Ultrasonic study of the elastic properties of calcium tungstate and other scheelites

Abstract

A study of the elastic properties of the scheelite structure crystals CaW0(_4), CaMo0(_4), ArMo0(_4) and PbMo0(_4) is presented. The seven independent components of the elastic stiffness constant tensor of CaW0(_4) have been determined between 1.5 K and 300 K by pulse superposition measurements of ultrasound velocities. A computer fitting procedure has been used to obtain the elastic constants from the velocity data; this has allowed the elastic constants to be determined even though large energy flux deviations prevented the measurements of the velocities of the quasi-shear modes propagated in the [100] and [110] directions. Experiments on SrMo0(_4) single crystals have shown that similar difficulties were the cause of inconsistencies in recently published velocity data; a new, correct set of elastic constants for SrMo0(_4) has been determined. Scheelites belong to the TII Laue group. The signs of C(_16) and S(_16) depend on the definition of the sense of the +z axis with recpect to the atomic arrangement. A convention previously used for CaMo0(_4) has bee adopted, the Z axis sensehas been found in SrMo0(+4) by an x-ray method: in each material C(_16) has been shown to be negative. Elastic behaviour and wave propagation characteristic, and their orientation dependence in the four materials, have been compared and contrasted. The work has provided a new in-sight into the acoustic properties of TI and TII Laue group materials; in the latter the “axes of acoustic symmetry” in the (001) plane do not coincide with the <100> and <110> crystallographic directions (as in TI's) but deviate from them by angles which are between 15 and 23 in the scheelites studied. Knowledge of the positions of these axes should facilitate further ultrasonic studies.