The Atomistic Origin of the Inverse Piezoelectric Effect in a-SiO₂ and a-GaPO₄

Jav Davaasambuu,^a Vasili Kochin,^a Andreas Pucher,^a Semen V.Gorfman,^a Vladimir G.Tsirelson,^a Peter Blaha^b and Ullrich Pietsch^c

^aQuantum Chemistry Department, Mendeleev University, Moscow, Russia; ^bInstitute of Materials Chemistry, Technical University of Wien, Austria; ^cInstitute of Physics, University of Potsdam, Potsdam, Germany (upietsch@ullipc.physik.uni-potsdam.de)

The inverse piezoelectric effect of a-quartz can be observed applying an external electric field parallel to the non-centrosymmetric [11.0] direction. In a previous paper we have shown that the model of field induced mutual displacement of ionic sublattices fails for the explanation of the atomic origin of the macroscopic measurable effect. Therefore we proposed an alternative model which is based on the rotation of nearly rigid SiO₄ tetrahedra under influence of the external electric field considering the strong covalent bond between silicon and oxygen.

Meanwhile this model has been verified by measuring the changes of integrated intensities of selected Bragg reflection DR/R of a-SiO₂ and the isostructural a-GaPO₄ under influence of a periodic external high electric field of E ≤ 8 kV/mm. For the first time a similar experiment was performed at low temperatures (50 < T < 300 K).

The received data were interpreted in terms of a semi-empirical structure model and by ab-initio calculations. Nine structural parameters of the semi-empirical model were refined using nine selected Bragg reflections which were measured at different field strength. For the refinement we used the constraint of rigid SiO₄ tetrahedra. In addition, the form factor variation was neglected because the quantum-mechanically predicted field dependence is two orders of magnitude smaller than the experimental data. Our model fits all measured DR/R in a qualitative right manner. At E=3kV/mm the Si-O-Si angle in direction parallel and perpendicular to the applied field change by about 0.05° and 0.02°, respectively. In GaPO₄ the Ga-O-P angles parallel to the field alter by about 0.12° reflecting the higher piezoelectric coefficient d₁₁₁ compared to a-SiO₂.

The temperature dependence of DR/R´s was measured down to 50 K. They can be interpreted mainly by the temperature dependence of Debye-Waller factors but an additional contribution caused by the field-induced rotation of SiO₄ and (Ga,P)O₄ tetrahedra, respectively.

Ab-initio calculations have be performed using the WIEN2k-package. Here we defined a supercell of reduced symmetry along the [11.0] direction of the quartz structure containing 72 atoms. The external electric field of about 5 kV/mm is modelled by an additional saw-like potential. The relaxed atomic positions within a sub-unit of the supercell with constant field strength were used as input for the semi-empirical model, mentioned above. Although the calculations are not finished yet, the results seem to verify our predictions.

References

V.G.Tsirelson , S.V.Gorfman, U.Pietsch, Acta Cryst A. submitted

J. Davasambuu, V.Kochin, A.Pucher, U.Pietsch, Europhys.Lett. 2002 submitted

J.Stahn , U.Pietsch, P.Blaha, K.H.Schwarz, Phys.Rev. B63, 165205