This book brings together a collection of chapters that focus on the relationship among electrical, chemical, and mechanical properties and the study of adjusting one property through the control of a

Mixed ionic and electronic conducting perovskites that can readily exchange oxygen with the atmosphere exhibit a chemo-mechanical coupling between their oxygen content and their lattice dimensions. The lattice dilation accompanying oxygen loss, termed “chemical expansion,” beneficially enables new techniques that use measures of strain to determine changes in oxygen content, but deleteriously causes large chemical stresses in devices during operation that can lead to mechanical failure. In this presentation I will describe our work aimed at understanding, across multiple length scales, which factors impact chemical expansion coefficients in perovskites, in order to develop design principles for controlling them. Polycrystalline gallate and titanate perovskites containing multivalent Ni, Fe, and Co have been studied using in situ thermogravimetry, diltometry, and diffraction to probe the chemical expansion process at macroscopic and crystal structure levels. Corresponding simulations using density functional theory, molecular dynamics, and empirical approaches have provided atomistic insight into changes taking place on the anion and cation sublattices during oxygen loss. Factors impacting the magnitude of the chemo-mechanical coupling, including oxygen vacancy radii, charge localization on cations, temperature, crystal symmetry, and defect ordering, have been identified.

Many modelling problems in materials science involve finite temperature simulations with a realistic representation of the interatomic interactions. These problems often necessitate the use of large simulation cells or long run times, which puts them outside the range of direct first-principles simulation. This is particularly the case for energy storage systems, such as batteries or supercapacitors. For battery materials, it is possible to introduce polarizable potentials for the interactions, in which additional degrees of freedom provide a representation of the response of the electronic structure of the ions to their changing coordination environments. Such force field can be built on a purely first principles basis. Here we discuss the example of a Li-ion conductor, and we show how the long molecular dynamics simulations are useful for characterizing accurately the conduction mechanism. In particular, strong cooperative effects are observed, which impact strongly the electrical conductivity of the material. In the case of supercapacitors, the full electrochemical device can be modelled. However, this leads to very large simulation cell, which does not allow using polarizable force fields for the electrolytes. For the electrodes, fluctuating charges are used in order to maintain a constant electric potential as in electrochemical experiments. These simulations have allowed for a deep understanding of the charging mechanism of supercapacitors. In particular, the desolvation of the ions inside the porous carbon electrodes and the fast dynamic of charging can now be understood at the molecular scale.

Strained oxide thin films are of interest for accelerating oxide ion conduction in electro-chemical devices. Although the effect of elastic strain has been uncovered theoretically, the effect of dislocations on the diffusion kinetics in such strained oxides is yet unclear. Here we investigate a 1/2<110>{100}edge dislocation by performing atomistic simulations in 4-12% doped CeO2 as a model fast ion conductor. At equilibrium, depending on the size of the dopant, trivalent cations and oxygen vacancies are found to simultaneously enrich or deplete either in the compressive or in the tensile strain fields around the dislocation. The associative interactions among the point defects in the enrichment zone and the lack of oxygen vacancies in the depletion zone slow down oxide ion transport. This finding is contrary to the fast diffusion of atoms along the dislocations in metals and should be considered when assessing the effects of strain on oxide ion conductivity.

In this work, chemical expansion in perovskite oxides was characterized in detail, motivated, inter alia, by a desire to understand the lower chemical expansion coefficients observed for perovskites in comparison to fluorite-structured oxides. Changes in lattice parameter and in local atomic arrangements taking place during compositional changes of perovskites, i.e., stoichiometric expansion, were investigated by developing an empirical model and through molecular dynamics and density functional theory atomistic simulations. An accurate empirical expression for predicting lattice constants of perovskites was developed, using a similar approach to previous reports. From this equation, analytical expressions relating chemical expansion coefficients to separate contributions from the cation and anion sublattices, assuming Shannon ionic radii, were developed and used to isolate the effective radius of an oxygen vacancy, rV. Using both experimental and simulated chemical expansion coefficient data, rV for a variety of perovskite compositions was estimated, and trends in rV were studied. In most cases, rV was slightly smaller than or similar to the radius of an oxide ion, but larger than in the fluorite structured materials. This result was in good agreement with the atomistic simulations, showing contractive relaxations of the closest oxide ions towards the oxygen vacancy. The results indicate that the smaller chemical expansion coefficients of perovskites vs. fluorites are largely due to the smaller change in cation radii in perovskites, given that the contraction around the oxygen vacancy appears to be less in this structure. Limitations of applicability for the model are discussed.

The effect of dislocations on the chemical, electrical and transport properties in oxide materials is important for electrochemical devices, such as fuel cells and resistive switches, but these effects have remained largely unexplored at the atomic level. In this work, by using large-scale atomistic simulations, we uncover how a ⟨100⟩{011} edge dislocation in SrTiO3, a prototypical perovskite oxide, impacts the local defect chemistry and oxide ion transport. We find that, in the dilute limit, oxygen vacancy formation energy in SrTiO3 is lower at sites close to the dislocation core, by as much as 2 eV compared to that in the bulk. We show that the formation of a space-charge zone based on the redistribution of charged oxygen vacancies can be captured quantitatively at atomistic level by mapping the vacancy formation energies around the dislocation. Oxide-ion diffusion was studied for a low vacancy concentration regime (ppm level) and a high vacancy concentration regime (up to 2.5%). In both cases, no evidence of pipe-diffusion, i.e., significantly enhanced mobility of oxide ions, was found as determined from the calculated migration barriers, contrary to the case in metals. However, in the low vacancy concentration regime, the vacancy accumulation at the dislocation core gives rise to a higher diffusion coefficient, even though the oxide-ion mobility itself is lower than that in the bulk. Our findings have important implications for applications of perovskite oxides for information and energy technologies. The observed lower oxygen vacancy formation energy at the dislocation core provides a quantitative and direct explanation for the electronic conductivity of dislocations in SrTiO3 and related oxides studied for red-ox based resistive switching. Reducibility and electronic transport at dislocations can also be quantitatively engineered into active materials for fuel cells, catalysis, and electronics.

Mixed ionic and electronic conducting oxides, employed in, e.g., catalysts and solid oxide fuel cells (SOFCs), often store and release large quantities of oxygen during operation. Upon oxygen release (i.e., during exposure to lower oxygen pressure or higher temperature), multivalent cations reduce their oxidation state, resulting in an expansion that typically outweighs the small lattice contraction around the oxygen vacancies that form [1]. This chemo-mechanical coupling between lattice expansion and change in chemical composition can be described quantitatively by the chemical coefficient of expansion (CCE). When materials with high CCEs are incorporated into operating devices, such as SOFCs, the large stresses accompanying stoichiometry changes can lead to mechanical failure and shortened device lifetimes. Therefore, CCEs of new materials need to be characterized, and factors controlling the chemical expansion need to be investigated in order to engineer materials with low CCEs. In this work the CCEs of two candidate SOFC cathodes, La0.9Sr0.1Ga1-xNixO3-δ (LSGN; 0 ≤ x ≤ 0.5) and SrTi0.65Fe0.35O3-α (STF), were determined as part of an ongoing effort to understand factors governing chemical expansion in perovskites. Prior computational simulations from our group identified that the degree of charge localization on the multivalent cations can play a significant role in determining the CCE, with delocalized charges (i.e., metallic behavior) resulting in decreased changes in cation radii upon reduction [2]. In this presentation, experimental evidence for the effect of charge localization on chemical expansion in LSGN, recently measured for the first time, will be discussed. Bulk samples prepared by the Pechini method were measured from 600 – 900 °C in N2/O2 mixtures by thermogravimetric analysis (TGA), to determine oxygen non-stoichiometry and defect equilibria, and by dilatometry and in situ X-ray diffraction, to determine the corresponding lattice expansion. For LSGN, increasing charge delocalization was achieved by increasing the Ni content, as demonstrated through electrical conductivity measurements [3] and subsequent analysis of electronic mobilities using carrier concentrations derived from TGA data with defect modeling. Correspondingly, the measured CCE decreased by 13% at 800 °C upon increasing the Ni concentration from 0.1 to 0.5 [4], in agreement with the theoretical prediction of decreasing CCE with increasing charge delocalization. Additionally, recent work on measuring the CCE for STF will be presented. STF displays similar chemical expansion behavior to LSGN, with the CCE at 800 °C being comparable to the highest value measured for LSGN. [1] D. Marrocchelli, S. R. Bishop, H. L. Tuller, and B. Yildiz, Advanced Functional Materials, 22 (9) 1958-1965 (2012). [2] D. Marrocchelli, S. R. Bishop, H. L. Tuller, G. W. Watson, and B. Yildiz, Physical Chemistry Chemical Physics, 14, 12070-12074 (2012). [3] N. J. Long, F.’ Lecarpentier, and H. L. Tuller, Journal of Electroceramics, 3 (4), 399-407 (1999). [4] N. H. Perry, J. E. Thomas, D. Marrocchelli, S. R. Bishop, and H. L. Tuller, ECS Transactions, 57 (1) 1879-1884 (2013).

Many energy-related materials rely on the uptake and release of large quantities of ions, for example, Li + in batteries, H + in hydrogen storage materials, and O 2− in solid-oxide fuel cell and related materials. These compositional changes often result in large volumetric dilation of the material, commonly referred to as chemical expansion. This article reviews the current knowledge of chemical expansion and aspires to facilitate and promote future research in this field by providing a taxonomy for its sources, along with recent atomistic insights of its origin, aided by recent computational modeling and an overview of factors impacting chemical expansion. We discuss the implications of chemical expansion for mechanical stability and functionality in the energy applications above, as well as in other oxide-based systems. The use of chemical expansion as a new means to probe other materials properties, as well as its contribution to recently investigated electromechanical coupling, is also highlighted.

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

Classical molecular dynamics simulations are performed on LiF in the framework of the polarizable ion model. The overlap repulsion and polarization terms of the interaction potential are derived on a purely non-empirical, first-principles basis. For the dispersion, three cases are considered: a first one in which the dispersion parameters are set to zero and two others in which they are included, with different parametrizations. Various thermodynamic, structural and dynamic properties are calculated for the solid and liquid phases. The melting temperature is also obtained from direct coexistence simulations of the liquid and solid phases. Dispersion interactions appear to have an important effect on the densities of both phases and on the melting point, although the liquid properties are not affected when simulations are performed in the NVT ensemble at the experimental density.

The coupling between the electrical, chemical and mechanical properties of materials, usually referred to as Electro-Chemo-Mechanics [1], has very important implications for energy related materials and devices. Indeed, this coupling can be beneficial, e.g. the ion conductivity enhancement observed in ceria and zirconia when these materials are strained [2], or detrimental, e.g. the lattice parameter expansion observed in ceria upon reduction [3]. For this reason a better understanding of this coupling is necessary in order to tailor the properties of these materials. Atomistic computer simulations represent a powerful tool to study the mechanical-electrochemical coupling, as they can provide information that is complementary to experiments. In this presentation, I will review some recent computational work in this field. First I will talk about chemical expansion in ceria, an example of chemo-mechanical coupling. I will show how, by combining Density Functional Theory and Molecular Dynamics Calculations with experimental data, we concluded that chemical expansion is caused by two competing processes, the formation of a vacancy (leading to a lattice contraction) and the cation radius change (leading to a lattice expansion). This information was then condensed in a simple analytical model, which was then used to predict materials compositions that minimize chemical expansion. Then I will present two more examples from my work: the first one on the study of co-doping strategies in ceria as a means to enhance its ionic conductivity (electro-chemical coupling) and the second one on the effects of dislocations in SrTiO3 on the defect chemistry and mobility of this material (electro-chemo-mechanical) coupling. References [1] Tuller and Bishop, Annu. Rev. Mater. Res. 41 369 (2011) [2] Kushima and Yildiz, J. Mat. Chem. 20 4809 (2011) [3] Marrocchelli et al. Adv. Fun. Mat. 22 1958 (2012)

In this paper we report a computational study of the effects of strain on the conductivity of Y-doped ceria (YDC). This material was chosen as it is of technological interest in the field of Solid Oxide Fuel Cells (SOFCs). The simulations were performed under realistic operational temperatures and strain (𝜖) levels. For bulk and thin film YDC, the results show that tensile strain leads to conductivity enhancements of up to 3.5 × and 1.44 × , respectively. The magnitude of these enhancements is in agreement with recent experimental and computational evidence. In addition, the methods presented herein allowed us to identify enhanced ionic conductivity in the surface regions of YDC slabs and its anisotropic character.

In this paper, we focus on the effect of processing‐dependent lattice strain on oxygen ion conductivity in ceria based solid electrolyte thin films. This is of importance for technological applications, such as micro‐SOFCs, microbatteries, and resistive RAM memories. The oxygen ion conductivity can be significantly modified by control of lattice strain, to an extent comparable to the effect of doping bulk ceria with cations of different diameters. The interplay of dopant radii, lattice strain, microstrain, anion‐cation near order and oxygen ion transport is analyzed experimentally and interpreted with computational results. Key findings include that films annealed at 600 °C exhibit lattice parameters close to those of their bulk counterparts. With increasing anneal temperature, however, the films exhibited substantial compaction with lattice parameters decreasing by as much as nearly 2% (viz, Δd600–1100 °C: –1.7% (Sc+3) > –1.5% (Gd+3) > –1.2% (La+3)) for the annealing temperature range of 600–1100 °C. Remarkably 2/3rd of the lattice parameter change obtained in bulk ceria upon changing the acceptor diameter from the smaller Sc to larger La, can be reproduced by post annealing a film with fixed dopant diameter. While the impact of lattice compaction on defect association/ordering cannot be entirely excluded, DFT computation revealed that the main effect appears to result in an increase in migration energy and consequent drop in ionic conductivity. As a consequence, it is clear that annealing procedures should be held to a minimum to maintain the optimum level of oxygen ion conductivity for energy‐related applications. Results reveal also the importance to understand the role of electro‐chemo‐mechanical coupling that is active in thin film materials.

Chemical expansion refers to the spatial dilation of a material that occurs upon changes in its composition. When this dilation is caused by a gradual, iso-structural increase in the lattice parameter with composition, it is related to the composition change by the stoichiometric expansion coefficient. In this work, three different approaches to defining the stoichiometric expansion coefficient (αS) are discussed. While all three definitions of αS given here are legitimate, we show that there are advantages to selecting certain ones for comparison across different crystal structures. Examples are provided for changes in oxygen content in fluorite, perovskite, and Ruddlesden-Popper (K2NiF4) phase materials used in solid oxide fuel cells.

Molecular dynamics simulations, based on polarizable interaction potentials, were performed to study the effects of Li-ion vacancies in LiMgSO4F. It was found that the diffusion coefficient of this material goes through a maximum, when 50% of the Li ions have been removed. The degree of cooperativity of the ionic conduction mechanism was monitored via the Haven ratio and found to decrease monotonically as a function of the number of Li ion vacancies in the crystal. This was explained in terms of a two-step conduction mechanism, in which a Frenkel pair has to be created first, followed by the diffusion of a Li ion to the nearest vacancy. The implications of our findings and some of the technical limitations and challenges are also briefly discussed.

Non-stoichiometric oxides are frequently used in SOFC electrodes due to the ease with which they exchange oxygen with the atmosphere over their entire surface, as compared to composites limited to three phase boundaries (i.e. LSM/YSZ). The large fluctuations in oxygen content these materials exhibit during operation lead, not only to significant changes in transport properties, but also to a defect induced expansion, known as chemical expansion, potentially contributing to mechanical failure. In this presentation, new insights into the origins of chemical expansion, with consequent development of methods for reducing its impact in non-stoichiometric oxides, facilitated by collaborations of the authors, will be discussed.

The defect-induced lattice expansion (chemical expansion), and corresponding relaxation patterns around oxygen vacancies, were examined as a function of host cation radius for HfO2, ZrO2, CeO2, UO2, ThO2, and Bi2O3 fluorite-structured oxides. Analysis of data from the literature, combined with new molecular dynamics simulations, found a maximum in the effective radius of an oxygen vacancy (related to the lattice contraction around a vacancy) for a host cation size close to that of cerium. In other words, ceria shows the highest chemical expansion, whereas the other studied materials, with either smaller or bigger host cations than Ce, undergo smaller chemical expansion. Significant asymmetric lattice relaxation around a vacancy for smaller cations and 2nd nearest neighbor cation relaxations around a vacancy for larger cations play a strong role in forming the maximum. The impact of this vacancy relaxation on ionic conductivity is discussed, and through careful analysis of the vacancy–anion radial distribution functions, an estimate of a critical vacancy concentration (c* = 0.025%), above which vacancy interactions exist, was derived.

The influence of electron localization on the chemical expansion coefficient was examined experimentally, using a model electrode material, (La,Sr)(Ga,Ni)O3-δ. Varying the Ni content yielded differing degrees of electron localization with resultant chemical expansion coefficients evaluated by dilatometry and thermogravimetric analysis in N2/O2 mixtures at 800 °C. In agreement with prior computational predictions, a decrease in chemical expansion coefficient was observed with electron delocalization.

For the first time, the role of isovalent Zr substitution in cerium oxide on the non-stoichiometry induced dilation (chemical expansion) was investigated. Chemical expansion was derived experimentally using HTXRD, dilatometry, and TGA measurements on Pr0.1Zr0.4Ce0.5O1.95-delta and computationally with DFT calculations on Zr0.5Ce0.5O2-delta. Though Zr was found to increase the reducibility and the corresponding chemical expansion of ceria in the studied range, the relationship between chemical expansion and non-stoichiometry (the chemical expansion coefficient) was significantly smaller (54% less) than that observed in ceria, and consistent with predictions from the authors' previous work. The origin of the reduced chemical expansion coefficient, associated with a larger contraction of the lattice around oxygen vacancies, is explained using DFT calculations and corroborated with prior investigations of enhanced reducibility of ceria-zirconia. Additionally, implications of this discovery for solid oxide fuel cells and heterogeneous catalyst systems are also discussed.