The atomistic origin of the inverse piezoelectric effect in α-quartz Original Research Article

Ab initio calculations have been carried out using the FP-APW+lo method in order to understand the atomic origin of the inverse piezoelectric effect in α-quartz. The external electric field was modelled by a saw-like potential Vext in order to achieve translational symmetry within a supercell (SC) containing 72 atoms. The original trigonal quartz structure was repeated along the [110] direction, which corresponds to the direction of the external field. An electric field with 550 kV/mm was applied and the atomic positions of the SC were relaxed until the forces acting on the atoms vanished. In parts of the SC, Vext changes almost linearly and thus the relaxed atomic positions can be used to determine the structural response due to the external electric field. The calculations provide the piezoelectric modulus of the correct order of magnitude. In contrast to previous models and in agreement with recent experimental results, the atomic origin of the piezoelectric effect can be described by a rotation of slightly deformed SiO4 tetrahedra against each other. The change of the Si–O bond lengths and the tetrahedral O–Si–O angles is one order of magnitude smaller than that of the Si–O–Si angles between neighbouring tetrahedra. The calculated changes of X-ray structure factors are in agreement with experiment when the theoretical data are extrapolated down to the much smaller field strength that is applied in the experiment (E<10 kV/mm).