Correlation between Lattice Constant and Magnetic Moment in 3d Transition Metal Alloys

An empirical relation between the lattice constant and the magnetic moment was found in binary solid solutions of 3d transition metals expressed as $\mathrm{a}(\mathrm{x}\mathrm{)=}{\mathrm{a}}_{\mathrm{A}}\text{\hspace{0.17em}(1−}\mathrm{x}\mathrm{)\hspace{0.17em}+\hspace{0.17em}}{\mathrm{a}}_{\mathrm{B}}\hspace{0.17em}\mathrm{x}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\mathrm{C}\mathrm{\hspace{0.17em}〈\mid \mu \mid 〉}$ , where $\mathrm{x}$ is the atomic fraction, ${\mathrm{a}}_{\mathrm{A}}$ , ${\mathrm{a}}_{\mathrm{B}}$ and $\mathrm{C}$ are parameters, $\mathrm{〈\mid \mu \mid 〉}$ the average magnitude of atomic magnetic moments. It is shown that the equation holds for all possible combinations of 3d transition metals which form solid solutions over a considerably wide range of concentrations. The analysis of lattice constants at high temperatures leads to the conclusion that localized atomic moments are retained above Tc in most 3d ferromagnetic alloys. The thermal expansion anomaly observed in the Invar alloy (${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ ) is explained as the result of collapse of localized moments above Tc. The physical meanings of the parameters are discussed in terms of the atomic size. It is shown that expansion of the atomic size is caused by the formation of the localized moment.