Elastic Moduli of Vanadium

Using the technique of zone melting by electron bombardment, $\frac{3}{8}$-in. diameter single crystals of vanadium were grown in a high vacuum. Two crystals were prepared from seeds such that their lengths were parallel to the [100] and the [110] crystal directions. With these orientations, the elastic moduli $C_{11}$, $C_{44}$, and $\frac{1}{2}(C_{11}-C_{12})$ were measured directly from 4.2°K to 300°K using the ultrasonic pulse-echo technique. The results are, in units of ${10}^{11}$ dyne ${\mathrm{cm}}^{-2\mathrm{}}$, The moduli at 4.2°K were used to calculate a Debye ${\theta }_0$ of 399.3°K which disagrees with the ${\theta }_0$ of 338°K obtained from calorimetry. The room temperature moduli agree very well with all other determinations. The moduli were used to calculate a phonon frequency distribution which is compared with the distribution measured by slow neutron scattering.