Theoretical predictions of polymorphic phase boundaries in BaTi1−xZrxO3 by first-principles calculations

The piezoelectric properties of BaTi1−xZrxO3 are investigated by first-principles calculations with virtual crystal approximation. The total energy, piezoelectric coefficient, elastic property and Born effective charge as a function of Zr doping level x of BaTi1−xZrxO3 are calculated in order to reveal the property of its polymorphic phase boundaries. Our results show that the polymorphic phase boundaries of BaTi1−xZrxO3 exist only in the range of x=0.077–0.088, which is coincident with the available experimental observation. And a high piezoelectric coefficient d33 at x=0.08 is shown in the tetragonal and orthorhombic BaTi1−xZrxO3. It is found that this high piezoelectric activity at the polymorphic phase boundaries is due to the flat free energy profile of BaTi1−xZrxO3. Moreover, as can be seen in our calculations, the enhancement of structural instability and Ti–O covalent bonding is responsible for the enhancement of piezoelectricity of BaTi1−xZrxO3. This study gives a fundamental understanding of polymorphic phase boundaries in BaTi1−xZrxO3, and may further serve the improvement of piezoelectric response in BaTi1−xZrxO3 from the application point of view.