Reinterpretation of the bond-valence model with bond-order formalism: An improved bond-valence-based interatomic potential for PbTiO${}_{3}$

Reinterpretation of the bond-valence model with bond-order formalism: An improved bond-valence-based interatomic potential for PbTiO $_{3}$

Shi Liu, Ilya Grinberg, Hiroyuki Takenaka, and Andrew M. Rappe

Phys. Rev. B 88, 104102 – Published 6 September 2013

Abstract

We present a modified bond-valence model of PbTiO $_{3}$ based on the principles of bond-valence and bond-valence vector conservation. The relationship between the bond-valence model and the bond-order potential is derived analytically in the framework of a tight-binding model. An energy term, bond-valence vector energy, is introduced into the atomistic model and the potential parameters are reoptimized. This model potential can be applied both to canonical-ensemble (NVT) and isobaric-isothermal ensemble (NPT) molecular dynamics (MD) simulations. This model reproduces the experimental phase transition in NVT MD simulations and also exhibits the experimental sequence of temperature-driven and pressure-driven phase transitions in NPT simulations. We expect that this improved bond-valence model can be applied to a broad range of inorganic materials.