Elastic Constants and Ultrasonic Attenuation of aβ-Tungsten-StructureV3Ge Crystal from 4.2 to 300°K

The longitudinal and transverse acoustic velocities and the ultrasonic attenuation of a $\beta$-tungsten ${\mathrm{V}}_3$Ge crystal with the $\beta$-tungsten structure have been measured by a pulse technique at a frequency of 10 MHz between 4.2 and 300°K. The room-temperature elastic moduli have been determined as $C_{11}=2.966\mathrm{}$, $C_{44}=0.6978\mathrm{}$, and $C_{12}=1.042\mathrm{}$ in units of ${10}^{12}$ dyn/${\mathrm{cm}}^2$. Contrary to the behavior of the $\beta$-tungsten-structure compounds ${\mathrm{V}}_3$Si and ${\mathrm{Nb}}_3$Sn, the adiabatic compressibility of ${\mathrm{V}}_3$Ge was found to be temperature-dependent. The elastic constant $C_{12}$ exhibits a lattice-softening phenomenon in the temperature interval between 75 and 300°K. The shear modulus $\frac{1}{2}(C_{11}-C_{12})$ displays a minimum at 75°K. At this temperature the longitudinal (in contrast to the shear) attenuation shows a sharp peak. The behavior of the elastic moduli and attenuation is discussed in terms of possible operation of an electron transfer mechanism. In addition, both the longitudinal and the shear attenuation behave anomalously at 168°K. A relaxational process is assumed. The limiting value of the Debye temperature is found to be 487°K. At room temperature, it is 471°K.