Research

Empirical Modeling of Perovskites

Perovskites
Many electroceramics are based on or related to the perovskite crystal structure.  The generic perovskite oxide formula is generally written as ABO3.  In the ideal cubic form, the A site is coordinated to 12 anions to form cuboctahedral coordination polyhedra.  The B site is coordinated to six anions, forming octahedra.  The anions are coordinated to just two B site cations, as the four nearest A-site cations are about 41% further away. The anion octahedra are corner shared, which is a key feature of all perovskites.

Perovskites abound both in nature and in the laboratory, and their wide compositional range renders a variety of useful properties such that perovskites are encountered in applications as disparate as electroceramics, superconductors, refractories, catalysts, magnetoresistors, and proton conductors.  They are also of interest for use as substrates or buffer layers for compound semiconductor heteroepitaxy.  The design of such advanced materials requires an understanding of the relationship between chemical composition and crystal structure.

Understanding the relationship between processing, structure, and properties is essential for designing perovskites. This class of materials has an incredibly high potential to produce beneficial properties (such as pyroelectricity, ferroelectricity, piezoelectric, photoelectricity, superconductivity, etc.) but unfortunately, this wide range of potential properties is found within an even wider compositional space and it is not feasible to measure every composition experimentally. Our work aims to solve this problem and quantify the effects produced by these relationships by producing empirical models that use published structural data to predict the resulting properties of the material.

Applications
There are currently about 224.3 million smart phone subscribers in the USA, and 4.6 billion cell phone users worldwide, making the cellular phone one of the fastest-selling consumer items in history and the most widely spread technology on the planet. There are three times as many mobile phones than PCs of any kind in the world and more mobile phones than cars. There are over twice as many mobile phone users as internet users, and more mobile phone users than people with a credit card. Twice as many people use SMS text messaging worldwide than use e-mail, with 75,000 messages sent every second in the USA!

Microwave resonators are used extensively in telecommunications equipment, including cellular telephones and satellite links, and are at the heart of this multi-billion dollar market.  Oxide ceramics are critical elements in these devices, and three properties are important in determining their usefulness as a dielectric resonator.  First, the material must have a high dielectric constant (εr) to enable size reduction, the size of a microwave circuit being proportional to εr-½.  Second, a high quality factor Q (low tanδ) means fine frequency tunability and more channels within a given band.  Third, these ceramic components play a crucial role in compensating for frequency drift because of their low temperature coefficients of resonant frequency (τf).  Optimizing all these properties in a single material is not a trivial problem, and a full understanding of the crystal chemistry of such ceramics is paramount to future development.  Many perovskite-structured ceramic materials are known to have useful microwave dielectric properties, with potential applications in the mobile telecommunications market.

MODELING THE EFFECT OF POINT DEFECTS IN PEROVSKITES

In this study, a solid-state processing method is used to synthesize single-phase perovskite ceramics with engineered defect concentrations. Powder samples are characterized via X-ray diffraction. The resulting products are then uniaxially pressed and sintered for microstructural analysis. The ultimate goal is to develop a predictive model, based solely on composition, for the effect of point defects on the structure and, by extension, dielectric properties of perovskites.

Point defects like vacancies can have a profound effect on the structure of perovskite ceramics, but the exact mechanisms by which they do this are unclear.  There is some evidence in a variety of perovskite systems that A-site vacancies increase the average A-O bond distance due to mutual electrostatic repulsion of anions across the negatively-charged vacant site, which increases as the number of vacancies increases. A predictive model for the pseudocubic lattice constant which accounts for A-site vacancies and the ionic radii in their correct coordinations (XII, VI, and II for the A, B, and X species respectively) has been recently developed and shown to work adequately in several systems.

MODELING THE EFFECT OF CHEMICAL ORDERING IN PEROVSKITES

Chemical ordering is a common structural feature in perovskites that have a mixed occupancy in one or more of their lattice sites. This is usually achieved by having multiple cations in either the A or B-site that spontaneously diffuse from random occupancy into an ordered structure however, the X-site (anion) can also posses chemical ordering and at high enough concentrations site specific vacancies can also form an ordered pattern in the crystal structure. not all cations will produce ordering when substituted into a perovskite crystal structure and it can be difficult to tell whether a specific composition will result in chemical ordering and what degree of ordering will result should ordering occur. Two variables that strongly contribute to chemical ordering are the difference in charge and radius between the ions with species possessing large differences being more likely to separate from each other and species with small differences being more likely to remain randomly interspersed with each other.

Ordering can occur over a short range or over a long range. Short range ordering consists of many small domains of order such that the structure appears to be ordered when viewed at a very small scale but when viewed at a large scale the ordered domains are small enough that the bulk material appears to be disordered. This type of ordering can be very difficult to detect with traditional measurement techniques such as X-Ray Diffraction (XRD) however it can still have a very distinct effect of the resulting properties. Long range ordering on the other hand appears ordered regardless of the scale at which it is viewed.

Chemical ordering can have a profound effect on the properties of a perovskite. Chemical Ordering increases the packing efficiency in the plane that the ordering is occurring on and decreases the packing efficiency in all other planes which can either result in a net volume shrinkage or volume expansion depending on the magnitudes of the volume shrinkage and expansion respectively.

The electronic band structure is also very sensitive to the degree and type of ordering present with perovskites of identical composition possessing very different band structures depending on whether they are disordered, partially short range ordered, completely short range ordered, partially long range ordered, or fully long range ordered. The degree of ordering present in the perovskite additionally produces a gradient of potential properties that prevents researchers from fully identifying the presence of said properties by measuring individual data points. This large amount of nuance present in the structure property relationship of a perovskite makes it nearly impossible to identify perovskite structures with desirable properties through blind trial and error. 

one particularly suitable technique for simplifying this process is empirical modeling. the advantages of empirical modeling are that it is able to quickly screen a vast amount of data identifying trends that would never be visible to a researcher who is only synthesizing a small number of compositions and that it is able to predict the properties that a composition would have with a specific type of ordering. This first benefit is critical to perovskites because with all of the elements that can be seamlessly included in a perovskite either entirely or partially substituted in, the list of potential compositions is effectively endless and researchers will undoubtedly require some sort of tool screen through all of them. This second feature is incredibly beneficial because some perovskites like Barium Strontium Magnesium Tantalate (BSMT) only posses beneficial properties (in this case Dielectric properties) when they have a very high degree of long range ordering but experimentally inducing such ordering is very time consuming and costly so it is very difficult to search for potential alternative compositions or even alternative ordering structures with the same composition.

A-Site Ordering

A-site ordering in perovskites typically occurs on the {001} planes in perovskites and has been shown to produce an atypical volume increase due to the effect of bond expansion in other planes outweighing the effect of bond compression in the ordered plane

Our lab has published multiple works on this topic including DOI: 10.1111/jace.14547 which is focused on empirically measuring the presence of and amount of A-site ordering in perovskites and DOI: 10.1111/jace.16168 which is focused on modeling the effects of A-site ordering in perovskites.

due to the fact that the majority of A-site ordering in perovskites is short range ordering which appears disordered over large distances and is difficult to identify with common measurement techniques such as XRD many of the A-site ordered perovskites have been understandably misclassified as disordered structures. We simulated the structure in Density Functional Theory (DFT) simulations to confirm that layered A-site ordering was indeed the lowest energy configuration. then our lab synthesized samples of x and measured them using XRD, SEM, TEM, and EDS to verify the structure and thoroughly confirm that there were no visible indications of long range ordering in the material. after that we used electron diffraction to index the peaks and identified smearing in the Bragg reflections that was indicative of some ordering being present. finally we accounted for the effects of A-site ordering in our empirical model and showed that it increased the predictive accuracy of said model.

building off of this model 15 compositions in the NaLiLaTiO3 (NLLT) system were synthesized and then analyzed using XRD and TEM. to collect structural data and asses the presence of long and short range ordering. by fitting an A-site size correction factor and a cation ordering parameter to these data points relationships between vacancy concentration, A-site size correction factor, and a cation ordering parameter became apparent. By modeling these relationships it is possible to predict the unit cell volume as a function of cation ordering. interestingly the models developed were surprisingly insensitive to vacancy ordering despite their dependence on vacancy concentration.

B-Site Ordering

B-site ordering in perovskites {111} planes is typically preferred and is usually either 1:1 (rock salt) ordered where the B-site species alternates between every cation or 1:2 ordered where the minority B-site species shows up every third site. B-site ordering typical produces the expected volume decrease. our lab has produced a model predicting the behavior of 1:1ordered perovskites. 

similarly to how the model for A-site ordering was produced four perovskite compositions that were expected to result in B-site order were synthesized. Unlike A-site ordering that is commonly short range, these compounds possessed long range ordering and thus could be easily detected with XRD measurements. With 38 additional 1:1 B-Site ordered compositions that were mined from literature it was possible to expand our empirical model such that it can account for the effects of 1:1 B-site ordering in perovskites by using a B-site size correction factor. Unfortunately, this model does not appear to effectively account for the effects of 1:2 B-site ordering in perovskites so further work will still be necessary.