Study On Pure Mode Axes Of Tetragonal System Cystals

When mechanical disturbance occur in a part of a crystal, elastic waves will spread in the crystal with the transmission of energy. Because a crystal is anisotropic, generally speaking, there are three different values of phase velocity in a certain spreading direction. Along the direction of a wave vector, there are three elastic waves. If the energy velocity and the wave vector are in the same direction, then the direction is called pure mode axis. When the acoustic waves propagate along its pure mode axis, there must be pure shear or pure longitudial waves. This characteristic is very useful to the design of transmitting transducer and receiving transducer. Based on the slowness surfaces of tetragonal crystal system, the pure mode axes have been studied and the piezoelectric effects have been considered.The direction of a radius vector on a slowness surface is the direction of a phase velocity. A normal direction on the slowness surface represents the direction of the energy velocity. Thus, the direction of a radius vector which is consistent with the normal direction on a three dimensional slowness surface is a pure mode axis. Matlab software is used to simulate slowness surface with a grid map. Each grid point represents the direction of phase velocity. A pure mode axis can be determined and figured out by comparing the directions of all the radius vectors and the corresponding normal directions. The higher the density of the grids is, the more accurate the data are. The pure mode axes of tetragonal system crystals have been studied by using this method. It is found that the pure mode axes of crystals with symmetry 4mm,422,42m,4/mmmare[001],[110] and other eight directions equivalent to them, respectively. The pure mode axis of crystals of 4,4,4/m class is [001]([001]) and other eight axes in XY plane. Let [001],[110]and axes equivalent to them rotate an angle around the Z axis. Eight axes in XY plane can be obtained. The angle of rotation changes with different kinds of crystals.For the piezoelectric transducer, piezoelectric effect of the crystal can not be ignored. The influence of piezoelectric effect on the pure mode axis has been investigated. When piezoelectric effect is considered, the independent components of elastic stiffness coefficient of crystals belonging to 4,4,422,4mm,42m class will change. The elastic stiffness coefficients has been calculated by using the modified formula. Then the slowness surface including the piezoelectric effect of crystals can be drawn and the new pure mode axis can be determined. Up to now, there are only the experiment data of pizeoelectric effect of the following crystals,i.e. BaTiO3 (4mm), ADP(42m)and TeO2 (422).The pure mode axes of three kinds of crystals stated above are calculated and figured out. It is found that there is no change by considering the piezoelectric effects. So it means that piezoelectric effect has no effect on the pure mode axes of these crystals.