First-principles study of the relaxor ferroelectricity of Ba(Zr, Ti)O₃

Ba(Zr, Ti)O₃ is a lead-free relaxor ferroelectric. Using the first-principles method, the ferroelectric dipole moments for pure BaTiO₃ and Ba(Zr, Ti)O₃ supercells are studied. All possible ion configurations of BaZr_0.5Ti_0.5O₃ and BaZr_0.25Ti_0.75O₃ are constructed in a 2× 2× 2 supercell. For the half-substituted case, divergence of ferroelectric properties is found from these structures, which greatly depends on the arrangements of Ti and Zr ions. Thus our results provide a reasonable explanation to the relaxor behavior of Ba(Zr, Ti)O₃. In addition, a model based on the thermal statistics gives the averaged polarization for Ba(Zr, Ti)O₃, which depends on the temperature of synthesis. Our result is helpful to understand and tune the relaxor ferroelectricity of lead-free Ba(Zr, Ti)O₃.