Crystallite Size Dependency of the Pressure and Temperature Response in Nanoparticles of Ceria and Other Oxides

Home , Crystallite, Crystallographic defect

Philip P. Rodenbough

Submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

Crystallite Size Dependency of the Pressure and Temperature Response in Nanoparticles of Ceria and Other Oxides

Philip P. Rodenbough

The short title of this dissertation is Size Matters. And it really does. Before diving into the original findings of this dissertation, this abstract starts by contextualizing their significance. To that end, recall that some of the earliest concepts learned by sophomore organic chemistry students include explaining physical properties based on carbon chain length, for example, and polymer length has enormous influence on macroscopic material properties. In the 1980s it was found that the electronic properties of small inorganic semiconductor crystallites can be rigorously tied to the physical size of the crystallites, and this understanding has led directly to the successful integration of so-called quantum dots into readily available technologies today, including flat screen televisions, as well as emerging technologies, such as quantum dot solar cells. Oxides, for their part, are important components of many technologies, from paints and cosmetics to microelectronics and catalytic converters. The crystallite size dependency of fundamental mechanical properties of oxides is the topic of this dissertation. First, this dissertation reports that consistent preparation methods were used to produce batches of specific crystallite sizes for a diverse family of five cubic oxides:

CeO2 (ceria), MgO (magnesia), Cu2O (cuprite), Fe3O4 (magnetite), and Co3O4. The size-based lattice changes for small crystallites was carefully measured with X-ray diffraction. Expanded lattice parameters were found in small crystallites of all five oxides (notably for the first time in Fe3O4). This behavior is rationalized with an atomic model reliant on differing coordination levels of atoms at the surface, and fundamental calculations of physical properties including surface stress and expansion energy are derived from the measured lattice expansion for these oxides. Then, the size dependency of the pressure response in ceria nanoparticles was measured using diamond anvil cells and synchrotron radiation. In a study unmatched in its comprehensiveness, it was found that the bulk modulus of ceria peaked at an intermediate crystallite size of 33 nm. This is rationalized with a core-shell model with a size dependent shell compressibility whose influence naturally grows as crystallite size shrinks. Complimentary thermal expansion measurements were carried out to probe the structural response of crystallites to heat. Overall, the thermal expansion of ceria decreased with crystallite size. Through careful heating cycles, it was possible to separate out quantitatively the two primary factors contributing to negative surface stress in ceria: ambient surface adsorbents and surface non-stoichiometry. These may be the first instances of such a calculation that provides this insight into the surface stress of oxide nanoparticles. Next, pressure and temperature studies parallel to those in ceria were carried out on magnesia as well. Magnesia is an important oxide to compare to ceria because it does not share ceria’s tendency to form oxygen vacancy defects with cation charge variances. Nonetheless, magneisa was shown to possess a peak (albeit a less dramatic peak) in bulk modulus at an intermediate crystallite size, about 14 nm. Magnesia, like ceria, also had decreased thermal expansion at smaller crystallite sizes. Finally, experiments on molecular oxygen exchange properties of a series of oxides were carried out using a thermocycling reactor system designed and built in-house, with the aim of developing materials to convert carbon dioxide to carbon monoxide.

Experiments were carried out under 1200°C, much lower than the 1500°C typically required for ceria oxygen exchange. It is thought that crystallite morphology could play an important role in dictating the eﬀectiveness of this catalytic process. The increased understanding of fundamental physical properties of oxide nanoparticles, as explored here, may lead to their more rational integration into such emerging technologies. Table of Contents

List of Figures ...... v List of Tables ...... viii Acknowledgements ...... x Dedication ...... xii

1 Lattice Expansion in Nanoparticles of CeO2, MgO, Cu2O, Fe3O4,

and Co3O4 1 1.1 Preface ...... 1 1.2 Introduction ...... 2 1.3 Understanding Lattice Parameter Shifts ...... 3 1.4 Materials ...... 11

1.4.1 CeO2 ...... 12 1.4.2 MgO ...... 16

1.4.3 Cu2O...... 20

1.4.4 Fe3O4 ...... 22

1.4.5 Co3O4 ...... 27 1.5 Lattice Expansion and Derived Calculations ...... 30 1.6 Discussion and Conclusions ...... 35

i 2 Crystallite Size Dependency of the Lattice Response to Pressure in

Nanoparticles of CeO2 39 2.1 Preface ...... 39 2.2 Introduction ...... 39 2.3 Experiments ...... 41 2.4 Results ...... 42 2.5 Literature Review ...... 46 2.6 Core-shell Model for Variable Bulk Modulus ...... 49 2.7 Conclusions ...... 52

3 Crystallite Size Dependency of the Lattice Response to Tempera-

ture in Nanoparticles of CeO2 53 3.1 Preface ...... 53 3.2 Introduction ...... 53 3.3 Experiments ...... 55 3.4 Results ...... 55 3.5 Discussion ...... 58 3.5.1 Crystallographic Defects in Ceria ...... 60 3.5.2 Simmons and Balluﬃ Experiment Review ...... 61 3.5.3 Atmosphere Considerations ...... 64 3.6 Calculations ...... 65 3.7 Relation to Bulk Modulus ...... 68 3.8 Conclusions ...... 69

ii 4 Crystallite Size Dependency of the Lattice Response to Pressure and Temperature in Nanoparticles of MgO 70 4.1 Preface ...... 70 4.2 Introduction ...... 71 4.3 Bulk Modulus Experiments and Discussion ...... 71 4.4 Thermal Expansion Experiments and Discussion ...... 76 4.5 Conclusions ...... 81

5 Thermal Oxygen Exchange Cycles in Manganese Perovskites 82 5.1 Background ...... 82 5.2 Introduction ...... 84 5.3 Materials ...... 86

5.3.1 MgMnO3 ...... 86

5.3.2 Mg0.5Al0.5MnO3 ...... 89

5.3.3 AlMnO3 ...... 89

5.3.4 CaMnO3 ...... 89

5.3.5 Ca0.5Sc0.5MnO3 and ScMnO3 ...... 90

5.3.6 SrMnO3 ...... 90

5.3.7 Sr0.5Y0.5MnO3 ...... 90

5.3.8 YMnO3 ...... 91

5.3.9 BaMnO3 ...... 91

5.3.10 Ba0.5La0.5MnO3 ...... 91

5.3.11 LaMnO3 ...... 91 5.4 Oxygen Cycling Results ...... 92

iii 5.5 Literature Review ...... 93 5.6 Conclusions ...... 95

References 96

iv List of Figures

1.1 Lattice contraction in halides as demonstrated by Boswell7 ...... 3 1.2 The linear relationship between lattice parameter and inverse crystallite diameter in gold, as demonstrated by Kuhlmann-Wilsdorf10,11 . . 4 1.3 Illustration explaining atomically how surface stress influences lattice changes in small crystallites of metals and ionic materials...... 7 1.4 Unit cell drawings ...... 12 1.5 Typical XRD patterns for large and small crystallites of ceria, with detail of (111) peak...... 15 1.6 Typical bright field TEM images for ceria nanoparticles...... 16 1.7 Typical XRD patterns for large and small crysatllites of magnesia, with detail of (220) peak...... 18 1.8 Typical bright field TEM images for magnesia nanoparticles, average

diameter ∼41 nm ...... 19 1.9 Typical XRD patterns for large and small crysatllites of magnetite, with detail of (440) peak...... 25 1.10 Typical bright ﬁeld TEM image for magnetite nanoparticles, average

diameter ∼23 nm...... 26

v 1.11 Typical XRD patterns for large and small crystallites of Co3O4, with detail of (440) peak...... 28

1.12 Typical bright ﬁeld TEM image for Co3O4 nanoparticles, average di-

ameter ∼13 nm...... 29 1.13 Lattice expansion as a function of crystallite size for ﬁve oxides. . . . 31

2.1 Plot of unit cell volume as a function of applied pressure, for ceria of diﬀerent crystallite diameters...... 44 2.2 Plot of bulk modulus as a function of crystallite size, for ceria. Dot- ted lines refer to the bulk modulus of large crystallite sizes from our experiments and from previous literature reports, as indicated. The curved line is a ﬁt using Equation 2.1 ...... 45

3.1 Cyclic temperature ramping experiments plotted out. Lattice parameter changes in small and large crystallites of ceria, as temperature

cycles back and forth twice between 50 and 400°C ...... 57 3.2 Detail of (511/333) peak shifts during thermal expansion or ceria, with

prominent Kα1/Kα2 splitting...... 58 3.3 Thermal experiments can be used to determine predominant defect types...... 61 3.4 The macroscopic length of aluminum increases more quickly than its lattice parameter under heat, indicating an increase in vacancy-type defects, as demonstrated by Simmons and Balluﬃ.113 No such diﬀer- ence is observed in ceria.114 ...... 63

vi 3.5 Brouwer diagrams relate defects to oxygen partial pressure and semiconductor behavior, as illustrated by Fergus117 ...... 64 3.6 The coeﬃcient of thermal expansion of the lattice parameter (CTELP) of ceria decreases for smaller crystallites...... 67

4.1 Plot of unit cell volume as a function of applied pressure, for magnesia of diﬀerent crystallite diameters...... 74 4.2 Plot of bulk modulus as a function of crystallite size, for magnesia. Dotted line refers to the bulk modulus of large crystallite sizes from our experiments and and solid straight line refers to bulk modulus from previous literature reports. The curved line is a ﬁt using Equation 2.1 75 4.3 Cyclic temperature ramping experiments plotted out. Lattice parameter changes in small and large crystallites of magnesia, as temperature

cycles back and forth twice between 50 and 400°C...... 78 4.4 The coeﬃcient of thermal expansion of the lattice parameter (CTELP) of magnesia decreases for smaller crystallites...... 79

5.1 XRD data for materials used in thermal oxygen cycle experiments. . . 87 5.2 Unit cell drawings for materials related to those used in thermal oxygen cycle experiments, with Hermann-Mauguin notation...... 88 5.3 Results of oxygen exchange experiments, indicating mmol of O exchanged per mol of material, in each of three cycles...... 92

vii List of Tables

1.1 Surface stress terminology...... 9

1.2 Typical preparation conditions and characterization data for CeO2 nanoparticles ...... 14 1.3 Typical preparation conditions and characterization data for MgO nanoparticles ...... 20

1.4 Typical preparation conditions and characterization data for Cu2O nanoparticles ...... 22

1.5 Typical preparation conditions and characterization data for Fe3O4 nanoparticles ...... 24

1.6 Typical preparation conditions and characterization data for Co3O4 nanoparticles ...... 29 1.7 Calculated surface stresses and expansion energies ...... 34

2.1 Experimental values for pressure versus volume of ceria unit cells of diﬀerent crystallite diameters...... 43 2.2 Details of the parameters used for calculated bulk modulus B, for ceria. 43

viii 3.1 Experimental values for thermal expansion of ceria crystallites of different diameters...... 56 3.2 Contributions to surface stress ...... 66

4.1 Details of the parameters used for calculated bulk modulus B, for magnesia...... 72 4.2 Experimental values for applied pressure versus volume of magnesia unit cells, for diﬀerent crystallite diameters...... 74 4.3 Experimental values for thermal expansion of magnesia crystallites of diﬀerent diameters...... 77

5.1 Materials explored for thermal oxygen exchange cycles...... 84 5.2 Oxygen exchange results ...... 92

ix Acknowledgements

I thank my doctoral dissertation sponsor Professor Siu-Wai Chan for providing me the opportunity to grow professionally. I also thank the Chemistry Department, the Applied Physics and Applied Mathematics Department’s Material Science and Engineering Program, and the Graduate School of Arts and Sciences of Columbia University for support. I thank the National Science Foundation Division of Materials Research Grant #1206764 for ﬁnancial support. I thank the Master of Science in Materials Science and Engineering students who have worked with me on the projects described in this dissertation. The 2013- 2014 MS students were Junhua (Hunter) Song, Ziying Ran, and Yanjun Yu. The 2014-2015 MS students were Chengjunyi (Tony) Zheng, Yuxuan (Ivan) Liu, and Chenyuan (Felix) Hui. The 2015-2016 MS Students were Ye (Mike) Wang, Jiaqi (Fiona) Xue, and Teng (Tom) Yang. I also thank Dr Misha Lipatov, who was a voluntary postdoctoral associate, and undergraduate students Yuxuan Xia and Bonnie Hu. In particular, Hunter worked on copper oxide, Yanjun and Tony worked on magnesium oxide, and Ziying, Felix, and Yuxuan Xia worked on cobalt oxide, and Ivan worked on iron oxide. Dr Misha Lipatov assisted with some calculations and ﬁttings. Students Aditya (Ishan) Varshnei and Robert Viramontes also helped with

x some impedance spectroscopy projects that do not appear in this dissertation, and Dr Joan Raitano helped with some very early material science lab familiarization. I thank the various synchrotron facility beamline scientists who assisted in gath- ering high energy X-ray diffraction data described in this dissertation: Drs Alastair MacDowell, Maritn Kunz, Bora Kalkan, and Jinyuan Yan at the Lawrence Berke- ley National Lab Advanced Light Source Beamline 12.2.2; Drs Zhounghou Cai and Stanislav Sinogeiken at the Argonne National Lab Advanced Photon Source Beamline 2-ID-D and HP-CAT; others at the Brookhaven National Lab National Synchtron Light Source I and the Cornell High Energy Syncthron Source. I thank the Shared Materials Characterization Lab at Columbia University, in particular Dr Daniel Paley who assisted with variable temperature X-ray diffraction experiments, and Professor Xavier Roy, who led the procurement of such instrumen- tation. I thank my advisory committee members, Professors Katayun Barmak and Louis Brus, for their guidance, and further thesis committee members Professors Xavier Roy and Latha Venkataraman for agreeing to review my dissertation. For further advice, I also thank Professors David Walker, Simon Clark, Robert Farrauto (and his group), Jingguang Chen (and his group), and Dr Michael Steigerwald. Finally, I thank all the other teachers, scientists, and mentors who in the preced- ing years have contributed to my scientific development up to the point of being able to write a doctoral dissertation, and I thank my family and friends for their support during my time in graduate school. They know who they are.

xi A` Norbert et `aEmmanuel.

Que cette th`esenous m`enevers les plus belles destinations.

xii Chapter 1

Lattice Expansion in Nanoparticles of CeO2, MgO, Cu2O, Fe3O4, and

Co3O4

1.1 Preface

Some parts of this chapter are based on a manuscript entitled “Lattice Expansion in Metal Oxide Nanoparticles: MgO, Co3O4, and Fe3O4,” by P. P. Rodenbough, C. Zheng, Y. Liu, C. Hui, Y. Xia, Z. Ran, Y. Hu, and S.-W. Chan, which has been recommended for publication in the Journal of the American Ceramic Society,1 and another manuscript entitled “Size-Dependent Crystal Properties of Nanocuprite,” by J. Song, P. P. Rodenbough, L. Zhang, and S.-W. Chan, which appears in the International Journal of Applied Ceramic Technology.2 CZ assisted with some MgO preparation and preliminary calculations, JS assisted with some Cu2O preparation,

1 YL assisted with some Fe3O4 preparation, and CH and YX assisted with some Co3O4 preparation. Dr Misha Lipatov helped verify some calculations.

1.2 Introduction

The elucidation of relationships between features at the atomic and larger levels is a fundamental aspect of chemistry and materials science. For example, the length of polymers can directly inﬂuence their macroscopic properties,3 and the discovery of the rigorous dictation of electronic properties from the crystallite size of small inorganic semiconductor crystallites has been key to the integration of these quantum dot materials into current technology.4,5 For crystalline ionic materials, the crystallite size is the diameter of the region of coherent crystallinity; typically such crystallites are the sole constituents of single dis- crete particles, or nanoparticles. When a single crystallite is the sole constituent of a particle, it may more accurately be referred to rather as a crystal, but in this dissertation the term crystallite is used in an inclusive sense, to refer to both monocrystalline particles, and the single-crystalline portions of a particle that may have aggregated several such crystals together in a reversible way. The lattice parameter refers to the length of the unit cell that describes the repeating 3D atomic pattern that makes up the crystal structure of the material.6 In many cases lattice parameter is thought of an intrinsic property, so much so that it is referred to in some contexts as the lattice constant. And indeed, for large crystallites whose diameters are on the order of at least microns, the lattice parameter does not typically change with crystallite size.

2 Figure 1.1: Lattice contraction in halides as demonstrated by Boswell7

1.3 Understanding Lattice Parameter Shifts

For crystallites whose diameters are on the order of nanometers, the lattice parameter can and does change with crystallite diameter. One of the earliest detailed reports of this phenomenon came from Frank Boswell in 1951.7 In a landmark study, he made careful electron diffraction measurements of the lattice parameter and crystallite size for a variety of ionic materials, as well as gold and (in less detail) bismuth. His measurements of thin films in vacuum revealed that for 2-3 nm crystallites of NaCl, KCl, NaBr, and LiF, the lattice contracted by 0.4-0.8 %, as illustrated in Figure 1.1. In that figure, deviation from X-ray values is understood to mean in this context deviation from large crystallites. Similar results were obtained for gold, which also featured lattice contraction for small crystallites. Boswell considers two primary explanations for this phenomenon. He rejects the idea that the lattice contraction is due to the failure of the theory behind the Madelung constant, noting that it was shown at least thirteen years prior that the Madelung constant for a 3 nm NaCl crystallite is the same as that for an infinite crystal to one part in 6,000.8 He does,

3 however, note that an isolated plane of a crystal may theoretically have a lattice constant a few percent less than that of a bulk crystal.9 He accepts that the surface layer of a small ionic crystallites may therefore exert a compressive force on the lattice, resulting in lattice contraction. To be precise, Boswell was actually measuring the crystallite grain size in thin ﬁlms, not the crystallite size of free monocrystalline nanoparticles that will often the subject of discussion in this dissertation, but the distinction probably matters little for the purposes here. Boswell’s results were taken forward in another landmark study by Doris Kuhlmann-Wilsdorf et al in 1968.10,11 Therein, she carefully laid the groundwork for an understanding of surface stress in solids as distinct from surface tension. Sur- face stress is understood, in one possible con-

Figure 1.2: The linear relationship be- text, to be the force per unit length which tween lattice parameter and inverse crys- must be applied to a terminating surface in tallite diameter in gold, as demonstrated 10,11 by Kuhlmann-Wilsdorf order to keep it in equilibrium. Kuhlmann- Wilsdorf then derived, from the equations for capillary pressure in a spherical particle (from the Young-Laplace equation) and compressibility of cubic lattices, a method for calculating the surface stress of material whose lattice contracts at small crystallite sizes. In particular, she reported a surface stress of 1175 dyn/cm (1.175 N/m) in gold, using the linear relationship between the change in lattice parameter and the inverse crystallite diameter for crystallites as small as 3.5 nm, as illustrated in

4 Figure 1.2. Some of Kuhlmann-Wilsdorf’s calculations and methods will be explored in more detail in Section 1.5. A modern interpretation of surface stress is given by Philip Manuel Diehm et al in 2012.12 His comprehensive framework accommodates not only lattice contraction, which had been known for over half a century, but also oxide lattice expansion. The phenomenon of oxide lattice expansion was in fact reported in MgO by Cimino as early as 1966,13 but it went unacknowledged and uncited in Kuhlmann-Wilsdorf’s seminal work on surface stress two years later (although she did mention the pos- sibility of negative surface stress, implying lattice expansion). Only more recently has oxide lattice expansion attracted more signiﬁcant attention. Small crystallites

14 of CeO2 were shown to exhibit lattice expansion as early as 1999, and Diehm thoughtfully catalogued the ﬂurry of reports that followed to highlight the general trend: small crystallites of metals and halides typically exhibited lattice contraction, whereas those of oxides typically exhibited lattice expansion. Diehm provided a framework more comprehensive, robust, and convincing than previous attempts.15 Diehm’s essential proposition can be understood quite intuitively. He proposes that both metals and ionic materials (including oxides) exhibit surface stress, and that the atomic origin of that stress is due to the diﬀerence in coordination at the surface and in the interior. At the surface, atoms are lowly coordinated (i.e. they have fewer neighbors) and so would prefer to have shorter bonds. In the interior, atoms are highly coordinated (i.e. they have many neighbors) and so would prefer to have longer bonds. This keeps the overall electron density as homogenous as possible. When crystallite size is large, the surface area to interior volume ratio is small, so there is no observable deviance from the interior’s ideal lattice parameter.

5 As crystallite size shrinks, however, the surface area to interior volume ratio increases, and since the surface and interior are mutually coherent in a uniform crystallite, the net eﬀect is that the surface layer compresses the lattice of the interior. Thus, in small crystallites of metals and ionic materials, lattice contraction is observed. The lattice expansion of oxides is explained with their unusual surface structure. Oxides are notorious for featuring oxygen vacancies and cation charge variances, especially at the surface, in addition to surface adsorbents such as H2O or CO2 cap- tured naturally under ambient conditions. Such adsorbents increase the coordination of atoms at the surface such that it surpasses that of atoms at the interior. Thus, the situation becomes reversed: atoms at the surface are highly coordinated, preferring longer bonds, and atoms at the interior are (relatively) more lowly coordinated, preferring shorter bonds. This results in lattice expansion for small crystallites. If cations are reduced at the surface, as they often are for nonstoichiometric oxides,

16 especially for CeO2, this further exacerbates lattice expansion: the reduced cations feature a larger ionic radius, which has the equivalent effect of creating a preference for longer bonds (in the same way as does surface adsorbents). Diehm also touches on the lattice variation in small covalent crystallites, which is complicated by the directionality of covalent bonding with specific orbitals (in contrast to the non-directionality of metallic or ionic bonding), but such materials are beyond the scope of the discussion in this dissertation. The framework outlining the difference between lattice contraction and expansion, however, is central to many of the following discussions, and so is illustrated in Figure 1.3, which is worthwhile to discuss in detail. Figure 1.3.a illustrates that lowly coordinated atoms prefer shorter bonds whereas highly coordinated atoms prefer

6 (a) Top: lowly coordinated atoms prefer shorter bonds. Bottom: highly coordinated atoms prefer longer bonds.

(b) Left: clean, stoichiometric surfaces. Middle: surfaces featuring adsorbed water molecules. Right: surfaces featuring reduced cations with larger ionic radii.

Figure 1.3: Illustration explaining atomically how surface stress inﬂuences lattice changes in small crystallites of metals and ionic materials.

7 longer bonds. Figure 1.3.b illustrates three distinct scenarios that may occur at the surface of a material. If the surface is clean and stoichiometric as in Figure 1.3.b.left, then the surface is more lowly coordinated than the interior. This means that the surface exerts a compressive stress on the interior, which, in small crystallites, results in a contracted lattice parameter. This is often referred to as “positive” surface stress. The surface in Figure 1.3.b.left can also thought to be under tensile stress from the core, but to describe the situation from such a perspective is probably more confusing than instructive. In Figure 1.3.b.middle, the surface features extensive water adsorbents. In this case, the surface atoms of the crystalline material are actually more highly coordinated than the interior. Thus, the surface prefers longer bonds, and exerts a tensile stress on the core, resulting in lattice expansion for small crystallites. This is sometimes referred to as “negative” surface stress. The surface in Figure 1.3.b.middle can also be described as under compressive stress from the core, but again, this terminology is probably more confusing than insightful, because the overall net eﬀect is lattice expansion (not compression). The surface in Figure 1.3.b.right features reduced cations with increased radii. Such cations would prefer longer bonds, and so the net eﬀect is similar to the case in Figure 1.3.b.middle. Figure 1.3.b.left typically describes the situation for most metals and ionic materials. Figure 1.3.b.middle and Figure 1.3.b.right typically describe the situation for most oxides. The terminology surrounding Figure 1.3 is important to get right. In this dissertation, we will conscientiously refer to surfaces exerting compressive stress on the core as positive surface stress. We will conscientiously decline to characterize such a situation as “tensile surface stress” as others have done12 because it is needlessly confusing: such a description is ambiguous about whether the surface is under a

8 Positive surface stress Negative surface stress Surface exerts stress on core compressive tensile Core exerts stress on surface tensile compressive Net result at small crystallite sizes is lattice contraction expansion

Table 1.1: Surface stress terminology. tensile stress from the core or whether it is exerting a tensile stress on the core. Our terminology is more speciﬁc. Similarly, we will refer to surfaces exerting a tensile stress on the core as negative surface stress. Such a positive/negative designation is ultimately arbitrary and is only chosen as such here to be consistent with most literature. Such terminology should not raise concerns about “negative” pressure that such a negative surface stress may imply for the Laplace-Young equation (or derivations thereof) because the Laplace-Young equation is concerned with pressure diﬀerences, not absolute pressures. The terminology is made unambiguously clear in Table 1.1. The greater framework described here is powerful in that it describes many of the size-dependent lattice changes catalogued by Diehm. For example, Diehm catalogues many instances of lattice expansion in small crystallites of CeO2, but in one instance

17 there is a report of lattice contraction in CeO2. Upon closer inspection, it can be seen that such lattice contraction is probably due to the particularly meticulous cleaning of CeO2 nanoparticles with nitric acid, which may not only remove surface adsorbents but also oxidize the surface more fully. As Figure 3 illustrates, a cleaner and more stoichiometric surface is more likely to exhibit lattice contraction for small crystallites. The actual state of the surface is therefore highly dependent on detailed conditions of experiments and is not necessarily an inherent function solely of the

9 chemical composition of the material. Diehm’s framework of lattice expansion and contraction is supported by rigorous Density Functional Theory calculations that show, for example, that clean stoichiometric CeO2 in fact has a positive surface stress, but when surface adsorbents are introduced, the surface stress becomes negative. Introducing cation reduction (and oxygen vacancies) is calculated to have a similar eﬀect, changing the sign of surface stress from positive to negative. Experimental evidence in MgO, from as far back as 1969, is also consistent with this framework: clean nanoparticles of MgO studied in vacuum exhibited lattice contraction, but the lattices expanded when exposed to ambient conditions (especially moist air).18 There are certainly some aspects of surface stress theory that have generated some controversy in the past,19–21 but in light of Diehm’s framework they are not concerning here. Mogensen in 200022 delivered a particularly thorough study of ceria defect thermodynamis in which he suggests that Vegard’s rule23,24 may apply to ceria. Vegard’s rule is that a linear relationship exists between the lattice parameter and solutes; Mogensen proposes that Ce3+ can be treated as a solute in ceria. Veg- ard’s rule is unlikely to be a good primary explanation for lattice changes in oxide nanoparticles as explored here, because it requires the solute to be homogenously dis- tributed in the solid and there is in fact good experimental evidence for the surface localization of such reduced cations.16,25

10 1.4 Materials

Five oxide systems are explored in this chapter: CeO2, MgO, Cu2O, Fe3O4, and

Co3O4. Their basic properties and preparations as executed in this dissertation are described in this section. Starting materials were typically purchased from Sigma Aldrich or Alfa Aesar and used without further purification. Purified water was prepared to 18 MΩcm with a Barnstead Nanopure Infinity system. X-ray diffraction (XRD) patterns were typically collected with a PANanalytical diffractometer with Cu-Kα radiation (λ = 0.15418 A)˚ under ambient conditions, with an accelerating voltage of 45 kV and emission current of 40 mA. XRD data was subsequently an- alyzed using the software programs XFit26 and Celref,27 or MAUD,28 to determine lattice parameter with peak fitting and Rietveld refinement.29 The Scherrer equation was typically used to estimate average crystallite size.30,31 Crystallite morphology was typically examined using transmission electron microscope (TEM), on a JEOL-2100 instrument. Images are typically taken under bright field. For such examination, dry nanoparticles were sonicated in ethanol and drop-cast onto an amorphous carbon film supported by a 300-mesh copper grid from Electron Microscopy Sciences. The crystallite size and size distribution were determined for each sample by using the software program ImageJ32 to measure sizes of more than 50 randomly selected nanoparticles with clear outline for each sample. Polydispersity is quantitatively described here as standard deviation in particle size over mean particle size. Illus- trations of the crystal structure of the materials studied here are presented in Figure 1.4.33

11 (a) CeO2 ceria (b) MgO magnesia (c) Cu2O cuprite (d) Fe3O4 magnetite

Figure 1.4: Unit cell drawings

1.4.1 CeO2

Cerium34 is a rare earth metal, although it is the most common of the rare earth

35 metals, and its primary oxide is CeO2, known alternatively as ceria, ceric oxide, or (in older mineralogy texts) cerianite. Here the material will mostly be referred to as

CeO2 or ceria. The next most important oxide of cerium is Ce2O3, but this oxide is typically not stable under normal conditions. CeO2 crystallizes in the ﬂuorite structure, shown in Figure 1.4.a. Its space group in Hermann-Mauguin notation is Fm3m,¯ and its space group number is 225. The Strukturbericht designation for the crystal structure of CeO2 is C1 and its Pearson symbol is cF12. Ceria is used in many technologies, most notably three-way catalytic converters found in virtually every modern consumer automotive vehicle.36 This fully mature technology takes harmful components of exhaust (CO, NOx, CHx) and converts them to more benign species (CO2,N2). The oxide systems used in such technologies are complex and typically include precious metal catalysts and alumina support, with ceria acting as a critical oxygen buﬀer. Ceria is also useful in emerging technologies

37 38 such solid oxide fuel cells and thermocyclic conversion of CO2 to CO, the latter of which will be discussed in more detail in Chapter 5.

12 There are a great many diﬀerent ways to synthesize oxide nanoparticles,39 including ceria.40 The easiest way, perhaps, the make ceria is to start with an aqueous solution of cerium (III) nitrate, and precipitate with base. The behavior of cerium species in aqueous systems has been studied intensely,41–43 but essentially, as with many non-alkali metals, aqueous cerium ions form insoluble hydroxides that dry to yield the oxide. Oxidation of free aqueous cerium ions from 3+ to 4+ happens as a matter of course from ambient dissolved oxygen. The base used in these studies was hexamethylenetetramine (HMT), whose cage-like structure is thought to contribute to the formation of particularly uniform nanoparticles.44 Size control is achieved by adjusting mixing time and (for larger particles) annealing temperature. Aspects of the preparation described here have been reported previously.45,46

Preparation of CeO2 Nanoparticles

In a typical preparation, 250 mL of aqueous 0.0375 M cerium (III) nitrate hexahydrate was prepared and stirred. Separately but simultaneously, 250 mL of aqueous 0.5 M HMT was prepared and stirred. After thirty minutes of independent stirring, the solutions and were combined and stirred for a time ranging from six hours to overnight. Shorter stirring times typically resulted in smaller nanoparticles, whereas longer stirring times typically resulted in larger nanoparticles. After stirring, the solution was then centrifuged at 10°C at 12 krpm for two hours. The supernatant was discarded, and the solid mass was left to dry in air overnight. The solid was then mechanically ground with a mortar and pestle. For some samples, a two hour annealing step was added afterward to achieve further increases in crystallite size. Results are detailed in Table 1.2.

13 Annealing temp Lattice parameter Crystallite size Mixing time (hrs) (°C) (A)˚ (XRD) (nm) 6 N/A 5.4312 7.1 24 N/A 5.4287 9.7 24 N/A 5.4329 10.0 24 500 5.4121 10.6 24 550 5.4180 11.8 24 600 5.4151 19.3 24 600 5.4146 32.8 24 650 5.4117 51.8 24 700 5.4117 59.9 24 700 5.4146 86.9 24 1200 5.4115 >100

Table 1.2: Typical preparation conditions and characterization data for CeO2 nanoparticles

Representative XRD and TEM Data for CeO2 Nanoparticles

Figure 1.5 shows typical XRD patterns for large and small crystallite ceria. The small crystallite sample is notable for its peak broadening (which indicates small crystallite size) and peak shift to the left (which indicates an expanded lattice parameter). XRD peaks are labelled with the corresponding reflection in (hkl) notation, and the y-axis is arbitrary units of intensity. Figure 1.6 shows typical TEM images for small and medium crystallite ceria. The smaller crystallites shown in this figure have an average diameter of about 9 nm, with good uniformity. The larger crystallites shown in this figure have an average diameter of about 33 nm, with only mild polydispersity. The crystallite sizes determined by TEM are typically in good agreement with those determined by the Scherrer equation and XRD. Full histogram sets are provided elsewhere.47

14 Figure 1.5: Typical XRD patterns for large and small crystallites of ceria, with detail of (111) peak.

15 (a) CeO2 nanoparticles, average diameter ∼9 nm (b) CeO2 nanoparticles, average diameter ∼33 nm

Figure 1.6: Typical bright ﬁeld TEM images for ceria nanoparticles. 1.4.2 MgO

Magnesium48 is an alkali earth that forms a single oxide, MgO,49 also known as magnesia, or periclase to mineralogists. This oxide crystallizes in the rock salt structure, which can be thought of as a pair of interlocking face-centered cubic lattices, as illustrated in Figure 1.4.b. Like ceria, the space group of magnesia in Hermann- Mauguin notation is Fm3m,¯ and its space group number is 225. The Strukturbericht designation for the crystal structure of MgO is B1 and its Pearson symbol is cF8. MgO ﬁnds use in cements and for refractory purposes in steelmaking. Some research has also been done on its crystallite size-dependent optical properties50 and its suitability as a substrate for superconductors,51 in addition to some catalysis studies.52 Two of the most signiﬁcant preparation methods for MgO nanoparticles are hy- drothermal53 and sol-gel methods.54 We have chosen the sol-gel method here. This particular sol-gel method features the dissolution of magnesium nitrate in ethanol,

16 followed by its precipitation with oxalate to form a gel. The gel is then annealed to yield decomposition of the organic oxalate coordinating group, yielding the oxide. This is one variation of many55 of the Pechini method.56 Crystallite size control is achieved through temperature variation.

Preparation of MgO Nanoparticles

MgO nanoparticles were typically prepared by first dissolving equimolar amounts of magnesium nitrate hexahydrate and oxalic acid dihydrate separately in ethanol, yielding two clear solutions. Then, upon mixing they yielded a thick white gel. The gel was stirred at room temperature for several hours and then dried without stirring at 100°C overnight. The dried precursor was then ground to a fine powder and annealed at different temperatures ranging from 500 to 1100°C for 2h in air. Results are detailed in Table 1.3.

Representative XRD and TEM Data for MgO Nanoparticles

Figure 1.7 shows typical XRD patterns for large and small crystallite magnesia. As with ceria, the small crystallite sample is notable for its peak broadening (which indicates small crystallite size) and peak shift to the left (which indicates an expanded lattice parameter). XRD peaks are labelled with the corresponding reﬂection in (hkl) notation, and the y-axis is arbitrary units of intensity. Stars represent peaks from the sample holder. Figure 1.8 shows a typical TEM image for nanoparticles of magnesia. This sample features crystallites sizes with an average diameter of about 41 nm. As with all of the materials discussed in this chapter, morphology is vaguely regular despite aggregation and crystallite size measurements agree with XRD estimations.

17 Figure 1.7: Typical XRD patterns for large and small crysatllites of magnesia, with detail of (220) peak.

18 Figure 1.8: Typical bright ﬁeld TEM images for magnesia nanoparticles, average diameter ∼41 nm

19 Crystallite Crystallite Annealing Lattice size (TEM) size (XRD) Polydispersity temp ( C) parameter (A)˚ ° (nm) (nm) 500 4.2247 7.6 8.2 0.21 550 4.2172 12.8 11.5 0.18 600 4.2162 10.8 12.1 0.18 650 4.2135 14.0 14.4 0.17 700 4.2129 14.4 15.5 0.17 750 4.2116 21.5 22.3 0.18 800 4.2101 27.6 31.1 0.13 850 4.2100 35.2 36.6 0.15 900 4.2096 47.9 51.1 0.12 950 4.2082 41.1 48.2 0.14 1000 4.2065 42.1 47.5 0.16 1100 4.2052 92.6 98.1 0.10 1200 4.2050 >100 >100 N/A

Table 1.3: Typical preparation conditions and characterization data for MgO nanoparticles

1.4.3 Cu2O

57 58 Copper forms two oxides: CuO and Cu2O. The latter is the main oxide of interest here and is known as cuprite (or cuprous oxide, copper(I) oxide). Cuprite’s cubic crystal structure is isostructural with Ag2O and is illustrated in Figure 1.4.c. This structure can be thought of as a cubic lattice with oxygen ions at the corners of the cube and an oxygen at the center with tetrahedral coordination to copper ions. The space group of cuprite in Hermann-Mauguin notation is Pn3m and its space group number is 224. The Strukturbericht designation for the crystal structure of cuprite is C3 and its Pearson symbol is cP6. Cuprite is useful as an antifouling agent and fungicide, and is seeing increasing interest as a potential component of nanoscale electronics and photovoltaics.59

20 Typically the 2+ form of copper is more stable in most ionic compounds, so most preparations of cuprite require some form of reduction. The preparation featured here are both precipitation methods, one of which features post-crystallization reduction, and one of which features pre-crystallization reduction. Aspects of the preparation described here have been reported elsewhere.2

Preparation of Cuprite Nanoparticles

The post-crystallization reduction method was typically carried as follows. Equal volumes of aqueous solutions of 0.0375 M copper (II) nitrate and 0.5 M HMT were combined and stirred at 40°C. After stirring, the solution was then centrifuged at 10°C at 12 krpm for two hours. The supernatant was discarded, and the solid mass was left to dry in air overnight. The solid was then mechanically ground with a mortar and pestle. Such a processed yielded CuO, which was reduced to Cu2O by brieﬂy annealing at 250°C in a ﬂow of 5% CO balanced with helium. Size control was achieved by adjusting the annealing time from 10 to 25 min. This yielded uniform cuprite nanoparticles with crystallite diameters ranging from 9 to 20 nm. The pre-crystallization reduction method was typically carried as follows. Three aqueous solutions were combined: 400 mL of 0.005 M copper (II) nitrate, 250 mL of 0.009 M ascorbic acid, and 400 mL of 0.038–0.900 M sodium hydroxide. Size control was achieved by varying the sodium hydroxide concentration. After stirring under ambient conditions, the solution was then centrifuged at 10°C at 12krpm for two hours. The supernatant was discarded, and the solid mass was left to dry in air overnight. The solid was then mechanically ground with a mortar and pestle. Such a process yielded cuprite nanoparticles directly without the need for further reduction.

21 NaOH CO annealing Lattice parameter Crystallite size concentration (M) time (A)˚ (XRD) (nm) - 10 4.2738 9 0.038 - 4.2682 14 - 15 4.2675 31 - 25 4.2662 55 0.170 - 4.2652 68 0.900 - 4.2654 >100

Table 1.4: Typical preparation conditions and characterization data for Cu2O nanoparticles

Results are detailed in Table 1.4. XRD patterns and TEM images for cuprite are not detailed here but elements of this data can be found elsewhere.2

1.4.4 Fe3O4

Iron60 is a transition metal that can form several diﬀerent oxides,61 but the oxide of interest in this report is Fe3O4, known as magnetite, which features a spinel structure. Magnetite’s spinel structure contains cations with diﬀerent charges and can

2+ 3+ 2- be alternatively written as Fe Fe2 O4 . These two diﬀerent oxidation states of iron are located at the tetrahedral and octahedral holes of the crystal structure. An illustration of the crystal structure is provided in Figure 1.4.d. The space group in Hermann-Mauguin notation is Fd3m,¯ and its space group number is 227. The Struk- turbericht designation for the crystal structure of magnetite is H1 and its Pearson symbol is cF56. Magnetite is of particular note for its potential biomedical applications and catalysis.62 Magnetite nanoparticles can be synthesized many diﬀerent ways.63 In this report, minor variations on Massart’s method64 are used in most cases, and Park’s method65 helps achieve the smallest crystallite sizes. The former method features

22 co-precipitation with appropriate ratios of iron cations in aqueous solution. Typical crystallite sizes under this method vary from 10 nm to 20 nm. The latter method features the decomposition of iron oleate in high boiling point solvent, which yields crystallite diameters less than 10 nm.

Preparation of Fe3O4 Nanoparticles

For the synthesis of magnetite nanoparticles, standard air-free techniques were used to achieve argon atmospheres. Typically, for the first method (Massart’s method), 1.7 mmol of iron (II) sulfate heptahydrate, and 3.3 mmol of iron (III) chloride hexahydrate were combined in deoxygenated water, which was further bubbled with argon. Then, 50 mL of aqueous alkaline solution was added dropwise into the iron solution at a controlled temperature. The alkaline solution was either sodium hydroxide, am- monium hydroxide, tetramethylammonium hydroxide, or some combination thereof. The solution was stirred for an additional hour. The black precipitate was collected with a magnet and washed with water and ethanol, yielding magnetite nanoparticles. Typically, for the second method (Park’s method), iron oleate was first synthesized using minor variations of a previously reported procedure.66 First, 120 g of 40 % potassium oleate paste was mixed with 100 mL ethanol and stirred until dissolved. Then 13.5 g of iron (III) chloride hexahydrate was added to the solution. Then 150 mL of hexane was poured into the flask, and the mixture was kept refluxing under vigorous stirring overnight. The hexane phase was then separated, washed with water 2 times, and concentrated under reduced pressure. After several subsequent cycles of washing with acetone and ethanol and then drying, the final product was a brown waxy solid of iron oleate.

23 Crystallite size Crystallite Size Lattice Reaction Conditions (TEM) (nm) (XRD) (nm) Parameter (A)˚ 1M NaOH, RT 10.0 11.3 8.3748 1M NaOH, 90°C 17.3 19.3 8.3712 1M NaOH + 1M NH3, RT 10.6 12.5 8.3738 25% TMAOH, RT 14.6 13.7 8.3723

1M NH3, 90°C 23.0 20.2 8.3691 1M NH3, post-anneal >100 >100 8.3679 Oleate Decomp. 5.9 6.0 8.3790

Table 1.5: Typical preparation conditions and characterization data for Fe3O4 nanoparticles

Then, 2.8 g of iron oleate was combined with 0.5 mL of oleic acid and 40 mL of hexadecane. The mixture was ﬁrst heated up to 100°C with continuous argon ﬂow for 2 hours, then to 200°C for another 1.5 hours. After cooling, acetone was added to accelerate the aggregation of the nanoparticles. The nanoparticles were collected with a magnet and washed with hexane and ethanol 3 times each. The product was grinded with a mortar and pestle, yielding magnetite nanoparticles. Micron-sized crystallites were achieved by annealing in argon at a high temperature.

Representative XRD and TEM Data for Fe3O4 Nanoparticles

Figure 1.9 shows typical XRD patterns for large and small crystallite magnetite. As usual, the small crystallite sample is notable for its peak broadening (which indicates small crystallite size) and peak shift to the left (which indicates an expanded lattice parameter). XRD peaks are labelled with the corresponding reﬂection in (hkl) notation, and the y-axis is arbitrary units of intensity. Figure 1.10 shows a typical TEM image for nanoparticles of magnetite. This

24 Figure 1.9: Typical XRD patterns for large and small crysatllites of magnetite, with detail of (440) peak.

25 Figure 1.10: Typical bright ﬁeld TEM image for magnetite nanoparticles, average diameter ∼23 nm.

26 particular sample features crystallites sizes with an average diameter of about 23 nm.

1.4.5 Co3O4

Cobalt67 forms two main oxides: CoO, which is isostructural with the previously discussed MgO, and Co3O4, which is isostructural with the preveiously discussed

Fe3O4 (magnetite). Co3O4 is the oxide of interest here. Research interest in Co3O4 includes applications in catalysis, batteries, and gas sensors.68,69 There are many ways

70 71 to synthesize Co3O4. We have chosen a variation of HMT precipitation here.

Preparation of Co3O4 Nanoparticles

Typically, Co3O4 nanoparticles were prepared by combining equal volumes of aqueous solutions of 0.5 M HMT and 0.5 M cobalt (II) nitrate hexahydrate. A few drops of

H2O2 (30 wt %) were added to assist with oxidation, and the solution was stirred at 80°C for 3 hours. The solution then centrifuged at 10°C at 12 krpm for 2 hours. The supernatant was separated and the remaining precipitate was allowed to dry in air. This precursor product mixture contained mainly Co3O4 with small amounts of

Co(OH)2 and CoO as deduced by XRD. When annealed for 2 hours in air at varying temperatures from 200-900°C, the product crystallized as single phase Co3O4 at varying crystallite sizes.

27 Figure 1.11: Typical XRD patterns for large and small crystallites of Co3O4, with detail of (440) peak.

28 Crystallite Crystallite Annealing Lattice size (TEM) size (XRD) Polydispersity temp ( C) parameter (A)˚ ° (nm) (nm) 200 8.0703 10.0 9.3 0.19 250 8.0664 12.1 10.5 0.09 300 8.0668 13.7 13.5 0.13 350 8.0672 13.4 13.0 0.14 400 8.0622 16.4 16.4 0.15 450 8.0634 17.3 16.7 0.20 500 8.0579 25.5 25.3 0.19 550 8.0558 40.2 41.6 0.27 600 8.0549 50.3 55.3 0.29 900 8.0576 >100 >100 N/A

Table 1.6: Typical preparation conditions and characterization data for Co3O4 nanoparticles

Figure 1.12: Typical bright ﬁeld TEM image for Co3O4 nanoparticles, average diameter ∼13 nm.

29 Representative XRD and TEM Data for Co3O4

Figure 1.11 shows typical XRD patterns for large and small crystallites of Co3O4. XRD peaks are labelled with the corresponding reﬂection in (hkl) notation, and the y-axis is arbitrary units of intensity.

Figure 1.12 shows a typical TEM image for nanoparticles of Co3O4. This sample features crystallites sizes with an average diameter of about 13 nm. The Co3O4 nanoparticles can seen to be particularly well-formed and uniform; this is possibly attributable to the use of HMT in their preparation.

1.5 Lattice Expansion and Derived Calculations

In all five materials (CeO2, MgO, Cu2O, Fe3O4, and Co3O4), lattice expansion is observed as crystallite size decreases. In the representative XRD data, both peak shifts to the left (indicating expanded lattice) and peak broadening (indicating small crystallite sizes) are evident. TEM studies carried out on samples typically revealed that polydispersity was low, indicating uniform crystallite batches. Figure 1.13 is the key figure of this chapter and summarizes the data by plotting lattice expansion against crysatllite size for all five oxide systems. A full review of precisely how to use X-ray diffraction data to obtain the lattice parameter is beyond the scope of this discussion but can be found elsewhere.29,72 The mean crystallite size of a powder sample was estimated with Scherrer equation:30,31

0.9λ d = (1.1) βcosθ

In this equation, d is the mean crystallite diameter, 0.9 is an approximation factor

30 Figure 1.13: Lattice expansion as a function of crystallite size for ﬁve oxides.

31 for the general spherical shape of the crystallite, λ is the X-ray wavelength, β is the line broadening at half the maximum intensity (full-width at half-max or FWHM), and θ is the Bragg angle. The nanoparticle crystallite diameters determined by this Scherrer equation and by TEM imaging here are typically in good agreement. Full histograms of TEM ceria nanoparticle diameter counts are presented as supplemental information elsewhere,33 and the polydispersity (standard deviation in particle size over mean particle size) is reported for MgO in Table 1.3. The cobalt oxide typically had uniformity as good or better than ceria and magnesia, whereas the polydispersity of cuprite and magnetite was typically larger. The Williamson-Hall equation73,74 was used to separate the lattice expansion eﬀect from the heterogeneous strain eﬀect on peak broadening:

∆d β cosθ = hkl hkl (1.2) dhlk 4sinθhkl

In this equation, d is the interplanar spacing of (hkl) planes, β is the line broadening, and θ is again the Bragg angle, of the (hkl) planes. The elastic strain in the [hkl] direction is represented, then, by ∆d/d. Typically there was no discernable positive slope for the Williamson-Hall plots, indicating the overall amount of heterogeneous strain to be negligible. The peak broadening is then mainly due to small crystallite size, which agrees with the evidence from TEM data. The surface stress is calculated using the rate of change of the lattice parameter with respect to crystallite diameter. Such a calculation was performed by Cimino in 196613 and reﬁned by Kuhlmann-Wilsdorf in 1968.10,11 Brieﬂy, from the equation for capillary pressure in a spherical particle (P = 4f/d, where P is pressure, f is surface

32 stress, and d is diameter, a variation of the Young-Laplace Equation) and from the deﬁnition of bulk modulus (B = −V0∆P/∆V , where B is bulk modulus and V is volume), we obtain:

−3B ∆a f = d (1.3) 4 a0

Where a, lattice parameter, has been exchanged (as a cubic system) for V with

∆V/V0 = 3∆a/a0, which works for small changes, and a0 represents the lattice parameter for the bulk. The last two terms, ∆a/a0 and d, can together be evaluated as the slope of the line of the plot of ∆a/a0 vs 1/d. We can also calculate the internal expansion energy of the unit cell against hydrostatic pressure for small nanoparticles. For this calculation, we start with the deﬁnition of PV work:

Z E = P dV (1.4)

Where E is energy. When we divide both sides by V and substitute out P using the deﬁnition of bulk modulus, we obtain:

E Z 1 ∆V = −B dV (1.5) V V V

Which we can then evaluate as:

E Z ∆V/V ∆V ∆V −B ∆V 2 −9B ∆a2 = −B d = = (1.6) V 0 V V 2 V0 2 a0

33 CeO2 MgO Cu2O Fe3O4 Co3O4 Bulk Modulus B (GPa) 220 155 110 185 190 Min crys size achieved d 7 7 9 6 9 (nm)

Lattice expansion ∆a/a0 0.37 0.47 0.19 0.13 0.19 Surface stress f (N/m) 5.41 4.12 1.56 1.26 3.09 Expansion energy E/V 13.9 15.3 1.92 1.46 2.12 (J/cm3) Expansion energy E (mEv/formula unit) 3.5 1.8 0.47 0.67 0.87

Table 1.7: Calculated surface stresses and expansion energies

Where in the last step we have again used the simple substitution ∆V/V0 =

3∆a/a0 which works for cubic systems. In Table 1.7, we have reported absolute values for both surface stress and expansion energy. It is understood in the cases studied here that the surface stress represents the surface exerting a tensile stress on the core (or the core exerting compressive stress on the surface), which is often denoted as “negative” surface stress. In any case, it nets lattice expansion. For expansion energy, again, the absolute value in this case represents the energy for the lattice parameter to increase. For these particular calculations, we have used standard literature values for the bulk modulus of these oxides,59,75–78 although we will revisit the wisdom of such a choice in Chapters 2 and 4.

34 1.6 Discussion and Conclusions

The experimental results obtained in this chapter are consistent with Diehm’s framework of surface stress. For all five oxide systems, lattice expansion was observed. In the case of ceria this is probably due to both surface adsorbents and surface cation reduction, as depicted in Figure 1.3.b.middle and 1.3.b.right. Micron crystallites of ceria under ambient conditions are almost completely stoichiometric, represented as CeO2, but it is well-documented that nanoscale crystallites have up to 6% of their surface cations in the Ce3+ state,16 and so these nanoparticles are in fact more accurately represented as CeO2-x, where x is small, and cerium exists in the Ce3+ state in addition to the Ce4+ state. This phenomenon is sometimes described as nonstoichiometry. The share of Ce3+ ions may further increase under vacuum for ceria, where such non-stoichiometry may perhaps more than suffice for a negative surface stress, despite the lack of adsorbents under vacuum conditions. We have conducted thermogravimetric studies, not detailed here, that are strongly suggestive of significant physical adsorption of ambient gasses (H2O and CO2) for ceria nanoparticles under ambient conditions—such adsorbents are shown to dissociate under mild heating in air, as will be discussed further in Chapter 3. These adsorbents are not present to any appreciable extent in micron crystallites. Our ceria nanoparticles were not cleaned or oxidized in any rigorous ways such as in reports that saw ceria nanoparticle lattice contraction,17 and so we would expect lattice expansion for otherwise ambient nanoparticles (as we did observe). Magnesia is different from ceria in that it is rigorously stoichiometric. We have conducted X-ray Photoelectric Spectrum (XPS) studies, not detailed here, that con-

35 ﬁrm the Mg2+ oxidation state (to the exclusion of any other oxidation state) across all crystallite sizes of magnesia. The lattice expansion in magnesia, then, is due exclusively to the present of surface irregularities such as hydroxides. Indeed, it is

79 well-documented that MgO has a tendency to form Mg(OH)2 at its surface, which probably increases the surface coordination of MgO in a way similar to adsorbents such as CO2 and H2O. We found, in fact, that if MgO nanoparticles were not characterized in a timely fashion or stored in conscientiously clean and dry conditions, they eventually decomposed from a single crystalline oxide phase to mixed hydroxylated- oxide phases that were poorly definable by XRD. The results here are also consistent with previous reports of MgO nanoparticles exhibiting contration under vacuum conditions, and expansion under ambient conditions.18 Our XRD studies were conducted under ambient conditions and so expansion would be expected (and was observed). For ceria, vacuum may exacerbate negative surface stress due to its facilitation of the formation of oxygen vacancies and cation reductions at the surface. For magnesia, vacuum serves only to clean the surface of adsorbents and hydroxides and hence changes the sign of the surface stress from negative to positive. The surface stress situation of cuprite is different from both ceria and magnesia. Like ceria, cuprite is capable of exhibiting oxygen non-stoichiometry. Unlike ceria, cuprite’s secondary phase is a more oxidized version, rather than a more reduced one. Put another way, ceria’s primary cation is Ce4+ but small crystallites are shown experimentally to contain a signification portion of reduced Ce3+, whereas cuprite’s primary cation is Cu+ but small crystallites are shown experimentally to have a significant portion of the oxidized Cu2+ cation. Put yet another way, ceria is

CeO2-x, whereas cuprite is Cu2O1+x. We have explored the oxidation state variation

36 of cuprite elsewhere, and have strong X-ray Absorption Near Edge Spectroscopy (XANES) evidence for the presence of Cu2+ in small crystallites of cuprite.2 We have modelled this excess Cu2+ to be surface-localized.80 Using a simple model of ionic size based on oxidation state, one might expect such a situation to yield positive surface stress in cuprite. In fact, the speciﬁc cubic crystal structure of cuprite is somewhat special. It features an O-Cu-O-Cu zig-zag chain with an unusually short Cu-O bond length of 1.85 A,˚ which is short relative to its low coordination and oxidation state. Monoclinic crystals of CuO, on the other hand, feature a Cu-O bond length of 1.88-

81 1.96 A,˚ which is longer than Cu2O. This is the opposite trend that one would expect based on abstracted ionic radius alone. Thus a careful consideration of bonds lengths in speciﬁc crystal structures indicates that it is distinctly possible that even if there is a surface layer of CuO in small crystallites of cuprite, as we posit there is, that this more oxidized layer in fact contributes to surface stress in the negative sense, and such a surface would in fact exert a tensile stress on the core and result in the lattice expansion seen experimentally here. Cuprite of course could also have surface adsorbents that further contribute to its negative surface stress.82

The isostructural Fe3O4 and Co3O4 are both in relatively oxidized states and a slightly reduced surface (as in ceria) would not be surprising for them. This would be consistent with the observed lattice expansion observed experimentally here. It may be instructive in future studies to conduct careful measurements the lattice changes in nanoparticles of other oxide materials, in a way parallel to the studies described here. In particular, it may be instructive to measure lattice changes in

CuO (although it is monoclinic, not cubic) to compare to the Cu2O results obtained here, and in CoO (which is often cubic but sometimes hexagonal) to compare to

37 83 the Co3O4 results here. This may be as simple as oxidizing Cu2O nanoparticles or reducing Co3O4 nanoparticles (or of course it may be much more involved). It may also be instructive to rigorously measure the lattice parameter expansion in

84 85 other oxides such as ZnO and Mn3O4, for which a fair amount of nanoparticle preparation knowledge has already been obtained. In carrying out such studies it would also be worthwhile to recall that a case of lattice contraction for an oxide would not be particularly surprising, if that oxide surface were particularly clean or stoichiometric or resistant to adsorption. A case of lattice contraction may also be observed for an oxide featuring a slightly increased oxidation state at the surface (as long as their crystal structures are not so special as cuprite). In fact such as case has already been observed for UO2, which tends to oxidize non-stoichiometrically as UO2+x and whose small crystallites see signiﬁcant contractions in lattice parameter.86 Rock salt CoO may be another good candidate to potentially observe lattice contraction in small oxide crystallites because it tends to oxidize to Co3O4. Lattice expansion has been observed for CoO nanoparticles when coated in organics,87 but perhaps cleaned nanoparticles will exhibit contraction due to an oxidized surface. All such cases are consistent with the framework described in this chapter.

38 Chapter 2

Crystallite Size Dependency of the Lattice Response to Pressure in Nanoparticles of CeO2

2.1 Preface

Some parts of this chapter are based on a manuscript entitled “Size dependent compressibility of nano-ceria: Minimum near 33 nm,” by P.P. Rodenbough, J. Song, D. Walker, S.M. Clark, B. Kalkan, and S.-W. Chan, which appears in Applied Physics

47 Letters. JS assisted with some CeO2 preparation. JS, SMC, and BK assisted with some synchrotron measurements. DW assisted with some data interpretation.

2.2 Introduction

It is well established that nano-structured materials often have physical and chemical properties that diﬀer from their larger counterparts.88 It is common, however, to treat bulk modulus as an attribute that does not change with crystallite size, particularly when explaining size dependent lattice parameter expansions or contractions in

39 nanomaterials. This happens consistently with otherwise sound explanations.10–12,89 It is important to use clear terminology in these studies. Bulk modulus refers to the reciprocal of a material’s relative volume decrease under hydrostatic pressure. It is not to be confused with compressibility and elasticity, which are separate (but related) terms. The term compressibility typically refers to the reciprocal of bulk modulus. Materials with a high bulk modulus have low compressibility, and vice versa. Elasticity is a term often used loosely but rigorously refers to the elastic modulus (also known as Young’s modulus), which is material’s change in length relative to force applied in one dimension. The elastic modulus should not be confused with elasticity in general, which often means mechanical reversibility, as opposed to plasticity, which refers to mechanical irreversibility. The more rigorous term for elasticity in this sense is actually compliance. In the studies discussed presently we are concerned with bulk modulus, for which applied pressure is three-dimensional and isotropic (for a material that can be treated isotropically). The term bulk modulus is also not to be confused as an indicator of crystallite size: large crystallites are sometimes referred to as bulk material, but the bulk modulus is a property of crystallites of any size. The response of a crystalline lattice to pressure, then, can be quantitatively measured as the bulk modulus. Oxides, whose lattices often expand with decreasing crystallite size, are useful as microelectronic circuits, sensors, piezoelectric devices, fuel cells, and catalysts,90 so it is probably worthwhile to understand how their bonding changes for nanoscale crystallites. In particular, physical mechanical properties of nanoparticles (like bulk modulus) are in some ways more poorly understood than electrical or optical properties.91,92 Good evidence has been mounting that bulk modulus of oxide nanoparticles

40 is diﬀerent from the same material at larger crystallite size,93,94 but few studies test over a large range of diﬀerent crystallite sizes, which is key to detailing trends.95 We present here experimental evidence that bulk modulus of ceria increases from the bulk to reach a maximum near a crystallite diameter of 33 nm, and then decreases for smaller crystallite sizes. We examine several potential explanations for this behavior, which together may lead to a better understanding of the bonding environment for oxide nanoparticles.

2.3 Experiments

45,46 Nanoparticles of CeO2 were prepared as described in Section 1.4.1 and elsewhere. For the bulk modulus measurements, high pressure x-ray diffraction measurements were performed at ambient temperature using a standard symmetric diamond anvil cell (DAC) which consists of two 300 µm culet diamonds with a rhenium gasket indented to 50 µm thickness near the sample chamber. Ceria powder, mixed with ruby chip pressure markers, was loaded in an 110 µm hole drilled at the center of the indentation. Helium or argon was used as the pressure transmitting fluid. X- ray diffraction data was collected on beamline 12.2.2 of the Advanced Light Source at Lawrence Berkeley National Lab.96 A Si(111) double-crystal monochromator was used for wavelength selection, and diffraction data was collected using a MAR345 image plate at an x-ray energy of 30 keV (0.4133 A)˚ and a sample-to-detector dis- tance 280 mm determined with a LaB6 standard. Diffraction data was integrated using Fit2d97 and unit cell lattice parameters and volumes were determined with Celref software.27 The volume of the unit cell calculated as the cube of the unit cell lattice parameter, since the lattice of ceria is cubic.

41 The pressure in the diamond anvil cell was adjusted by turning the screws on the DAC and the pressure was measured with ruby ﬂuorescence. The ruby ﬂuores- cence spectra typically showed a sharp doublet throughout the measurements, with no measurable broadening of the peaks. The sharpness of the doublets and the uniformity of the pressures recorded indicate that any non-hydrostaticity that might be present in our measurements was, for the most part, below a measurable level over the entire range of pressures investigated in this study.

2.4 Results

The collected high-pressure XRD data is detailed in Table 2.1 and plotted in Figure 2.1. For Table 2.1, the header is crystallite diameter. Pressure P refers to the ruby fluorescence reporting the pressure inside the DAC and is given in gigapascals (GPa). Volume V refers to the volume of the unit cell for ceria sample as calculated from the XRD pattern, and is given in cubic angstroms (A˚3). The data, although neither perfectly linear nor a perfect fit with a Birch-Murnaghan equation of states, is free from drastic discontinuities and sharp slope changes sometimes seen in other reports on ceria nanoparticles.94 We attribute this to selection of the pressure-transmitting medium (PTM) as helium or argon. Experimenters who have chosen a mixture of methanol and ethanol as a PTM sometimes see significant and sharp deviations from linearity (especially above 15 GPa) which may come from the non-hydrostaticity of the PTM solidifying. These PTM-artifact deviations hinder study of the analyte of interest. The arrows in Figure 2.1 indicate the greatest response to pressure (arrow a, the 6 nm sample) and the least response to pressure (arrow b, the 33 nm sample), corresponding respectively to the lowest and highest bulk modulus, further detailed

42 6nm 13nm 20nm 26nm 33nm 52nm 87nm >100nm PV PV PV PV PV PV PV PV 0.0 159.4 0.0 159.8 4.2 157.0 6.0 154.5 0.0 158.3 0.4 157.7 0.6 158.5 0.0 159.8 1.3 158.0 3.9 156.5 5.3 156.3 7.7 153.9 3.7 156.3 1.1 157.6 3.9 156.6 3.9 156.5 2.0 158.4 4.7 157.5 6.9 155.5 8.8 153.5 3.9 156.2 1.8 157.4 7.6 154.9 6.5 155.6 3.1 157.1 6.5 155.6 8.4 154.9 10.1 153.0 5.3 155.4 1.9 157.1 9.3 154.0 8.1 154.4 4.4 155.9 8.1 154.4 11.5 154.0 11.2 152.1 6.9 154.8 3.5 156.5 10.3 153.2 9.3 153.5 5.5 155.7 9.3 153.5 13.5 153.1 13.5 150.9 7.7 154.7 4.2 156.3 11.6 152.5 11.6 152.7 6.8 153.7 11.6 152.7 14.4 152.3 16.2 149.6 8.7 155.1 7.5 154.7 13.0 151.9 13.0 151.8 8.1 152.8 13.0 151.8 15.2 152.3 19.1 147.7 10.3 154.8 8.2 154.4 15.6 150.8 14.7 151.0 9.5 151.8 14.7 151.0 17.2 151.4 20.7 146.8 14.0 153.5 8.7 154.0 19.0 148.9 15.5 150.2 11.4 150.7 15.5 150.2 17.4 151.4 23.1 145.1 16.5 152.3 12.7 152.2 19.8 148.7 16.8 149.1 14.2 148.8 16.8 149.1 19.8 151.0 14.1 151.6 21.0 148.1 17.9 148.8 14.9 148.6 17.9 148.8 21.0 150.7 16.2 150.5 23.8 146.4 19.2 148.2 16.5 148.3 19.2 148.2 22.7 150.1 18.4 149.9 26.4 145.4 20.1 147.7 18.6 147.1 20.1 147.7 25.6 149.2 21.2 148.9 21.1 146.6 26.0 147.9 18.6 174.4

Table 2.1: Experimental values for pressure versus volume of ceria unit cells of diﬀerent crystallite diameters. shortly. The bulk modulus, B, was calculated several diﬀerent ways. First, it was calculated simply as B = −V0∆P/∆V , over the range of data. Then, it was calculated using the Birch-Murnaghan (BM) equation of state (EoS),98,99 with software EoSFit7100. Finally, the bulk modulus was calculated with f-F plots.101 We readily acknowledge that for the BM EoS,

Crystallite some of the fits were not perfect. It was decided diameter B0 ’ V0 B (nm) 6 4 160.00 193 that the best representation of the bulk modu- 13 4 159.66 221 20 12 159.22 290 lus came from using the parameters detailed in 26 0 158.34 342 33 8 158.43 383 52 4 158.43 326 Table 2.2. For that table, B0’ is the pressure 87 4 158.43 259 >100 4 158.78 217 derivative of B and V0 represents the manually Table 2.2: Details of the parameters fixed initial volume based on a compromise be- used for calculated bulk modulus B, tween ambient XRD results and goodness of fit for ceria. with the BM EoS. We have decided that these parameters are appropriate because

43 Figure 2.1: Plot of unit cell volume as a function of applied pressure, for ceria of diﬀerent crystallite diameters.

44 Figure 2.2: Plot of bulk modulus as a function of crystallite size, for ceria. Dotted lines refer to the bulk modulus of large crystallite sizes from our experiments and from previous literature reports, as indicated. The curved line is a fit using Equation 2.1 they fit the experimental data best while still adhering to non-negative values for B0’ and reasonable values for V0. It is worthwhile to recall that these nanoparticles by their nature have broader XRD peaks and so the precision of the lattice parameter is inherently less than in large crystallite material. All three of these methods for calculating the bulk modulus produced the same general trend: as crystallite size decreased, bulk modulus first increased, then reached a peak at 33 nm, and then reached the lowest value from our set at 6 nm. And indeed

45 this is the general trend seen in Figure 2.1: the data is bound on the upper end by the 33 nm sample and on the lower end by the 6 nm sample. This gives us confidence that the trend we report is real. The differences between the bulk modulus values using different calculation methods, however, are concerning. Even within the BM

EoS method, values can change substantially through the tradeoﬀ between B0 and

B0’. In the end, we have the most confidence in the BM EoS values as reported in Table 2.2, where the bulk modulus and crystallite diameter are plotted in Figure 2.2. It is evident that with decreasing crystallite size, bulk modulus first increases and then decreases, reaching its maximum near 33 nm. The fit line in Figure 2.2 is not just a guide for the eyes and was in fact derived with some rigor which will be discussed later. The straight dotted lines in Figure 2.2 represent the bulk modulus of large crystallite (bulk) material: experimenetally determined in this experiment and taken from previous literature reports, as indicated.

2.5 Literature Review

There are several diﬀerent explanations that have been proposed for changes in bulk modulus for small crystallites. Z. Wang et al in 2001102 reported that the structure of their ceria nanoparticles (with crystallites 9-15 nm in diameter) started to change from ﬂuorite to orthorhombic α-PbCl2 at 22 GPa. Our experiments did not reproduce such a phase change. We do note that our maximum pressure (∼25 GPa) was much lower than Z. Wang’s maximum pressure in this case (∼38 GPa). Their 2001 studies also indicated that the bulk modulus of their ceria nanoparticles was enhanced relative to the micron-sized material: their ceria nanoparticles had a bulk modulus of 328 GPa, whereas their large-crystallite ceria had a bulk modulus of 230

46 GPa. In a follow-up study in 2004,103 Z. Wang et al reported noticeable discontinuities in their P vs V data for their ceria nanoparticles, starting at 20 GPa. They used no PTM for these experiments. Their conclusions are complicated by the proposal of in-situ particle coarsening, as evidenced through XRD peak sharpening, which was not evident in our experiments. Such coarsening may be related to synthesis method or absence of PTM. In continued studies reported in 2007,104 Z. Wang et al experimented with very small nanoparticles (3 nm), and found the bulk modulus of these particles to be enhanced relative to the large crystallites. They also postulated (through arguments based on homogenous stress field distributions and unusual behavior of defects and vacancies) that there may be a critical size where bulk modulus of nanoceria may suddenly become very enhanced; they estimate the critical size to be 7-18 nm. Ge et al reported in 201493 sudden changes in compressibility of their ceria nanoparticles at 10 GPa using methanol-ethanol-water as their PTM. Specifically, they saw their volumes become less responsive to pressure, indicating an increase in bulk modulus. Such apparent changes may be due to solidifying media. They followed their methanol-ethanol-water studies with N2 as their PTM, obtaining similar results. Their nanoparticles (4.7 and 5.6 nm diameter) were smaller than the ones used here, so it is possible that they are observing a separate phenomenon, but the PTM of helium or argon was not tested. Such results may also be related to the relative quantities of material and PTM in the cell, which experimentally is difficult to control with precision. Their explanation for the sudden bulk modulus increase has to do with increasing surface energy for smaller nanocrystals, which leads to hardening at small sizes. Ge’s interpretation is insufficient to explain the results

47 obtained here, as it accounts only for an increased bulk modulus as size decreases, and not for a peak in bulk modulus at intermediate size. Q. Wang et al reported in 201494 that the compression curve for their ceria nanoparticles was irregular above 12 GPa using silicon oil as the PTM. They sup- posed that good PTMs like helium or neon would be too soft to hinder the grains from touching each other and thus would be functionally equivalent to no PTM. Our results suggest that the selection of helium or argon as PTM is ﬁne. Their core-shell interpretation of their data is focused on explaining sharp slope sign changes, which are not seen in our data. Their core-shell interpretation is distinct from the core-shell model of Bian et al,105 which will be discussed shortly. None of these works on ceria nanoparticles consider crystallites over a wide range of diameters, whereas Chen et al reported in 200995 the bulk modulus of anatase titania nanoparticles over a very wide range of crystallite diameters, and their results are similar to ours. They measured 12 samples of diﬀerent sizes. The smallest was 3 nm and the largest was 45 nm (and then micron crystallites). As their crystallite size decreases, they see an initial increase in bulk modulus, followed by a decrease, with bulk modulus peaking near 15 nm crystallite diameter. They use hardening from dislocation networks to explain the increase in bulk modulus, and then they propose that the particles become too small to sustain such dislocations, which results in a decreasing bulk modulus after 15 nm. Further studies on anatase titania nanoparticles raise concerns over some experimental details,106 but Chen’s work was probably cor- rect in revealing such a trend of bulk modulus peaking at an intermediate crystallite size. A similar trend was observed by Bian et al in 2014105 for a wide size-range of

48 PbS nanoparticles. They describe a core-shell model. They take special note that they have achieved high-quality crystallites that are defect-free, as evidenced by high- resolution TEM, and therefore Chen’s explanation of bulk modulus trends depending on dislocations is less convincing. Explanations that rely on diameter-dependent lattice expansion also do not apply here, because the lattice of ceria only expands at small diameters, which does not ﬁt bimodal bulk modulus behavior. Furthermore, Bian shows that expanding lattice parameter of PbS nanoparticles is quantitatively inadequate to explain the magnitude of the changes in bulk modulus. As a sidenote, the lattice expansion that Bian observed in most likely due to the presence of oleate passivating groups at the surface of the PbS nanoparticles.107

2.6 Core-shell Model for Variable Bulk Modulus

We use Bian’s core-shell model to understand the trend observed in our ceria nanoparticles. This model is distinct both from the bulk modulus model proposed by Q. Wang94 and the model used to understand surface stress in Section 1.3. Under this core-shell model for understanding variable bulk modulus, ceria has a shell region and a core region. The core region has a constant bulk modulus, equal to that of large crystallites, while the shell region has a size-dependent bulk modulus. In a large crystallite, the bulk modulus of the shell is higher than that of the core, because of surface reconstruction and higher packing density at the surface. The concept of shorter and stronger Ce-O bonds at the surface of ceria is supported by some ﬁrst-principle electronic calculations.102 But at large crystallite sizes, this counts little overall because of the small surface area to volume ratio. As crystallite size decreases, the shell becomes more important, as the surface area to volume ratio

49 increases, and the consequence is an increased effective bulk modulus up to a peak near 33 nm. At diameters smaller than 33 nm, the size-dependency of the bulk modulus of the shell begins. The shell bulk modulus is expected to decrease with smaller nanocrystal sizes because of curvature effects. The bulk modulus of a surface shell is greatest in a flat slab, and decreases as surface curvature becomes more severe and radius decreases. The surface ions have fewer partners to bond with even under the most favorable reconstruction. Overall, this core-shell empirical qualitative model satisfactorily explains the peaking of bulk modulus at an intermediate crystallite diameter in all three inorganic crystallites considered here: ceria, titania, and lead sulfide. We completed a fit of our data with the crystallite size dependent bulk modulus function detailed by Bian. The fitted line is featured in Figure 2.2. In Bian’s original notation, the function is:

c(Kc − Ks) Keff = Ks + (2.1) 1 + (1 − c) (Kc−Ks) (Ks+(4Gs/3))

Where Keff is the effective bulk modulus, Ks is the bulk modulus of the shell region, c is the volume fraction of the core, Kc is the bulk modulus of the core region, and Gs is the shear modulus. The thickness of the shell region is embedded in c. The fit that we achieved provides the same trend as the experimental data, and matches only slightly worse than Bian’s fit for PbS (which is imperfect to start with). It is possible that non-stoichiometry of ceria may be responsible for some of the poorness of the fit: non-stoichiometry is not part of Bian’s model. The fit line shown here uses a flat shell layer bulk modulus of 350 GPa and a shell thickness of 9 nm.

50 There are important differences between this core-shell model for understanding bulk modulus and the framework for understanding surface stress as presented in Chapter 1. In particular, this core-shell bulk modulus model uses surface reconstruction and higher electron densities at the surface (which suggests shorter stronger bonds and positive surface stress) to explain the higher bulk modulus of the surface for low curvatures. The very data provided by Bian, however, indicates that his PbS nanoparticles in fact have increased lattice parameter at small crystallite sizes, which implies a negative surface stress. It is not clear how to reconcile these observations coherently within both frameworks. Additionally, the framework presented in Sec- tion 1.3 relies on surfaces that are coherent with their core, not reconstructed as the core-shell bulk modulus model supposes. It should also be noted that the core-shell bulk modulus model treats nanoparticles as perfect spheres, but of course small nanoparticles have facets that are very important. A model that incorporates the faceted nature of nanoparticles may be more accurate. The core-shell bulk modulus also incorporates a constant shell thickness, but there is no real reason why the shell thickness should remain constant across all crystallite sizes. It is very possible that the shell thickness could be changing and a model that allows for this may better fit the data. Although it is on some level satisfying to have an explanation of variable bulk modulus to which a curve can be fitted, it is on another level unsatisfying to have questions left regarding the precise role of the surface, in terms of how surface stress and non-stoichiometry help determine bulk modulus. We also note that the crystallite size dependent bulk modulus complicates the calculations presented in Section 1.5, for which only standard large-crystallite bulk modulus values were used.

51 2.7 Conclusions

We have presented experimental evidence of the crystallite size dependence of the bulk modulus of ceria, illustrated the importance of testing nanomaterials over a range of sizes, and emphasized the importance of using a suitable PTM for high- pressure XRD studies. Our results are consistent with a core-shell theoretical explanation for the observed experimental behavior. This ﬁnding of bulk modulus ex- tremum in ceria nanoparticles helps further understand their characteristics, which may aﬀect their use in applied technologies such as heterogeneous catalysis.

52 Chapter 3

Crystallite Size Dependency of the Lattice Response to Temperature in Nanoparticles of CeO2

3.1 Preface

Dr Misha Lipatov assisted with some of the calculations in this chapter. A manuscript of this chapter is currently in preparation for submission to an academic journal.

3.2 Introduction

While bulk modulus represents the response of a crystalline lattice to pressure, the coeﬃcient of thermal expansion represents the response of a crystalline lattice to temperature. In some contexts, thermal expansion refers to macroscopic expansion of polycrystalline or large single-crystal materials at elevated temperatures. In the context of this chapter, however, thermal expansion refers to the temperature-based expansion of atomic spacing (or more precisely, the unit cell) within crystallites as measured by XRD. The thermal response is another mechanical property, like

53 pressure response, that remains poorly characterized and understood in nanoscale materials, especially in comparison to electronic and optical properties. In many engineering applications, it is often preferable to use materials that feature minimal thermal expansion. Invar, for example, is famous for its low thermal expansion.108 Other modern materials feature a negative thermal expansion, in which heating causes contraction, a phenomenon that is only starting to be fully understood.109 Thermal expansion is also related to other important material properties such as resistance to thermal shock, a variant of thermal expansion that incorporates timescale and thermal conductivity, and a property to which borosilicate glass (the material of modern standard laboratory glassware) owes much of its popularity.110 We readily acknowledge that grain boundaries are essential to the function of such macroscopic applications of materials, and our study of monocrystalline nanoparticles does not address how they would behave in composite form. But the behavior of monocrystalline lattices is probably an important prerequisite (that is currently lacking) for any such broader understanding. This chapter features the careful measurements of thermal expansion for ceria nanoparticles across a wide range of crystallite sizes. Such an experiment probing the crystallite size dependency of thermal expansion has virtually no precedence in literature. We found that as crystallite size decreases, the coeﬃcient of thermal expansion decreases as well. This means that when small crystallites are heated, they expand less than larger crystallites do, under the same conditions. We are also able to separate diﬀerent contributing factors to the surface stress of CeO2 nanoparticles.

54 3.3 Experiments

Nanoparticles of ceria were prepared as described in Section 1.4.1. Variable-temperature (VT) XRD experiments were performed on a Panalytical XRD isntrument with an integrated temperature control and heating apparatus. Samples were heated from

50°C to 400°C, with pauses to take a set of XRD scans at 50°C intervals. XRD scans were collected up to 100° 2Θ. Typically, two heating and cooling cycles were performed on the same sample in immediate succession. The experiments were performed in air under ambient pressure. Lattice parameter was determined from XRD measurements as described in Section 1.4 and 1.5.

3.4 Results

Table 3.1 provides the full data set collected. Figure 3.1 features a representative plot of selected data. The coefficient of thermal expansion was typically calculated as the slope of the plot of expansion (∆a) vs temperature, for an average of the heating and cooling cycles. Since the smaller crystallites usually feature sharp discontinuities in lattice changes during the first heating cycle, the coefficient of thermal expansion was typically calculated from the second heating/cooling cycle. We note that thermal expansion (or coefficient thereof) is sometimes expressed in K-1 (as calculated from

∆a/a0) and other times in A/K˚ (as calculated from ∆a); we have chosen the latter expression here. Crystallite size was monitored throughout the VT XRD process (as indicated by peak width) and was found to be constant within stochastic variability noise (typically no more than ± 0.5 nm). The maximum temperature of 400°C was speciﬁcally

55 lattice parameter (A)˚ for crystallite size provided Step- Temp 5.3nm 6.3nm 8.0nm 8.8nm 12.0nm 17.2nm 26.2nm 38.4nm 51.6nm 68.5nm >100nm (°C) 1-50 5.4291 5.4288 5.4244 5.4241 5.4164 5.4163 5.4189 5.4156 5.4177 5.4174 5.4151 2-100 5.4302 5.4319 5.4246 5.4249 5.4180 5.4182 5.4208 5.4181 5.4202 5.4197 5.4180 3-150 5.4364 5.4366 5.4293 5.4268 5.4185 5.4201 5.4235 5.4206 5.4228 5.4228 5.4204 4-200 5.4344 5.4373 5.4299 5.4270 5.4212 5.4221 5.4255 5.4235 5.4248 5.4251 5.4232 5-250 5.4324 5.4349 5.4261 5.4224 5.4226 5.4250 5.4284 5.4258 5.4281 5.4282 5.4257 6-300 5.4317 5.4319 5.4214 5.4181 5.4248 5.4267 5.4296 5.4285 5.4299 5.4302 5.4280 7-350 5.4334 5.4325 5.4224 5.4179 5.4273 5.4294 5.4317 5.4309 5.4326 5.4326 5.4304 8-400 5.4357 5.4354 5.4275 5.4221 5.4314 5.4320 5.4336 5.4332 5.4348 5.4348 5.4330 9-350 5.4328 5.4324 5.4257 5.4206 5.4282 5.4295 5.4310 5.4303 5.4318 5.4320 5.4301 10-300 5.4317 5.4282 5.4236 5.4170 5.4259 5.4274 5.4287 5.4274 5.4292 5.4298 5.4267 11-250 5.4293 5.4272 5.4219 5.4160 5.4233 5.4253 5.4264 5.4250 5.4264 5.4273 5.4238 12-200 5.4269 5.4267 5.4202 5.4143 5.4216 5.4230 5.4241 5.4222 5.4240 5.4234 5.4217 13-150 5.4268 5.4260 5.4189 5.4155 5.4197 5.4206 5.4216 5.4198 5.4217 5.4212 5.4194 14-100 5.4255 5.4289 5.4175 5.4136 5.4177 5.4183 5.4193 5.4174 5.4192 5.4189 5.4162 15-50 5.4246 5.4281 5.4162 5.4124 5.4155 5.4156 5.4171 5.4150 5.4168 5.4160 5.4138 16-100 5.4248 5.4314 5.4182 5.4140 5.4178 5.4187 5.4199 - 5.4197 5.4193 5.4170 17-150 5.4281 5.4275 5.4200 5.4170 5.4207 5.4213 5.4223 - 5.4221 5.4218 5.4197 18-200 5.4281 5.4348 5.4262 5.4185 5.4225 5.4239 5.4250 - 5.4255 5.4239 5.4219 19-250 5.4318 5.4356 5.4242 5.4185 5.4265 5.4264 5.4278 - 5.4272 5.4277 5.4242 20-300 5.4323 5.4372 5.4261 5.4216 5.4249 5.4282 5.4303 - 5.4302 5.4304 5.4274 21-350 5.4325 5.4390 5.4278 5.4225 5.4299 5.4304 5.4326 - 5.4325 5.4335 5.4304 22-400 5.4362 5.4395 5.4296 5.4256 5.4321 5.4324 5.4347 - 5.4348 5.4359 5.4330 23-350 5.4346 5.4361 5.4274 5.4231 5.4284 5.4298 5.4319 - 5.4321 5.4327 5.4304 24-300 5.4320 5.4354 5.4250 5.4211 5.4259 5.4275 5.4291 - 5.4291 5.4299 5.4271 25-250 5.4315 5.4324 5.4228 5.4192 5.4232 5.4254 5.4265 - 5.4268 5.4270 5.4236 26-200 5.4279 5.4296 5.4206 5.4171 5.4216 5.4230 5.4240 - 5.4242 5.4239 5.4217 27-150 5.4273 5.4302 5.4194 5.4169 5.4198 5.4207 5.4216 - 5.4216 5.4213 5.4187 28-100 5.4247 5.4298 5.4178 5.4140 5.4174 5.4184 5.4193 - 5.4195 5.4196 5.4168 29-50 5.4273 5.4312 5.4167 5.4123 5.4155 5.4162 5.4170 - 5.4167 5.4168 5.4135

Table 3.1: Experimental values for thermal expansion of ceria crystallites of diﬀerent diameters.

56 Figure 3.1: Cyclic temperature ramping experiments plotted out. Lattice parameter changes in small and large crystallites of ceria, as temperature cycles back and forth twice between 50 and 400°C

57 chosen to be under the temperature at which ceria is known to coarsen. To reiter- ate: crystallite size was monitored throughout the heating process for all samples (with the Scherrer equation), and the particle size only displayed stochastic variation within a window of about 1 nm, and the particles did not coarsen throughout the heating process.

3.5 Discussion

The large crystallite samples feature very regular thermal expansion. Rep- resentative XRD scans of the (511/333) peak in large crystallites are detailed in Figure 3.2, where a clear shift to the left can be seen for the heating process (these peaks also feature Kα1/Kα2 splitting). This is followed by a shift back to the right for the cooling process. This is standard thermal response Figure 3.2: Detail of (511/333) peak shifts during thermal expansion or ceria, with behavior to be expected for large crys- prominent Kα1/Kα2 splitting. tallites. The small crystallite samples feature thermal expansion as well, but their behavior is more complicated. First, recall that such small crystallites typically start oﬀ with a larger lattice parameter, as detailed in Chapter 1. Second, recall that due to the extensive peak broadening, the precise determination of the lattice parameter of such samples is inherently less certain, due simply to the nature of ﬁtting broad peaks

58 versus sharp peaks. Two of the most salient features of the thermal expansion of small crystallites of ceria are the sharp discontinuities upon the first heating cycle, and the smaller lattice parameter at the starting temperature for the second cycle. This behavior can be explained using the framework described in Chapter 1. Recall that small crystallites of ceria have increased surface adsorbents (principally H2O and CO2, but also peroxides, superoxides, and hydroxyl groups,111 and also organics) that play important roles in determining surface stress and lattice parameter deviations. In particular, HMT decomposes slowly to formaldehyde and ammonia in water, so these likely have a residual presence in ceria nanoparticles. During the first heating cycle, such adsorbents are burnt off, and so the first heating cycle represents the ceria under dynamic conditions in which the surface environment is changing drastically.

After the first cooling cycle, when the temperature has returned to 50°C, the lattice parameter is significantly smaller than its starting value. This is to be expected. The surface has effectively been cleaned by heating, and recall from Figure 1.3 that a cleaner surface contributes to lattice contraction. Even after a cycle of heating, however, the lattice parameter of small crystallites is still greater than that of large crystallites. This effectively gives us a way to separate out the effects of lattice expansion due to surface adsoprtion (Figure 1.3.b.middle), and lattice expansion due to oxygen vacancies and cation charge variances at the surface (Figure 1.3.b.right). We suggest that although heating in air at ambient pressure to such moderate temperatures will remove surface adsorbents, such a treatment will not significantly affect the oxygen vacancies and cation charge environment of the surface of ceria.

59 3.5.1 Crystallographic Defects in Ceria

Before going further, it is worthwhile to discuss the defect chemistry of ceria in detail. The characteristic crystallographic defect in ceria is an oxygen vacancy coupled with two cerium cation reductions, which can be notated generally as:112

1 [2Ce4+, O2−] → [2Ce3+,V ] + O (3.1) O 2 2(g)

In more rigourous Kroger-Vink notation, such a defect is is notated as:

0 1 −−−→CeO2 2Ce + 3Ox + V •• + O (3.2) ∅ Ce O O 2 2(g)

Where ∅ represents the defect-free crystal structure. Such a defect in Equation 3.2 is distinct from the classical Schottky and Frenkel defects, which in theory for ceria would be represented (respectively) as:

CeO2 0000 •• ∅ −−−→ VCe + 2VO (3.3)

CeO2 x x •• 00 ∅ −−−→ CeCe + OO + VO + Oi (3.4)

Where in this case the Frenkel defect is an oxygen migrating to an interstitial site (although other theoretical iterations such as cerium migration could also be classiﬁed as Frenkel-type).

60 (a) Constant defect case, ∆a/a0 = ∆l/l0 (b) Increasing interstitial case, ∆a/a0 > ∆l/l0

Figure 3.3: Thermal experiments can be used to determine predominant defect types. 3.5.2 Simmons and Balluﬃ Experiment Review

It is important to note that such Schottky and Frenkel defects are often not experimentally understood to occur in ceria, but they form an important framework in understanding defect chemistry more generally. In a classic materials science experiment, Ralph Simmons and Robert Balluﬃ in 1960113 measured the lattice expansion and total expansion in polycrystalline aluminum under heat. From such experiments, it is often possible to distinguish which type of defect is characteristic in a material. As Figure 3.3 details, information can be gathered if there is an increase in defects with temperature for a macroscopic polycrystalline bar of material. If atoms tend to vacate their original location and move to the surface, then the overall length of the bar will increase more quickly than the lattice parameter. If instead atoms tend to move instead from the surface to interstitial locations, then the lattice parameter will increase more quickly than the total physical length of the bar. Thermodynamic calculations can be done to determine the precise concentration of defects in either of these two cases.

61 If the defect concentration does not change with temperature, however, then no quantitative information can be gathered from this type of experiment. Simmons and Balluffi’s original experiments were done on metals, most prominently aluminum, shown in Figure 3.4. Note that Schottky and Frenkel defects are typically used to describe compounds, not metals, and so the two defect cases Simmons and Balluffi instead referred to in their original work were simply vacancies versus interstitials (although their surface localization is important). Raymond Fournelle et al in 1993114, however, carried out similar experiments on ceria. He noted no difference in the relative expansion of the lattice parameter and the total length of a bar of polycrystalline ceria under heat. Instead of positing that there was no change in the concentration of defects with temperature (which is unlikely), rather he reasoned that the very nature of nonstoichiometric oxide defects renders these kinds of experiments ineffective. An increased defect concentration for nonstoichiometric oxides usually means oxygen vacancies and reduced cations as described in Equation 3.2. Oxygen, when creating a vacancy in such a manner, neither migrates from the core to the surface to increase the length of the bar, nor migrates from the surface to the core to inserts itself interstitially (which are the two possible scenarios envisioned by Simmons and Balluffi); it instead leaves as gaseous diatomic molecular oxygen. The cation reduction from Ce4+ to Ce3+ would contribute equally to a and l and so no difference would be expected. The non-difference between unit cell expansion and total bar length expansion is therefore good evidence for characteristic nonstoichiometric oxide defects of the type in Equation 3.2. Further evidence for such vacancies is provided by meticulous high-resolution STM studies.115 It is important to have a historical contextual understanding of these defects. For

62 Figure 3.4: The macroscopic length of aluminum increases more quickly than its lattice parameter under heat, indicating an increase in vacancy-type defects, as demonstrated by Simmons and Balluffi.113 No such difference is observed in ceria.114 example, although Fournelle’s results are highly suggestive that ceria forms defects according to Equation 3.2, it is classically understood that fluorite oxides typically form anion-Frenkel defects as in Equation 3.4. This is in contrast to rock salt oxides such as MgO which are typically classically understood to form Schottky defects (akin to Equation 3.3).116 We do not explore the possible effects that such Schottky and Frenkel defects may have, if they are indeed present, on lattice parameter and surface stress, although it is certainly an interesting line of thought.

63 3.5.3 Atmosphere Considerations

It is also noteworthy that the thermal expansion experiments in this chapter were conducted in air under ambient pressure. It is well known that the defect concentrations of oxides is closely tied to oxygen partial pressure. Brouwer diagrams118 reﬂect the relationship between oxygen partial pressure and defect concentration in oxides, and they often indicate under what oxygen parital pressure regime what kind of defect (Schottky, Figure 3.5: Brouwer diagrams relate defects to oxygen partial pres- Frenkel, or otherwise) will dominate. They also sure and semiconductor behavior, as illustrated by Fergus117 indicate the oxygen partial pressure regime under which an oxide material will behave as an n-type or p-type semiconductor, depending on the relative share of oxygen interstitials or vacancies. An example, idealized Brouwer diagram117 is provided in Figure 3.5 for a hypothetical oxide prone to Frenkel defects (note that this is not the case for ceria). Bauwer diagrams, it should be noted, are for a single temperature. Ellingham diagrams,119 meanwhile, use basic thermodynamics to illustrate the relationship between the free energy of formation of oxygen and temperature, for the reduction of CeO2 to Ce metal (or Ce2O3). Such a diagram does not speak to any kinetic considerations, but rather only addresses thermodynamics. Such a diagram is not detailed here. For the temperatures explored in this chapter in particular, and for the ambient atmosphere conditions employed, we do not expect signiﬁcant variations in the defect

64 concentration in our ceria samples over the course of these experiments. It would certainly be interesting to try similar thermal expansion experiments under diﬀerent atmospheres with control of oxygen partial pressure.

3.6 Calculations

We calculate the thermal expansion coeﬃcients as plotted in Figure 3.6. For the 5.3 and 8.0 nm ceria, we take a detailed look at the thermal expansion, as shown in Table

3.2. The start point is understood to be the first 50°C measurement, and the end point is understood to be the second 50°C measurement after one heating and cooling cycle. At the start, we understand the lattice expansion of ceria to be due to both surface adsorbents and surface nonstoichiometry. At the end point, we posit that the surface adsorbents have been removed, and the lattice expansion is due primarily to surface nonstoichiometry only (nonstoichiometric oxide type defects, Equation 3.2). So, then, we calculate the respective contributions to surface stress, in Table 3.2. For simplicity’s sake we have used the standard bulk modulus values from Chapter 1 in these calculations, although we acknowledge that the bulk modulus for such small crystallites may in fact be different, as detailed in Chapter 2. Surface stresses are reported in absolute values, although this is understood to be the surface exerting a tensile stress on the core (negative surface stress). We have suggested in past chapters that as ceria crystallite size decreases, both surface adsorbents and surface nonstoichiometry increase. Kuhlmann-Wilsdorf and Diehm’s theory of surface stress, however, suggests that surface stress is in fact constant across crystallite size, and only begins to have an observable effect on lattice parameter at small crystallite sizes due to increased surface-to-volume ratios. This

65 5.3nm 8.0nm >100nm start end start end start end lattice 5.4291 5.4246 5.4244 5.4162 5.4151 5.4138 parameter (A)˚

∆a/a0 0.00258 0.00199 0.00171 0.00044 - - Total Surface Stress for 5.3nm Crystallite (N/m) 2.261 From Surface Adsorbents 0.516 22.8% From Surface Nonstoichiometry 1.745 77.2% Total Surface Stress for 8.0nm Crystallite (N/m) 2.267 From Surface Adsorbents 1.682 74.2% From Surface Nonstoichiometry 0.585 25.8%

Table 3.2: Contributions to surface stress implies that the causative agents of surface stress (i.e. surface adsorbents and surface oxygen vacancies with cation charge variances) are also constant across crystallite size. It is not easy to reconcile these two concepts (constancy versus increase in surface stress components with size). For now, we have calculated surface stress here using individual values for a/a0 and d instead of as a slope for a set of data. The surface stress values for 5.3 and 8.0 nm ceria presented here agree with each other. The ﬁnding of an increased contribution to negative surface stress from surface non- stoichiometry at smaller crystallite sizes is consistent with the stronger evidence from XANES and XPS for such a surface environment,16,25 compared to the somewhat more anecdotal evidence for increased surface adsorbents at smaller crystallite sizes from TGA not detailed in this dissertation. The calculations presented here suggests that reduced ceria surfaces actually have fewer surface adsorbents, a phenomenon that may merit further study in future experiments. The general trend of decreased thermal expansion for smaller crystallites, as

66 Figure 3.6: The coeﬃcient of thermal expansion of the lattice parameter (CTELP) of ceria decreases for smaller crystallites.

67 shown in Figure 3.6 can be thought of an already-expanded lattice having little capacity to further expand under heat. We have ﬁt the data with a simple y = A−B/x ﬁt. The solid straight line in Figure 3.6 represents the experimentally determined thermal expansion of large crystallite (bulk) ceria.

3.7 Relation to Bulk Modulus

We note that thermal expansion and bulk modulus are traditionally related by the Gr¨uneisenparameter120 as follows:121

γC α = V (3.5) 3B

Where α is the coeﬃcient of thermal expansion of the lattice parameter, γ is the

Gr¨uneisenparameter, CV is the constant-volume heat capacity, and B is the bulk modulus. We note that in this expression, B has units of Pa, CV has units of J/K, and γ is dimensionless, which means that α would need to be expressed in m3/K, whereas we have used A/K˚ throughout this chapter. More importantly, we note that such a relation implies that, if γCV /3 is constant, so must be αB. Instead, as detailed in this chapter and in Chapter 2, both α and B decrease for crystallites under ∼15 nm, which quickly decreases the product of these two values. It is likely that Equation 3.5 is therefore insuﬃcient for accurate descriptions across wide ranges of crystallite sizes, and only good for a treatment of bulk material.

68 3.8 Conclusions

Through variable temperature experiments, the two contributing factors to negative surface stress can be separated. It is also found that small crystallites tend to have decreased thermal expansion coeﬃcients. It may be interesting in future experiments to control atmosphere, or to try similar experiments for crystallites with positive surface stress. It may also be interesting in the future to conduct experiments on the size dependency of heat capacity, as this may allow additional insight into the relationship between α, B, and CV . Finally, the relationship between surface adsorbents and surface non-stoichiometry, as evidenced in the calculations in this chapter, are highly suggestive that further studies on this topic may be interesting for applications of ceria nanoparticles in heterogenous catalysis.

69 Chapter 4

Crystallite Size Dependency of the Lattice Response to Pressure and Temperature in Nanoparticles of MgO

4.1 Preface

Some of the nanoparticle preparations reported here were assisted by Chengjunyi (Tony) Zheng, Ye (Mike) Wang, Yuxuan Xia, and Jiaqi (Fiona) Xue. The synchrotron studies were completed at Lawrence Berkeley National Lab’s Advanced Light Source, Beamline 12.2.2, with the guidance of Dr Jinyuan Yan and the as- sistance of Ye (Mike) Wang and Yuxuan Xia, and Argonne National Lab’s Ad- vanced Photon Source, Beamline 2-ID-D and HP-CAT, with the guidance of Drs Cai Zhonghou and Stanislav Sinogeikin.

70 4.2 Introduction

As has been explored previously, MgO diﬀers from CeO2 in important ways (especially in regards to non-stoichiometry tendancies). It will be interesting, therefore, to explore how the lattice of MgO responds to pressure and temperature, in comparison to the response of CeO2 as explored in Chapters 2 and 3.

4.3 Bulk Modulus Experiments and Discussion

Preparation of MgO nanoparticles was carried out as described in Chapter 1. Mea- surement of the bulk modulus was carried out mostly as described in Chapter 2. In- stead of using a PTM of helium, neon, or argon, we chose a PTM of methanol-ethanol for these experiments because it was easier to prepare. We avoided solidification of the PTM by staying mostly under 12 GPa. Measurement of the thermal expansion was carried out as described in Chapter 3. The bulk modulus data is detailed in Table 4.2, in which P represents the pressure of the interior of the diamond anvil cell as reported by ruby fluorescnece in units of GPa, and V represents the volume of the unit cell of magnesia for the crystallite 3 size of interest as determined by XRD in units of A˚ . A plot of the data is provided in Figure 4.1, in which arrow a highlights the particularly low volumes achieved by 9 nm magnesia at high pressure, arrow b draws attention to the particularly high volume achieved by 14 nm magnesia, and arrow c points to the medium volume achieved by large crystallite magnesia. Indeed, these cursory observations of the data are carried through the more rigorous BM EoS calculations, which are provided in Table 4.1, in which V0 is allowed to float. As plotted in Figure 4.2, magnesia

71 achieves a maximum in bulk modulus at 14 nm crystallite diameter, and the smallest bulk modulus observed was for the smallest crystallite size of 9 nm. The solid line represents the experimental large-crystallite bulk modulus of 153 GPa, whereas the dotted line represents previously reported bulk modulus of magnesia of 155 GPa.76 It may be noted that the peak in bulk modulus for magnesia is siginificantly less dramatic than the peak observed in ceria. We also note that these bulk modulus calculations for magnesia were carried out with fewer data points than those for ceria. This was a conscious choice. We wanted to use our limited synchrotron time to get data for as many different crystallite sizes as possible, even if the precision and certainty for each bulk modulus measurement was less than ideal. We acknowledge that this is a tradeoff between quantity (of sizes) and quality (of data for an individual size), but given the importance of measuring across a wide variety of crystallite sizes (as we have illustrated in Chapter 2 for ceria), we think we made the right choice. The crystallite size dependency of the bulk modulus

Crystallite of magnesia was studied previously by Marquardt et al in diameter B0 ’ B (nm) 122 9 3 77 2011. They used an acoustical method (Brillouin spec- 11 4 126 12 3 153 troscopy) very different from the method employed here. 14 4 166 20 2 152 23 4.5 150 They found that small crystallites of magnesia had a de- 26 5 155 creased bulk modulus compared to standard large crys- Table 4.1: Details of the parameters used for calcu- tallites. Their findings are consistent with the findings lated bulk modulus B, for reported here. magnesia. When magnesia is compared to the other materials reviewed in Chapter 2 (ceria, titania, and lead sulfide), it appears that the phenomenon of a peak in bulk modulus is relatively common. It is worthwhile perhaps to think of the relation to lattice

72 changes at small crystallite sizes. Ceria, magnesia, and lead sulfide all exhibit lattice expansion under most experimental conditions (which include surface hydroxyl groups for magnesia and oleate passivating groups for lead sulfide). Anatase titania is tetragonal, not cubic, and most reports for its size-dependent lattice changes indicate expansion in a offset by contraction in c.12 All these materials feature a peak in bulk modulus at an intermediate crystallite size in at least some studies.

86 Urania (UO2), on the other hand, features lattice contraction due to its over-

123 oxidized surface (UO2+x). Zvoriste-Walters et al found in 2013 that the bulk modulus of urania decreases monotonically with crystallite size. It is interesting to speculate that this very different bulk modulus behavior in urania may be related to its positive surface stress. Titania nitride (TiN), however, features both a positive surface stress and a peak in bulk modulus at intermediate crystallite size,94 so there may certainly be more to the story. Further complicating the story are the isostructural pair γ-Fe2O3 and γ-Al2O3, the former of which is reported to have a bulk modulus that peaks at an intermediate crystallite size,124 and the latter of which is reported to have a bulk modulus that decreases monotonically with crystallite size.125 A comprehensive explanation for the crystallite size dependency of bulk modulus remains elusive for now. As Figure 4.2 illustrates, the bulk modulus behavior for magnesia is similar to the behavior seen in ceria, and so such behavior at least cannot be due to nonstoichiometry (which is absent in magnesia). The bulk modulus of magnesia reaches a peak at an intermediate crystallite size, and decreases thereafter. We have fit the magnesia bulk modulus data with the same equation as in Chapter 2 in accordance with the core-shell model for crystallite size dependent bulk modulus. The fit line uses a flat

73 9nm 11nm 12nm 14nm 20nm 23nm 26nm >100nm PV PV PV PV PV PV PV PV 0.2 77.3 3.4 74.1 0.2 75.1 2.3 74.7 1.0 75.5 0.1 74.6 7.3 72.4 0.4 74.6 3.8 74.1 4.6 73.8 10.1 71.1 4.9 73.4 3.9 74.0 3.7 73.2 10.2 71.5 3.3 73.3 7.5 71.9 9.2 71.1 9.2 71.4 7.1 72.8 7.9 72.4 7.0 71.5 8.4 72.0 9.2 71.0 9.9 69.8 8.3 71.7 7.9 71.7 11.2 71.4 12.2 70.8 10.6 70.3 5.9 73.0 7.6 71.4 8.2 70.6 7.2 72.1 5.9 73.1 8.4 72.3 9.9 71.1 9.0 70.9 4.2 73.7 3.8 73.1 6.1 71.4 6.3 72.3 3.6 73.6 5.7 73.3 6.5 72.2 6.5 71.5 1.9 74.7 1.3 74.3 5.0 73.2 1.3 75.3 2.0 74.8 0.3 75.2

Table 4.2: Experimental values for applied pressure versus volume of magnesia unit cells, for diﬀerent crystallite diameters.

Figure 4.1: Plot of unit cell volume as a function of applied pressure, for magnesia of diﬀerent crystallite diameters.

74 Figure 4.2: Plot of bulk modulus as a function of crystallite size, for magnesia. Dotted line refers to the bulk modulus of large crystallite sizes from our experiments and and solid straight line refers to bulk modulus from previous literature reports. The curved line is a ﬁt using Equation 2.1

75 shell layer bulk modulus of 170 GPa and a shell thickness of 4 nm. The solid line in Figure 4.2 represents the experimentall determined bulk modulus of large cyrstallite magnesia, whereas the dotted line represents the bulk modulus of large crystallite magnesia from previous literature reports.

4.4 Thermal Expansion Experiments and Discus- sion

Magnesia nanoparticles were prepared as described in Chapter 1, and thermal expansion experiments were carried out as described in Chapter 3. We note that very small crystallites of magnesia have a significantly reduced coefficient of thermal expansion, whereas larger crystallites have a coefficient of thermal expansion closer to that of the bulk. Similar to Chapter 3, we have fit the data in Figure 4.4 with a simple y = A − B/x and although the fit is not as good at for ceria, it is still satisfactory. We take a detailed look at the representative thermal expansion of a small crystallite and a large crystallite of magnesia in Figure 4.3, where the large crystallite data (which is highly regular) has been duplicated over two cycles. There is some discontinuity in the first heating cycle, but in notable contrast to ceria, the lattice parameter of small-crystallite magnesia returns to the same value after a single heating and cooling cycle. There are two reasons for this behavior. The first reason is that as a matter of preparation methods, all magnesia nanoparticles are annealed at at least

500°C. Whatever weakly adsorbed material that may have stuck to the particles may have already been burnt oﬀ (which is not the case for most ceria nanoparticles). The astute observation at this point would be to say that the magnesia nanoparticles are

76 lattice parameter (A)˚ for crystallite size provided Step-Temp 9.1nm 12.3nm 13.6nm 23.5nm 34.0nm >100nm (°C) 1-50 4.2438 4.2340 4.2437 4.2216 4.2184 4.2150 2-100 4.2557 4.2168 3-150 4.2569 4.2194 4-200 4.2619 4.2219 5-250 4.2622 4.2245 6-300 4.2603 4.2272 7-350 4.2599 4.2297 8-400 4.2582 4.2321 9-350 4.2544 4.2297 10-300 4.2536 4.2272 11-250 4.2505 4.2248 12-200 4.2501 4.2222 13-150 4.2488 4.2197 14-100 4.2451 4.2173 15-50 4.2438 4.2311 4.2275 4.2196 4.2177 4.2151 16-100 4.2463 4.2328 4.2294 4.2218 4.2198 17-150 4.2481 4.2352 4.2323 4.2240 4.2220 18-200 4.2501 4.2370 4.2348 4.2260 4.2241 19-250 4.2521 4.2390 4.2368 4.2283 4.2263 20-300 4.2535 4.2402 4.2391 4.2301 4.2287 21-350 4.2543 4.2429 4.2422 4.2337 4.2310 22-400 4.2572 4.2443 4.2438 4.2342 4.2331 23-350 4.2535 4.2423 4.2410 4.2328 4.2308 24-300 4.2514 4.2397 4.2385 4.2298 4.2284 25-250 4.2498 4.2387 4.2356 4.2281 4.2263 26-200 4.2484 4.2362 4.2336 4.2257 4.2240 27-150 4.2471 4.2341 4.2309 4.2237 4.2221 28-100 4.2452 4.2307 4.2286 4.2211 4.2196 29-50 4.2440 4.2316 4.2267 4.2189 4.2178

Table 4.3: Experimental values for thermal expansion of magnesia crystallites of diﬀerent diameters.

77 Figure 4.3: Cyclic temperature ramping experiments plotted out. Lattice parameter changes in small and large crystallites of magnesia, as temperature cycles back and forth twice between 50 and 400°C.

78 Figure 4.4: The coeﬃcient of thermal expansion of the lattice parameter (CTELP) of magnesia decreases for smaller crystallites.

79 cleaned and non-stoichiometric, so they should exhibit lattice contraction, whereas the data shows expanded lattice parameters for small crystallites of magnesia compared to larger ones, even after heating and cooling cycles. This is easily explained using a detailed understanding of the surface structure of magnesia. In a detailed study in 1995, Keith Refson described the surface of magnesia as follows:“Supporting evidence is provided by well-crystallized natural growths of

Mg(OH)2 on MgO.... We conclude that the (111) hydroxyl, rather than the bare (001) is the normal surface of MgO under ambient environmental conditions. A (001) MgO surface will chemisorb water and reconstruct except under ultrahigh vacuum or high temperature. Dehydroxylation is experimentally observed only under UHV: indeed hydration reactions occur under lesser vacuum in the TEM at a partial pressure of water of 10 Pa. Upon heating dehydroxylation begins at 200°C but is gradual with residual hydroxyls persisting until over 700°C.”79 Thus, under our experimental conditions, the surface of magnesia still features extensive hydroxylation, even after moderate heating, which contributes to negative surface stress. This is in contrast to ceria, whose surfactants are more easily burnt off. Outlining how the bulk modulus relates to the thermal expansion for magnesia is an exercise parallel to that of ceria as described in Chapter 3. Both α and B decrease for very small crystallites, which means either that Equation 3.5 in insufficient or that γ and CV are also changing with crystallite size. There are certainly some thoughts suggestive that γ (and even γ for MgO specifically) may change under certain conditions.126–128 This would make an excellent area for further investigation.

80 4.5 Conclusions

In ways similar to ceria, the pressure and temperature response in magnesia has been investigated. It has been shown that bulk modulus of magnesia also has a peak at an intermediate crystallite size, although the peak is less dramatic. This suggests that nonstoichiometry cannot be the sole reason behind such bimodal behavior. Furthermore, the temperature studies illustrated that magnesia’s surface adsorbents and reconstructions are stable up to at least 400°C, consistent with the idea that magnesia’s negative surface stress is due to such surface abnormalities.

81 Chapter 5

Thermal Oxygen Exchange Cycles in Manganese Perovskites

5.1 Background

The unchecked burning of fossil fuels is not sustainable, and it is important to in- vestigate strategies to increase the value of waste CO2. One such strategy is to use thermal cycles of solid oxides to reduce CO2 to CO (and H2O to H2), as demonstrated

38 in a seminal report by William Chueh et al in 2010. CO and H2 are together known as syngas, and they can be very easily converted in synthetic fuels and other products via the Fischer-Tropsch process.129 Cheuh’s thermal cycle of ceria for carbon dioxide reduction featured two steps as follows:

δ 1500°C: CeO2(s) → CeO2-δ(s) + O2(g) (5.1) 2

900°C: CeO2-δ(s) + δCO2(g) → CeO2(s) + δCO(g) (5.2)

The high temperature step is carried out under inert gas ﬂow, which sweeps away the evolved oxygen, and the low temperature step features the re-oxidation of ceria

82 using CO2 (or H2O) as an oxidant, which produces CO (or H2). Such processes will be referred to generally here as thermal oxygen cycles, since they feature the ejection and subsequent injection of oxygen atoms for a solid oxide system.

The temperature used for this process (especially the 1500°C high temperature step) is extraordinarily high. For reference, steel often melts at a temperature of about 1370°C. Although it is possible to use solar concentrators to reach these temperatures, such a feat requires very high quality solar concentrators and exceptional reactor engineering. And such a CO2 cycling system only makes sense if it is driven by renewable (solar) energy. Thus it is of interest to engineer oxide systems that may exhibit such thermal oxygen cycles at lower temperatures, so that simpler solar concentrator systems may be employed. Ceria certainly has a host of physical and chemical properties that make it interesting, especially for oxygen exchange, and there have been efforts in doping ceria to achieve lower temperature results.130 An increasing amount of attention is being paid, however, to manganese perovskite systems,131 some of which are reported to operate at temperatures as low as 1200°C.132 It is thought that the perovskite crystal structure is more amenable to chemical doping and substitution, and thus represents a wider chemical space to explore, compared to the fluorite structure of ceria.131 Manganese, with its variable oxidation state, is particularly amenable to adopt- ing perovskite structures when paired with fixed oxidation state elements. Such perovskites are typically represented as ABO3, where A is an element with a fixed oxidation state, and B is manganese. The suitability of manganese as a constituent element

133,134 of such mixed oxide compounds for CO2 reduction has been explored some, but a systematic understanding of the inﬂuence of its partner element is lacking.

83 Reversible Oxygen Material Successfully Synthesized? Exchange Demonstrated?

MgMnO3 Yes Yes

Mg0.5Al0.5O3 Yes No

AlMnO3 No N/A

CaMnO3 Yes Yes Ca0.5Sc0.5O3 Yes No ScMnO3 Yes No SrMnO3 Yes Yes Sr0.5Mn0.5O3 Yes Yes YMnO3 Yes No

BaMnO3 No N/A

Ba0.5La0.5MnO3 Yes No LaMnO3 Yes Yes

Table 5.1: Materials explored for thermal oxygen exchange cycles. 5.2 Introduction

We report here a systematic study of perovskite compounds of the type ABO3, where A is a fixed-oxidation state element (2+ or 3+) and B is manganese, for use in thermal cycling reactions. To study both oxygen evolution and CO2 dissociation steps together represents an unwieldy task, so we have concentrated here on the oxygen exchange properties with the understanding that the CO2-splitting step could later be studied in a similarly systematic way. Indeed it has been suggested previously132 that different elements on the B-site of ABO3 perovskites influence the oxygen non- stoichiometry and CO2-splitting capabilities of a material separately. Table 5.1 lists the materials considered here. Each of the eight fixed-oxidation state elements were chosen as an A-element, along with 50/50 mixtures of 2+/3+ partners from the same row. The materials were synthesized with a modified Pechini

84 method55,56,132 and annealed in air at 1200°C. The materials were characterized by XRD, and the perovskite structure (or minor variations thereof) was confirmed in each case. The materials were then studied with a custom-built flow reactor system featuring mass flow controllers, a furnace, a gas chromatograph, and a continuous oxygen monitoring system specially supplied by Enerac. The continuous monitoring system used IR and electrochemical methods to sample the gas flow every five seconds and determine the concentration of oxygen, carbon dioxide, and carbon monoxide. Typically, the materials was heated slowly under argon flow until oxygen evolution was detected. The first sign of oxygen represented the “low” temperature for that material, and the “high” temperature was typically 1200°C. The material was then cycled several times: heating to 1200°C, recording oxygen evolution, cooling to the low temperature, exposing to oxygen briefly, flushing thoroughly with argon, and then heating 1200°C and recording subsequent oxygen evolution. The equation being studied, then, is the following:

δ 1200°C: ABO3(s) → ABO3-δ(s) + O2(g) (5.3) 2 δ Lowtemp : ABO + O → ABO (5.4) 3-δ(s) 2 2(g) 3(s)

Total amounts of oxygen were determined from the gas ﬂow rate and the concentrations recorded by the Enerac instrument. GC was used nonquantitatively to spot-check for oxygen presence, verifying the Enerac instrument.

85 5.3 Materials

Materials were synthesized from nitrate starting materials using the Pechini method as described elsewhere.55,56,132 XRD data (with arbitrary y-axes) for the following section is provided in Figure 5.1, and drawings of unit cells are provided in Figure

5.2. A unit cell drawing of CaTiO3, the original perovskite structure from which the structure type derives its name, is provided in Figure 5.2.a for comparison purposes, but this was not a material tested for thermal oxygen exchange. It should be noted that not all structures explored here adhere strictly to the formal atomic arrangement of the perovskite structure, but rather to the general ABO3 formula characteristic of the perovskite structure.

5.3.1 MgMnO3

This material has been traditionally been studied for its magnetic properties. Pre- vious reports describe its defective cubic spinel structure, featuring magnesium ions

135 that spill onto the B site. MgMnO3 is isostructural with MgAl2O4, featuring the

2+ 2+ 4+ defect spinel structure [Mg ][Mg1/3Mn4/3 1/3]O4. In our experiments, MgMnO3 evolved oxygen at temperatures above 600°C. Reversible oxygen exchange was successfully demonstrated in cycling experiments at 600-1200°C. The unit cell image provided in Figure 5.2.b is MgAl2O4, which is isostructural with MgMnO3, space group Fd3m, Crystallography Open Databse (COD) ID 1010129.

86 (a) MgMnO3 (b) Mg0.5Al0.5MnO3 (c) CaMnO3

(d) Ca0.5Sc0.5MnO3 (e) ScMnO3 (f) SrMnO3

(g) Sr0.5Y0.5MnO3 (h) YMnO3 (i) Ba0.5La0.5MnO3

(j) LaMnO3

Figure 5.1: XRD data for materials used in thermal oxygen cycle experiments.

87 (a) CaTiO3, Pm3m (b) MgAl2O4, Fd3m (c) CaMnO3, Pnma

(d) SrMnO3, P63/mmc (e) YMnO3, P63cm (f) LaMnO3, Pbnm

Figure 5.2: Unit cell drawings for materials related to those used in thermal oxygen cycle experiments, with Hermann-Mauguin notation.

88 5.3.2 Mg0.5Al0.5MnO3

This material was found in our studies to have a structure analogous to MgMnO3 but with a slightly smaller lattice parameter, as would be expected from the presence of the smaller Al3+ cation. The XRD of this material suggests that its crystallinity was poorer than the MgMnO3 and perhaps as a result the material did not exhibit reversible oxygen exchange.

5.3.3 AlMnO3

This material appears to exist only as a theoretical compound, as it has been suggested that the Al3+ cation would be too small to support the perovskite structure, and that the synthesis of this compound would require prohibitively high pressure.136 Indeed, the Pechini method used here did not successfully yield this material.

5.3.4 CaMnO3

This material has been previously studied for its oxygen non-stoichiometry.137 Un- der ambient conditions the material features an orthorhombic structure and is stoichiometric. As noted by others, the material expels oxygen at 896°C to shift to a tetragonal structure, and again at 913°C to shift to a cubic phase.138 To capture these oxygen shifts, this material was cycled at 750-1200°C in our experiments, at which temperatures reversible oxygen exchange was demonstrated. CaMnO3 has space group Pnma, and the unit cell image provided in Figure 5.2.c is generated from COD ID 1525994.

89 5.3.5 Ca0.5Sc0.5MnO3 and ScMnO3

Both of these materials appear to be virtually unknown in literature. Materials were made whose XRD patterns are plausibly those of these perovskite materials.

5.3.6 SrMnO3

This material has previously been studied in terms of magnetic properties.139 Its oxygen non-stoichiometry has been reported previously.140 The material was successfully cycled in the experiments reported here at 900-1200°C. SrMnO3 has space group P63/mmc, and the image provided in Figure 5.2.d is generated from COD ID 1529598.

5.3.7 Sr0.5Y0.5MnO3

This material has previously been reported to split CO2 at 900-1200°C cycling temperatures.134 Although we observed oxygen evolution at 1200°C, when we exposed the reduced material to CO2 at 900°C, we did not observe CO2 splitting under our experimental conditions. Reversible oxygen exchange, however, was observed. This material is particularly noteworthy in this study because although it is a mixed Sr-Y manganese oxide, it exhibits a crystalline structure distinct from both SrMnO3 and

YMnO3.

90 5.3.8 YMnO3

This material has mostly been studied for magnetic properties,141 although oxygen storage properties have been explored as well.142 In our studies, this material evolved oxygen at very low temperatures (as low as 400°C) but did not exhibit reversible oxygen exchange under the conditions explored here. YMnO3 has space group P96cm, and image provided in Figure 5.2.e is generated from COD ID 7217215.

5.3.9 BaMnO3

This material appears to be accessible through a laborious synthesis process143 but not via our Pechini method.

5.3.10 Ba0.5La0.5MnO3

This material has a structure analogous to LaMnO3 but with a larger lattice parameter as may be expected from the presence of the larger Ba2+ cation. The material’s

XRD indicates a poor crystallinity in comparison to LaMnO3, and, perhaps as a result, the material did not cycle oxygen well.

5.3.11 LaMnO3

This material has known oxygen non-stoichiometry properties.144 We cycled the material at 850-1200°C. LaMnO3 has space group Pbnm, and image provided in Figure 5.2.e is generated from COD ID 1006141.

91 Material MgMnO3 CaMnO3 SrMnO3 Sr0.5Y0.5MnO3 LaMnO3 Cycling Temp Lo-Hi (°C) 600-1200 750-1200 900-1200 900-1200 850-1200 1° 10,052 9004 938 669 788 cycle (113.0) (115.0) (15.9) (11.4) (17.0)

µLO2 ej / g mtl 2° 2362 785 912 343 227 (mmol O / mol mtl) cycle (26.7) (10.0) (15.5) (5.8) (4.9)

3° 1860 620 881 323 93.2 cycle (21.1) (7.9) (14.9) (5.5) (2.0)

% dropoﬀ 81.5 93.1 6.1 51.7 88.2

Table 5.2: Oxygen exchange results

Figure 5.3: Results of oxygen exchange experiments, indicating mmol of O exchanged per mol of material, in each of three cycles. 5.4 Oxygen Cycling Results

The results of oxygen cycling experiments are presented in Table 5.2 and Figure 5.3.

These results suggest that SrMnO3 may be a good material to conduct further experiments on, in order to develop it for carbon dioxide splitting, since this material showed moderate oxygen exchange with very little dropoﬀ between cycles.

92 5.5 Literature Review

All of the materials listed in Table 5.2 were tested with CO2 as an oxidant (in addition to the O2 oxidant results detailed). None of the materials split CO2; neither CO evolution nor O2 upon reheating in inert atmosphere were observed. There are several ways in which the results presented here diﬀer from previous literature reports. Sunita Dey et al described in 2015 reports134,145 that both

La0.5Ca0.5MnO3 and Y0.5Sr0.5MnO3 split CO2 at 900-1200°C cycles. Their only evidence, however, is thermogravimetric analysis (TGA). This only detects weight changes and does not directly detect CO. This method is incapable of distinguishing between physical gas adsorption and CO2 splitting to CO. The custom reactor built in-house for our studies, however, directly detects O2, CO2, and CO, with an integrated IR-electrochemical sensor. We were successful in preparing La0.5Ca0.5MnO3 and Y0.5Sr0.5MnO3, but when tested under conditions similar to those reported by Dey, we did not observe any CO.

132 Alexander Bork, in 2015, reported CO2 splitting for La0.6Sr0.4Cr0.8Co0.2O3 at 800-1200°C cycles. They did confirm the presence of CO with IR. Although we were able to successfully synthesize La0.6Sr0.4Cr0.8Co0.2O0.3, we were not able to confirm its oxygen evolution or CO2 splitting properties with our reactor. Bork suggests that the B-site of ABO3 may control its CO2 splitting capability, whereas the A-site may control initial O2 production. Since the latter has been explored in depth here, it may be useful in future experiments to explore B-site doping to trigger CO2 splitting. Qingqing Jiang in 2014 reported146 a curious difference between a material’s abil- ity to exchange oxygen versus split CO2. Specifically, they found that certain per-

93 ovskites, most notably LaFe0.7Co0.3O3, expelled oxygen but did not split CO2. When combined with a support (such as SiO2), however, the materials were subsequently able to split CO2. Their experiments are complicated by phase mixing between active and support materials. We tried mixing SrMnO3 with SiO2 and CeO2 support, but did not see CO2 splitting activity emerge. We have shown elsewhere, however, the power of using support materials for certain hetergenous redox processes.80 Andreas Stein et al in 2013 and 2014 reported147,148 on how the microstructure of CeO2 impacted its activity in catalytic thermocycles. In 2013 he found that templating CeO2 with poly(methyl methactrylate) (PMMA) during preparation gave it microstructure that greatly enhanced its CO2 splitting activity at low temperatures: successful CO2-splitting cycles were demonstrated at 850-1200°C. In a follow up study in 2014, he reported that really it was as easy as templating CeO2 with wood. This helped form interconnected channels and pores of micrometers in diameter, similar to the PMMA templating. The wood-templated material successfully split CO2 at 800-1200°C cycles, whereas non-templated material did not do so. It should be noted that his experiments were carried out in a reactor that used very rapid laser heating. Preparation of both CeO2 and SrMnO3 with sawdust did not enhance catalytic activity in our reactor. The results detailed in this chapter are a small part of the wider interest in ex- amining the known catalytic properties of oxide materials and tailoring the crystallographic details of their corresponding nanostructures to achieve targeted results.149 DFT and computational methods could also be used to identify new oxide families for use in these thermocycles.150

94 5.6 Conclusions

It has been shown through experiments here, after testing a wide range of potential manganese perovskite materials, that SrMnO3 may hold promise if further developed to split CO2. This material features good oxygen exchange properties that do not diminish very much over multiple cycles. It is still possible that a SrMnO3 material might be made to split CO2 with our in-house reactor. As Bork suggests, it may be worthwhile to try cobalt doping at the B-site, and as Stein suggets, it may be worthwhile to template the material with PMMA during preparation. It may be an interesting challenge to prepare nanoparticles of this material with a template in such a way that the nanoparticles do not coarsen at such high temperatures. It is possible that the nanoparticles may have enhanced catalytic activity. Such a project would be very challenging, given the tendency of such oxide nanoparticles to coarsen at high temperatures.

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