Temperature and particle-size dependence of the equilibrium order parameter of FePt alloys

First, second, and third nearest-neighbor pair mixing potentials for equiatomic FePt alloys were calculated from first principles by the Connolly-Williams method within the canonical cluster expansion formalism. It was demonstrated that these Connolly-Williams potentials (based on completely ordered states) and the corresponding Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) potentials (based on completely disordered states) can be brought into very close correspondence to each other simply by increasing the magnitude of the strain-induced interactions added to the KKR-CPA potential. Using the mixing potentials obtained in this manner, the dependence of equilibrium L1(0) ordering on temperature was studied for bulk and for (approximately) spherical nanoparticles ranging in size from 2.5 to 6 nm. The order parameter was calculated using Monte Carlo simulations and the analytical ring approximation. The calculated order-disorder temperature for bulk (1495-1514 K) was in relatively good agreement (4% error) with the experimental value (1572 K). For nanoparticles of finite size, the (long-range) order parameter changed continuously from unity to zero with increasing temperature. Rather than a discontinuity indicative of a phase transition, we obtained an inflection point in the order as a function of temperature. This inflection point occurred at a temperature below the bulk phase transition temperature and decreased as the particle size decreased. Our calculations predict that 3.5-nm-diam particles in configurational equilibrium at 600 degrees C (a typical annealing temperature for promoting L1(0) ordering) have an L1(0) order parameter of approximately 0.84 (compared to a maximum possible value equal to unity). According to our investigations, the experimental absence of (relatively) high L1(0) order in 3.5-nm-diam nanoparticles annealed at 600 degrees C or below is primarily a problem of kinetics rather than equilibrium.