The Effect of Dislocations on Magnetization Near Saturation

The effect of dislocations on the magnetization curve at high fields is calculated by direct use of dislocation theory. The deviation from saturation is assumed to be due to magnetostrictive forces, localized in the stress field about the dislocation rather than at the dislocation itself; their effect is more complicated than that of the simple "line concentrations of force" considered in an earlier article. Pairs of dislocations of opposite sign, separated by a short distance, contribute a term $\frac{a}{H}$ to the deviation from saturation; in this respect they resemble line concentrations. Pairs separated by a long distance and surplus dislocations of one sign contribute a term $\frac{b}{H^2}$, with $b$ theoretically not a constant but a logarithmically varying function of $H$. From data on the variation of the empirical $a$ and $b$ with plastic strain, it is possible to calculate the density of dislocations and the "block" length if a value is assumed for the distance $Y$ between the members of a dislocation pair. The orders of magnitude obtained agree with those obtained in the theory of hardening if $Y$ is taken $\cong 2\times {10}^{-6\mathrm{}}$ cm. It appears that all but about 1 percent of the dislocations are members of such pairs.