The ElastiC constants of Nickel Single Crystals

Abstract

Single crystals of nickel, of a slender cylindrical rod form, were prepared by the method of slow solidification, and Young's moduli of elasticity of annealed crystal specimens having various orientations were measured by the method of magnetostrictive oscillation at room temperature. The relation between the reciprocal of the modulus,1/E, and orientations(γ1, γ2, γ3)was found to be 1/E = 0.8349 − 2 × 0.6739 × 10-12 cm2/dyne, where γ1, γ2 and γ3 are direction cosines of the rod axis of a crystal specimen referred to the tetragonal axes; Young's moduli in directions of the three principal crystallographic axes,[100],[110], and [111], are E[100] =1.198 × 1012,E[110] = 2.008 × 1012, and E[111] = 2.592 × 1012 dynes/cm2, respectively. Then, principal elastic parameters, Sik, were determined by the use of the reliable measured data for the volume compressibility of polycrystalline nickel, which was O.535 × 10-12 cm2/dyne;results obtained are S11 = 0.835 × 10-12, S12 = − 0.328 times 10-12, and S44 = 0.978 times 10-12cm2/dyne. The rigidity moduli in directions of the three principal crystallographic axes, computed from the above-determind principal elastic parameters, are G[100] = 1.022 × 1012, G[110] = 0.605 × 1012, and G[111] = 0.533 × 1012 dynes/cm2. Hence, the elastic anisotropies are E[111]/E[100] = 2.16 and G[100]/G[111] = 1.92, being nearly the same as those of iron crystals. Further, three principal elastic constants, Cik, were computed to be C11 = 2.44 × 1012, C12 = 1.58 × 1012, and C44 = 1.02 × 1012 dynes/cm2; so-called Cauchy's relation C12 = C44 does not hold. The elastic moduli of quasi-isotropic polycrystalline nickel were calculated from the elastic constants of single crystals by theories of Voigt, Reuss, Huber and schmid, and Bruggeman, and the calculated values were compared with the measured ones. It was found that theories of Voigt and, particularly, of Bruggeman gave the most accurate values, which were 2.07 × 1012 and 1.92×1012 dynes/cm2, respectively, for Young's modulus and 0.78 × 1012 and 0.72 × 1012 dynes/cm2, respectively, for the rigidity modulus. Further, Debye's characteristic temperature was calculated by the use of the computed values for Poisson's ratio, 0.315 and 0.329, which were obtained by the theories of Voigt and Bruggeman, and the results were 451 and 432 ° K, respectively. © 1942, The Japan Institute of Metals. All rights reserved.