Modeling Strain Distribution at the Atomic Level in Doped Ceria Films with Extended X-ray Absorption Fine Structure Spectroscopy

Abstract

Ceria doped with trivalent dopants exhibits nonclassical electrostriction, strong anelasticity, and roomtemperature (RT) mechanical creep. These phenomena, unexpected for a ceramic material with a large Young's modulus, have been attributed to the generation of local strain in the vicinity of the host Ce cations due to symmetrybreaking point defects, including oxygen vacancies. However, understanding why strain is generated at the host rather than at the dopant site, as well as predicting these effects as a function of dopant size and concentration, remains a challenge. We have used the evolutionary-algorithm-based reverse Monte Carlo modeling to reconcile the experimental data of extended X-ray absorption fine structure and X-ray diffraction in a combined model structure. By extracting the details of the radial distribution function (RDF) around the host (Ce) and trivalent dopants (Sm or Y), we find that RDF of the first-nearest neighbor (1NN) of host and dopant cations as well as the second-nearest neighbor (2NN) of the dopant are each best modeled with two separate populations corresponding to short and long interatomic distances. This heterogeneity indicates that fluorite symmetry is not preserved locally, especially for the dopant first-and second-NN sites, appearing at surprisingly low doping fractions (5 mol % Sm and 10 mol % Y). Given that Ce rather than dopant sites act as the source of local strain for electrostriction and RT creep, we conclude that the environment around the dopant does not respond to electrical and mechanical excitations, likely because of its similarity to the double fluorite structure which has poor electrostrictive and anelastic properties. The trends we observe in the RDFs around the Ce sites as a function of dopant size and concentration suggest that the response of these sites can be controlled by the extent of doping: Increasing dopant size to increase strain magnitude at the 1NN shell of Ce and decreasing dopant fraction to decrease strain propagation to the 2NN shell of Ce should produce stronger electrostrictive response and RT creep.

A review of defect structure and chemistry in ceria and its solid solutions

“…The average nearestneighbor distances of doped ceria show that the lattice strongly deviates from fluorite symmetry at the unit cell level. 58,59 This stands in a seeming contradiction with the XRD studies which average over all unit cells and indicate fluorite symmetry for acceptor doping levels up to 20 mol%. 35,[60][61][62] It is evident that the global average does not provide the full structural description and a multimodal approach, combining the XRD and EXAFS studies to provide a picture of actual structure, is needed.…”

“…In addition, EXAFS-and XRD-derived interatomic distances disagree and result in the calculation of unphysical Cat-V O distances under the assumption of a uniform fluorite phase. This finding is supported by the combination of EXAFS and XRD data in a simulated structure (using reverse Monte-Carlo-EXAFS modelling 58 ), which reveals bi-modal distance distributions for Ce-O, Do-O and Ce-Do. The assumption of local fluorite symmetry must therefore be incorrect for ceria solid solutions at low-to-moderate doping levels.…”

“…It has long been known that for dopants larger than B102 pm, such as Gd 3+ and Sm 3+ , the average lattice parameter in the fluorite phase, as obtained using X-ray diffraction methods, increases with doping concentration. 157,158 However, several studies conducted on doped ceria using local probes, such as EXAFS, 58,107,116,136,[140][141][142] have found that cation-oxygen distances Cat-O, labeled a and c in Fig. 10, do not follow the average lattice parameter and contract as a function of increasing dopant concentration.…”

“…Recently, a Reverse Monte Carlo (RMC) based approach was implemented to the analysis of undoped and doped ceria EXAFS data. 58,171 The basic principle involves the extraction of a theoretical EXAFS spectrum from a simulated 3D model structure. The structure then continues to evolve through random atomic displacements, until theoretical and experimental spectra reach maximal agreement.…”

“…In a step towards multiscale modeling, Clark et al 171 employed RMC modeling to EXAFS as well as neutron total scattering to model undoped ceria powder material. More recently XRD lattice parameters and EXAFS data were consolidated in a single model structure, 58 for a series of Y-and Sm-doped ceria solid solutions. Here sputter deposited thin films were investigated.…”