Flux Synthesis of Zintl Phases and Feas Related Intermetallics Josiah Mathieu

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2013 Flux Synthesis of Zintl Phases and FeAs Related Intermetallics Josiah Mathieu

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COLLEGE OF ARTS AND SCIENCES

FLUX SYNTHESIS OF ZINTL PHASES AND FeAs RELATED INTERMETALLICS

JOSIAH MATHIEU

A Dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Fall Semester, 2013 Josiah Mathieu defended this dissertation on August 13th, 2013

The members of the supervisory committee were:

Susan Latturner Professor Directing Dissertation

Eric Hellstrom University Representative

Naresh Dalal Committee Member

Oliver Steinbock Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.

ACKNOWLEDGEMENTS

I would like to thank Dr. Latturner for the opportunity to work in her lab and pursue my interests in solid state chemistry. It has been everything I hoped if not more. I also appreciate the opportunity to have made a small contribution to the field of superconductivity, which is where my interest in the solid state came from originally. I would also like to thank Dr. Evan Benbow and Dr. Milorad Stojanovic for the numerous consultations about my work, as well as the time they spent training me on all the instrumentation necessary for it. Lastly, I would like to thank the rest of the Latturner group for their support.

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TABLE OF CONTENTS

List of Tables ...... vi List of Figures ...... vii Abstract ...... ix 1. INTRODUCTION: METAL FLUX SYNTHESIS AND ZINTL PHASES ...... 1 2. THEORETICAL AND TECHNICAL BACKGROUND FOR CHARACTERIZATION TECHNIQUES OF SOLID STATE MATERIALS USED IN THIS WORK ...... 7 2.1 Scanning Electron Microscopy and Energy Dispersive Spectroscopy ...... 7 2.2 X-ray Diffraction ...... 9 2.3 Heat Capacity Measurements and Thermal Excitation Processes in Solids ...... 12 2.4 Electrical Measurements ...... 18 2.5 Magnetic Measurements ...... 21 2.6 Nuclear Magnetic Resonance Spectroscopy ...... 26

3. FLUX GROWTH AND ELECTRONIC PROPERTIES OF Ba2In5Pn5 (Pn = P, As): ZINTL PHASES EXHIBITING METALLIC BEHAVIOR ...... 38 3.1 Introduction ...... 38 3.2 Experimental Section ...... 39 3.2.1 Synthesis ...... 39 3.2.2 Structure Refinements ...... 40 3.2.3 Differential Scanning Calorimetry–Thermogravimetric Analysis...... 42 3.2.4 Resistivity Measurements ...... 43 3.2.5 Nuclear Magnetic Resonance ...... 43 3.2.6 Electronic Structure Calculations ...... 44 3.3 Results and Discussion ...... 44 3.3.1 Synthesis ...... 44 3.3.2 Structure ...... 45 3.3.3 Transport Properties ...... 49 3.3.4 NMR Studies ...... 50 3.3.5 Electronic Structure Calculations ...... 52 3.4 Conclusion ...... 53

4. ZINTL PHASE AS DOPANT SOURCE IN THE FLUX SYNTHESIS OF

Ba1-XKXFe2As2 TYPE SUPERCONDUCTORS ...... 55 4.1 Introduction ...... 55 4.2 Experimental Procedure ...... 59 4.2.1 Synthesis ...... 59 4.2.2 Elemental Analysis ...... 59 4.2.3 Crystallographic Characterization of Ba1-x-yKxSnyFe2As2 Phases ...... 60

4.2.4 Magnetic Susceptibility Measurements ...... 61 4.3 Results and Discussion ...... 62 4.3.1 Structure Determination ...... 62 4.3.2 Magnetic Susceptibility Measurements ...... 64 4.4 Conclusion ...... 64

5. FLUX GROWTH AND PHYSICAL PROPERTIES OF A/Ni/Sb PHASES (A = Eu OR Sr) ...... 66 5.1 Introduction ...... 66 5.2 Experimental Procedure ...... 67 5.2.1 Synthesis ...... 67 5.2.2 Elemental Analysis ...... 67 5.2.3 Structure Refinements ...... 68 5.3 Discussion ...... 71 5.3.1 Synthesis and Crystal Growth ...... 71 5.3.2 Structure ...... 72 5.3.3 Magnetic Properties ...... 75 5.4 Conclusions ...... 79

6. FUTURE WORK ...... 80 7. REFERNCES ...... 81 8. BIOGRAPHICAL SKETCH ...... 87

LIST OF TABLES

3.1. Crystallographic Data for Ba2In5Pn5 Phases ...... 41

3.2 Atomic Positions for the Ba2In5Pn5 Phases ...... 42

3.3. Selected Bond Lengths (Å) ...... 48

4.1. Reaction ratios and product stoichiometries, unit cells, and superconducting transition temperatures for Ba1-x-yKxSnyFe2As2 phases...... 61

4.2. Atomic positions and occupancies for Ba0.598(6)K0.381(1)Sn0.044(5)Fe2A2...... 61

5.1. Crystallographic data for A/Ni/Sb phases...... 69

5.2 Atom positions for EuNi1.78Sb2 ...... 69

5.3 Atom positions for SrNi1.78Sb2...... 70

5.4 Atom positions for EuNi2Sb2 ...... 70

5.5 Atom positions for Eu2Sb5Ni7 ...... 70

5.6 Selected bond lengths for A/Ni/Sb phases ...... 73

LIST OF FIGURES

1.1 Reaction setup with the two crucibles in a sealed quartz tube...... 4

2.1 Characteristic X-ray formation and labeling...... 9

2.2 Visual derivation of Bragg’s Law...... 11

2.3 Simple block diagram for metals, semiconductors, and insulators...... 13

2.4 Representative heat capacity for a typical metal...... 14

2.5 The Fermi-Dirac distribution and its behavior in a metal at different temperatures...... 16

2.6 Resistivity plot for YAgSb2, which is representative for a normal metal...... 19

2.7 Wiring diagram for the four point probe method, showing the contacts on a piece of material...... 21

2.8 Simple illustration of the temperature intercept for Curie Weiss plots...... 24

2.9 Magnetic hysteresis plot for Co7(TeO3)4Br6, which is representative of a typical ferromagnet...... 25

2.10 Spin axis system, where the thick arrow denotes the direction of the nuclei being studied..29

2.11 Plot of signal versus pulse times used to find the 180o pulse time...... 30

2.12 NMR pulse sequence used to find the T1 relaxation time...... 31

2.13 Plot of signal vs. delay time (d1) used to find the T1 relaxation time for Ba2In5P5 at 248.15 K...... 31

2.14 Picture of solid-state NMR rotor and end cap showing fins used for spinning...... 34

3.1 (a) Ba2In5Pn5 structure, viewed down the b-axis. Large gray spheres are Ba; small dark blue spheres are pnictogen atoms; and red spheres are indium atoms. (b) Coordination environment of the two barium sites...... 46

3.2 Other II−III−V Zintl phase structures. (a) BaGa2Sb2 features pentagonal channels defined by Ga−Ga bonds; the ethane-like building block Sb3Ga-GaSb3 is a common motif. (b) Ba4In8Sb16 structure also features pentagonal channels but these contain Sb−Sb bonds. (c) EuIn2P2 structure features hexagonal channels defined by P3In−InP3 units...... 48

3.3 Single-crystal electrical resistivity data for the Ba2In5Pn5 phases...... 49

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115 3.4 In MAS-NMR spectra of Ba2In5Pn5, spinning at 5000 Hz ...... 51

3.5 31P MAS-NMR spectra of Ba2In5P5, spinning at 5000 Hz ...... 52

3.6 Plot of inverse 31P spin−lattice relaxation vs temperature. The linearity of the data agrees with the Korringa relation and indicates that Ba2In5P5 has metallic conductivity ...... 52

3.7 Total density of state calculations for Ba2In5Pn5 phases. The Fermi level is set at 0 eV...... 53

+ 4.1 Structure of K4Sn4, featuring Sn44- tetrahedra (white spheres are Sn, purple spheres are K ions) ...... 58

4.2 Magnetic susceptibility data for Ba1-x-yKxSnyFe2As2 phases, collected with an applied field of 10 G...... 62

4.3 Structure of Ba1-x-yKxSnyFe2As2; large blue spheres represent the Ba/K mixed site. The 4e sites partially occupied by tin are indicated by grey clouded spheres...... 63

5.1 SEM images of SrNi2-xSb2 (left) and EuNi2-xSb2 (right). These pictures are taken looking down the c-axis of the crystal...... 68

5.2 Structures of a) EuNi2Sb2 (I4/mmm, ThCr2Si2 type), b) Eu2Ni7Sb5 (I4/mmm, stuffed variant of La2NiGa10 structure type), c) EuNi2Sb2 (P4/nmm, CaBe2Ge2 type). All structures are viewed down the a-axis; magenta spheres represent Eu, orange represents Sb, and white or green represents Ni………………………………………………………….. 73

5.3 Temperature dependence of magnetic susceptibility for a crystal of EuNi1.8Sb2 oriented with its c-axis either parallel or perpendicular to the applied field of 10 G...... 76

5.4 Temperature dependence of magnetic susceptibility for a crystal of EuNi1.7 Sb2 oriented with its c-axis perpendicular to the applied field, collected at applied fields of 10 G (triangles) and 2 T (filled squares)...... 76

5.5 Field sweeps in both directions with respect to the c-axis of EuNi1.7Sb2 at 1.8 K...... 77

5.6 Showing the magnetization when EuNi1.7Sb2 is orientated with the c-axis perpendicular to the field between -2 T and 2 T to get a better view of the hysteresis that occurs between 1 and 2 T...... 77

5.7 Heat capacity data for EuNi1.76Sb2 collected with different applied magnetic fields...... 78

5.8 Resistivity plot for EuNi1.76Sb2...... 79

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ABSTRACT

Metal flux synthesis was used to discover new Zintl phase materials and to grow crystals of superconducting phases. Reactions of barium and the pnictide elements Pn = P or As in indium melts produced new Zintl phases Ba2In5Pn5. This structure features indium arsenide slabs separated by barium cations. The connectivity of the indium and the arsenide leads to charge 2+ − + 0 4− balancing according to the Zintl-Klemm concept ((Ba )2[(4b-In )5(4b-Pn )(3b-Pn )4] ). Band structure calculations indicate that these phases should be semiconducting, but resistivity and NMR studies show them to be metals. This may be due to very small amounts of excess indium doping onto Pn sites.

Reactions of barium, iron, and arsenic in tin flux yield the phase BaFe2As2. This can be converted into a superconductor by doping with potassium. The difficulty in handling the volatile and reactive potassium metal was solved by using a Zintl phase, K4Sn4, as a potassium source. Varying amounts of this compound were combined with barium, iron, and arsenic in tin flux reactions, producing a series of KxBa1-xFe2As2 crystalline products. The superconducting transition temperature varied with x as expected, but the use of tin flux added the complication of incorporating small amounts of tin; this also affected the Tc.

Lead flux was used to synthesize ANi2Sb2 phases. (A = Sr, Eu) which crystallized in either the ThCr2Si2 and CaBe2Ge2 structure types. Products forming with the ThCr2Si2 type consistently showed vacancies on the nickel site (ANi2-xSb2, x < 0.3) whereas the CaBe2Ge2 type products did not show these defects. Another ternary phase was also isolated, Eu2Ni7Sb5, with a new structure that is a stuffed variant of the La2NiGa10 structure type. EuNi2-xSb2 exhibits metallic behavior as given from resistivity data, and exhibits an antiferromagnetic transition at 5.8 K, which can be partially suppressed by applying an external magnetic field perpendicular to the c-axis. No suppression of the antiferromagnetic transition was found by applying an external magnetic field parallel to the c-axis up to 5 T.

CHAPTER 1

INTRODUCTION: METAL FLUX SYNTHESIS AND ZINTL PHASES

This work involves the synthesis of solid state intermetallics and pseudo-metallic Zintl phases using a non-traditional molten flux synthesis method that is gaining traction in the materials field among both chemists and physicists alike. Intermetallics are compounds that contain two or more metals; typically with differing sizes and electronegativities that leads to significant ionic or covalent bonding character. This is as opposed to alloys which are comprised of metals of similar sizes and electronegativities. These exhibit metallic bonding, in which completely delocalized valence electrons serve to maintain the structure through their electrostatic interactions with the metal atoms.1 Traditional solid state synthesis methods typically involve mixing powders of starting materials in various stoichiometric quantities and grinding them together, in some cases utilizing an inert volatile solvent and making a slurry to ensure that the mixing is carried out completely. The materials are pressed into a pellet and then placed in a container that can withstand very high temperatures, typically near 1000 ºC and sometimes higher. The container with the materials is usually then placed in the furnace where the high temperatures facilitate the diffusion of the solid powders. Typically the products from these reactions will not achieve sufficient mixing and resulting products will either be insufficient for full characterization or contain significant impurities. The solution is typically to regrind the materials and then place them back in the furnace. This routine can require multiple repetitions. While this method is useful for the synthesis of some compounds, for many it is not.1 In the case of the synthesis of intermetallics it is common to use the metal elements themselves as the starting materials. The mixing process is further complicated by the purchased forms of the elements. Many of the elements are air sensitive and it is usually convenient to purchase these elements in large pieces to decrease the surface to volume ratio, otherwise they may oxidize more rapidly, and even storage in a dry box may not completely preserve the materials. Many of them are malleable and cannot be ground down to a powder, making reliance on diffusion even more problematic. Mixing of the elements may require the use of arc melting equipment, or complete reliance on an element with a low melting or boiling point to facilitate

1 the mixing and diffusion of the other elements. Reliance on these mixing processes can result in lost material through evaporation, or a final product with impurities. Occasionally such losses can be accounted for by adjusting the starting molar ratios, or by adjusting the molar ratios to achieve a higher purity of the material after an identification of the desired or targeted product is obtained. In some cases losses of material or incomplete mixing can provide scientifically interesting results or become a desired reaction pathway, but there is typically a need to adjust the initial molar ratios of the reactants to obtain a pure enough sample of the desired phase for physical property measurements.1,2 Traditional solid state synthesis has other scientific limitations. The high temperatures lead to products that are thermodynamically favorable, and many products formed are so favored thermodynamically that that they cannot be avoided despite change in the starting molar ratios or changes in the reaction conditions. These thermodynamically favored products tend to be binary or simple ternary phases and due to the difficulty of the diffusion process and the high temperatures needed there is little room for kinetic control.1 A method for getting around the thermodynamic barriers and the difficulty of solid state diffusion lies in the molten flux synthesis method. This method relies on the use of an excess of a low melting metal to act as a solvent for the synthesis of intermetallics. As with traditional solution chemistry, the low melting metal solvent allows increased diffusion, as well as occasionally acting as a reactant itself. This method allows lower temperatures to be used in synthesis, and promotes more kinetic control by enabling different concentrations of materials to be used, as opposed to being limited to specific starting molar ratios. It has proven useful in giving products that cannot be predicted by traditional electronic counting schemes. It also provides a route to grow single crystals of known materials that could not be effectively studied in their polycrystalline forms.1 The requirements for a metal to be viable as a candidate for molten flux synthesis are that it should melt at a reasonably low temperature, such that normal heating profiles and containers can be used. There should be a large difference between the melting point and the boiling point temperatures of the metal. It should be possible to separate the flux from the products by chemical dissolution, filtration while the metal is still in the liquid state, or by mechanical removal. Lastly, it should not form highly stable binary compounds with any reactants. While these are good rules to follow, they should by no means be considered hard laws. It is not

2 necessary for the reactants to fully dissolve, as the molten metal flux can act as a transport medium.1 Experimentally, this process is carried out by putting the flux and the reactants into a crucible. The crucible is then sealed in a quartz tube under vacuum to provide an inert environment for the reaction to take place. The crucible used must not undergo extensive reaction with the liquid metal. Resources are available to determine which types of crucibles should be used depending on the metal being used as a flux. In this work, the main metals used as a flux were indium and tin.3 Both of these are fairly non-reactive, however, at high temperatures over extended periods of time it is possible that either of these metals may react with the quartz. Therefore alumina crucibles were used in this work. In order to save on lab expenses, alumina crucibles were made from cut alumina tubes with bottoms made from a cement composed predominantly of SiO2, Al2O3, and TiO2, but contains traces of other elements. The cement was frequently compromised during reactions, so it was replaced after each reaction. The reactions were generally loaded into the crucible with minor reactants being placed in between a bottom and top layer of the flux metal. This is done in order to maximize the contact of the flux with the other reactants in order to facilitate dissolution. Once the crucible is loaded, a second smaller crucible containing Corning Fiberfrax® is placed on top. They are loaded into a quartz tube which is then sealed under vacuum. An illustration is given in figure 1.1. The reaction ampoules are then heated in a programmable furnace to anywhere from 800 ºC to 1000 ºC and then cooled to around 500 ºC to 650 ºC over a period of a few days to a week and a half. The ampoules are taken out when the minimum programmed temperature was reached and then centrifuged to remove the flux. This typically results in the flux pooling into the bottom of the quartz, while the other reaction products remain in the reaction crucible. Gentle scraping of the bottom crucible will usually loosen the products so they can be collected. The molten flux method is not without its own drawbacks. Often, droplets of the flux will adhere to the surfaces of the crystals produced. This can cause problems with certain physical property measurements, so it may be necessary to physically scrape the flux off or place the crystal in dilute acid for awhile to remove the flux. Soaking the crystals in acid unfortunately places the crystals at risk of being dissolved as well, so care must be taken when using this method to remove the flux. Flux can also get trapped within the crystals as they grow; these flux

Figure 1.1 Reaction setup with the two crucibles in a sealed quartz tube.

occlusions can lead to unusual or unexpected results in physical property measurements, which was the case with the Zintl phases produced in this work. Lastly, depending on the concentrations used in the reaction, the flux may be over-saturated and lead to a solid chunk with any products produced difficult to separate from the flux.2 In this work the flux method was used to synthesize polar intermetallics called Zintl phases and then later, after the reports of discovery of iron arsenide superconductors, this method was studied as a possible way to control the potassium used as a dopant to induce the superconductivity. Zintl phases are a class of compounds that are electronically positioned between traditional intermetallics and insulating valence compounds. Zintl phases were originally a result of the studies of Eduard Zintl, who studied reactions of group 13-17 elements in liquid ammonia solutions of alkali metals. He observed that elements to the right of group 13 tended to form polyatomic anions in liquid ammonia, whereas elements to the left of group 14 formed insoluble metal phases. It was through these reactions that phases such as Na4Pb9 (which 4- contains Pb9 anions) were discovered, which were found to have salt-like structures and tended to be line compounds. These observations of the salt-like structures led to the electronic classification of Zintl phases, named after Zintl. These phases fall somewhere between traditional intermetallics and insulating compounds. The marked difference occurs from the phases having a combination of ionic and covalent bonding within the same structure: the

4 electropositive cations transfer their electrons to a covalently bonded network of anions or individual anions or clusters.4 There are general guidelines that Zintl phases tend to follow. First, there should be well- defined relationship between their chemical and electronic structures, which means for Zintl phases the total number of electrons transferred from the electropositive elements should account for the charge and valence bonding of the anions in the structure. In general, the octets of all the individual anions should be filled, either by bonds or lone pairs. Zintl phases should typically be semiconductors, though a few metallic Zintl phases now exist in literature, and the phases in this work are metallic due to impurities. Lastly, Zintl phases should typically be diamagnetic. This follows from the fact they are usually semiconducting, but paramagnetism can occur if elements like europium, ytterbium, or manganese are part of the structure. Again, there are a few metallic Zintl phases that would also be an exception to this.4 Zintl phases come in three general structure classifications that are dependent on the cation to anion ratio. Where the ratio is heavily in favor of anions, the anions typically exist as extensive 3-dimensional networks with the cations locked into cavities, as exemplified by 5,6 clathrate phases such as Ba8Ga16Ge30. A slight ratio in favor of anions generally gives layered structures, with alternating cation and anion layers, as seen in EuIn2P2, although various distortions such as puckering can occur.7,8 When the ratio reaches around one to one or more in favor of the cations, the anions tend to form isolated covalently bonded clusters, or occasionally 9,10 as isolated anions, as seen respectively in K4Sn4 or Ca2Si. The elements incorporated in any Zintl products will also have an effect on the structure, as group 13 elements generally require more covalent bonds and bonding networks as they are more electron deficient than group 15 elements. In this work targeting novel ternary Zintl phases, the main elements selected for use as molten metal fluxes were gallium, indium, tin, and lead. All four of these elements possess the ideal properties of having low melting points as well as high boiling points. These fluxes are also appealing because each of these elements is a main group metal which has been observed to incorporate into previously reported Zintl phases (for instance EuGa2As2, EuIn2As2, and 11,12,13 Na4Sn9). These flux metals will be present in great excess, so it is the ratio of the two non- flux reactants which will be critical for controlling the stoichiometry and structure of any Zintl phases produced. Layered or two dimensional Zintl phases are of particular interest given the

5 unusual properties of layered superconductors such as YBa2Cu3O7-x, MgB2, and KxBa1- 14,15,16 xFe2As2. Zintl phases such as Y2AlGe3, Ba2Sn3Sb6, and SrSn3Sb4 have been found to be superconducting. While they are not layered, they show that Zintl phases can be superconducting.17,18

CHAPTER 2

THEORETICAL AND TECHNICAL BACKGROUND FOR CHARACTERIZATION TECHNIQUES OF SOLID STATE MATERIALS USED IN THIS WORK

2.1 Scanning Electron Microscopy and Energy Dispersive Spectroscopy

These two experimental techniques will be discussed together since the two techniques are typically done concurrently, as an energy dispersive spectrometer (EDS) is an add-on to a scanning electron microscope (SEM). SEM is typically used a tool to analyze the surfaces of materials. It has an advantage over a traditional microscope since the imaging is done with electrons rather than light. Electrons have a shorter wavelength than light photons which allows for far better magnification, and resolution can typically approach 40 Å. SEM images also maintain a 3D appearance due to the high field depth. Energy dispersive spectroscopy is used to do semi-quantitative elemental analysis, which is a key technique in this work as without it x-ray diffraction becomes largely speculative as to the elements included in a structure due to the mixture of reactants used in the synthetic methods employed.19 The basic components of an SEM are a vacuum system, electron gun, detection system, and a computer to interact with the instrument and display the images and output data. The vacuum system typically consists of a diffusion pump backed by a rotary pump. The purpose of pump is to rid the entire system of air. This minimizes the scattering of electrons from the electron gun by gas molecules and slows down the oxidation of the tungsten filament used to produce the electrons. The electron gun consists of an electron source, a number of magnets which are used to focus the beam, and an anode to produce an electric potential gradient that accelerates the electrons towards the sample being studied. The electron source is typically a tungsten filament; incandescent heating will cause the filament to emit electrons. The beam is typically 25,000-30,000 Å in diameter and must be narrowed and focused through a series of magnetic lenses in order to achieve spot sizes in the 50-200 Å range. The sample sits on a conductive substrate (typically an aluminum puck in the work done here), in order to facilitate a

7 connection to ground. The sample stage is capable of movement in all three translational directions, and has the ability to rotate and tilt.19 When the electrons hit the sample they will either collide elastically or inelastically with the atoms that they encounter. Elastic collisions produce backscattered electrons which produce topographic and compositional information. The probability () that a backscattered electron will occur is given by equation 2.1, which shows that the mean atomic weight (Z) or density of the (2.1)19 material being investigated is the single factor of importance. Back scattered electrons are detected by a combination of an aluminum scintillator, typically called a Everhart-Thornley detector, and solid state BSE detectors. Evenhart-Thornley detectors convert backscattered electrons to photons to produce an image, while solid state BSE detectors work similarly to a photodiode and a current is produced against a bias voltage by the formation of electron-hole pairs when struck by the backscattered electrons. Due to the 90º angle with respect to the sample stage that Everhart-Thornley detectors are placed in they cannot be used very well for back scattered electron detection, therefore multiple solid state BSE detectors are generally used and placed in favorable areas with respect to the line of sight of the backscattered electrons.19 Inelastic collisions deposit electrons into the sample which results in a number of processes which return the material to the ground state. Secondary electrons produced by this process result in the typical image seen by the SEM. Secondary electrons are lower in energy than the beam produced by the electron gun and are facilitated by being a partial means of recovery to the ground state by the material. Secondary electrons are typically collected using a Everhart-Thornley detector. Since they are not as sensitive to line of sight as backscattered electrons, that detector is sufficient to obtain an image.19 The most important inelastic process that occurs is the generation of characteristic X- rays, produced as another means of the sample reaching its ground state. These are created from deep in the area where the sample is being probed and therefore require an accelerating voltage that is one and a half to three times the critical excitation energy required to eject an inner shell electron. The subsequent hole is then replaced by an outer shell electron; this results in emission of an X-ray. The energy of the emitted X-ray depends on the inner shell electron ejected, and

8 which outer shell the replacement electron is from. A figure showing a couple of these processes is shown in figure 2.1. For instance, if the electron is ejected from the n=1 energy level the

Figure 2.1 Characteristic X-ray formation and labeling.

transition is designated with a “K”. If the replacement electron comes from the second energy level it is more specifically defined as “K”, whereas if the replacement electron comes from the third energy level it is specifically designated as “K". An electron ejected from the second energy level is designated with a "L", with the and  terms being derived from higher energy levels as before. The energy of the X-rays are specific to the levels of a particular atom, making them useful for elemental analysis. For instance, the K X-ray for germanium has an energy of 9.874 keV and that of arsenic is 10.530 keV. The highest detectable X-rays typically fall in the 10-20 keV range. The detection of the X-rays is typically done with a thin film diode made of lithium doped silicon connected to a series of amplifiers and ultimately an analog to digital converter in order to display the data on the computer.19

2.2 X-ray Diffraction

In addition to being utilized for elemental analysis, X-rays also play a distinct role in the determination of the structure of solid state materials. In the X-ray tube of a diffractometer the characteristic X-ray of a particular element is utilized, typically copper or molybdenum. The X- rays are produced in the same fashion as the X-rays produced for EDS. An electron gun is aimed in this case at a copper or molybdenum plate to produce X-rays, though it is important to note

9 that this process results in more than one wavelength of X-rays as discussed in section 2.1. In order to create monochromatic X-rays for diffraction, only the "K" X-rays are sent to the sample for diffraction, while the others are filtered off with a piece of metal foil.20 The X-rays are then aimed at a crystal which is mounted on a goniometer, which allows the crystal to be positioned in almost any orientation for data collection. Diffracted X-rays are collected by a charge coupled device (CCD) camera on modern instruments. The cameras are capable of collecting both intensity and spatial information about the diffracted X-rays. This information is used to create electron density maps which are in turn used to interpret the crystal structure. In modern crystallography, the data is typically interpreted by a software package, with human input for the final stages of structure refinement. Structural refinement is possible because of two things, the spatial information provided by the diffraction itself, and the varied intensities from atomic scattering factors. Crystals are treated as being layers of planes that act is semi-transparent mirrors that are separated by specific distance, hence the diffraction of a beam of X-rays at an angle  to the incident beam will be governed by the wavelength of the beam. As the crystal is rotated into different positions, many different sets of planes will diffract to provide as much information as possible. The conditions for diffraction are typically referred to as Bragg's Law. A visual derivation for Bragg's Law is shown in figure 2.2. Two X-ray beams approach two adjacent planes, and must satisfy the same diffraction condition. The equations governing the diffraction condition are shown in equations 2.2 and 2.3. In order for the two beams to have constructive interference the additional path traveled by the beam diffracting of the lower plane in figure 2.2, xyz , must be equal to a whole

(2.2)20

(2.3)20 number wavelength so that the two beams are in phase after diffraction. Bragg's Law is shown in equation 2.3, shows the diffraction condition as it is commonly defined.20 X-ray diffraction intensity is generated by atomic scattering factors which result from coherent scattering with electrons.15 Therefore, atoms with more electrons give more intense diffraction spots. The spot intensities are compared relatively to each other for atomic identification purposes, which is why elemental analysis should be done on a sample prior to an X-ray diffraction experiment. It is also why it is difficult to tell the difference between atoms

Figure 2.2 Visual derivation of Bragg’s Law.

with a similar number of electrons, as the difference in intensities may be negligible. Another effect caused by this property is that in ionic compounds certain cations and anions can become indistinguishable. An example of this would be potassium chloride, where potassium and chlorine both have eighteen electrons after potassium donates one of its valence electrons complete the octet of the chlorine atom. This also plays a role in structure determination. Once all the data has been collected, computer software will run algorithms to decipher the information and come up with several initial structure models. While the computer software does much of the structure determination work, it is critical for any human user to have knowledge of basic crystallography, be familiar with common bond lengths and structures, and have a good foundation in the chemistry of the type of material being studied. Crystals can be viewed as arrays of 7 different types of unit cells. A unit cell is a three dimensional unit that is repeated throughout the entire crystal. Unit cells can contain one or more atoms and atom positions, and can come in many different arrangements. Consideration of symmetry expands those seven crystal systems to 14 lattice types, and 230 space groups. Ultimately, all crystal structures will be labeled with one of the 230 space groups. Each space group is associated with different sets of diffraction conditions. In crystals the lattice planes are arranged in three dimensions, and atoms can be located at different positions within the unit cell. Therefore the diffraction patterns collected will differ from phase to phase depending on the

11 atom types and arrangements found within them. Bragg's Law, as it was discussed previously, was based on whole number multiples of the wavelength of the X-ray beam. However, symmetry elements associated with different space groups introduce additional planes of atoms which can result in destructive interference of diffracting X-rays. This gives another type of systematic absence which can occur in phases such as potassium chloride, where peaks that would normally be seen in the diffraction pattern for the structure can be masked by the atoms having the same atomic scattering factors and producing extra phase shifts of 180° which cancel some diffraction peaks.20 Once the software has chosen the best starting model for the structure, it is up to a human user to identify the atom types in the structure, and their placement. Additional corrections are made for absorption of X-rays and thermal motion of the atoms. What indicates whether the final refinements are correct is the R-factor, which is a measure of how well the data matches up with the refined structural model. In general an R-factor of 0.02 to 0.06 is regarded to mean the structure is correct. Additional things such as bond distances and arrangement of atoms based on electronegativity differences should be considered to ensure that solved structures make sense chemically.

2.3 Heat Capacity Measurements and Thermal Excitation Processes in Solids

Central to the study of solids is the study of thermal properties. The thermal properties are governed by the thermal excitation of both electrons and phonons, the lattice vibrations in a solid. While atomic and molecular systems tend to display discrete energy levels and give characteristic information based on specific internal and external quantum mechanical interactions, that privilege is lost as we go to the solid state. In a crystalline solid the number of interactions increases almost infinitely. This results in the shift from being able to identify specific rotational, vibrational and electronic interactions to having to look at bulk interactions. On a purely mathematical note, this concentration of interactions allows the use of integrals as opposed to sums in order to determine quantitative thermodynamic totals, and is also largely justified by the use of the approximations utilized for solid state calculations. Instead of vibrational modes composed of motions of specific bonds in molecules, extended solids exhibit phonons, or the lattice vibrations within a solid material. The thermal

12 equilibrium occupancy of these phonons with temperature are then described by the Planck distribution function as seen in equation 2.4, where ℏ is Planck's constant (ħ=h/2),  is the 

(2.4)21

frequency of identical harmonic oscillators, kB is the Boltzmann constant, and T is the temperature.21 Similarly, the increased number of interactions of atomic orbitals in extended solids results in minimized energy differences between different interacting atomic orbitals. This results in the formation of bands. In the block diagram shown in figure 2.3, we see the basic views for

Figure 2.3 Simple block diagram for metals, semiconductors, and insulators.

bands in solid materials like metals, semiconductors, and insulators. The behavior of electrons with temperature in metals is described by the Fermi-Dirac function which is given in equation 2.5, where  is the orbital energy, and  is a temperature dependent function.The Fermi-Dirac (2.5)21 distribution explains the behavior of particles with odd half integer spins (1/2, 3/2, ...), that

13 follow the Pauli exclusion principle, and whose wave functions are anti-symmetric. All of these conditions are met by electrons. In each model there are two bands; the bottom band is the valence band, and the top band is the conduction band. In a typical metal the valence band stops at the Fermi level which denotes the division between the electron filled valence band and the electron empty conduction band. In semiconductors and insulators the Fermi level lies about 3/5 of the way to the conduction band from the valence band. The energy of the Fermi level is also known as the Fermi energy.21 Representative heat capacity data for a metal is shown in figure 2.4. While this plot shows examples for two models, the Debye model is discussed here and provides a more accurate prediction of the T3 behavior of the heat capacity at low temperatures. At low

Figure 2.4 Representative heat capacity for a typical metal.22

temperatures there is a dominant cubic feature in CV, the heat capacity at constant volume. At high temperatures the heat capacity levels off. The high temperature behavior is known as the

Dulong and Petit value, which is 3Nkb. In order to describe the low temperature behavior, the density of states for the phonons must be determined.21 In order to calculate this a 3-dimensional particle in a box model is used, with sides of length L, based on a primitive monoatomic lattice as well as the utilization of identical harmonic

14 oscillators. The familiar test function eikx is applied in 3-dimensions yielding typical wavevector values of 2n/L. The result is that one unit of k is allowed per (2/L)3 of volume in k space. The number of modes N in a sphere of radius k is then calculated as shown in equation 2.6. The derivative is then taken with respect to the oscillator frequency to give the density of states for

(2.6)21 the phonons in the system as shown in equation 2.7. From here an additional assumption is

(2.7)21 made; it is assumed at low temperatures that only low energy and long wavelength vibrations such that kbT >> ħ are the only active phonon modes. Due to the long wavelength these modes can be thought of as similar to a classical elastic continuum, therefore a dispersion relation as shown in equation 2.8 where v is the velocity of sound, a constant, is used. The density of states (2.8)21 for this case then becomes V2/22v3. The total thermal energy of the system can then be calculated as shown in equation 2.9, where the integral goes from 0 to D, which is a cutoff (2.9)21 frequency with a corresponding cutoff wavevector kD. The Debye temperature, the temperature above which CV should approach the Dulong and Petit value, is defined as , where ħD/kB. At this point the Debye approximation can only be analytically solved at very low temperatures or high temperatures. For kbT >> ħthe integral can be solved yielding the solution for CV given in equation 2.10, where it explains the cubic behavior of CV at low temperatures. At high

(2.10)21 temperatures where ħ >> kBT the Debye approximation approaches the expected 3NkB value of Dulong and Petit.21 While the phonon heat capacity seems to fully explain experimental heat capacity results, there is an additional contribution from the conduction electrons. Based on the Drude model it was originally thought that all electrons in a metal were conducting and should contribute a value of (3/2)NkB to CV, however it was always determined that the additional contribution to CV was

Figure 2.5 The Fermi-Dirac distribution and its behavior in a metal at different temperatures.23

0.01 of this value. The Fermi-Dirac distribution sheds light on this. Figure 2.5 shows the behavior of the Fermi-Dirac function at different temperatures. There is little change between the temperatures of 0 K, where the Fermi-Dirac function is equivalent to a step function with the full electron population below the Fermi level, and 500 K. Even at 500 K the Fermi-Dirac function has not deviated much from its step function form and only the electrons within kBT of the Fermi energy take part in conduction.21 With the development of the free electron model the change in the total thermal energy from the conduction electrons when heated from 0 K to T could be calculated using equation 2.11. Here, the density of states is constructed similarly to the method used to compute the (2.11)21 density of states for the phonon modes, where the only difference is an additional factor of 2 due to the ability of two electrons, one spin up and one spin down, to occupy each state.

F is the Fermi energy.With similar approximations such as kbT << F and the assumption that

16 the density of states at the Fermi level does not change with temperature, the contribution to CV from the conduction electrons can be calculated as shown in equation 2.12 to show that it is directly proportional to T. The approximations hold since the temperatures that the metals are (2.12)21

21 studied at are much lower than these. TF is a constant defined by F BTF.

The heat capacity at constant volume CV is most pertinent when≡ k discussing solids, but it should be noted that the experiment is typically done under conditions of constant pressure to give CP. Since a solid is already relatively compressed unlike a gas or a liquid, the approximation that CP CV holds fairly well. The heat capacity experiment as done on a Quantum Design

PPMS involves≌ placing a sample immersed in grease on a platform through which wires send a known amount of heat to the sample, and this is then followed by a cooling period. The temperature response of the sample is measured by a thermocouple and the heat capacity is then evaluated based on equation 2.13. The model for the equation is based on the idea that there is (2.13)24 good thermal contact between the sample and the platform. Ctotal is the total heat capacity of the sample and platform, Kw is the thermal conductance of the supporting wires, Tb is the temperature of the thermal bath, and P(t) is the power applied by the heater. In order to determine the heat capacity of the sample itself, a measurement is done with just the grease, and the result of that measurement is simply subtracted off.24 2 Once the experiment is done, the data is typically plotted as CV/T versus T . This is because of the two contributions to CV, where the linear term is from the conduction electrons and the cubic term from the phonon contributions give equation 2.14. Dividing each side of the (2.14)21 equation by T gives equation 2.15. By performing a curve fitting function we can extract the (2.15)21 constants  andthe latter is often called the Sommerfeld parameter and gives an indication of the effective mass of the conduction electrons compared to the mass of the electron based on the free electron model, it can also be used to calculate the density of states at the Fermi level as

(2.16)21 shown in equation 2.16. A can be used to calculate the Debye temperature as shown in equation 2.17.16

(2.17)21

2.4 Electrical Measurements

Resistivity or conductivity measurements are another characterization technique where the thermal excitation of electrons and phonons once again play an important role. Typical resistivity measurements are done by recording the resistivity of a sample versus temperature. Since this research involves the study of Zintl phases it is also important to discuss the thermal excitation of electrons in semiconductors as well. The conductivity σ is defined in equation 2.18 where n is the electron concentration, e is (2.18)21 the charge of the electron, and is the mobility of the electron. Resistivity and conductivity are inverse functions of each other, or σ The resistivity is dominated at room temperature by collisions of electrons with other electrons and phonons, while at low temperatures it is dominated by impurity scattering. A characteristic resistivity plot for a metal is shown in figure 2.6. At low temperatures the resistivity reaches a minimum value due to only impurity scattering, this value is referred to as the residual resistivity. A typical practice is to calculate the residual resistivity ratio (RRR), which is the ratio of the room temperature resistivity to the residual resistivity. This is a convenient way to approximate the impurity concentration in a sample. In a typical sample a residual resistivity of 1 ohmcm per percent of impurity will occur.21 For a semiconductor we need to work with the Fermi-Dirac function in equation 2.5 and consider the case where -kBT, which falls into the region that semiconductors are typically studied. At these temperatures the Fermi-Dirac distribution is reduced to what is seen in equation 2.19. The corresponding energy for a conduction electron in the conduction band is the sum of

(2.19)21

25 Figure 2.6 Resistivity plot for YAgSb2, which is representative for a normal metal.

energy at the conduction band edge, plus the additional kinetic energy as suggested by the free electron model. However, in a real material, conductivity can also carried out by vacant orbitals, or holes. Overall conductivity of a material is then brought about by the sum of the contributions from the electrons and holes. In a semiconductor the role of holes is more exaggerated, given the nature of the space between the valence and conduction bands as seen in figure 2.3. When an electron is excited from the valence band to the conduction band, the orbital once occupied by the electron becomes a hole.21 In real materials, typically the electron and hole concentrations are unequal and are determined by impurities in the material, however the theory for the thermal excitation of an electron from the valence band to the conduction band in a semiconductor is best understood by working the case where the numbers of electrons and holes are equal, as in the case of an intrinsic semiconductor. In this case the density of states must be determined for both the electrons and holes. Again, this is similar to the method used in the heat capacity section, although separate masses are used, one for holes and one for electrons, and the range for the integration is unchanged. Conduction electrons are found in the energy range from the edge of the conduction band and higher, whereas the holes are found from the valence band edge and lower. The equilibrium concentrations of the electrons and holes are then calculated and multiplied together to determine the equilibrium relationship. The energy gap (Eg) results from the difference in the energies between the edges of the conduction and valence bands, Ec-Ev. Despite the fact that not all

19 semiconductors are intrinsic, this model holds well because the main assumption is that Eg >> 21 kBT. In resistivity measurements this is important as the concentration of holes or electrons conforms to an equation like that seen in equation 2.20, where E g is inside an exponential

(2.20)21 function. Resistivity is the inverse of conductivity as shown in equation 2.21. By assuming the T3/2 part is offset by the temperature dependence of the mobility and dominated by the

(2.21)21 exponential function, the natural log of 2.21 can then be taken giving equation 2.22. By then

(2.22)21 grouping the first term to be a constant "b", giving equation 2.23. From 2.23 A plot of lnvs.

+b (2.23)21

1/T should give a linear plot in the region where the resistivity behaves exponentially, allowing 21 Eg to be calculated from a resistivity measurement. Resistivity measurements are typically conducted using a four-point probe method as shown in figure 2.7. In this setup the two outside probes serve as the current sources with one being the I+ and I- contacts. Two probes in the middle serve only to record a voltage drop between each other. The four contacts are typically connected with a metal paste or solder typically made of highly conductive metals like gold, silver, or indium in order to minimize contact resistance. The reason for the four probe measurement as opposed to a two-probe measurement (i.e. combination of current source and voltage measurements on the same probe) is to prevent the input resistance of the current source from drawing a voltage itself. By isolating the voltage contacts, this insures that the voltage measured provides a more accurate relation to Ohm's law, V = IR. In order to go from voltage drop across the probes to resistivity, one must know the current used in the measurement to get the resistance. From there the length and cross section of the crystal is used to calculate the resistivity as shown in equation 2.24, where A is the

Figure 2.7 Wiring diagram for the four point probe method, showing the contacts on a piece of material.

(2.24) cross section of the crystal and l is the length between the voltage probes. While resistivity can be plotted against a number of independent variables, the only such measurement done in this work was against temperature.

2.5 Magnetic Measurements

In this work we are studying materials that are semiconductors or metals, and contain transition and rare earth metals. We also look at superconductors, which will be discussed in a later chapter. A variety of magnetic susceptibilities will be encountered, including the susceptibility of the core diamagnetism of the atoms themselves, paramagnetism of conduction electrons, as well as behavior which results from unpaired electrons in d and f orbitals. All atoms display an internal diamagnetic behavior due to an induced current that persists in the presence of an applied field due to the electronic shielding of the nucleus by electrons. This is typically explained by the Larmor theorem which states that additional movement of electrons around the nucleus will be induced by the applied field as stated in equation 2.25,

(2.25)21 where is the angular frequency, e is the charge of the electron, B is the total magnetic field. The additional induced current is given in equation 2.26, where Z is the number of electrons

(2.26)21 around the atom. The corresponding magnetic moment based on a current loop with an area of is shown in equation 2.27. In a solid this individual atomic result becomes complicated and

(2.27)21 susceptibility is calculated per unit volume as is shown in equation 2.28, where n is the concentration of atoms per unit volume and is the permeability of free space which is a (2.28) the magnetic constant with the value of 4×It is important to denote that diamagnetism is a weak negative susceptibility on the order of 10-6 emu·mol-1 The rest of the magnetic phenomena to be discussed in this chapter have to do with unpaired electrons in the material. Typically unpaired electrons are found in metals, as well as compounds containing transition and rare earth elements. All materials exhibit the previously mentioned diamagnetic contribution, but it is typically overshadowed by the paramagnetic or positive magnetic susceptibility contributions. Non-interacting localized electrons exhibit Curie-Weiss behavior. The electrons may interact at extremely low temperature; however if we look at the area where the temperature energy is much greater than the electron interaction energy, kBT >> the electrons can be viewed as noninteracting. The interaction energy in this case is -·for each moment in the system. Since each spin is independent of each other and the temperature is high enough that the field has little effect on the spin orientation, we get a net magnetization in the direction of the field as shown in equation 2.29, where N is the number of spins. The cosine function in brackets signifies that it is (2.29)26 the thermodynamic average value. Since this is a fairly standard statistical thermodynamic calculation, the result is given in equation 2.30. The corresponding magnetic susceptibility is

(2.30) given in equation 2.31, the Curie Law, which results naturally from the derivative of the

(2.31)

22 magnetization with respect to field at constant temperature. The molar magnetic susceptibility can be calculated, giving equation 2.32. From this we can calculate the magnetic moment per

(2.32) mole in Bohr magnetons of the material, as shown in equation 2.33, where C is the Curie

(2.33) constant, which gives a value that can be compared to theoretically expected values in literature.21,26 From equation 2.33 we see that the molar susceptibility is an inverse function of the temperature. It is customary to plot 1/m vs. T which allows for fitting with an equation of the form in equation 2.34, where the magnetic moment can be calculated from m as shown in (2.34) equation 2.35 where the plot shows a linear function, and is best interpreted at higher

(2.35) temperatures well above any apparent ordering interactions. The Bohr magneton values that are calculated in equation 2.35 are typically compared to known experimental values for different atoms. The atoms that have localized electrons are typically those in the d and f blocks of the periodic table. Tables of theoretical and measured values for various atomic configurations can be found in various textbooks. It is important to note the type of material being studied. Rare earth electrons typically behave as expected due to the contracted f-orbitals that do not participate in chemical bonding, and hence tend to be truly localized. D-block elements on the other hand are susceptible to crystal field splitting and Jahn- Teller distortion which distorts degeneracy of the d-orbitals and tend to negate the effects of spin-orbit coupling. They also have a greater tendency to interact to form bonds, which may lead to itenerant magnetism of electrons in d-orbital derived bands.21

At temperatures where kBT is not much greater than electron interaction energy of a material then magnetic ordering of the electrons may be observed. Typical magnetic ordering phenomenon that might be encountered at lower temperatures are antiferromagnetism and ferromagnetism. These ordering transitions are driven by magnetic coupling interactions between

23 localized spins. The presence of these coupling forces was ignored in the previous derivations. Taking these forces into account, the Curie Law can be modified as shown in equation 2.36. In this arrangement the denominator contains an extra term the Weiss constant, which typically

(2.36)21

reflects the interaction strength. This modification also means that the plot of 1/m vs. T is more like equation 2.37, where the extra C term is analogous to an “x-intercept”. Figure 2.8 shows the two cases where is either negative in the case of antiferromagnetism, or positive in the case

(2.37)

of ferromagnetism. In the case of a ferromagnetic interaction  is often similar to TC, the Curie temperature, which is the temperature that a spontaneous alignment of the spins occurs under an applied magnetic field. Plots of real data are not as simple as what is shown in figure 2.8. In most materials, if magnetic susceptibility data is collected is collected at low enough temperatures then low temperature interactions will obstruct the Curie-Weiss behavior. It is therefore

Figure 2.8 Simple illustration of the temperature intercept for Curie Weiss plots.

customary to only make a plot of 1/m vs. T using the data in which Curis-Weiss behavior is followed, then use a linear fit of the data to extrapolate the point at which the data would intercept the temperature axis.

These interactions require proper experimental technique in order to be properly observed. Due to the nature of the instrumentation used to perform magnetic susceptibility measurements, it is often necessary to center samples between the pickup coils at temperatures where electron interactions occur, and since the only way to elicit a signal for this technique is to apply a magnetic field, a sample could be put in a ferromagnetic or other type of interacting state. It is therefore common to warm the sample to room temperature after centering it, before cooling it back down to low temperature before starting to record data. The process of cooling the sample without applying an external magnetic field is known as zero field cooling (ZFC), and the process of cooling the sample while an external field is applied is known as field cooled (FC). For most basic magnetic susceptibility measurements the proper way to perform the experiment is under ZFC conditions. Ferromagnetism is typically observed as a spontaneous jump in the susceptibility at a particular temperature, the Curie temperature (TC), when measured from low temperature to high

27 Figure 2.9. Magnetic hysteresis plot for Co7(TeO3)4Br6, which is representative of a typical ferromagnet.

temperature. A feature of ferromagnetism known as hysteresis can be observed by measuring the susceptibility with respect to field. A typical hysteresis loop is shown in figure 2.9. The width of the field in which it takes to flip the spins in the material is the coercivity, which is a measure of

25 the ferromagnetic strength. The loop is actually recorded across five quadrants, with the data from the first quadrant typically being omitted, as the sample is being magnetized in the first step; though Figure 2.9 does include the measurement of the initial quadrant. Antiferromagnetism is typically observed as a hump, or susceptibility maximum at low temperatures followed by Curie-Weiss behavior at higher temperatures. The temperature where 21 the maximum occurs is known as the Neel temperature (TN). An additional property that must be considered in this work, since the materials studied were metals, is that the d-orbitals participate in bonding, and therefore form bands. We must therefore take into account the effect of conduction electrons, which further reduces the localized behavior of the d-block electrons. Pauli paramagnetism, or the susceptibility of the conduction electrons in a metal, is a temperature independent positive susceptibility of order 10-4 emu/mol that is explained by a combination of the theories used in the thermal conductivity of conduction electrons and Curie-Weiss behavior to give equation 2.38. The equations shows that the value of

(2.38)21 the Pauli paramagnetism is essentially proportional to the density of states at the Fermi level.16 It is important to note that in real materials these phenomena can occur concurrently, and can be difficult to distinguish from magnetic susceptibility measurements alone. The susceptibility of any given material is the sum of all the individual susceptibilities. For example, since metals were studied in this work, sometimes the Pauli susceptibility and the Curie-Weiss susceptibility can mask each other, and hence it is not uncommon to deconvolute the two contributions with a software fitting program. Equation 2.39 shows how this can be done. Since

(2.39) the core diamagnetism contribution is generally orders of magnitudes smaller than other susceptibilities, it is often ignored.

2.6 Nuclear Magnetic Resonance Spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy takes advantage of the interaction of energy with the magnetic moment (spin) of the nucleus. Nuclear spin varies from nucleus to

26 nucleus, but is quantized, and always a half integer multiple value of ħ. The ability to carry out an NMR experiment will depend on the natural abundance, nuclear spin values, nuclear magnetic moment, and magnetogyric ratio of the nucleus that is to be studied. If a nucleus has a nuclear spin state of zero it is impossible to do NMR spectroscopy on that particular nucleus. This information, combined with information about the state and structure of the sample will determine what type of experiment will be conducted. Most NMR spectrometry is done on organic molecules that are dissolved in solvent; protons are typically the nucleus of interest. These experiments are used mainly as a tool to deduce structure and purities from the products of an organic synthesis. In this work the samples that were studied were solid intermetallics, which make the NMR experiments more difficult. NMR samples are placed in the center of a magnet, which splits the energy levels of the nucleus into 2I+1 states where I is the spin quantum number. The populations of the various energy levels within the magnetic field at equilibrium are estimated from the Boltzmann distribution which is given in equation 2.40. The distribution is usually shown as ratio between two energy levels, N1 and N2, where N is the population of the spins at that energy level. At

(2.40)28 infinitely high temperatures, all the energy levels are equally populated, whereas at absolute zero only the lower energy level is populated. The energy under an applied magnetic field is the interaction of the component of the nuclear magnetic moment that is parallel to the direction of the applied magnetic field, typically labeled as the z-direction, and the applied magnetic field strength. For any system the lowest level has an energy of -zH, while the energy of the highest level is zH, where µz is nuclear magnetic moment in the z-direction and H is the applied magnetic field strength. The separation between the energy levels of any system is zH/I. The spin system is constantly precessing with respect to the applied magnetic field28 In order to get a signal for NMR, energy in the radio frequency (RF) range is directed at the sample through a probe, which contains the RF signal transmission and receiving coils, in order to induce a spin transition from a lower energy level to a higher energy level. Therefore, the strength of the signal depends on the population of the lower energy levels as opposed to the higher levels, prior to radiating the sample with RF energy. There are two ways to increase the population ratio. One way is to lower the temperature; however the equipment to do this is both

27 costly and requires a lot of care. The second way is to apply a stronger magnetic field, and increase the separation between the energy levels. Modern spectrometers utilize superconducting magnets, which produce one particular field strength. This static field will produce a characteristic resonance frequency for a 1H nucleus; this frequency is also used to denote the strength of the spectrometer. For example, a 500 MHz spectrometer means that magnetic field strength of the magnet is about 11.74 tesla. This calculation can be done for any spectrometer using the Larmor equation in equation 2.41 and using the magnetogyric ratio for a proton.

(2.41)28

Subsequently, the resonance frequency for any other nuclei can be calculated for a particular instrument by using its magnetic field strength and the magnetogyric ratio for the nucleus being studied.28 Once a sample is in the magnet all of the nuclei will approach equilibrium according to the Boltzmann distribution and there will be a net alignment with the magnetic field of the spectrometer. In order to induce a spin transition, RF energy at a frequency tuned to interact with the nucleus under study is directed at the sample which moves the nuclear spins of interest out of equilibrium. This is due to the fact that the field from the external magnet is constantly moving the spin system back towards equilibrium. The spin system is also always rotating with respect to the axis of the external field as the system moves toward equilibrium, which is a process known as precession.28 The total process in which the spin system goes back to the equilibrium position is referred to as a relaxation. Typically, the dominant relaxation process is referred to as T1 relaxation, or spin-lattice relaxation. The spin-lattice relaxation is the method by which the spin system relaxes by transferring the energy gained from the RF pulse to the lattice in order to go back to the equilibrium position. The samples presented in this work were metallic, so the dominant relaxation process was likely the nuclear spins transferring their energy to the conduction electrons. Since this process is quick, as opposed to other dominant mechanisms found in non-conducting solid samples, this work simply utilized direct observation techniques, as opposed to cross polarization or other special NMR techniques. For comparison it should be noted that liquid or dissolved samples have quick T1 relaxation times due to being able to rotate

28 freely and transfer the RF energy to the solvent or sample itself. Since solid samples cannot rotate, this slows the relaxation process significantly.28 Once the sample is positioned in the center of the magnet, and all of the final probe tuning procedures have been completed. RF energy with the frequency of the nucleus of study is directed at the sample, while a large bandwidth is recorded in order to detect the signal. Keeping in mind relaxation time, repeated experiments are performed and the signal is essentially zoomed in on, recording only the stretch of bandwidth necessary to get whole signal and maximize the signal resolution. The spin system is usually represented with a 3-D axis system as shown in figure 2.10, where the equilibrium is shown to be along the z-axis, which is also the 0º pulse position. The NMR spectrometer utilizes a phase sensitive detector along the xy-axis to pick up the nuclear spin signal. In order to produce an NMR signal the NMR pulse must essentially move the spin to the 90º mark using what is referred to as a 90º pulse. The phase sensitive detector records a signal as long as the spin has a magnitude in the xy-axis. A 90º pulse time is generally found by

Figure 2.10 Spin axis system, where the thick arrow denotes the direction of the nuclei being studied.

finding the 180º pulse time and then halving the time of it. Typically, a series of different pulse times are tested out to see the progression of the magnitude of the spin in the xy-plane. A series of signals like the one in figure 2.11 is produced, and the pulse time is carefully found for the 180º pulse. The reason this is done is because it is easier to find no signal, as opposed to the absolute maximum. 29

It is important to find the T1 relaxation time of the sample in order to maximize the efficiency of collecting the best possible spectrum in least amount of time, as well as utilize the

T1 value to asses certain physical properties of the sample. In a typical pulse sequence there is a delay time between each measurement which is supposed to be of a duration 5 times the T1 relaxation time. The T1 relaxation time is essentially used as a measure of the rate of system relaxation, however after such a time, only about 63% of the nuclear spins are actually back at

Figure 2.11. Plot of signal versus pulse times used to find the 180o pulse time.29

28 equilibrium. At 5 times T1 roughly 99% of the spins are back at equilibrium. The T1 time is typically found by using the inversion recovery technique, where a 180º pulse is followed by a first delay time, then followed up by a 90º pulse, and lastly a very long second delay time. This pulse sequence, as shown in figure 2.12, is repeated with the first delay time going from very short to longer, with a range of signals like that shown in figure 2.13. The first signals produced in the series have a negative magnitude. These correspond roughly to 270º pulses, in which the spin magnitude still has a net component in the xy-plane, but are precessing 180º out of phase with a 90º pulse.

Figure 2.12. NMR pulse sequence used to find the T1 relaxation time.

The T1 relaxation rate is essentially the rate of change of the magnitude of the spin system along the z-axis, where the 90º pulse in the inversion recovery sequence basically moves the nuclei at the equilibrium position to the xy-plane. Therefore, the final signal produced in the

Fig 2.13. Plot of signal vs. delay time (d1) used to find the T1 relaxation time for Ba2In5P5 at 248.15 K.

series should be equivalent to applying a 90º pulse after which all of the nuclei have reached equilibrium. This relaxation process is a first order process, such that equation 2.42 represents (2.42)28 the rate of change of the magnitude of the spin system along the z-axis; where Mz is the variable magnitude, M0 is the equilibrium magnitude, k is a proportionality constant, and t represents

31 time. When integrated with respect to the magnitude and time, as well as setting k equal to 1/T1 you get equation 2.43 which represents the exponential growth of the spin magnitude with

(2.43)28 increasing first delay time. In an actual experiment, a plot of the amplitude against the first delay time is made and the curve is fitted to equation 2.42.

Utilizing the proper T1 technique in itself does not guarantee success, as peak broadening can hamper the acquisition of clean signals. In samples, there exists a spatially dependent dipolar coupling interaction of which the properties follow the physics of a textbook magnetic dipole- dipole interaction. The part of the overall Hamiltonian pertaining to the scenario between two isolated spin 1/2 nuclei under an applied external magnetic field along the z-axis is given in equation 2.44. 1 and 2 are the two magnetogyric ratios of the two nuclei, and m1 and m2 are the

(2.44)28 respective magnetic dipole moments of the two nuclear spins. The two important parts of this equation are the angle dependence, and the dot product of the two nuclear spin magnitudes. The effect of this interaction results in line broadening, which may obscure the peak structure in the NMR signal.28 The dot product of the magnetic dipole moments between two spin 1/2 nuclei is a special case where the angle dependence becomes the dominant part of the equation, whereas in the case where one or more nuclei are quadrupolar, the directionality of the magnetic dipole-dipole interaction may no longer be along the direction of the external applied field. In the case where the angle dependence is dominant, the dipolar interaction can be removed by rotating at the angle at which the angle dependent term goes to zero, which occurs at 54.74º. In cases with quadrupolar nuclei, the directionality of the magnetic dipole-dipole interaction may prevent the ability to remove such interactions.28 One more line broadening factor is the chemical-shift interaction. Electronic shielding of the nucleus is not always isotropically distributed, and therefore the alignment of the molecular or crystalline axis with respect to the axis of the external applied magnetic field can have an effect on how the nuclei precess back to equilibrium. This is more of a problem for solid samples with multiple peaks or powders where the broad distribution of chemical orientations produces

32 multiple chemical shifts within close range of each other. Multiple site occupancies usually produce more than one peak, and depending on the electronic conditions of each site, these peaks may also run together. They are often able to be distinguished qualitatively, but integration is usually impossible, although certain software packages may be able to deconvolute the peaks and provide a usable estimate. In the case where a nucleus is shielded anisotropically, an asymmetric signal is collected. The sum of all the chemical-shift interactions in a material can be represented by the Hamiltonian in equation 2.45, where σZZ is the chemical-shift tensor. The chemical shift (2.45)28 tensor is given in equation 2.46, the individual σ’s are the principal values of the chemical-shift (2.46)28 tensor along the fixed axes in the material, while the ’s are the direction cosines of the fixed axes in the material with respect to the external magnetic field.28 In liquids or dissolved samples free rotation contributes to the ability to obtain a signal with time averaged chemical-shift interactions due to molecular tumbling, giving isotropic signals that are relatively easy to interpret. This tumbling also shortens the T1 relaxation time, which helps reduce line broadening, and allows for more experiments to be done in a shorter period of time. Anisotropic chemical-shift interactions in solids provides additional challenges, and while it is possible to do NMR spectroscopy on a single crystal, in which case the chemical shift anisotropy can be controlled and evaluated; it is not always a useful technique, because a 100 mg single crystal is often difficult to attain. Therefore, it is most common to do NMR spectroscopy on powder samples, and since all crystal orientations will then be present, they will give an isotropically averaged signal. The isotropic signal in liquids is simply a natural byproduct of the free rotational motion, opposed to solids which do not rotate freely, but in a way can be rotated artificially. In order to simulate free rotation of materials and gain a more isotropic chemical-shift interaction, magic angle spinning (MAS) was developed in order to simultaneously remove dipolar coupling and reduce broadening from the chemical-shift interaction by giving an isotropically averaged signal. MAS-NMR involves filling a rotor with the material being studied and then spinning it rapidly with a compressed gas, while aligned at a 54.74° angle with respect to the external magnetic field.28

Rotors are essentially hollow tubes made out of a special material. It is best to use a rotor made of a material that does not contain the nucleus being studied in order to avoid conflicting signals. Common rotor materials are Al2O3, BN, and ZrO2. These materials do not deform when spun, and can withstand wear and tear well. On each end of the rotor are caps to hold in the material and help stabilize the spinning at the high speeds that are used, with the cap on the side towards the gas-jets typically having fins in order to facilitate spinning. A rotor and an end cap for the gas-jet side is shown in Fig. 2.14. The rotor is placed in a stator for spinning, which is

Fig. 2.14 Picture of solid-state NMR rotor and end cap showing fins used for spinning.

typically attached to the top of the probe. The stator houses the gas-jets, and provides a housing so that the rotor can spin rapidly with little turbulence.28 Turbulence must also be avoided by careful sample preparation. In some cases it may be possible to perform MAS-NMR on a single crystal or nicely shaped object for study, but in general powders are what are studied with this technique. Powders must be finely ground and tightly packed into the rotor in order to ensure that the sample remains in place during spinning. If there is not enough material to fill the rotor then either the sample must be mixed with an innocuous additive or spacers can be used to fill the extra rotor space. In the case of this work an ionic salt was mixed in with a metallic sample to facilitate spinning, as the conduction electrons may produce eddy currents in response to the external magnetic field, which could counteract the

34 spinning of the rotor. There is generally an area in the middle of the rotor that receives the most homogenous RF pulse, so it is important to fill at least this area with material for study. While MAS-NMR decreases the amount of peak broadening, it does have one drawback. The direction cosines in equation 2.45 have a time-dependent component, and upon spinning, spinning sidebands can arise. If the spinning rate is not faster compared to the frequency width of the anisotropic chemical-shift interaction then the direction cosines become time-dependent and the result is additional peaks on either side of the main isotropically averaged peak that are spaced at the spinning speed of the rotor. The only way to remove sidebands is to spin the rotor fast enough that they do not appear. In order to spin the rotor faster safely, smaller rotors are used. Using a smaller rotor has the drawback of containing less sample for study, which results in a weaker NMR signal overall. It is up to the experimenter to determine whether or not using more or less material, or spinning at higher or lower speeds provides any reasonable trade-off when in most cases NMR experiment time is at a premium. It is therefore common and acceptable for sidebands to appear in published literature despite their unwanted nature.

MAS-NMR was used to study the Ba2In5Pn5 (Pn = P, As) Zintl phases in chapter 3 due to the fact that resistivity measurements performed on the Ba2In5Pn5 (Pn = P, As) Zintl phases indicated that these compounds were metallic. As Zintl phases are expected to be semiconductors, MAS-NMR was used as a secondary verification of the phases' metallic properties. It was also scientifically interesting as Zintl phases have little history of study by NMR. The verifications of the metallic behavior was done by observing the Knight Shift of the material and showing that the materials satisfied the Korringa Relation. The Knight Shift is named after Walter Knight, who observed that copper NMR signals occurred at different frequencies depending on whether the signal was obtained from copper metal or copper (I) chloride. In particular, the peak from the metallic copper occurred at a frequency 0.23 percent higher than of the peak from CuCl. This property was found to occur for all metals when compared to diamagnetic compounds containing the metal. The Knight Shift has typically been measured in frequency by physicists, but as more chemists do NMR work, ppm is becoming the more common unit of measure for chemical shifts. The units of ppm are also more convenient as they hold the same value regardless of the strength of the external magnetic field used in the experiment. They make more sense for the recording of Knight Shifts as ppm is a fractional unit of measurement which helps to make sense of the values obtained for Knight

Shifts. The units of ppm are obtained by taking the measurement of interest in Hertz and then dividing by the magnet strength in MHz, hence giving parts per million as ppm suggests.30 Knight Shifts follow a number of observable rules. The frequency shift of a metal relative to diamagnetic reference compound is always positive. The fractional Knight Shift is both field and temperature independent, and is larger depending on the atomic number of the nucleus being studied. These properties arise from the hyperfine interaction between the nuclei and the conduction electrons in the material. The overall Hamiltonian consists of three interactions and is given in equation 2.47. Assuming that the interactions between the nuclei act to add an additional (2.47)30 magnetic field to the environment, and assuming that electrons are noninteracting with each other, a Hamiltonian that represents this hyperfine interaction is presented in equation 2.48. Of interest here is the delta function which involves the positions of electrons relative to the (2.48)30 nuclei. Given that this interaction is weak, only electrons that reach the site of the nucleus, s- electrons, have an effect on the Knight shift. In conjunction with with the Fermi-Dirac function, only the electrons at the Fermi level participate in conduction giving equation 2.48, which is the overall simplification of equation 2.49 for each individual nuclear spin. The compound effect on (2.49)30 each nucleus gives the shift from the additional field, and the final equation for the Knight shift 2 is given in equation 2.50. In this equation the term |uk (0)| which represents the density of (2.50)30

S electrons at the Fermi level, which is temperature independent for “good” metals, and e is the susceptibility of the conduction electrons.30 The Korringa relation has to do with the number of nuclear transitions per second that occur from the time the RF pulse is turned off to the time that the nuclei in the system of study return to the equilibrium state. In the case of a metallic solid as studied in this work, the number of nuclear transitions per second is based on the transfer of the nuclear energy to the conduction electrons, which results in the scattering of the conduction electrons. The main interaction equation is given in equation 2.51. Again, the elections which participate in this interaction are

(2.51)30 the ones at the Fermi level, as well as the ones with significant s-state character. This interaction equation is part of a larger equation that represents the number of nuclear transitions per second.

This larger equation is given in equation 2.52, where Wmks,nk's' represents the number of transitions per second . This equation is only concerned with the transfer of energy from the nuclei as they go through an energy transition and transfer it to the electrons to scatter them. (2.52)30

Assumptions for this equation include the system being in thermal equilibrium such that the system can be represented by a finite temperature T, allowing for the use of any of the major physical statistical models that utilize exponential functions. This allows the system to be represented by a single exponential function, as opposed to using quantum mechanical calculations which require each interaction to be described by separate equations. This assumption is valid when the individual interaction energies are much less that of the temperature energy, and the transfer of energy between the spins are more rapid than the transition of energy to the lattice. This allows the number of transitions per second to be computed with a simple Boltzmann-like expression. Add this to the fact that only conducting electrons within kBT can participate in the scattering process, and the final equation that describes the Korringa Relation is given in equation 2.53. Substituting this equation with the

(2.53)30 equation for the Knight shift , equation 2.50, then simplifies it even more as shown in equation

2.54. In this equation we get an inverse relationship between the T 1 relaxation rate and

(2.54)30 temperature. Everything else such as the fractional shift and the number of electrons at the Fermi level are temperature independent.30

Experimentally, the T1 relaxation rate is found at multiple temperatures and then a plot of the inverse of the T1 relaxation rate is plotted against temperature. A metal should produce a linear plot.

CHAPTER 3

FLUX GROWTH AND ELECTRONIC PROPERTIES OF Ba2In5Pn5 (Pn = P, As): ZINTL PHASES EXHIBITING METALLIC BEHAVIOR

3.1 Introduction

Use of molten metal fluxes is an appealing option for exploratory synthesis, as this is a lower-temperature technique that allows for isolation of kinetically stabilized or metastable phases.31 Indium has a low melting point of 157 °C as well as a large difference between its melting point and boiling point, which makes it a viable flux for reaction chemistry, and it can easily be separated from its products through centrifugation. Indium flux reactions have yielded 1,31 metallic phases (YbCoIn5, RCu2Si2, RIn3) as well as semiconductor crystals (Ge, Si, InP). In this work, reactions in indium flux produce materials that seem to bridge these classifications-- Zintl phases that appear to be poor metals. Zintl phases are saltlike compounds in which electropositive metals donate their valence electrons to clusters or networks made up of electronegative metalloid elements that generally come from groups 13-15, but can occasionally include transition metals. They have a well- defined relationship between their chemical and electronic structures as explained by the Zintl- Klemm concept. Because of the fact that that the electropositive element is assumed to transfer all of its valence electrons to the electronegative elements, Zintl phases are considered to be closed-shell compounds.4 They are therefore expected to be diamagnetic semiconductors (with the exception of those containing paramagnetic cations such as europium). A number of exceptions exist; for instance, SrSn3Sb4, Ba3Sn4As6, and EuIn2P2 can be explained in terms of their bonding by the Zintl-Klemm concept, but they have been found to have a weakly metallic resistivity.7,8,32 Metallic behavior is also observed in Zintl phases with small band gaps that are doped by impuritites or slight variations in stoichiometry, such as the clathrate phases 33,34 Ba8Ga16Ge30 and Ba8Al15Si31.

In this chapter, synthesis and properties are described for Ba2In5As5 and Ba2In5P5, two Zintl phases with a new structure type. This structure can be rationalized by the Zintl-Klemm concept, and band structure calculations imply that the materials should be semiconductors.

However, transport measurements indicate metallic behavior. NMR studies of Knight shifts and the Korringa relations, seldom investigated for Zintl phases, also support the classification of these compounds as poor metals. These data are evaluated in light of previous reports on metallic Zintl phases and the potential for doping inherent in the flux growth technique.

3.2 Experimental Section

3.2.1 Synthesis

Ba2In5As5 was originally made in a reaction of the elements Ba, In, Ge, and As in a 0.5:15:1:1 mmol ratio with indium acting as a flux. Starting materials for the preparation of this compound were Ba rods (Acros-Organics, 99+%), In shot (Alfa-Aesar, 99.9%), Ge powder (Cerac, 99.999%), and As powder -20 mesh (Cerac, 99%). Once it was determined that germanium was not incorporated, the reaction was repeated without Ge. Because of the toxicity of arsenic, gloves and masks were used when handling the reactant and the reactions were carried out in a furnace located in a hood. All elements were combined in an alumina crucible with half the indium flux loaded on the bottom and half on top of the rest of the reactants. The crucible was placed in a fused silica tube; another alumina crucible was filled with Fiberfrax ceramic fiber and inverted on top of the reaction crucible in the silica tube to act as a filter during centrifugation. The fused silica tube was sealed under a vacuum of 1 × 10-2 Torr, and then heated to 1000 °C in 10 h, held at this temperature for 48 h, cooled to 850 °C in 150 h, held for 24 h, cooled to 800 °C in 50 h, held for 24 h, cooled to 700 °C in 50 h, held for 24 h, and finally cooled to 600 °C. At this temperature, the silica tubes were removed from the furnace, inverted and quickly placed in a centrifuge to remove excess molten flux from the mass of needle shaped crystalline product. Many of the crystals are covered with patches of indium flux. Small amounts of InAs and barium arsenide phases are also obtained as side products. Elemental analysis was performed on the crystals using a JEOL 5900 scanning electron microscope (SEM) with energy-dispersive spectroscopy (EDS) capabilities. The crystals were mounted on carbon tape and analyzed using a 30 kV accelerating voltage and an accumulation time of 10-20 s. An average of eight crystals gave a rough stoichiometry of Ba1In3As4. Because germanium was not incorporated into the product, the synthesis was done again without this

39 element, heating at 60 °C/h to 1000 °C, holding for 48 h, cooling at 2 °C/h to 600 °C, and then centrifuging.

Ba2In5P5 was synthesized the same way using phosphorus (Alfa-Aesar, 99%) instead of arsenic (Ba:In:P reaction ratio of 0.5:15:1 mmol) and with a modification of the previous heating profile. The reaction tube was heated at 60 °C/h to 500 °C, and held there for 1 h to facilitate mixing; heating continued at 60 °C/h to 1100 °C, where the reaction was kept for 48 h. It was then cooled at 2 °C/h to 600 °C and centrifuged. EDS analysis yielded a rough stoichiometry of

Ba2In7P7 for an average of 5 crystals. Crystals of InP are typically obtained as side-products from this reaction, as well as some as yet unidentified grayish-red powder. Attempts to make these phases from stoichiometric reactions of the elements failed, yielding instead InP and InAs.

3.2.2 Structure Refinements

Samples for X-ray diffraction were selected from the SEM plate after elemental analysis and fragments of the large needle shaped crystals were mounted on glass fibers for diffraction. Single-crystal X-ray diffraction data were collected at room temperature using a Bruker AXS SMART CCD diffractometer equipped with a Mo radiation source. Processing of the data was accomplished with the use of the program SAINT; an absorption correction was applied to the data using the SADABS program.35 Refinement of the structure was performed using the SHELXTL package.36 The crystallographic data is summarized in Tables 3.1 and 3.2. Additional details regarding the crystallographic refinements can be found in the Supporting Information. Powder X-ray diffraction data was collected on several samples using a Rigaku Ultima III Powder X-ray diffractometer with a Cu radiation source and a CCD detector.

Table 3.1. Crystallographic Data for Ba2In5Pn5 Phases

Ba2In5P5 Ba2In5As5 fw (g/mol) 1003.63 1223.38 space group Pnma Pnma a (Å) 17.257(3) 17.461(2) b (Å) 4.1599(6) 4.2905(4) c (Å) 17.490(3) 17.961(2) V (Å3) 1255.5(3) 1345.6(2) 3 dcalcd (g/cm ) 5.31 6.04 Z 4 4 T (K) 298 298 radiation Mo Kα Mo Kα

2θmax 56.56 56.62 index ranges −22 ≤ h ≤ 22 −23 ≤ h ≤ 23 −5 ≤ k ≤ 5 −5 ≤ k ≤ 5 −22 ≤ l ≤ 23 −23 ≤ l ≤ 23 no. of reflns collected 16 653 17 871 unique data/params 1770/73 1894/74 (mm−1) 15.8 26.3

R1/wR2* (I > 4σ(Fo)) 0.0376/0.0690 0.0390/0.0844

R1/wR2 (all data) 0.0464/0.0718 0.0404/0.0850 residual peaks/hole 2.13/−1.4λ 5.3λ/−1.λ1 2 2 2 2 2 1/2 * R1 = ∑(|Fo| − |Fc|)/∑|Fo|; wR2 = [∑[w(Fo − Fc ) ]/∑(w|Fo| ) ] .

* Table 3.2 Atomic Positions for the Ba2In5Pn5 Phases ** atoms x y z Ueq

Ba2In5P5 Ba1 0.01951(4) 1/4 0.62099(4) 0.0095(1) Ba2 0.04209(4) 1/4 0.12983(4) 0.0134(2) In1 0.15747(4) 1/4 0.81018(4) 0.0099(2) In2 0.31328(4) 1/4 0.77710(4) 0.0095(2) In3 0.17218(4) 1/4 0.44118(4) 0.0103(2) In4 0.33002(4) 1/4 0.47180(4) 0.0103(2) In5 0.28948(4) 1/4 0.12583(4) 0.0087(2) P1 0.1044(2) 1/4 0.3087(2) 0.0086(5) P2 0.3852(2) 1/4 0.0113(2) 0.0079(5) P3 0.3919(2) 1/4 0.2354(2) 0.0088(5) P4 0.5834(2) 1/4 0.5589(2) 0.0090(5) P5 0.3023(2) 1/4 0.6253(2) 0.0083(5)

Ba2In5As5 Ba1 0.02046(4) 1/4 0.62073(4) 0.0116(2) Ba2 0.04258(4) 1/4 0.13045(4) 0.0150(2) In1 0.15773(5) 1/4 0.81209(2) 0.0128(2) In2 0.31191(5) 1/4 0.77898(5) 0.0125(2) In3 0.17319(5) 1/4 0.44182(5) 0.0129(2) In4 0.32928(5) 1/4 0.47149(5) 0.0132(2) In5 0.28915(5) 1/4 0.12686(4) 0.0094(2) As1 0.10370(7) 1/4 0.30931(7) 0.0104(3) As2 0.38575(7) 1/4 0.01156(7) 0.0092(3) As3 0.39297(7) 1/4 0.23718(7) 0.0103(3) As4 0.58216(7) 1/4 0.55705(7) 0.0101(3) As5 0.30407(7) 1/4 0.62603(6) 0.0088(3) * All atoms are on 4c Wyckoff sites.

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

3.2.3 Differential Scanning Calorimetry−Thermogravimetric Analysis (DSC−TGA)

DSC−TGA for Ba2In5P5 and Ba2In5As5 were performed using a TA instruments SDT 2960 Simultaneous DSC−TGA. A total of 30–40 mg sample masses of single crystals were

42 placed in alumina sample containers; an empty alumina sample container was placed on the reference side of the detector. Each sample was heated under a N2 gas stream to 1100 °C at 10 °C/min and held there for 5 min, followed by cooling at −10 °C/min to room temperature. After the analysis, the solid in the sample container was removed, ground to powder, and analyzed using powder X-ray diffraction.

3.2.4 Resistivity Measurements

DC conductivity measurements were performed on a Quantum Design PPMS. The surfaces of the crystals were carefully scraped to remove excess indium (attempting to remove the indium with an acid etch led to dissolution of the crystals). Contacts were made with gold wire and silver paste in a standard four-probe configuration along the b-axis of the crystals. The dimensions of the Ba2In5As5 and Ba2In5P5 crystals were 1 × 0.013 × 0.018 and 1 × 0.020 × 0.024 3 mm , respectively. A current of 200 and 2500 Α was used for Ba2In5As5 and Ba2In5P5, respectively. The measurements were run from 1.9 to 317 K. Minor kinks in the data around 250−260 K were seen in several samples and appear to be an artifact of annealing of the silver paste. No structural transitions for the title compounds were apparent in diffraction data taken in this temperature range.

3.2.5 Nuclear Magnetic Resonance

Magic angle spinning (MAS) NMR data were collected on a Varian Inova 500 widebore spectrometer. In an argon-filled drybox, crystals of Ba2In5Pn5 phases were ground with KBr in 50:50 mixtures by volume to facilitate spinning; these mixtures were packed into 4 mm zirconia rotors sealed with airtight screwcaps. In between measurements the filled rotors were stored in 115 the drybox. The external references used were 0.1 M aqueous In(NO3)3 for In (I = 9/2, 95.84% abundant) and 15 M phosphoric acid for 31P (I = 1/2, 100% abundant). Data was collected at room temperature and a spinning rate of 5kHz, using a one-pulse sequence (pulse length 5 s and relaxation delay 500 ms). 31 The temperature dependence of the P T1 relaxation time of Ba2In5P5 was investigated to further explore the possibly metallic nature of the material by determining if the Korringa

43 relation was followed. T1 values were measured using the inversion recovery method. Data was collected over a temperature range from 144.9 to 323.2 K with a spinning rate of 5 kHz. During variable temperature operation of the spectrometer, the temperature controlling gas as well as the MAS probe is run completely with nitrogen (as opposed to air under normal conditions) in order to achieve low temperatures as well as prevent oxidation of sensitive electronics at high temperatures. To maintain proper temperature equilibration, we performed constant flow rate monitoring.

3.2.6 Electronic Structure Calculations

Density functional theory-based electronic structure calculations were performed on both compounds using the linear muffin tin orbital method within the local spin density approximation.37 Atom positions from the experimental crystal structures were used as inputs for the calculations, which were performed on a 4 × 12 × 4 k-point grid (63 irreducible k-points).38

3.3 Results and Discussion

3.3.1 Synthesis

Flux synthesis in an excess of indium seems to be required to isolate the title phases. Stoichiometric reactions led to indium phosphide or indium arsenide as predominant products, with no evidence of the Ba2In5Pn5 phases in the powder XRD patterns. The failure of stoichiometric synthesis is evidence that these phases are metastable or peritectic in nature; this is also indicated by their melting point behavior (vide infra). Flux synthesis is known to facilitate the isolation of such materials.1,2 InP and InAs are also produced in the flux syntheses, comprising up to 30−40% of the solid product; the triangular crystals are easily distinguishable from the needle shaped Zintl phase crystals. In the arsenide synthesis, use of higher soak temperatures (1000 °C) seems to promote formation of more of the Zintl phase and less InAs (5–

10% of the solid product). A possible byproduct that was surprisingly NOT seen is the BaIn2P2 Zintl phase reported by the Kauzlarich group.39 That compound was also synthesized in In flux, but the reaction ratio was more indium-rich (Ba:In:P mmol ratio of 3:110:6, compared to the

44 ratio used in our work of 0.5:15:1 mmol, which corresponds to 3.7 : 110 : 7.3). In addition, the temperature profile was different, with the Kauzlarich synthesis heating to a maximum temperature of 1100 °C and centrifuging at 900 °C, compared to the lower temperatures used in this work (maximum temperature of 1000 °C and centrifuging at 600 °C). These variations in the synthesis procedure are apparently sufficient to shift the reaction toward the Ba2In5P5 product instead of the BaIn2P2 compound.

The Ba2In5Pn5 compounds form as very thin silvery needles with metallic luster. In crystalline form they are somewhat stable to water and dilute acids due to formation of an oxide coating, indicated by a reddish coloration on the crystal surface. In powder form, the phosphide compound degrades in air rapidly; the arsenide is more robust. Ba2In5P5 is stable under nitrogen until about 900 °C when the mass of the sample began to decrease slightly, possibly due to evaporation of excess indium flux coating the crystals. At 935 °C the melting point is reached. A recrystallization is seen at 902 °C; however, the XRD pattern of the product after this process indicates a mixture of predominantly InP and In metal. The compound is therefore incongruently melting. Ba2In5As5 appears to melt at 889 °C, again accompanied by crystallization at 863 °C into InAs and other unidentifiable phases. Syntheses of analogues with divalent metals Sr and Eu were explored, as was replacement of phosphorus and arsenic with the heavier elements in the pnictide family.

Attempts to make Sr and Eu analogues resulted in phases with the hexagonal EuIn2P2 structure 6 type instead (P63/mmc, a = 4.2055(3) Å, c = 17.887(2) Å for EuIn2As2; a = 4.0896(3) Å, c =

17.783(3) Å for SrIn2P2; and a = 4.2145(7) Å, c = 18.067(6) Å for SrIn2As2). InAs and InP were also observed products. An antimony analogue Ba2In5Sb5 could not be obtained; instead, a highly air-sensitive barium antimonide phase formed.

3.3.2 Structure

The two title phases have a new structure type (shown in Figure 3.1) which can be analyzed using the standard Zintl−Klemm charge balancing rules. The two crystallographically distinct barium atoms donate their valence electrons to the main group element layer. The structure can thus be understood as comprising anionic slabs separated by layers of Ba2+ cations.

In the anionic main group slabs, all of the indium atoms (there are 5 unique In sites; see Table 3.2) have roughly tetrahedral coordination. Because they are bonded to 4 atoms, the In can be

Figure 3.1. (a) Ba2In5Pn5 structure, viewed down the b-axis. Large gray spheres are Ba; small dark blue spheres are pnictogen atoms; and red spheres are indium atoms. (b) Coordination environment of the two barium sites.

can be thought of as In−. Among the five pnictide sites, four of them are in capping sites for the anionic layer, coordinated to 3 indium atoms, and are therefore neutral in the charge counting scheme. The remaining Pn site, Pn(5), is in a very distorted tetrahedral arrangement, bonded to 4 In atoms, and has a +1 charge by the Zintl−Klemm counting rules. The overall charge balancing 2+ − + 0 4− scheme is therefore (Ba )2[(4b-In )5(4b-Pn )(3b-Pn )4] . This structure resembles other Zintl phases comprising similar elements. Many compounds have been synthesized from the combination of a divalent cation (Eu, Ba, Sr), a

46 group III or trielide metal (Ga, In), and a group V or pnictide metalloid (P, As, Sb; use of arsenic is less common presumably because of toxicity). The importance of different synthetic methods is demonstrated by the fact that new compounds continue to be discovered in this phase space. 2+ Materials with a high ratio of M : main group (such as Sr3InAs3, Ba3In2P4, and Ba14InP11) have structures with anionic 1D ribbons of main group elements, usually comprised of trielide 2+ 40 centered tetrahedra (units such as InP4) linked together, surrounded by M cations. Compounds with a lower M2+: main group ratio, such as the title compounds, tend to feature 2D layers or 3D networks of linked main group elements. The structures of EuIn2P2, BaGa2Sb2, and 7,40 Ba4In8Sb16 are shown in Figure 3.2 for comparison. In general, the trielide element is tetrahedrally coordinated, and the divalent metal cation is coordinated by the more electronegative pnictide element. The coordination environment for the two Ba sites in Ba2In5P5 is shown in Figure 3.1. Ba(1) interacts with seven P atoms with bond lengths ranging from 3.226 to 3.275 Å. Ba(2) has a distorted octahedral coordination to six P atoms at longer distances in the 3.24λ−3.3λ8 Å range, with a seventh phosphorus atom at a distance of 3.503 Å (see Table 3.3). The longer distances around Ba(2) reflect the vicinity of this cation to the distorted tetrahedral phosphorus site, which has its own formal positive charge according to the Zintl−Klemm counting rules. Other structural features common to the title compounds and the other II/III/V Zintl phases are trielide–trielide bonds and resulting pentagonal and hexagonal channels in the structure. In Ba2In5Pn5, ethane-like Pn3In−InPn3 linkages are aligned parallel to each other and bridged by pnictogen atoms; this produces hexagonal channels along the b-axis direction. The In−In bond lengths are almost identical in the phosphide and arsenide, ranging from 2.75 to 2.78

Å. The Pn3M-MPn3 unit is also observed in the BaGa2Sb2 and EuIn2P2 structure types, with the latter having a similar In−In bond length to the compounds studied here. Pn3In−InPn3 linkages also form sections of the pentagonal channels of Ba2In5Pn5; these pentagons include the highly distorted tetrahedral Pn(5) site. The distortion is reflected in both the angles and the bond lengths; for instance, most of the In−P bonds in the phosphide compound are in the 2.58−2.62 Å range, but the bonds to the P(5) atom include two longer bonds of 2.662(3) and 2.727(3) Å.

Figure 3.2. Other II−III−V Zintl phase structures. (a) BaGa2Sb2 features pentagonal channels defined by Ga−Ga bonds; the ethane-like building block Sb3Ga-GaSb3 is a common motif. (b) Ba4In8Sb16 structure also features pentagonal channels but these contain Sb−Sb bonds. (c) EuIn2P2 structure features hexagonal channels defined by P3In−InP3 units.

Table 3.3. Selected Bond Lengths (Å)

Ba2In5P5 Ba2In5As5 Ba1−Pn 3.227(2), 3.266(2), 3.272(2), 3.275(3) 3.299(1), 3.336(1), 3.344(1), 3.356(1) Ba2−Pn 3.249(2), 3.307(3), 3.377(3), 3.398(2), 3.329(1), 3.385(2), 3.432(1), 3.438(2), 3.532(2) 3.503(3) In−In 2.750(1), 2.776(1) 2.757(1), 2.777(1) In−Pn 2.579(2) to 2.617(2) 2.6590(9) to 2.695(2) In−Pn5 2.614(2), 2.662(3), 2.727(3) 2.6929(9), 2.751(2), 2.811(2)

3.3.3 Transport Properties

The single-crystal resistivity data for both Ba2In5P5 and Ba2In5As5 show the temperature dependence characteristic of metallic materials (Figure 3.3). The phosphorus analogue has a room temperature resistivity almost an order of magnitude lower than the arsenic phase; ρRT = −3 −3 6.1 × 10 Ω cm for Ba2In5As5 and ρRT = 1.0 × 10 Ω cm for Ba2In5P5. The poor metal nature observed for these materials is unusual for technically charge-balanced Zintl phases, which are normally semiconductors. It is also surprising that the phosphide is more conducting than the arsenide (this was reproducible over several samples); use of a heavier element in a semiconductor usually leads to a smaller band gap and lower resistivity. Indium flux occlusions within the Ba2In5Pn5 crystals or on the surface are evidenced by the observation of traces of

Figure 3.3. Single-crystal electrical resistivity data for the Ba2In5Pn5 phases.

49 superconductivity at 3 K, but it is unlikely that these are acting as complete electrical shorts, given that the measured resistivity above 3 K is much higher than that of metallic indium.

3.3.4 NMR Studies

NMR measurements were carried out to further investigate the electronic properties of the Ba2In5Pn5 materials and determine if the observed conductivity was a result of occlusions or characteristic of the bulk phase. The interaction of conduction electrons with an applied magnetic field produces an extra effective field on the nuclear magnetic moment, resulting in a large paramagnetic shift the Knight shift.41 Likewise, conduction electrons in a metal have a characteristic effect on the temperature dependence of the relaxation of the nuclear spins; this is observed as a linear dependence of the inverse of the spin−lattice relaxation time T1 with temperature T and is known as the Korringa relation.30 The 115In chemical shifts observed for the title compounds (referenced to aqueous

In(NO3)3 at 0 ppm) are 625 ppm for Ba2In5As5 and 799 ppm for Ba2In5P5. The five indium sites in the crystal structure should lead to five peaks in the 115In NMR spectrum (Figure 3.4), but only one broad peak is seen. This is likely due to the large quadrupole moment of indium nucleus and the similar but highly asymmetric sites of the indium atoms in the lattice. The magnitudes of the shifts are smaller than those seen for pure indium metal in bulk or occlusion form (ca. 8000 ppm) and are also well below the values reported for indium intermetallics such as AuIn2, NiIn, and 42-46 Li3In, which tend to range from 3000−λ000 ppm. However, the observed shifts are much larger than the negative values or small positive values seen for ionic indium (as observed for − 41 InX4 ions in solution, where X = halide). Shifts in the 300−800 ppm range have been observed for indium in III−V semiconductors; however, these shifts are very dependent on doping.48,49 The

600−800 ppm range observed for the Ba2In5Pn5 compounds can be roughly assigned to the doped semiconductor/poor metal regime, with the higher shift of the phosphide reflecting its higher conductivity compared to the arsenide. 31 For further characterization, P data for Ba2In5P5 at various temperatures were collected to investigate the Korringa effect. The room temperature 31P resonance is observed at −180 ppm relative to phosphoric acid reference at 0 ppm; this shift remains constant at temperatures ranging from 144.9 to 323.2 K. Again, only one broad peak is observed, although it shows

50 significant asymmetry (Figure 3.5.) This may indicate slightly different chemical shifts for the five phosphorus sites, as would be expected comparing the distorted tetrahedral environment of P(5) to the more regular trigonal environments of the other four phosphorus atoms. The value of

115 Figure 3.4. In MAS-NMR spectra of Ba2In5Pn5, spinning at 5000 Hz.

the chemical shift is close to the range observed for phosphorus in small band gap 50,51 semiconductors such as CdSnP2, ZnSiP2, and Sn17Zn7P22I8 (−30 to −170 ppm). The unusually 31 2 short T1 relaxation time observed for the P nuclei in this material (ca. 1 × 10 ms) is several orders of magnitude faster than normally seen for this nucleus; this is an indication of rapid relaxation caused by conduction electrons. The temperature dependence of this relaxation time is also characteristic of a metal, as it follows the linear Korringa relationship (Figure 3.6). This data also supports the classification of Ba2In5P5 as a poor metal or heavily doped semiconductor.

31 Figure 3.5. P MAS-NMR spectra of Ba2In5P5, spinning at 5000 Hz.

Figure 3.6. Plot of inverse 31P spin−lattice relaxation vs temperature. The linearity of the data agrees with the Korringa relation and indicates that Ba2In5P5 has metallic conductivity.

3.3.5 Electronic Structure Calculations

Band structure calculations were carried out on the Ba2In5Pn5 phases to determine if the apparent metallic behavior is due to structural features or impurities. As shown in Figure 3.7, based on the crystal structure, these compounds are expected to be semiconductors, with a band gap of 0.6 eV for the phosphide and 0.4 eV for the arsenide. This indicates that impurities or structural defects act as dopants and result in the metallic conductivity evidenced in the transport measurements and NMR data.

Figure 3.7. Total density of state calculations for Ba2In5Pn5 phases. The Fermi level is set at 0 eV.

3.4 Conclusion

Although most Zintl phases reported in the literature are by all measures semiconductors, there have been several cases where metallic resistivity was observed. These compounds are either very small band gap semiconductors, doped semiconductors, or true metals. EuIn2P2 has a −3 resistivity of ρRT = 2 × 10 Ω cm and the temperature dependence typical of a metal at high temperatures. However, data at low temperatures makes it apparent that this can be attributed to thermal excitation across a very small band gap.7 Doped semiconducting behavior leading to metallic resistivity data has been observed in some off-stoichiometry or deliberately doped Zintl phases. One example is Eu5In2−xZnxSb6, a zinc-doped variant of the semiconducting Eu5In2Sb6 parent phase.52 Off-stoichiometry is a common occurrence in clathrate Zintl phases; the presence of framework vacancies and small changes from the ideal charge-balanced stoichiometry

Ba8M16T30 (M = trielide such as Al, Ga; T = tetrelide such as Si, Ge) leads to metallic behavior in Ba8Al14Si31 and Ba8Ga16−xGe30+x. These phases can also be deliberately doped to produce 33,34 metallic variants, as in the Ba8Ga16+xSbxGe30−2x series of compounds. On the other hand, the

Zintl phases SrSn3Sb4 and Ba3Sn4As6 are reported as being true metals. Their resistivity is similar to that of the title compounds (in the 1 × 10−3 Ω cm range), also increasing with temperature. But the lack of a band gap in these tin-containing phases is confirmed by DOS calculations and is attributed to band broadening due to the heavy main group elements and structural features that cross-link the channel structures.8,32

The exact nature of the defects that cause metallic behavior in the title Ba2In5Pn5 phases is currently unknown, but it is likely that they are slightly off-stoichiometry, or doped with very small amounts of impurities. Since these compounds were grown from indium flux, the presence of excess indium in the structure, substituting on pnictide sites, is a possibility. The semiquantitative SEM-EDS elemental analysis technique is not accurate enough to determine small stoichiometry variations. The level of substitution is also too low to be seen in the crystal structure refinement. During the final cycles of the structure solution, the occupancies of all the atoms were allowed to vary and did not change significantly from unity. Low levels of doping/substitution would be averaged out in a crystal structure, but might be enough to result in metallic behavior. Flux synthesis as a source of stoichiometry variations has not been greatly investigated. In the case of Zintl phases, such defects are particularly surprising because the products are expected to be charge balanced. However, in several of the aforementioned cases, a certain level of flexibility is available in the anionic framework, allowing for incorporation of different elements (Zn in the Eu5In2Sb6 case, Sb in the Ba8Ga16Ge30 case) as well as vacancies and 33,34,52 substitutions. It is notable that the off-stoichiometry clathrate phase Ba8Al14Si31 is synthesized in aluminum flux, and the doped Ba8Ga16+xSbxGe30−2x series are grown in gallium flux. It is clearly possible that in this work, synthesis in indium flux may have led to

Ba2In5+xPn5−x, a slightly off-stoichiometry metallic variant of the ideal semiconducting phase.

CHAPTER 4

ZINTL PHASE AS DOPANT SOURCE IN THE FLUX SYNTHESIS OF

Ba1-xKxFe2As2 TYPE SUPERCONDUCTORS

4.1 Introduction

Superconductivity is the term related to materials that demonstrate an immeasurable or zero resistance. Superconductivity was first discovered by Kammerlingh Onnes in 1911 shortly after his lab developed the first method for liquefying helium. Upon performing transport measurements at low temperature on mercury he observed a sudden drop to zero in the resistivity at a specific temperature. Upon testing other metals he found that many other metals also had sudden drops to zero in their resistivity at specific temperatures. The temperature at which these materials' resistivities falls to zero is referred to as the critical temperature or TC. TC's for some common metals are 4.15 K, 0.4 K, 3.7 K, 7.19 K, and 9.25 K for mercury, titanium, tin, lead, and niobium respectively. Niobium has the highest TC of all metals, and only about half the metals in the periodic table exhibit superconductivity. Onnes tried to deliberately destroy the effect by doping samples with impurities, only to find that these "dirty" metals still exhibited superconductivity.53 The lack of resistance and the resulting stable current in a superconductor gives rise to the Meissner effect, in which the application of an applied exterior magnetic field is repelled by the superconductor. The Meissner effect is most commonly demonstrated by magnetic levitation, in which a magnet placed on top of a piece of superconducting material will levitate above the superconductor since the magnetic field of the magnet is repelled by the superconductor. In analysis of superconductors, this effect is observed in magnetic susceptibility measurements as a sharp drop in the susceptibility as the sample is cooled below its TC. Below this temperature, the compound is strongly diamagnetic, since the superconducting electrons are paired (these are referred to as Cooper pairs).53 Superconductors can only expel an external magnetic field to a certain extent, however, and as a consequence can only tolerate so much of a current as well. This gives rise to the commonly measured quantities Tc, Bc, and Ic; the critical temperature, critical magnetic field, and

55 critical current respectively. These values have come to be measures of strength of various superconductors. Superconductors also come in two types, type I and type II. Type I superconductors are typically elemental metals. Therefore, most superconducting compound materials are type II superconductors. Type II superconductors range from doped elemental metals (dirty metals) to alloys, intermetallics, and certain ceramic materials. Type II superconductors consist of the purely superconducting state as described earlier, as well as a normal state where the material is not superconducting at all. The difference in these materials is that as they transition from the superconducting state to the normal state by way of the vortex state. The vortex state is essentially a state in which the material consists of areas of normal behavior and areas of superconducting behavior.53 The vortex state can be observed by covering a disk-shaped piece of type II superconducting material with fine magnetic powder and placing it in an SEM, and cooling it below its superconducting transition temperature. As the temperature of the sample is then increased, small circular areas of normal conductivity (vortices) will start to appear on the surface of the material, and the magnetic powder will move accordingly. As the material gets warmer the areas of the vortices increase until the superconductivity of the sample is entirely destroyed.54 This vortex state of Type II superconductors is characterized not only by temperature dependence, but also by field and current dependence. These compounds therefore have additional measures of strength, Bc2 and Ic2. As a type II superconductor that is cooled below its critical temperature is placed in an increasing external magnetic field, it passes from the full superconducting state to the vortex state at Bc1, then from the vortex state to the normal state at

Bc2. Superconductors are widely known for their use in Nuclear Magnetic Resonance (NMR) spectrometers, and magnetic resonance imaging (MRI) devices. The superconductors are fashioned into coils; the superconducting current produces a strong, steady magnetic field utilized in these devices. The most commonly used material in these instruments is NbTi or

Nb3Sn, both are type II superconductors with Tc's of 9.2 K and 18.3 K respectively, and Bc2's of roughy 15 T and 30 T respectively. NbTi as an alloy, has the advantage of being ductile and can be bent and shaped into wires and coils easily, while Nb3Sn requires special processing techniques to obtain the coil shapes needed for spectrometers.55 Therefore there is a need for

56 nuclear magnetic resonance spectrometers with fields greater than 15 T that can be shaped in a simpler fashion. An additional disadvantage for NbTi and Nb3Sn are their low TC’s; they require liquid helium to cool to a superconducting state, and liquid helium is quickly being depleted and its price constantly increasing. And since the discovery of superconductivity there has always been the desire to revolutionize the world with room temperature superconducting materials.

One of the largest breakthroughs came in 1986 with the discovery YBa2Cu3O7+x, or 56,57 YBCO. The ceramic material has a Tc of 90 K, and a Bc2 of 140 T. The Tc of 90 K is significant because it can be cooled with liquid nitrogen, which is easier to obtain as well as less costly than helium. Unfortunately, as a ceramic material it is difficult to work with. It is not ductile, so shaping the material into wires and coils is not an easy task. The superconductivity and quality of the material is also affected by the amount of oxygen in the material, as well as secondary non-superconducting phases that can develop in the material during its growth process. So while exploration of the copper oxide family of ceramics have led to higher Tc’s

(with the highest found in HgBa2Ca2Cu3O8 with a Tc of 132.5K), there is a need for intermetallic superconductors which are more easily processed into useful forms.58 New superconducting compounds based on PbO-type iron arsenide layers have been of 59 great interest since the initial reports on LaFeAs(O1−xFx) in 2008 and KxBa1-xFe2As2 in 2009.

BaFe2As2 has the ThCr2Si2 structure type, with the iron arsenide slabs separated by a layer of 2+ Ba cations. This compound becomes superconducting when hole-doped (Ba1−xMxFe2As2, where M = K or Rb) or electron-doped (Co- or Ni-substitution into iron sites).60 Hole-doping by substitution of potassium for barium has been explored most extensively, with Tc increasing with 16,61 potassium content up to a maximum of 38 K for Ba0.55K0.45Fe2As2. However, potassium metal is extremely volatile and attacks commonly used reaction vessels such as alumina crucibles and quartz tubing. This behavior makes it difficult to control the amount of potassium incorporated into the product, in both stoichiometric and flux syntheses. A variety of methods have been explored to minimize these problems, including carrying out reactions under partial pressures of argon, lowering the maximum reaction temperature, use of alumina inlays, use of very rapid heating, and devising sealed zirconia crucible configurations.62 However, attack on reaction vessels and loss of potassium is still observed. In this work we describe the use of a potassium/tin Zintl phase as a potassium source in the tin flux synthesis of Ba1−xKxFe2As2. This technique allows for the avoidance of gas phase potassium and produces crystals of this

57 compound with much less attack on reaction vessels; it is potentially a far more controllable method of potassium doping than the use of elemental potassium metal.

The Zintl phase KSn (also referred to as K4Sn4 to more accurately depict its structural building blocks, Figure 4.1) can be synthesized from a stoichiometric reaction. The structure 4− 63 features Sn4 tetrahedra surrounded by potassium ions. Such Zintl phases have been used as sources of small clusters of tetrel elements, for instance, as precursors for formation of nanoparticles (from oxidation of NaGe), organozintl clusters, oligomers, and mesoporous 64 compound semiconductors (from reaction of K4Ge9). While thermal decomposition of MTt (M = Na, K, Rb, Cs; Tt = Si or Ge) results in the formation of clathrate structures, KSn is found to be stable up to 740 °C, at which point it melts incongruently.65 However, when dissolved in 4− excess tin (as in a tin flux), the Sn4 anions will dissociate and the tin atoms will form more of a loose network in the melt, releasing the potassium atoms to react with other species in the flux.66

4- Figure 4.1 Structure of K4Sn4, featuring Sn4 tetrahedra (white spheres are Sn, purple spheres are K+ ions)

4.2 Experimental Procedure

4.2.1 Synthesis

In an argon-filled glove box, elemental potassium and tin were combined in a 1.1 : 1 mmol ratio (slight excess of potassium) in a pyrex tube which was sealed off under vacuum. This reaction tube was placed in a 100 °C oven for 1 day, removed, and the contents were shaken to facilitate mixing. The tube was then placed into a 200 °C furnace for 1 day to yield the Zintl phase, which forms as a dull grey powder. Powder XRD confirms the tetragonal structure of this phase, but also indicates the presence of unreacted tin. KSn is highly air sensitive and must be stored and handled under argon.

This compound was used as a reactant in subsequent flux syntheses of Ba1−xKxFe2As2 phases. For each reaction, iron, arsenic, barium, and KSn were placed in an alumina crucible between layers of tin in stoichiometries listed in Table 4.1. Each crucible was placed in a fused silica tube; another alumina crucible was filled with Fiberfrax ceramic fiber and inverted on top of the reaction crucible to act as a filter during centrifugation. The silica tubes were sealed under vacuum. These ampules were heated to 850 °C in 3 hours and held there for 3 hours. They were cooled to 550 °C over 36 hours and then removed from the furnace and quickly centrifuged. This procedure produces well-formed silver crystals with a thin plate-like morphology up to 1 mm on a side and 0.1 mm thick. Tin from the flux is incorporated into the products, indicated by both elemental analysis and crystallographic studies (vide infra). A small amount of potassium vapor is produced by decomposition of the KSn in the flux, evidenced by a slight brownish discoloration of the fused silica ampule. This is in contrast to the dark coating and microcracks in silica tubes jacketing syntheses using elemental potassium, some of which fail completely during the reaction.

4.2.2 Elemental Analysis

4.2.3 Crystallographic Characterization of Ba1-x-yKxSnyFe2As2 Phases

Diffraction data was collected on a Bruker APEX2-CCD single crystal X-ray diffractometer with graphite-monochromated Mo Kα radiation ( = 0.71073 Å) with 20 second frames at 298 K. The data collections were carried out using the suggested programs calculated by the APEX2 software based on the initial matrix collections which determine unit cell size and Bravais class. Unfortunately, since these compounds have small unit cells of high symmetry and therefore inherently fewer diffraction peaks, for several of the crystals the calculated program led to low data completeness and resulted in less than optimal data:parameter ratios. For small high symmetry unit cells, collection of an entire full sphere of data is recommended. The data was integrated by SAINT and was corrected for absorption effects using the empirical method (SADABS).35 Space group assignment was done by XPREP, and structure refinement was 36 carried out using SHELXTL. The initial structure was based on BaFe2As2 as a starting model. All of the atoms were refined anisotropically, with Ba and K constrained to be on the same site with the same thermal parameters. The resulting R1 value was in the 7-8% range for all the data sets; the electron density maps all featured a large Q-peak at a 4e site near the Ba/K occupied 2a site. This extra peak is too far away from the Ba/K site to be caused by thermal motion of that atom. Single crystal analysis reported on a related phase (Ba1-xRbxFe2As2) by Bukowski, et al. found similar areas of electron density in the same location, finding that the site was the appropriate distance away from neighboring As atoms for a Sn-As covalent bond, and hence determined that in the absence of Ba/K, a Sn atom would be located at the site of the electron density.16,61,67 The 4e site and its symmetry equivalent are on opposite sides of the Ba/K site, and are too close to each other to allow for a Sn-Sn dimer. Therefore, only one of the two symmetry equivalents can be occupied. In our refinement, the multiplicity of this site was halved, and the occupancy was constrained along with the Ba/K occupancy using the SUMP command (occupancy of Ba on 2a + occupancy of K on 2a + half occupancy of Sn on 4e = 1). After this our R1 values were found to be in the 2-4% range (see Table 4.1). The anisotropic refinement of the thermal parameters of the Sn site was constrained to match that of the Ba/K site; when refined separately, the thermal parameters of tin became unreasonably large, despite a slight improvement in the R-value.

Table 4.1. Reaction ratios and product stoichiometries, unit cells, and superconducting transition temperatures for Ba1-x-yKxSnyFe2As2 phases. a Reactant ratio Product stoichiometry Unit cell parameters R1/wR2 Tc KSn/Ba/Fe/As/Sn a (Å) c (Å) (K)

0/0.5/1/1/10 Ba0.899(4)Sn0.101(4)Fe2As2 3.929(1) 13.158(3) 0.0287 / 0.0725 -

1.2/0.3/1/1/20 Ba0.777(9)K0.12(1)Sn0.097(6)Fe2As2 3.922(2) 13.285(7) 0.0226 / 0.0596 22

3.2/0.3/1/1/20 Ba0.683(8)K0.24(1)Sn0.073(5)Fe2As2 3.946(2) 13.431(9) 0.0232 / 0.0558 26

2.4/0.3/1/1/20 Ba0.606(9)K0.35(1)Sn0.044(5)Fe2As2 3.906(1) 13.352(4) 0.0260 / 0.0621 27

1.2/0.3/1/1/8.8 Ba0.545(8)K0.426(9)Sn0.028(6)Fe2As2 3.9021(5) 13.354(2) 0.0378 / 0.0908 30

2.0/0.3/1/1/10 Ba0.34(1)K0.66(1)Fe2As2 3.8822(4) 13.540(2) 0.0391 / 0.1102 27 a 2 Crystallographic structure refinement R-values for I > 4I data. R1 = ║Fo│–│Fc║/  │Fo║. wR2 = [Σ w(Fo – 2 2 2 2 1/2 2 2 2 –1 2 2 Fc ) / Σ w(Fo ) ] , w = [ (Fo ) + (A·p) + B·p] ; p = (Fo + 2Fc )/3; A = 0.0067, B = 0.

Table 4.2. Atomic positions and occupancies for Ba0.598(6)K0.381(1)Sn0.044(5)Fe2As2. ** atoms Wyckoff site x y z occ Ueq Ba 2a 0 0 0 0.59(2) 0.0148(6) K 2a 0 0 0 0.38(2) 0.0148(6) As 4e 0 0 0.35425(9) 1 0.0098(4) Fe 4d 0 0.5 0.25 1 0.095(5) Sn 4e 0 0 0.095(3) 0.022(3) 0.0148(6)

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

4.2.4 Magnetic Susceptibility Measurements

Magnetic susceptibility measurements were carried out on a Quantum Design MPMS XL SQUID magnetometer. Single crystals were placed in Kapton tape with the a,b-plane parallel to the length of the tape. The tape was then kinked to align the crystals with the c-axis perpendicular to the length of the Kapton tape, and subsequently to the applied field. Because this is a manual method, some offset from the desired alignment may occur. Zero-field cooled data were collected from 2 to 60 K with an applied field of 10 G; results are shown in Figure 4.2.

-5

-10

-15

Ba0.78K0.13Sn0.10Fe2As2

Susceptibility (emu/mol) Susceptibility -20 Ba0.68K0.24Sn0.07Fe2As2 Ba0.61K0.35Sn0.04Fe2As2 Ba0.53K0.43Sn0.03Fe2As2 Ba0.34K0.66Fe2As2 -25 0 10 20 30 40 50 Temperature (K)

Figure 4.2. Magnetic susceptibility data for Ba1-x-yKxSnyFe2As2 phases, collected with an applied field of 10 G.

4.3 Results and Discussion

4.3.1 Structure Determination

Single crystal X-ray diffraction was carried out on small shards cleaved from larger crystals in each batch. The tetragonal I4/mmm symmetry was confirmed; unit cell parameters of representative samples are listed in Table 4.1, and atomic positions for one analog are listed in Table 4.2. The structure solutions indicate a mixture of K+ and Ba2+ on the 2a site. They also show an extra peak in the electron density at a 4e site (0,0,z) close to the Ba/K site, which is not occupied in the parent structure. This was also reported in a tin flux synthesis of Ba1-xRbxFe2As2, and was assigned as a partially occupied site resulting from incorporated tin atoms from the flux.67 This is supported by the suitable bond lengths to the nearby As atoms; in the data sets studied here, they are consistently within a narrow range of 2.83 – 2.89Å. The Sn site is 2.3 – 2.5Å away from its symmetry equivalent; this is too short for a Sn-Sn bond, so the presence of Sn-Sn dimers is unlikely. The cages defined by the puckered FeAs layers are therefore filled

62 either by a mixed Ba/K site, or by an off-center Sn atom; see Figure 4.3. The resulting Ba1-x- yKxSnyFe2As2 stoichiometries are listed in Table 4.1. Similar incorporation of atoms of a flux element in voids usually occupied by an electropositive ion is observed in the structure of the 8, 68 Zintl phase Ba3Sn4As6 and in intermetallics such as Gd0.67Pt2Al5 and DyNi3Al9. The amount of tin incorporated into the structure appears to be related to the Ba/K ratio. As the amount of potassium increases, the occupancy of the 4e Sn site drops, confirmed by both elemental analysis and crystallographic refinement results. A maximum of 11% tin occupancy on this site is seen in the barium analog, dropping to zero in the most potassium-rich phase studied here, Ba0.34K0.66Fe2As2. These values are all within the 0-2 mole percent range of Sn incorporation reported for other flux growth syntheses of these phases.62a,62c,69 Addition of tin into the structure changes the expected trend in unit cell parameters. With increasing potassium doping, a decrease in the a-axis and an increase in the c-axis of the BaFe2As2 parent compound lattice is usually observed.16,61 The additional effect of tin on the unit cell parameters obfuscates this trend. This is likely due to the interaction between tin and arsenic limiting the variation of

Figure 4.3. Structure of Ba1-x-yKxSnyFe2As2; large blue spheres represent the Ba/K mixed site. The 4e sites partially occupied by tin are indicated by grey clouded spheres.

63 the As-Fe-As angles in the iron arsenide layers. When Ba2+ is replaced by a larger K+, the c-axis expands; this is usually counteracted by a shrinking of the As-Fe-As angle, which brings the iron atoms closer together in the square net of iron sites and shrinks the a,b axes. With bonding interactions to tin atoms on the 4e site, the ability of the As-Fe-As angles to adjust is reduced, so the a,b axes will increase along with the c-axis. Since the As-Fe-As angle and the corresponding vicinity of the iron atoms in their square net are important factors controlling the antiferromagnetic ordering in the parent compound and the superconducting transition in the doped compounds, incorporation of tin will affect both of these phenomena.

4.3.2 Magnetic Susceptibility Measurements

Magnetic susceptibility measurements were carried out on these compounds to determine their superconducting transition temperature. For tin-free Ba1-xMxFe2As2 phases synthesized stoichiometrically, Ba0.55K0.45Fe2As2 has the highest transition temperature, 38 K.

Our flux-grown sample with a similar Ba/K ratio has the highest observed Tc in this study (30 K), with the transition temperature dropping as the amount of potassium is increased or decreased. The dependency of Tc on Ba/K ratio appears to be maintained in these tin flux grown samples, but the incorporation of tin into the structure causes all the transitions to occur at lower temperatures. The susceptibility data also indicates significant inhomogeneity in these phases, a problem which has been noted in several other reports.62a,62c,67,69a Despite the fact that these measurements are carried out on single crystals, the superconducting transitions are broad, and secondary transitions below Tc are seen for some of the samples. This is due to the micaceous nature of the crystals; they have been shown to have varying compositions from layer to layer.62a,62c Traces of residual tin flux are present on the crystal surface of several of the samples, indicated by sharp transitions at 4 K (the Tc of elemental Sn).

4.4 Conclusion

In summary, a new method of synthesizing potassium-doped BaFe2As2 has been devised, using KSn as a non-volatile potassium source. This allows for synthesis of heavily doped phases without the use of specialized reaction vessels. It is possible that this methodology could be

64 expanded to tin-free reactions; for instance, K3As could be used as the dopant source in FeAs flux growth of BaFe2As2. Work is underway to optimize the synthesis of KSn (using sealed metal crucibles and higher temperatures to eliminate unreacted tin). Use of pure KSn as a reactant will enable better control of the amount of potassium in the flux reaction. We are also expanding this technique to Rb and Cs doping, using the Zintl phases RbSn and CsSn as sources of these alkali metals. Another important result of the current study is a better understanding of the incorporation of tin into the structure, an often overlooked aspect of flux growth.69b The location of the tin site is consistent in all the Ba1-x-yKxSnyFe2As2 analogs studied here and its occupancy is found to be inversely proportional to the amount of potassium included in the product. A remaining problem inherent with these phases is inhomogeneity; recent reports indicate that annealing at low temperatures improves the compositional uniformity.62c

CHAPTER 5

FLUX GROWTH AND PHYSICAL PROPERTIES OF A/Ni/Sb PHASES (A = EU OR SR)

5.1 Introduction

As shown in the previous chapter, potassium doped BaFe2As2 can readily be grown in 16,61 metal flux. The parent compound BaFe2As2 crystallizes in the ThCr2Si2 structure type, a structure which features PbO-type layers of transition metals and main group elements, separated by cations of the electropositive metal. This structure type is exhibited by over 700 different intermetallic phases and it is the subject of a large amount of research. Phases containing PbO- type FeAs layers are of particular interest as potential superconductors.70,71 Phases with PbO- type transition metal phosphide layers, such as BaNi2P2, have also been shown to be superconducting.72 Recent theoretical work on model compounds containing iron antimonide layers indicated they may also lead to superconductivity and that synthesis of such phases might be worth exploring.73 We explored multiple reaction systems, using gallium, indium, tin, and lead fluxes with different combinations of electropositive metals, transition metals, and pnictides. Unfortunately most reactions resulted in binary transition metal pnictide phases or known Zintl phases with the electropositive metals combining with the flux material and the pnictide. We were not able to grow any FeSb phases. We did find we could grow large crystals of the known phases EuNi2- xSb2 and SrNi2-xSb2 out of a lead flux and decided to focus our study on these compounds. While these phases were previously reported by reported by Jeitschko and Pöttgen, no physical property measurements have been performed on single crystals.74,75 We also discovered a structurally related phases, EuNi2Sb2 and Eu2Ni7Sb5, although the latter compound was not reproducible.

5.2 Experimental Procedure

5.2.1 Synthesis

Crystals of SrNi2-xSb2 and EuNi2-xSb2 were originally produced by a reaction of (Eu or Sr)/Ni/Sb/Pb at 0.5/1/1/10 mmol ratios; however, after optimization, the final reactant ratios of

0.29/1/1/20 were used for EuNi2-xSb2 and 0.7/1/1/20 for SrNi2-xSb2 as these ratios were found to produce larger crystals. These elements are placed in a crucible in three layers with half of the flux going in the top and bottom layer, while the remaining reactants are placed in the middle layer. The crucible is placed in a quartz tube and another crucible containing a wool-like silica material (Fiberfrax®) is placed on top. The quartz tube is then sealed off under vacuum. The tube is placed in a furnace and heated to 850° C over three hours, held there for three hours, and cooled to 650° C over 36 hours. Afterward, the tube is centrifuged to separate the flux from the products. On occasion structural variants of the europium containing phase were produced usually giving EuNi2Sb2, but were once pleasantly surprised with the phase Eu2Ni7Sb5 .

5.2.2 Elemental Analysis

Elemental analysis was carried out using a JEOL 5900 scanning electron microscope with EDS capabilities, using a 30 eV accelerating voltage and 60 second collection time; crystals were shattered to expose internal regions for analysis. For EuNi2-xSb2 and SrNi2-xSb2 an average of multiple crystals gave rough stoichiometries of Eu1Ni1Sb2 and Sr1Ni1Sb2. Crystals of the structural variants EuNi2Sb2 and Eu2Ni7Sb5 give ratios of Eu4Ni7Sb9 and EuNi2Sb2 respectively.

Figure 5.1 SEM images of SrNi2-xSb2 (left) and EuNi2-xSb2 (right). These pictures are taken looking down the c- axis of the crystal.

5.2.3 Structure Refinements

Samples for X-ray diffraction were selected from the SEM plate (Figure 5.1) after elemental analysis and fragments of the large plate shaped were mounted on glass fibers for diffraction. Single-crystal X-ray diffraction data were collected at room temperature using a Bruker AXS SMART CCD diffractometer equipped with a Mo radiation source. Processing of the data was accomplished with the use of the program SAINT; an absorption correction was applied to the data using the SADABS program.35 Refinement of the structure was performed using the SHELXTL package.36 The crystallographic data is summarized in Tables 5.1 through 5.6. Powder X-ray diffraction data was collected on several samples using a Rigaku Ultima III Powder X-ray diffractometer with a Cu radiation source and a CCD detector.

Table 5.1. Crystallographic data for A/Ni/Sb phases

EuNi1.78Sb2 SrNi1.78Sb2 EuNi2Sb2 Eu2Ni7Sb5 fw (g/mol) 499.96 435.61 512.87 1415.34 space group I4/mmm I4/mmm P4/nmm I4/mmm a (Å) 4.3690(3) 4.4212(7) 4.480(2) 4.391(2) b (Å) 4.3690(3) 4.4212(7) 4.480(2) 4.391(2) c (Å) 10.654(2) 10.757(2) 10.169(4) 26.299(6) V (Å3) 203.4 210.3 204.1 507.2 3 dcalcd (g/cm ) 7.99 7.08 8.34 8.67 Z 2 2 2 4 T (K) 298 298 298 298 radiation Mo Kα Mo Kα Mo Kα Mo Kα

2θmax 64.43 57.67 56.07 56.05 index ranges −5 ≤ h ≤ 5 −5 ≤ h ≤ 5 −5 ≤ h ≤ 5 −5 ≤ h ≤ 5 −6 ≤ k ≤ 6 −6 ≤ k ≤ 4 −5 ≤ k ≤ 5 −5 ≤ k ≤ 5 −10 ≤ l ≤ 15 −12 ≤ l ≤ 14 −13 ≤ l ≤ 13 −33 ≤ l ≤ 33 no. of reflns collected 1034 1568 2267 2818 unique data/params 135/10 105/10 181/17 228/21 (mm−1) 35.4 33.8 18.5 37.8

R1/wR2* (I > 4σ(Fo)) 0.0198/0.0435 0.0276/0.0644 0.0358/0.0727 0.0289/0.0499

R1/wR2 (all data) 0.0246/0.0435 0.0287/0.0644 0.0369/0.0727 0.0324/0.0499 residual peaks/hole 1.65/−1.26 1.10/-2.03 2.12/-4.84 1.93/-1.59 2 2 2 2 2 1/2 * R1 = ∑(|Fo| − |Fc|)/∑|Fo|; wR2 = [∑[w(Fo − Fc ) ]/∑(w|Fo| ) ] .

Table 5.2 Atom positions for EuNi1.78Sb2 ** atoms Wyckoff site x y z occ Ueq Eu1 2a 0 0 0 1 0.0137(3) Sb1 4e 0 0 0.36014(9) 1 0.0243(3) Ni1 4d 0 0.5 0.25 0.89(2) 0.0271(6)

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

Table 5.3 Atom positions for SrNi1.78Sb2 ** Wyckoff site x y z occ Ueq Sr1 2a 0 0 0 1 0.0160(5) Sb1 4e 0 0 0.35882(9) 1 0.0250(5) Ni1 4d 0 0.5 0.25 0.891(8) 0.0290(8)

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

Table 5.4 Atom positions for EuNi2Sb2

atoms Wyckoff site x y z occ Ueq**

Eu1 2c 0.25 0.25 0.74291(7) 1 0.0108(4)

Sb1 2c 0.25 0.25 0.3734(9) 1 0.0117(4)

Sb2 2a 0.75 0.25 0 1 0.1165(5)

Ni1 2c 0.25 0.25 0.1235(2) 1 0.140(6)

NI2 2b 0.75 0.25 0.5 1 0.155(6)

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

Table 5.5 Atom positions for Eu2Sb5Ni7 ** atoms Wyckoff site x y z occ Ueq Eu1 4e 0 0 0.34996(5) 1 0.0110(3) Sb1 4e 0 0 0.10343(6) 1 0.0093(4) Sb2 4d 0 0.5 0.25 1 0.0188(4) Sb3 2b 0 0 0.5 1 0.0399(8) Ni1 4e 0 0 0.2002(2) 1 0.0172(6) Ni2 8g 0 0.5 0.05156(8) 1 0.0273(6) Ni3 2a 0 0 0 1 0.0114(8)

** Ueq is defined as 1/3 of the trace of the orthogonalized Uij tensor.

5.3 Discussion

5.3.1 Synthesis and Crystal Growth

These A/Ni/Sb (A = Sr, Eu) phases tend to grow as large plate shaped crystals. As appears to be common, nickel containing ThCr2Si2 phases seem to have a preference to grow out of a lead flux.76, 77 Due to the synthesis method used and the fact that these crystals appear to grow layer by layer, occasionally droplets of metal flux can get trapped between the layers or coat some of the surface of the crystal. Lead has a superconducting transition (Tc=7 K), and it can mask transitions in the actual sample, particularly at low temperatures and when low magnetic fields are applied to the crystal. In situations like this sometimes the flux can be etched off the crystals using a basic or acidic solution. There is typically a trade off as the crystals could be slightly damaged or destroyed in this process. In this case we used 1M acetic acid to etch the lead coating from the surface; soaking overnight in this solution removes the lead and does not degrade the crystals. This was found to work for sufficiently large crystals, but for smaller crystals the acid etching was too destructive. After initial magnetic measurements on larger crystals, using magnetic fields above the transition was found to be more convenient. The synthesis procedure used by Jeitschko was the combination of the elements in a 1:1:2 Eu:Ni:Sb ratio, heating for 1 week at 800°C, followed by grinding of the product powder which was then pressed into a pellet and melted in a high frequency furnace and then quenched.74 Pöttgen also used a stoichiometric procedure, although the elements were combined in a 1:2:2 Eu:Ni:Sb ratio and arc melted several times.75 Products of both these synthetic methods were predominantly polycrystalline powder, although in the earlier report by Jeitschko, some small single crystals were isolated for SCXRD when the melted product was fractured.74 The lead flux synthesis used in our work enables growth of the product as predominantly large crystals, facilitating X-ray studies and measurements of directional dependence of magnetic and electronic properties. Both Jeitschko and Pöttgen indicate the presence of nickel defects in their product. Given the 1:1:2 Eu:Ni:Sb ratio used by Jeitschko, vacancies on the nickel site are understandable and were confirmed by single crystal diffraction studies, which indicated a stoichiometry of 74,75 EuNi1.53Sb2. In the work by the Pöttgen group, a synthesis ratio of 1:2:2 is used, so it might

71 be expected that the resulting product would have fewer nickel defects. However, the compound was characterized only by powder diffraction; and given the similarity to the unit cell parameters previously reported by Jeitschko (a = 4.340 Å and c = 10.597 Å for Jeitschko’s product, and a= 4.381Å and c = 10.681Å for Pottgen’s product), the authors assumed their compound had an identical stoichiometry. These unit cell parameters are actually not that similar, so this assumption may have been erroneous.75 Our work confirms the presence of nickel defects in this compound, and the isolation of large single crystals allows for the determination of an accurate stoichiometry. The reaction of 0.29:1:1 mmoles of Eu, Ni, and Sb in 20 mmoles of lead flux consistently yields stoichiometries in a small range between EuNi1.70(3)Sb2 and EuNi1.80(6)Sb2, with unit cell parameters of a = 4.3690(3)Å and c = 10.654(2)Å, which are in between those reported for Jeitschko and Pottgen.

Given that this indicates a higher nickel content than seen in the EuNi1.53Sb2 samples produced by Jeitschko, it is likely that the Pöttgen group sample was also more nickel-rich. Similar vacancies on the transition metal site have been reported in other phases with this structure type, such as Bi-flux grown La0.969(4)Bi0.031(4)Co1.91(1)As2; the cobalt sites in the Co/As layers 78,79 consistently show vacancies and EuNi2As2 is known to have a defect on the nickel site.

5.3.2 Structure

The ANi2-xSb2 (A = Sr, Eu) phases form in the tetragonal ThCr2Si2 structure type, while a primitive CaGe2Be2 structure type variant was found with europium, EuNi2Sb2. Eu2Ni7Sb5 exhibits a different structure type. It is also tetragonal and contains ThCr2Si2-type layers, but these layers are separated by an extra Ni/Sb slab. Both structure types have very similar a-axes, but the c-axis of Eu2Ni7Sb5 is longer. In both structures, the rare earth is coordinated by 8 nearest 2+ neighbors. These are all Sb in the ANi2-xSb2 phase; in Eu2Ni7Sb5, the Eu ions are coordinated by four Ni and four Sb atoms. Eu2Ni7Sb5 bears a strong resemblance to the La2NiGa10 structure type, and can be viewed as a stuffed variant of this structure. The ratio of rare earth to (transition metal + main group) atoms is 2:11 in La2NiGa10 and 2:12 in Eu2Ni7Sb5. The additional atom in the latter is found in a cubic interstitial site highlighted in dark green in figure 5.2. All the Ni-Sb bond lengths in Eu2Ni7Sb5 are found to be similar to Ni-Sb bond distances found in

Table 5.6 Selected bond lengths for A/Ni/Sb phases Select Bond Distances (Å)

EuNi1.78Sb2 SrNi1.78Sb2 EuNi2Sb2 Eu2Ni7Sb5 Eu-Eu 4.37 4.421 4.48 4.39 PbO Intralayer Bonding Ni-Sb 2.4797(5) 2.5015(6) 2.541(3) – 2.580(2) 2.544(4) – 2.585(2) PbO Interlayer Bonding Ni-Sb 2.541(3) 2.544(4) Sb-Sb 2.980(2) 3.037(2)

Exclusive to Eu2Ni7Sb5 Bonds to stuffed nickel site Ni-Ni 2.580(2) Ni-Sb 2.580(2)

(a) (c)

(b)

Figure 5.2 Structures of a) EuNi2Sb2 (I4/mmm, ThCr2Si2 type), b) Eu2Ni7Sb5 (I4/mmm, stuffed variant of La2NiGa10 structure type), c) EuNi2Sb2 (P4/nmm, CaBe2Ge2 type). All structures are viewed down the a-axis; magenta spheres represent Eu, orange represents Sb, and white or green represents Ni.

EuNi2Sb2 (Table 5.6), including the antimony bonded to interstitial nickel site. Eu2Ni7Sb5 is structurally similar to the CaBe2Ge2 type phase, with the structure consisting of CaBe2Ge2 type

73 lattices sandwiched in between planar nickel antimony layers. The Eu-Eu distances are more like that of the ThCr2Si2 structure type, so it is likely the Eu atoms would order magnetically.

Small crystals of a related phase, EuNi2Sb2 with the CaBe2Ge2 structure type, were occasionally produced in this work. This structure type is also tetragonal and is related to the

ThCr2Si2 structure. Both structures feature square grids of europium cations separated by puckered PbO-type layers. However, the I4/mmm symmetry of the ThCr2Si2-type EuNi2-xSi2 is lost by inverting the siting of Sb and Ni; as a result, the EuNi2Sb2 has P4/nmm symmetry. (See figure 5.2). EuNi2Sb2 was usually a minority phase; the product was predominantly the ThCr2Si2 type EuNi2-xSb2. Many of the early lanthanoid nickel arsenide 1-2-2 phases can form in both the 79-81 ThCr2Si2 and CaBe2Ge2 structure types, such as CeNi2As2. The synthesis procedure and particularly the reactant ratio used appears crucial in determining which structure is formed. For instance, Jeitschko studied several RNi2As2 phases (R = La-Sm) which can exhibit both structure types, and found that the nickel to arsenic ratio was critical to determining which structure type was formed. He found that a Ni:As ratio greater than 1 produced phases of the CaBe2Ge2 structure type, while ratios less than 1 produced phases of the ThCr2Si2 structure type. In this work the Ni:Sb ratio used was always 1:1, however this work uses molten metal synthesis, whereas Jeitschko performed stoichiometric reactions.79 We also routinely found NiSb as a side product, just as Jeitschko found when synthesizing phases of the ThCr2Si2 type. In this work, only one heating profile was used for EuNi2Sb2 synthesis; additional exploration of synthetic parameters is needed.

For the ThCr2Si2-type phases EuNi2-xSb2 and SrNi2-xSb2, the phase width appears to be small, with an average value of x = 0.22, much smaller than the defect content seen in Jeitschko’s products. However, Jeitschko’s values were determined from powder data, and the intensities of the diffraction peaks in a powder pattern may not be as accurate as those afforded by single crystal diffraction data.79 Several crystals of the europium analog were characterized by

SEM-EDS and single crystal XRD; the stoichiometries ranged from EuNi1.74Sb2 to EuNi1.80Sb2. However, these phases were made with similar Eu:Ni:Sb synthesis ratios; further investigation of possible control over nickel content is needed.

5.3.3 Magnetic Properties

For magnetic susceptibility measurements, the large plate-shaped crystals of EuNi2-xSb2 grown in lead flux were oriented with their c-axis either parallel or perpendicular to the applied field. Data was collected at fields at 1000 G or higher when acceptable to eliminate spurious signals from the superconducting transition of lead, which may be incorporated on the surface or as inclusions in these crystals. The temperature dependence of magnetic susceptibility for crystals with c-axis perpendicular to the field shows a characteristic antiferromagnetic transition at 5.8 K (see Figure 5.3). Orienting the crystal with its c-axis parallel to the field results in similar data; the lack of a distinct difference in susceptibility for these two orientations indicates that the europium moments are not directly aligned along the c-axis. At high temperatures the compound is paramagnetic and displays Curie-Weiss behavior. Fitting this data results in magnetic moment of 7.70 B per formula unit for both orientations, with a Weiss constant θ = - 6.41 K for the parallel orientation and θ = -1.87 K for the perpendicular orientation. The moment per formula unit is close to the theoretical value expected for Eu2+ ions (7.94 B) which indicates that the europium ions are divalent and the nickel atoms are not magnetic in this phase. This is in agreement with other studies on RNi2-xM2 phases such as CeNi2As2 and SrNi2As2, which also contain non-magnetic nickel.76,80 The small and negative Weiss constant indicates the presence of weak antiferromagnetic coupling forces between the Eu2+ ions, in accordance with the observation of antiferromagnetic ordering at 5.8K. Susceptibility data collected at larger fields indicates a change in spin orientation. Figure

5.4 shows the temperature dependence of the susceptibility of EuNi2-xSb2 crystal with c-axis perpendicular to the applied field, comparing data with applied fields of 10G and 2 T. At low applied fields, a distinct antiferromagnetic cusp is seen, but at 2 T, the transition is less distinct. This is in agreement with field dependence data collected at 1.8 K (Figure 5.5), which shows a subtle metamagnetic transition occurring between 1-2 T, accompanied by slight hysteresis. This likely corresponds to a field-induced spin reorientation. This phenomenon does not result in a completely ferromagnetic state, since no saturation is seen. It may involve formation of a canted antiferromagnetic system. A similar metamagnetic transition was observed in the field dependence data reported for CeNi2As2, with the authors inferring a possible spin-flop transition. Neutron diffraction data would be required for a better understanding of these ordered states.

0.7

0.6 perpendicular to c 0.5 parallel to c

0.4

0.3 (emu/mol) m

c0.2

0.1

0 0 50 100 150 200 250 300 Temperature (K)

Figure 5.3. Temperature dependence of magnetic susceptibility for a crystal of EuNi1.8Sb2 oriented with its c-axis either parallel or perpendicular to the applied field of 10 G.

Figure 5.4. Temperature dependence of magnetic susceptibility for a crystal of EuNi1.7Sb2 oriented with its c-axis perpendicular to the applied field, collected at applied fields of 10 G (triangles) and 2 T (filled squares).

Figure 5.5. Field sweeps in both directions with respect to the c-axis of EuNi1.7Sb2 at 1.8 K.

Figure 5.6. Showing the magnetization when EuNi1.7Sb2 is orientated with the c-axis perpendicular to the field between -2 T and 2 T to get a better view of the hysteresis that occurs between 1 and 2 T.

The heat capacity temperature dependence data (Figure 5.7) collected at several fields metamagnetic transition between 1 – 2 T. Datasets collected at 0 G and 1000 G applied fields are identical to each other, but the data collected at higher fields varies as the field-induced spin reorientation occurs. The magnetic ordering phenomenon is also apparent in the resistivity data

(Figure 5.8). EuNi2-xSb2 exhibits resistivity behavior typical of a metal at high temperatures; resistivity drops as the temperature is lowered. At the Neel temperature of 5.8 K, a kink is seen and the resistivity drops as the magnetic ordering of the europium moments reduces magnetic scattering of the conduction electrons. The low residual resistivity ratio (300K/10K) of EuNi2- xSb2 is 1.4, which is lower than BaFe2As2 (RRR = 4), BaNi2As2 (RRR = 8), and BaRh2As2 (RRR 82, 83 = 5.3) due to the nickel vacancies in the compound.

Figure 5.7. Heat capacity data for EuNi1.76Sb2 collected with different applied magnetic fields.

Figure 5.8. Resistivity plot for EuNi1.76Sb2.

5.4 Conclusions

Several A/Ni/Sb phases were grown from reactions of strontium or europium with nickel and antimony in lead flux. Isolation of ThCr2Si2 type or CaBe2Ge2 type structures depends on subtle changes in reactant ratio and possibly heating profile. All of the europium phases contain square grids of europium cations, with slightly different Eu-Eu distances (see table 5.6). It would be of interest to compare the magnetic ordering of Eu2+ moments in the defect-containing

EuNi2-xSb2 and its behavior in the defect free CaBe2Ge2-type EuNi2Sb2. Further work is needed to optimize synthesis of EuNi2Sb2 and Eu2Ni7Sb5 to allow for characterization of their magnetic and electronic properties.

CHAPTER 6

FUTURE WORK

This work shows the versatility of the metal flux synthesis method in discovery and crystal growth of intermetallic compounds. Molten metals can dissolve a wide variety of elements, facilitating the growth of complex phases ranging from semiconducting Zintl phases to superconductors. Several new compounds were discovered in this work, and the synthesis and crystal growth of known phases was optimized, enabling improved physical properties measurements.

The discovery of the new phase Ba2In5P5, which is very similar in composition to previously reported BaIn2P2 (both synthesized in In flux), indicates that subtle changes in temperature and reaction stoichiometry may allow for growth of new compounds.39 Further work can be done in the Ba/In/P system, exploring the specific conditions which direct the reaction toward one product over the other. Parameters of interest include the Ba:P ratio, maximum reaction temperature, and even the centrifuge temperature. Reports on the gallium flux synthesis of the phases Ce2PdGa12 and CePdGa6 show that these compounds form from identical reaction ratios by utilizing different heating profiles and centrifugation temperatures.84 Similar behavior may be occurring in the Ba/In/P system.

The use of K4Sn4 as a source of potassium dopant in the tin flux growth of KxBa1-xFe2As2 indicates that non-volatile Zintl phases can be viewed not only as products of flux growth, but also as potential reactants. Initial attempts were made to synthesize K3As to use as a source of both arsenic and potassium in the flux growth of KxBa1-xFe2As2 (for the reaction K3As + Fe + Ba in tin flux). However, this precursor compound proved difficult to isolate due to the volatility of both K and As.85 Further exploration of possible precursors to use as potassium sources is warranted.

The Eu2Ni7Sb5 phase described in Chapter 5 is a new structure which may feature magnetic ordering of Eu2+ ions. However, this phase was always found in too low a yield for physical measurements. Further work needs to be done exploring different heating profiles and different stoichiometries in order to reproduce this phase in larger quantities or as large single crystals in order to perform magnetic measurements on it.

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BIOGRAPHICAL SKETCH

Josiah Lee Mathieu

Field of Interest Interested in solid state chemistry, synthesis, and the study of material properties.

Education Ph.D. Candidate, Physical Chemistry Defended August 13th Florida State University Tallahassee, FL

ACS Certified Bachelor of Science, Chemical Physics June 2004 University of California, San Diego San Diego, CA

Minor, Mathematics June 2004 University of California, San Diego San Diego, CA

Research Experience Graduate Advisor: Dr. Susan E. Latturner March 2005 – August 2013 Department of Chemistry and Biochemistry, Florida State University Tallahassee, FL Flux synthesis of inorganic solids using molten metals and molten salts. Studied Zintl phases and

BaFe2As2 superconductors (including potassium and rubidium doping). Studied Zintl phases as reactants in metal flux reactions. Used multiple characterization tech: single crystal and powder x-ray diffraction, SEM/EDS, DSC-TGA, SQUID magnetometer, resistivity, and heat capacity. Served one year as Lab Safety Coordinator. Trained newer graduate students on instrumentation used for research. Assisted in planning and moving of the research lab. Familiar with the handling of toxic and hazardous materials (arsenic, lead, selenium. hydrochloric acid, etc.)

Teaching Experience Florida State University Directed Undergraduate Research, Ashley Rutstein, Spring 2010 Organic Chemistry, CHM 3210L, Teaching Assistant, Summer 2005 Analytical Chemistry, CHM 3120, Teaching Assistant, Fall 2005 Analytical Chemistry, CHM 4130L, Teaching Assistant, Spring 2006, Summer 2006, Fall 2006 Physical Chemistry, CHEM 4411L, Teaching Assistant, Spring 2007, Spring 2009 Physical Chemistry, CHM 4410 L, Teaching Assistant, Fall 2007, Fall 2008 General Chemistry, CHM 1046, Teaching Assistant, Spring 2008

Presentations and Posters "Zintl Phases as Dopant Sources in the Flux Synthesis of Iron Arsenide Superconductors." Talk, Materials Research Society Spring Meeting, San Francisco, CA, April 6th, 2010.

"Flux Synthesis of Iron Arsenide Superconductors using Zintl Phases as Precursors." Talk, Florida Inorganic and Materials Symposium (FIMS), Gainesville, FL, October 2, 2009.

"Flux Growth and Electronic Properties of Ba2In5Pn5 (Pn=P,As): Zintl Phases Exhibiting Metallic Behavior." Poster, Florida Annual Meeting and Exposition (FAME) of the American Chemical Society, Orlando, FL, May 2008.

Publications Mathieu, Josiah L.; Latturner, Susan E. "Zintl phase as dopant source in the flux synthesis of

Ba1-xKxFe2As2 type superconductors." Chemical Communications 2009, (33), 4965-4967.

Mathieu, Josiah; Achey, Randall; Park, Ju-Hyun; Purcell, Kenneth M.; Tozer, Stanley W.;

Latturner, Susan E. "Flux Growth and Electronic Properties of Ba2In5Pn5 (Pn = P, As): Zintl Phases Exhibiting Metallic Behavior." Chemistry of Materials 2008, 20(17), 5675-5681

Professional Organizations American Chemical Society Member, Joined in 2003