Dresden 2009 – wissenschaftliches Programm
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DF: Fachverband Dielektrische Festkörper
DF 12: Poster II
DF 12.4: Poster
Mittwoch, 25. März 2009, 09:30–12:30, P5
Visualization of elastic properties by use of the slowness surface — •Leonore Wiehl and Eiken Haussühl — Institut für Geowissenschaften, Goethe-Universität Frankfurt, D-60438 Frankfurt
The elastic properties of crystals are described by a tensor of forth rank, which may have up to 21 different components, depending on symmetry. In general the inspection at a first glance of just these coefficients gives no detailed idea, how elasticity varies with crystal direction. Therefore representation surfaces are used for visualization, which help to correlate elastic properties with other physical properties and with the crystal structure. For this purpose most often the longitudinal elastic stiffness is plotted, which represents the elastic "hardness" of a crystal in direction of the applied pressure. More detailed information, though seldom used, provides the refraction surface, or slowness surface [1]. It represents the reciprocal phase velocities of elastic waves. The slowness surface is a surface of 6th degree in the velocities and consists of three separate sheets corresponding to the three elastic waves which propagate in each wave normal direction (one quasi-longitudinal and two quasi-transverse). A program was written, which calculates from the measured elastic coefficients of a crystal with arbitrary symmetry the wave velocities and polarization vectors for a given wave normal by solving the Christoffel equation and plots sections through the slowness surface in any desired orientation. As an example, the elastic properties of (C5H11NO2)2(CuCl2)3·2H2O are discussed.
[1] F. I. Fedorov: Theory of Elastic Waves in Crystals. Plenum Press, New York, 1968