No abstract

Structural response of crystals to an applied external perturbation is important as a key for understanding microscopic origin of physical properties. Experimental investigation of structural response is a great challenge for modern structure analysis. We demonstrate how advanced X-ray diffraction techniques facilitate probing tiny (10 -4 Å) distortions of bond lengths under a permanent electric field. We also discuss details of the experimental procedure essential for reaching such precision. We ask whether the experiment can be used to evaluate * Dr. S. Gorfman

Piezoelectric lithium sulfate monohydrate, Li2SO4.H2O, was analyzed with respect to the relationship between the static structural properties of the crystal and its response to an external electric field. The static electron density was determined via standard low-temperature X-ray data collection at 90 (5) K using an Enraf-Nonius CAD-4 diffractometer, Mo Kalpha radiation and multipole model refinement. Then a synchrotron-radiation experiment using the D3 beamline at HASYLAB was conducted in order to investigate the structural deformations in Li2SO4.H2O caused by an applied external electric field. In particular, the shifts of Bragg-peak positions induced by the electric field were measured and the piezoelectric constants d211, d222, d233 and d213 of Li2SO4.H2O were obtained from the shifts. With the same experimental setup the variations of more than 100 Bragg intensities were measured under an applied electric field. The data were used to refine the corresponding displacements of individual atoms within the unit cell. The distortions of the cation-anion bond lengths in the LiO4, LiO3(H2O) and SO4 tetrahedra were evaluated and then analyzed in terms of the electron-density-related properties of the Li-O and S-O bonds. The two lithium structural units were found to be strongly deformed by the applied electric field, while the SO(4) tetrahedron changed less. This is in agreement with the low bond strength of the Li-O bonds.

Time-resolved measurements of the macroscopic and microscopic strains in piezoelectric crystals were performed with a novel data acquisition technique implemented on the basis of a field programmed gate array system. Both types of strains were induced in a crystal by an applied periodic high voltage with fast (within 100 ns) switches between opposite polarities and measured simultaneously by respective angular shifts and integrated intensities of synchrotron x-ray diffraction rocking curves. The time resolution achieved with the developed data acquisition system was 100 ns. The paper demonstrates the particular application of this technique for the investigations of time dynamics of lattice constants and atomic positions in a unit cell for piezoelectric BiB3O6 and Li2SO4 center dot H2O crystals. It has been found that 100 ns fast rising time of an applied external electric field induces oscillations of the crystal lattice constants, visible as oscillations of Bragg peak angular positions. At the same time, these oscillations are not observed for the Bragg intensities, i.e., for fractional positions of atoms in the unit cell and correspondingly for bond lengths. The results allow suggesting a model for the mutual interconnection between the deformation of bond lengths and lattice constants in piezoelectric crystals. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3480996]\u

We have determined all eight components of the piezoelectric tensor of a monoclinic crystal, BiB3O6, by means of synchrotron X-ray diffraction technique. The experiments have been performed on a four circle goniometer using the ω-scan method introduced by Graafsma [1] which is universal in the choice of appropriate reflections. The determined values of the piezoelectric tensor are in good agreement with those obtained earlier for BiB3O6 with the use of an optical Michelson interferometer.