Magnetostriction of Polycrystalline Aggregates

Abstract

The magnetostriction constant of the polycrystal λ_s can be written as a linear combination of the constants of the cubic crystallites; λ_s = αλ₁₀₀ + (1‐α)λ₁₁₁. The almost universally used approximation α = ⅖ is a poor one. It is based on the assumption of uniform stress through the aggregate (analogous to the Reuss approximation for the polycrystalline shear modulus). The alternative approximation of uniform strain (analogous to the Voigt approximation of the shear modulus) gives α = 2/(2+3c), where c = 2c₄₄/(c₁₁‐c₁₂) is a measure of the elastic anisotropy of the microcrystals. However, both approximations lie outside upper and lower bounds which have been derived by Hashin and Shtrikman for the elastic case (although the magnetostrictive analogs have not been calculated). A physically reasonable approximation (the analog of Kroner's spherical stress approximation which lies between the Hashin and Shtrikman bounds in the elastic case) was given in a little known paper by Vladimirsky. Here the local stress is approximated by that in a spherical microcrystal surrounded by a homogeneous material with the isotropic properties of the polycrystalline aggregate. We show that for physically interesting elastic constants the rather complicated Vladimirsky result can be represented simply by α = ⅖ − (lnc)/8. The available experimental data are compared with these various approximations; they favor the latter very strongly over the more commonly used α = ⅖.