We formulate a method of understanding the intrinsic piezoelectric properties of a perovskite system on an atomistic level using a density functional theory (DFT) methodology implemented into the electron density code CASTEP.
First we consider the basic unary perovskites; barium titanate, lead titanate and potassium niobate. Geometry optimisation, elastic compliance, linear response, and simulated strain calculations are performed and the polarisation and piezoelectric coefficients are calculated. We then define the partial piezoelectric coefficient and demonstrate a way to generate the electron density shift, two novel methods in the understanding of intrinsic piezoelectric properties.
We then study the binary piezoelectric lead titanate, performing the same calculations and analysing the electron density shift and partial piezoelectric
coefficient in order to identify new features of binary systems, the equalisation between basic perovskite units and the "sawtooth" bonding asymmetry between the different B-site ions.
Then the feasibility of these calculations is evaluated for bismuth ferrite, a material showing multiferroic properties. The conversion of non-orthonormal lattice axes to a cartesian coordinate system is addressed. We discuss the phonon and electric field calculations, and evaluate what is and is not possible. We find that structural and electron calculations are possible and report the optimised geometry, the elastic compliance, total electron density and spin maps, and the electron density shifts. We identify the symmetry, non-locality, and rotational modes in rhombohedral bismuth ferrite and suggest future research based on these properties.
