Monte Carlo simulation of equilibrium L10 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 (1495-1514 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 which decreased as the particle size decreased. Our calculations predict that 3.5-nm diameter particles in configurational equilibrium at 600 deg. 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 deg. C or below is primarily a problem of kinetics rather than equilibrium