Compositional phase diagram and microscopic mechanism of Ba 1-x Ca x Zr y Ti 1-y O 3 relaxor ferroelectrics.

With extensive first-principles density-functional calculations, we construct a three-dimensional compositional phase diagram of Ba1-x Cax Zry Ti1-y O3 (BCZT) with the Ca and Zr content in the ranges of 0 ≤ xCa ≤ 0.2 and 0 ≤ yZr ≤ 1. Our calculations show that, when the Zr content increases, the difference in energy and difference in the structural parameters of the cubic, tetragonal, orthorhombic, and rhombohedral phases of BCZT are reduced. Eventually, all four phases merge into a multiphase with coexisting cubic structures (MPCCS) under Zr-rich conditions, indicating that BCZT undergoes phase transition from a normal ferroelectric (NFE) to a relaxor ferroelectric (RFE), consistent with experimental observations. The 3D diagram shows that the regions of merged and separated energy surfaces correspond to the regions of the RFE and NFE, respectively, which suggests that a MPCCS corresponds to a RFE. In addition, with the MPCCS model and Landau-Devonshire theory, we provide an interpretation of the high electromechanical properties of the BCZT relaxor ferroelectric and apply it to the classical local random field and micro-macro domain transition models.