Virtual-crystal approximation that works: Locating a composition phase boundary in Pb(Zr_{1-x}Ti_3)O_3

TL;DR

This paper introduces an improved virtual crystal approximation (VCA) method for modeling disordered solid solutions, accurately predicting phase boundaries in Pb(Zr_{1-x}Ti_x)O_3 by overcoming previous limitations.

Contribution

The authors develop a new potential for VCA that yields averaged atomic properties, enabling accurate phase boundary predictions in ferroelectric oxides.

Findings

The new VCA method accurately predicts phase energies.

It correctly identifies the ground state at x=0.4.

Results agree with superlattice calculations and experiments.

Abstract

We present a new method for modeling disordered solid solutions, based on the virtual crystal approximation (VCA). The VCA is a tractable way of studying configurationally disordered systems; traditionally, the potentials which represent atoms of two or more elements are averaged into a composite atomic potential. We have overcome significant shortcomings of the standard VCA by developing a potential which yields averaged atomic properties. We perform the VCA on a ferroelectric oxide, determining the energy differences between the high-temperature rhombohedral, low-temperature rhombohedral and tetragonal phases of Pb(Zr_{1-x}Ti_x)O_3 at x=0.5 and comparing these results to superlattice calculations and experiment. We then use our new method to determine the preferred structural phase at x=0.4. We find that the low-temperature rhombohedral phase becomes the ground state at x=0.4, in agreement with experimental findings.