Elastic Constants of Magnesium Thorium Alloy

The longitudinal and shear wave velocities in a polycrystalline sample of magnesium thorium alloy were measured by a pulse transmission technique as a function of temperature. Temperatures ranged from 25 C to about 350 deg C for longitudinal wave measurements and to about 220 deg C for shear measurements. The resulting velocity data were used to calculate various elastic properties of the material, including Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio. The resulting least squares fits for these data are: Longitudinal velocity, c_l = 5.749 − 3.987 × 10⁻⁴T − 1.139 × 10⁻⁶T²mm/μsec; shear velocity, c_t = 3.108 − 1.421 × 10⁻⁴T − 2.588 × 10⁻⁶T²mm/μsec; bulk modulus, B = 3.576 × 10^″ − 2.744 × 10⁷T + 1.187 × 10⁵T² dynes/cm²; Young’s modulus, E = 4.435 × 10^″ − 1.415 × 10⁷T = 6.037 × 10⁵T² dynes/cm²; shear modulus, G = 1.716 × 10^″ − 7.994 × 10⁶T − 2.619 × 10⁵T² dynes/cm²; Poisson’s ratio, σ = 0.293 − 6.459 × 10⁻⁶T + 3.392 × 10⁻⁷T².