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 cuboctahedra.  The B site is coordinated to six anions, forming corner-shared octahedra.  The anions are coordinated to just two B site cations, as the four nearest A-site cations are about 41% further away.

Perovskites abound both in nature and in the laboratory, and their wide compositional range enables a variety of useful properties such that perovskites are encountered in applications as disparate as ferroelectrics, 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 propensity to exhibit beneficial properties, but this wide range of potential properties is found within an equally wide compositional space; and it is not feasible to experimentally synthesize and test every composition. Our work aims to solve this problem and by producing empirical models that use published structural data to predict the resulting properties of a perovskite material.

Applications
Many perovskite-structured ceramic materials are known to have useful microwave dielectric properties, with potential applications in the mobile telecommunications market.  Just one example application of perovskites is as microwave resonators, which are at the heart of the multi-billion dollar market for telecommunications equipment, including cellular telephones and satellite links.  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!

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.

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 has been recently developed and shown to work well 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, ordering can also occur on the anion site.  At high enough concentrations, otherwise randomly distributed site-specific vacancies can order.  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 order 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 on 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. It increases the packing efficiency in the plane on which the ordering occurs and decreases the packing efficiency in all other planes, which can either result in a net volume shrinkage or expansion depending on the magnitudes of the shrinkage/expansion.

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 the degree of short/long-range ordering. Different degrees of ordering present in the perovskite additionally produce property gradients which make it impossible to measurement these properties with an individual data point. This large amount of nuance present in the structure-property relationship of perovskites makes it very difficult to identify perovskite structures with desirable properties through blind trial and error alone.

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 substitutions, the list of potential compositions is effectively endless and researchers require some sort of tool to 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.

A-Site Ordering

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

Due to the fact that the majority of A-site ordering in perovskites is short-range, it is often difficult to identify with common measurement techniques such as XRD. Indeed, many A-site ordered perovskites have been misclassified as disordered structures for this reason. 

B-Site Ordering

B-site ordering in perovskites {111} planes is typically preferred and is usually either in the ratio 1:1 (rock salt) or 1:2.  B-site ordering typically produces a volume decrease. Unlike A-site ordering that is commonly short range, these compounds possessed long range ordering which could thus be easily detected via XRD measurements. Our lab has produced a model predicting the behavior of both 1:1 and 1:2 B-site ordered perovskites.