P.E. Armstrong

The elastic properties of polycrystalline HfC0.967, NbC0.964, TaC0.994, and WC1.007 were determined at 23°C, and the data were corrected to theoretical density. In units of 1012 dyn/cm2, the Young's moduli are 4.619, 4.884, 5.377, and 6.237; the shear moduli, 1.953, 1.987, 2.168, and 2.633; and the bulk moduli, 2.426, 3.008, 3.448, and 3.295, respectively. The Poisson's ratios are 0.183, 0.229, 0.240, and 0.185, respectively. The specific electrical resistivities (micro-ohm centimeters at 20°C, corrected to theoretical density) are 24.6, 49.1, 25.6, and 17.8, respectively.

The elastic properties of molybdenum single crystals have been measured using thin-rod resonance techniques as a function of temperature from −198° to over +650°C. Molybdenum behaves in a normal manner over this temperature range. Its elastic stiffness coefficients, with the exception of C12 which increased 3%, decreased in a nearly linear manner. The decrease was 8% for C44, 11% for C11, and 18% for C′. From these data the temperature dependence of the bulk modulus, the shear coefficient C′, the anisotropy ratio, and the Young's and shear modulus of isotropic polycrystalline molybdenum were calculated.

The elastic constants of thorium single crystals have been determined at ultrasonic frequencies employing both resonance and pulse-echo techniques. The values at 300°K in units of 1011 dyne/cm2 are, C11=7.53, C12=4.89, and C44=4.78. The constants C11 and C44 increase and C12 decreases with decreasing temperature and extrapolate to 7.79, 4.82, and 5.13, respectively, at 0°K. The Cauchy relation C12=C44 occurs, quite probably fortuitously, at 271°K. The anisotropy factor 2C44/(C11–C12) at room temperature is 3.6 which is comparable to the values for lead and gold. Calculated Poisson's ratios, σ100 and σ111, indicate a much stronger resistance to contraction in the close-packed planes than in the less densely packed (100) planes.