Effect of three-body interactions on the ordering of bcc binary alloys

The composition dependence of the order—disorder critical temperature is investigated for a model binary alloy equivalent to an Ising system with both the nearest-neighbor interactions ($J$) and the three-particle interactions ($P$) present. Using a real-space renormalization-group method for calculating the phase diagram, we find that for small three-body forces, the maximum critical temperature shifts from the 50-50 atomic percent composition proportionally to $\frac{P}{J}$. The proportionality constant is determined both from the renormalization-group method and from Griffith's smoothness postulate. The results of the two calculations agree with each other, and they are used to estimate the relative strength of the three-body potentials in iron cobalt. The estimate $\frac{P}{J}=0.11\mathrm{}\pm 0.06$ indicates that three-body forces are small, so that the nearest-neighbor Ising model is a good first approximation for the description of ordering in FeCo.