First principles soft mode lattice dynamics of PbZr${}_{0.5}$Ti${}_{0.5}$O${}_3$ and shortcomings of the virtual crystal approximation

Abstract

A comparative study between PbTiO${}_3$, PbZrO${}_3$, and the solid solution PbZr${}_{0.5}$Ti${}_{0.5}$O${}_3$ is performed on the soft mode lattice dynamics within the first Brillouin Zone. We consider the six unique B-site orderings for PbZr${}_{0.5}$Ti${}_{0.5}$O${}_3$ representable within the 2$\times$2$\times$2 primitive perovskite supercell as well as the virtual crystal approximation (VCA) to extract the phonon dispersion relations of a high-symmetry cubic-constrained form using density functional perturbation theory. We find that the most unstable modes in the rock-salt ordered structure and the VCA, like pure PbZrO${}_3$, are antiferrodistortive (AFD) whilst lower symmetry arrangements are dominated by $\Gamma$-point ferroelectric (FE) instabilities like pure PbTiO${}_3$. 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 rock-salt 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.

arXiv comment14 pages, 5 figures

References in corpus (17)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Phonons and related properties of extended systems from density-functional perturbation theory
• Optimized norm-conserving Vanderbilt pseudopotentials
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• A monoclinic ferroelectric phase in the Pb(Zr1-xTix)O3 solid solution
• The virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites
• Libxc: a library of exchange and correlation functionals for density functional theory
• O(N) methods in electronic structure calculations
• Lattice dynamics of BaTiO3, PbTiO3 and PbZrO3: a comparative first-principles study
• Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA
• Virtual-crystal approximation that works: Locating a composition phase boundary in Pb(Zr_{1-x}Ti_3)O_3
• Multiple soft-mode vibrations of lead zirconate
• First-principles study of the multi-mode anti-ferroelectric transition of PbZrO3
• Lattice instabilities of PbZrO3/PbTiO3 [1:1] superlattices from first principles
• Interplay of epitaxial strain and rotations in PbTiO${}_3$/PbZrO${}_3$ superlattices from first principles
• Dynamic Stimulation of Superconductivity With Resonant Terahertz Ultrasonic Waves

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