Theory of rare-earth alloys

A mean-field random alloy theory combined with a simple calculation of the exchange interaction $J(c,Q)\mathrm{}$ is shown to quantitatively account for the phase diagrams for alloys of rare-earth metals with Y, Lu, Sc, and other rare-earth metals. A concentration-dependent $J(c,Q)\mathrm{}$ explains the empirical 2/3. law and reconstitutes the idea of de Gennes scaling. The phase diagrams exhibit examples of both bicritical and tetracritical points. No significant deviations from the mean-field calculation can be detected with the present experimental accuracy. A linear interpolation of $J\left(Q\right)\mathrm{}$ for Gd and Er is found to account for all alloys except the Sc based. The exceptional behavior of the Sc alloys is due to a low density of states for Sc. A brief discussion is given of the effect on the mean-field results of changes in volume or $\frac{c}{a}$ ratio and of critical fluctuations. Since the physical mechanisms of these ideal alloys are well documented they may serve as good candidates for studies of statistical effects such as multicritical phenomena or spin-glass phenomena.