Determination of the shear constants of the cubic crystals

Abstract

As a result of the research, formulas for calculating shear elastic constants of cubic crystals, based on the resonant frequency of torsional vibrations of samples c 44 and C' with square and rectangular cross-section in the method of the composite piezoelectric vibrator was obtained. Despite the fact that the resonance method does not need a large single crystals, the calculation formulas for the samples most simple to manufacture prismatic either incomplete or completely unknown. For example, there is data on the calculation of the c 44 and C' of the natural frequencies of torsional vibrations of the rods only circular cross-section. An exception is the ultrasonic pulse method for measuring the elastic constants, but it requires to measure single-crystal samples of sufficiently large size. The calculation is reduced to finding the proper expressions for rotating mechanical torque, which is more or less complex function of the cross-section and the elastic constants of the sample material. At the same time it takes into account the amendment to the warping of the cross-section of anisotropic samples under torsion. Then calculates the natural frequencies of torsional vibration samples of square and rectangular cross-section and the corresponding shear elastic constants. As an example, the calculation of shear considered constant C' on the basis of the pitch frequency of torsional vibrations of square cross-section sample of nickel-titanium NiTi.