Empirical Modeling of Structural Distortions in Perovskite Ceramics
Authors: Smith Evan Connor 
Published: June 2020

Predictive models for composition-structure-property relationships are essential to realizing the
full potential of electroceramic materials; however, the electroceramics industry has largely failed
to invest in predictive models in favor of simple rules of thumb or expensive, time-consuming
trial-and-error methods. Empirically derived predictive models have the potential to significantly
improve and guide future research in a more cost-effective and timely manner. It may even be possible
to predict some intrinsic properties (e.g., polarization) on the order of a unit cell using
only the charge and size of each chemical component. Scientists and researchers may ultimately be able
to use these types of models to produce compositional recipes from desired property or structural data
or conversely predict properties and structures from compositional data. Moreover, empirical models
allow for the investigation and discovery of trends in properties and structures that would be
practically unobservable via either expensive experimental or computationally demanding first-principles
methods. The main focus of this work will be the use of empirical data to derive predictive models for
ceramics with the perovskite crystal structure and thereby glean crystallochemical insights which explain them.

Chapter one lays the foundation for this work. A general overview of perovskites is provided and the
seemingly endless degree of applications and properties that perovskite exhibit are explored including
ferroelectricity, piezoelectricity, pyroelectricity, superconductivity, ionic conductivity, etc.
It should be noted that the development of general correlative models which encompass all of these various
properties and structural effects would be well beyond the scope of this work. Instead, this work concentrates
on developing models for the effects of layered A-site ordering, rock salt B-site ordering, trigonality,
and oxygen vacancies on the perovskite structure. Additionally, previous empirical modeling efforts are
introduced to lay the groundwork for the development of the correlative models within this work.

Chapter two examines the effect of layered A-site ordering on the perovskite structure. 15 compositions
in the [(NayLi1-y)(1-3x)/2La(1+x)/2)TiO3 (NLLT)
system (y = 0.25, 0.5, and 0.75; x = 0, 0.0533, 0.1, 0.1733, and 0.225) were produced.
Long-range ordering for x >/ 0.1 was observed via X-ray diffraction, while short-range ordering was shown
to exist even for x < 0.1 via electron diffraction. Overall, the degree of ordering was observed
to decrease as x increased. The A-site ordering parameter (η) and the resultant expansion
(ΔrA) were each modeled for every y series of compositions in the NLLT
system. Two general models were developed based on these system specific models, which allow for the prediction
of η and ΔrA in layered A-site ordered perovskites with any arbitrary degree of
ordering using only published ionic radii data.

Chapter three investigates the effects of 1:2 B-site ordering in the BaMg1/3Ta2/3O3
(BMT) perovskite system. BMT is an ideal compound for the study B-site ordering because the degree of B-site ordering
increases with increasing annealing time. Thus, BMT powders were synthesized and annealed incrementally from 0 to
40 hours at 1500°C. The resulting structures were increasingly ordered on the B-site, which also caused a
trigonal distortion within the structure. An empirical model was developed which describes the degree of
ordering in terms of the B-site shrinkage or the annealing time, which allows for the prediction of the
ordering parameter (η) in BMT using only experimental input. This work has major implications in that
this modelling technique may be expanded to include other B-site ordered complex perovskites, which could
allow for the prediction of the degree of ordering and resultant volume shrinkage in B-site ordered
perovskites in general using only published ionic radii data or experimentally-derived pseudocubic lattice
constants.

Chapter four analyzes the effects of 1:1 rock salt B-site ordering in general. Four compositions were
synthesized in the AZn0.5Ti0.5O3 system (A = Nd, Sm, Nd0.5La0.5,
Nd0.5Gd0.5). Long-range 1:1 rock salt cation ordering on the B-site was shown to exist for all
four compositions via X-ray diffraction. Additional data was mined from literature for another 38 rock salt B-site
ordered perovskites. This data was sorted according to the Bsite species and empirical models were developed which
describe the B-site shrinkage (ΔrB) for each of these systems. From these system specific
models, a general model was developed for rock salt B-site ordering, which allows for the prediction of
ΔrB in rock salt B-site ordered perovskites using only published ionic radii data.

Chapter five focuses on the development of a general correlative model for perovskite trigonality. A data
mining approach was employed to gather published structural data for trigonally distorted perovskites. These
perovskites were sorted into specific systems, and empirical models were developed for the degree of
trigonality for each of these systems, which can be expressed a function of the ratio of the pseudocubic
lattice constant (αpc) to the B-X bond length (rBX). From these
system specific models, general models were developed for trigonal perovskites with either
R3c or R3c symmetry which describe the
degree of trigonality as a function of the modified tolerance factor. Additionally, a general model was
developed which allows for the prediction of the intrinsic polarization in R3c
trigonal perovskites.

Chapter six describes the effects of oxygen vacancies in perovskite ceramics. Eight compositions in the
CaTi1-xFexO3-x/2 system
(x = 0.05, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, and 0.45), and eleven compositions in the
SrTi1-xFexO3-x/2 system
(x = 0, 0.025, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, and 0.45) were synthesized.
A data mining approach was used to supplement this data with more oxygen vacant perovskite systems. Empirical
models were developed for each of these oxygen-deficient systems which describe the effective oxygen vacancy
size (rV) and the bond deformation (DB). In addition,
a general model was developed for the modified tolerance factor, which allows for the prediction of the tolerance
factor in oxygen vacant perovskites. In turn, this allows for the accurate prediction of the effective anion size
(rX) and pseudocubic lattice constant (αpc) in oxygen vacant perovskites.