Monte Carlo simulation of equilibrium L1 ordering in FePt nanoparticles

First, second, and third nearest-neighbor mixing potentials for FePt alloys were calculated from first principles using the Connolly–Williams approach. Using the mixing potentials obtained in this manner, the dependency of equilibrium L10 ordering on temperature was studied for bulk and for a spherical nanoparticle with a 3.5-nm diameter at equiatomic composition by use of Monte Carlo simulation and the analytical ring approximation. The calculated order-disorder temperature for bulk (1495–1514K) was in relatively good agreement (4% error) with the experimental value (1572K). 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 which decreased as the particle size decreased. Our calculations predict that 3.5-nm diameter particles in configurational equilibrium at 600°C (a typical annealing temperature for promoting L10 ordering) have an L10 order parameter of 0.83 (compared to a maximum possible value equal to unity). According to our investigations, the experimental absence of a (relatively) high L10 order in 3.5-nm diameter nanoparticles annealed at 600°C or below is primarily a problem of kinetics rather than equilibrium.