Shi Liu, Hiroyuki Takenaka, Tingting Qi, Ilya Grinberg, Andrew M. Rappe
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 bond-valence energy and bond-order potential is derived analytically in the framework of a tight-binding model. A new energy term, bond-valence vector energy, is introduced into the atomistic model and the potential parameters are re-optimized. The new model potential can be applied to both canonical ensemble ($NVT$) and isobaric-isothermal ensemble ($NPT$) molecular dynamics (MD) simulations. This model reproduces the experimental phase transition temperature 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.
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http://arxiv.org/abs/1211.5166
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