First-principles soft-mode lattice dynamics of PbZr0.5Ti0.5O3 and shortcomings of the virtual crystal approximation

Abstract

A comparative study between PbTiO3, PbZrO3, and the solid solution PbZr0.5Ti0.5O3 is performed on the soft mode lattice dynamics within the first Brillouin Zone. We consider the six unique B-site orderings for PbZr0.5Ti0.5O3 representable within the 2×2×2 primitive perovskite supercell as well as the virtual crystal approximation (VCA) to extract the phonon dispersion relations of a high-symmetry cubic-constrained form using density functional perturbation theory. We find that the most unstable modes in the rock-salt ordered structure and the VCA, like pure PbZrO3, are antiferrodistortive (AFD) whilst lower symmetry arrangements are dominated by Γ-point ferroelectric (FE) instabilities like pure PbTiO3. Despite similarities in the phonon dispersion relations between the rock-salt ordered supercell and the VCA, the character of modes at high symmetry points are found to be different. In particular, the a 0 a 0 c − & a 0 a 0 c + AFD instabilities of the rocksalt ordering are replaced with a − b − c − & a + b + c + instabilities within the VCA. Such a rotation pattern is not seen in any of the supercell-based calculations thus serving as a quantitative example of the inability of the method to represent accurately local structural distortions. Single modes are found exhibiting dual order parameters. At the zone centre, some arrangements show mixed FE & antipolar soft modes (due to Pb motion tansverse to the polar axis) and at long wavelengths all arrangements have soft modes of a mixed antipolar & AFD character. These are described with direct analysis of the eigendisplacements.

Polar Morphologies from First Principles: PbTiO3Films on SrTiO3Substrates and the p(2×Λ) Surface Reconstruction

“…Since our method is general to any atomic system, we can extend to other problems for the perovskite oxides (and beyond) including highly disordered configurations, such as the popular solid solution families AB x C 1−x O 3 , (1 − x)ABO 3 − xCDO 3 where DFT methods used to circumvent the need for large supercell calculations fail in the reproduction of local structural distortions. [ 78 ]…”

A re-examination of antiferroelectric PbZrO$_3$ and PbHfO$_3$: an 80-atom $Pnam$ structure

“…While the phonon dispersion of P m 3m PZO (Figure 1, blue lines) has been discussed elsewhere [18,35], we briefly remark on some important features and compare with the P m 3m PHO dispersion (Figure 1, orange lines). With a focus on the imaginary branches (indicative of dynamical instabilities) we see that both materials are firmly unstable throughout the entirety of the first BZ.…”

“…With a focus on the imaginary branches (indicative of dynamical instabilities) we see that both materials are firmly unstable throughout the entirety of the first BZ. In turn, this gives rise to a large number of unique unstable modes which are discussed in [18]. We can see clearly the strong instabilities at the R and Σ-points known to comprise the majority of the distortion defining the P bam AFE phase [5,36].…”

“…2 making the task of accurate structure refinement a challenging one. Recently, first principles calculations were used to show that a large number of unique and increasingly incommensurate dynamical instabilities were present in the phonon dispersion relations of cubic PZO and ordered models of near-morphotropic PbZr x Ti 1−x O 3 (PZT, x = 0.5) [18]. We then ask: do any further modes of this type condense within the low temperature ground state of PZO and PHO?…”

Large scale and linear scaling DFT with the CONQUEST code

“…It is well known that both Si and Ge are mechanically anisotropic, with the Young's modulus in the [1 1 1] direction distortions [113]. The study of ferroelectric domains in thin films is another problem requiring large-scale electronic structure calculations and accurate structural relaxations.…”