Dennis L. Jackson, David Roundy
We model the dielectric properties of the relaxor ferroelectric perovskite solid solution BaTiO$_3$ - Bi(Zn$_{1/2}$Ti$_{1/2}$)O$_3$ (BT-BZT) using ab initio methods combined with an Ising-like model. BT-BZT has both A-site and B-site disorder, which makes it a challenging material to model. The polarization of all possible 2x2x2 supercells of BT-BZT are determined using ab initio methods. The cells are then arranged on a lattice in an Ising-like model to determine long-range dielectric properties. This enables us to predict the long-range disorder effects of relaxors, while keeping the accuracy of ab initio methods. This new model enables us to work with orders of magnitude more atoms than other models such as molecular dynamics. We analyze the Monte Carlo data for a single lattice configuration using the multiple histogram method, and develop a new modified histogram technique to combine data from multiple lattice configurations. Experiments qualitatively agree with our models predicted values of dielectric constant and polarization.
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http://arxiv.org/abs/1209.0033
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