In attempting to explain the unusual magnetic properties of the iron-nickel alloys, single crystals of alloys containing 35 to 100 percent nickel were prepared, and measurements made of the magnetic crystal anisotropy and magnetostriction as dependent on cooling rate. It is confirmed that there is a large effect of cooling rate on the anisotropy in the region near Fe${\mathrm{Ni}}_3$, but the experiments show also a substantial effect between 50 and 85 percent nickel. Two magnetostriction constants, ${\lambda }_{100}$ and ${\lambda }_{111}$, were measured on the same crystals. The effect of cooling rate on magnetostriction was found to be substantial only in the composition range 70 to 80 percent nickel. When the specimens are quenched, ${\lambda }_{111}$ goes through zero for a nickel content just below 80 percent nickel, a composition very close to that for highest permeability. This is understandable because the magnetostrictive strain caused by movement of the boundary between two domains, each magnetized spontaneously in a [111] direction, depends on ${\lambda }_{111}$ alone. The same physical picture predicts that near 45 percent nickel, where [100] is the direction of easiest magnetization and ${\lambda }_{100}$ goes through zero, the permeability vs composition curve should again have a maximum. Such a maximum is known to exist, and initial permeabilities as high as 15 000 have been observed.

Although simple theory suggests that domain-rotation should occur in very weak fields when the crystal anisotropy is very small (75 percent nickel in quenched alloys), nevertheless, rotation involves magnetostrictive strains which prevent ${\mu }_0$ from becoming infinite. Internal poles are also likely to be formed. In slowly cooled alloys the anisotropy is zero at about 63 percent nickel; here there are random strains caused by magnetostriction and possibly also by atomic ordering.

The principal changes in magnetic properties with composition are explained in terms of the crystal anisotropy and magnetostriction, and their change with heat treatment.

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