A Phenomenological Derivation of the First- and Second-Order Magnetostriction and Morphic Effects for a Nickel Crystal

In order to account for experimental results which showed that the saturation elastic constants of a single nickel crystal varied with the direction of magnetization, a phenomenological investigation has been made of the stress, strain, and magnetic relations for single nickel crystals. The variation in elastic constants is shown to be a "morphic" effect caused by the change in the crystal symmetry due to the magnetostriction effect. In the energy equation this effect is represented by additional terms which involve squares and products of both the magnetic intensities and stresses. These terms are as large as the magnetostrictive terms when the stresses are of the order of ${10}^{10}$ dynes/${\mathrm{cm}}^2$. The energy equation has been used to derive the first- and second-order magnetostrictive effect, and the resulting terms agree with Becker and Döring's empirical constants for saturation conditions. For smaller magnetic intensities the terms divide up into first- and second-order terms which vary differently with magnetic field intensity. It is shown that the morphic effects involve six measurable constants, and some of these are evaluated experimentally.