Interpretation of Torsional Frequencies of Crystal Specimens

Abstract

A crystalline cylinder when subjected to a harmonically varying twisting moment in general not only twists but bends. A correct interpretation of the response frequencies is important in dynamical determinations of the elastic constants of crystals, and it is desirable that the measurements be made under such conditions that a simple formula, similar to that for isotropic materials, may be used without fear of serious error. In static measurements two such formulas are required, one for twist with bending prevented and the other for twist with bending unrestrained. It is shown here that each of these is a good approximation in dynamic measurements over certain ranges of frequencies and of specimen lengths, and formulas are derived by which the errors may be estimated. A simple straight-line plot based on approximate values of the elastic constants gives all the information that is needed for the selection of good working conditions in the final measurements. For the sodium and copper-gold crystals on which measurements have been reported, the pure torsion formula is a good approximation when no parasitic response frequencies are observable; but it would cease to be a good approximation for specimen lengths below about 3 cm.