M. Mezouar, J. Phys. Chem. B, 2003, 107, 5922–5925. 280 A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov and S. I. Shylin, Nature, 2015, 525, 73–76. 281 M. Einaga, M. Sakata, T. Ishikawa, K. Shimizu, M. I. Eremets, A. P. Drozdov, I. A. Troyan, N. Hirao and Y. Ohishi, Nat. Phys., 2016, 12, 835–838. 282 N. Morita, T. Endo, T. Sato and M. Shimada, J. Mater. Sci. Lett., 1987, 6, 859–861. 283 B. G. Müller, Naturwissenschaften, 1979, 66, 519–520. 284 A. Tressaud, J. L. Soubeyroux, H. Touhara, G. Demazeau and F. Langlais, Mater. Res. Bull., 1981, 16, 207–214. 285 B. G. Müller, J. Fluor. Chem., 1982, 20, 291–299. 286 Z. Mazej, A. Tressaud and J. Darriet, J. Fluor. Chem., 2001, 110, 139–143. 287 K. H. . Jack and R. Maitland, Proc. Chem. Soc., 1957, 232.

167

288 C. Billy and H. M. Haendler, J. Am. Chem. Soc., 1957, 79, 1049–1051. 289 A. Grzelak, J. Gawraczyński, T. Jaroń, D. Kurzydłowski, A. Budzianowski, Z. Mazej, P. J. Leszczyński, V. B. Prakapenka, M. Derzsi, V. V. Struzhkin and W. Grochala, Inorg. Chem., 2017, 56, 14651–14661. 290 K. Kusaba and T. Kikegawa, Solid State Commun., 2008, 145, 279–282. 291 A. I. Zaslavskii, Y. D. Kondrashev and S. S. Tolkachev, Dokl. Akad. Nauk SSSR, 1950, 75, 559–561. 292 J. Haines, J. M. Léger, F. Gorelli, D. D. Klug, J. S. Tse and Z. Q. Li, Phys. Rev. B, 2001, 64, 134110. 293 R. D. Shannon, Acta Crystallogr. Sect. A, 1976, 32, 751–767. 294 G. Liu, H. Wang, Y. Ma and Y. Ma, Solid State Commun., 2011, 151, 1899–1902. 295 R. L. Sass, E. B. Brackett and T. E. Brackett, J. Phys. Chem., 1963, 67, 2863–2864. 296 X. Wang and J. Li, Europhys. Lett., 2013, 102, 36002. 297 S. M. Dorfman, F. Jiang, Z. Mao, A. Kubo, Y. Meng, V. B. Prakapenka and T. S. Duffy, Phys. Rev. B - Condens. Matter Mater. Phys., 2010, 81, 174121. 298 A. E. Austin, J. Phys. Chem. Solids, 1969, 30, 1282–1285. 299 D. Kurzydłowski, Crystals, 2018, 8, 140. 300 E. Stavrou, Y. Yao, A. F. Goncharov, Z. Konôpková and C. Raptis, Phys. Rev. B, 2016, 93, 054101. 301 L. C. Ming, M. H. Manghnani, T. Matsui and J. C. Jamieson, Phys. Earth Planet. Inter., 1980, 23, 276–285. 302 L. M. Lityagina, S. S. Kabalkina and L. F. Vereshchagin, Sov. Phys. JETP, 1972, 35, 353–354. 303 J. A. Barreda-Argüeso, S. López-Moreno, M. N. Sanz-Ortiz, F. Aguado, R. Valiente, J. González, F. Rodríguez, A. H. Romero, A. Muñoz, L. Nataf and F. Baudelet, Phys. Rev. B - Condens. Matter Mater. Phys., 2013, 88, 214108. 304 J. C. Jamieson and A. Y. Wu, J. Appl. Phys., 1977, 48, 4573–4575. 305 C. Kürkçü, Z. Merdan and H. Öztürk, Russ. J. Phys. Chem. A, 2016, 90, 2550–2555. 306 L. Ming and M. H. Manghnani, Geophys. Res. Lett., 1978, 5, 491–494. 307 S. López-Moreno, A. H. Romero, J. Mejía-López, A. Muñoz and I. V. Roshchin, Phys. Rev. B, 2012, 85, 134110. 308 J. B. Boyce and B. A. Huberman, Phys. Rep., 1979, 51, 189–265. 309 D. A. Keen, S. Hull, A. C. Barnes, P. Berastegui, W. A. Crichton, P. A. Madden, M. G. Tucker and M. Wilson, Phys. Rev. B, 2003, 68, 014117. 310 O. Ohtaka, H. Takebe, A. Yoshiasa, H. Fukui and Y. Katayama, Solid State Commun., 2002, 123, 213–216. 311 Y. H. Han, H. B. Wang, I. A. Troyan, C. X. Gao and M. I. Eremets, J. Chem. Phys., 2014, 140, 044708. 312 J. Wang, G. Zhang, H. Liu, Q. Wang, W. Shen, Y. Yan, C. Liu, Y. Han and C. Gao, Appl. Phys. Lett., 2017, 111, 031907. 313 S. Hull and P. Berastegui, J. Phys. Condens. Matter, 1998, 10, 7945–7955. 314 M. Catti, Phys. Rev. B - Condens. Matter Mater. Phys., 2006, 74, 1–9. 315 Y. Li, L. J. Zhang, T. Cui, Y. W. Li, Y. Wang, Y. M. Ma and G. T. Zou, J. Phys. Condens. Matter, 2008, 20, 195218. 316 S. Hull and D. Keen, Phys. Rev. B, 1999, 59, 750–761. 317 C. N. Louis, K. Iyakutti and P. Malarvizhi, J. Phys. Condens. Matter, 2004, 16, 1577– 1592. 318 O. Madelung, Semiconductors: Data Handbook, Springer Berlin Heidelberg, Berlin, Heidelberg, 2004. 319 S. Miyatani, J. Phys. Soc. Japan, 1981, 50, 3415–3418.

168

320 A. Sulaev, P. Ren, B. Xia, Q. H. Lin, T. Yu, C. Qiu, S.-Y. Zhang, M.-Y. Han, Z. P. Li, W. G. Zhu, Q. Wu, Y. P. Feng, L. Shen, S.-Q. Shen and L. Wang, AIP Adv., 2013, 3, 032123. 321 Y. Zhang, Y. Li, Y. Ma, Y. Li, G. Li, X. Shao, H. Wang, T. Cui, X. Wang and P. Zhu, Sci. Rep., 2015, 5, 14681. 322 Z. Zhao, S. Wang, A. R. Oganov, P. Chen, Z. Liu and W. L. Mao, Phys. Rev. B - Condens. Matter Mater. Phys., 2014, 89, 1–6. 323 Z. Zhao, H. Wei and W. L. Mao, Appl. Phys. Lett., 2016, 108, 261902. 324 J. Zhu, A. R. Oganov, W. X. Feng, Y. G. Yao, S. J. Zhang, X. H. Yu, J. L. Zhu, R. C. Yu, C. Q. Jin, X. Dai, Z. Fang and Y. S. Zhao, AIP Adv., 2016, 6, 085003. 325 J. Zhang, C. Liu, X. Zhang, F. Ke, Y. Han, G. Peng, Y. Ma and C. Gao, Appl. Phys. Lett., 2013, 103, 082116. 326 A. Werner and H. D. Hochheimer, Phys. Rev. B, 1982, 25, 5929–5934. 327 A. L. Goodwin, D. A. Keen and M. G. Tucker, Proc. Natl. Acad. Sci., 2008, 105, 18708– 18713. 328 W. Cai and A. Katrusiak, Nat. Commun., 2014, 5, 1–8. 329 W. Grochala, J. Mol. Model., 2011, 17, 2237–2248. 330 A. Jayaraman, Rev. Mod. Phys., 1983, 55, 65–108. 331 W. Bassett, High Press. Res., 2009, 29, 163–186. 332 A. Jayaraman, Rev. Sci. Instrum., 1986, 57, 1013–1031. 333 G. J. Piermarini, S. Block, J. D. Barnett and R. A. Forman, J. Appl. Phys., 1975, 46, 2774–2780. 334 H. K. Mao, J. Xu and P. M. Bell, J. Geophys. Res., 1986, 91, 4673–4676. 335 Y. Akahama and H. Kawamura, J. Phys. Conf. Ser., 2010, 215, 043516. 336 F. Birch, Phys. Rev., 1947, 71, 809–824. 337 P. Vinet, J. Ferrante, J. H. Rose and J. R. Smith, J. Geophys. Res., 1987, 92, 9319–9325. 338 K. Brister, Rev. Sci. Instrum., 1997, 68, 1629. 339 A. Katrusiak, Acta Crystallogr. Sect. A Found. Crystallogr., 2008, 64, 135–148. 340 M. I. McMahon, Top. Curr. Chem., 2012, 315, 69–110. 341 W. Paszkowicz, Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms, 2002, 198, 142–182. 342 T. Palasyuk and M. Tkacz, Solid State Commun., 2004, 130, 219–221. 343 M. A. Kuzovnikov and M. Tkacz, Int. J. Hydrogen Energy, 2017, 42, 340–346. 344 P. M. de Wolff, J. Appl. Crystallogr., 1968, 1, 108–113. 345 A. Le Bail, H. Duroy and J. L. Fourquet, Mater. Res. Bull., 1988, 23, 447–452. 346 H. M. Rietveld, J. Appl. Crystallogr., 1969, 2, 65–71. 347 G. M. Sheldrick, Acta Crystallogr. Sect. A Found. Crystallogr., 2008, 64, 112–122. 348 W. A. Dollase, J. Appl. Crystallogr., 1986, 19, 267–272. 349 V. Petříček, M. Dušek and L. Palatinus, Zeitschrift für Krist. - Cryst. Mater., 2014, 229, 345–352. 350 G. Shen and H. K. Mao, Reports Prog. Phys., 2017, 80, 016101. 351 A. Mujica, A. Rubio, A. Muñoz and R. J. Needs, Rev. Mod. Phys., 2003, 75, 863–912. 352 E. Zurek and W. Grochala, Phys. Chem. Chem. Phys., 2015, 17, 2917–2934. 353 K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276. 354 M. Wojdyr, J. Appl. Crystallogr., 2010, 43, 1126–1128. 355 L. J. van der Pauw, Philips Res. Reports, 1958, 13, 1–9. 356 W. K. Chan, Rev. Sci. Instrum., 2000, 71, 3964. 357 A. A. Ramadan, R. D. Gould and A. Ashour, Thin Solid Films, 1994, 239, 272–275. 358 H. K. Mao and P. M. Bell, Rev. Sci. Instrum., 1981, 52, 615–616. 359 R. L. Reichlin, Rev. Sci. Instrum., 1983, 54, 1674–1677. 360 J. Gonzalez, J. M. Besson and G. Weill, Rev. Sci. Instrum., 1986, 57, 106–107.

169

361 C. Gao, Y. Han, Y. Ma, A. White, H. Liu, J. Luo, M. Li, C. He, A. Hao, X. Huang, Y. Pan and G. Zou, Rev. Sci. Instrum., 2005, 76, 1–5. 362 A. Dewaele, P. Loubeyre and M. Mezouar, Phys. Rev. B, 2004, 70, 094112. 363 C. Prescher and V. B. Prakapenka, High Press. Res., 2015, 35, 223–230. 364 R. M. Hazen, H. K. Mao, L. W. Finger and P. M. Bell, Carnegie Inst. Yearb., 1980, 79, 348–355. 365 R. J. Hemley, C. S. Zha, A. P. Jephcoat, H. K. Mao, L. W. Finger and D. E. Cox, Phys. Rev. B, 1989, 39, 11820–11827. 366 V. Scatturin, P. L. Bellon and A. J. Salkind, J. Electrochem. Soc., 1961, 108, 819. 367 H. Meyer and H. Müller‐Buschbaum, ZAAC ‐ J. Inorg. Gen. Chem., 1978, 442, 26–30. 368 A. Grzelak, J. Gawraczyński, T. Jaroń, M. Somayazulu, M. Derzsi, V. Struzhkin and W. Grochala, Inorg. Chem., 2017, 56, 5804–5812. 369 G. Kresse and J. Hafner, Phys. Rev. B, 1993, 47, 558–561. 370 G. Kresse and J. Hafner, Phys. Rev. B, 1994, 49, 14251–14269. 371 G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50. 372 G. Kresse and J. Furthmüller, Phys. Rev. B, 1996, 54, 11169–11186. 373 G. Kresse and D. Joubert, Phys. Rev. B, 1999, 59, 1758–1775. 374 K. Parlinski, Z. Q. Li and Y. Kawazoe, Phys. Rev. Lett., 1997, 78, 4063–4066. 375 A. Togo and I. Tanaka, Scr. Mater., 2015, 108, 1–5. 376 J. Perdew, A. Ruzsinszky, G. Csonka, O. Vydrov, G. Scuseria, L. Constantin, X. Zhou and K. Burke, Phys. Rev. Lett., 2008, 100, 136406. 377 J. Kanamori, J. Phys. Chem. Solids, 1959, 10, 87–98. 378 S. Iijima, Nature, 1991, 354, 56–58. 379 Y. R. Hacohen, E. Grunbaum, R. Tenne, J. Sloan and J. L. Hutchison, Nature, 1998, 395, 336–337. 380 K. Kholiya, Indian J. Phys., 2013, 87, 339–343. 381 D. Kurzydłowski, M. Derzsi, P. Barone, A. Grzelak, V. Struzhkin, J. Lorenzana and W. Grochala, Chem. Commun., 2018, submitted. 382 J. Tong, F. Kraus, J. Köhler, A. Simon, J. Liu and M.-H. Whangbo, Zeitschrift für Anorg. und Allg. Chemie, 2011, 637, 1118–1121. 383 P. G. Johannsen and W. B. Holzapfel, J. Phys. C Solid State Phys., 2000, 16, L1177– L1179. 384 G. L. Bottger and A. L. Geddes, J. Chem. Phys., 1967, 46, 3000–3004. 385 Y. Chen, S. Sun, Y. Wu, S. Gao, Z. Li, S. Ouyang, D. Li, Z. Men, M. Zhou and C. Sun, Phys. Status Solidi Basic Res., 2012, 249, 2113–2117. 386 H. Haller and S. Riedel, Zeitschrift fur Anorg. und Allg. Chemie, 2014, 640, 1281–1291. 387 R. Brückner, H. Haller, M. Ellwanger and S. Riedel, Chemistry, 2012, 18, 5741–7. 388 S. W. Hu, Z. X. Wang, F. Qu, T. W. Chu and X. Y. Wang, J. Phys. Chem. A, 2011, 115, 13452–13466. 389 J. Taraba and Z. Zak, Inorg. Chem., 2003, 42, 3591–3594. 390 Y. Quan and W. E. Pickett, Phys. Rev. B - Condens. Matter Mater. Phys., 2015, 91, 035121. 391 A. Dewaele, F. Datchi, P. Loubeyre and M. Mezouar, Phys. Rev. B - Condens. Matter Mater. Phys., 2008, 77, 1–9. 392 M. Monthioux and V. L. Kuznetsov, Carbon N. Y., 2006, 44, 1621–1623.

170