Ab-Initio Multiscale Simulation
of Piezoelectric Response

Kaxiras and Rice have done multiscale simulations with the Quasicontinuum method to predict the response of materials to competing strain and electric fields in qualitative agreement with experiment. The figure illustrates the simulated response of a piezoelectric material (lead titanate) under competing external mechanical and electrical loads: the pressure (vertical black arrows) tends to align the polarization on the horizontal axis (large blue arrows), the external field from the applied voltage tends to align the polarization on the vertical axis (large red arrow). The multiscale simulation, based on an ab-initio quantum mechanical Hamiltonian and the Quasicontinuum Finite Element Method, reveals the microscopic pattern of polarization (small colored arrows). The figures on the left show theoretical (top) and experimental (bottom) strain-versus-electric field curves, which are in excellent qualitative agreement.