Temperature and particle size dependence of equilibrium order parameter   of FePt
  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. Using the mixing potentials obtained in this manner, the dependency of equilibrium L1_0 ordering on temperature was studied for bulk and for (approximately) spherical nanoparticles ranging in size from 2.5 to 6nm. The order parameter was calculated using Monte Carlo simulation and the analytical ring approximation. 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 3.5nm diameter particles in configurational equilibrium at 600 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 3.5nm diameter nanoparticles annealed at 600 C or below is primarily a problem of kinetics rather than equilibrium 
R. V. Chepulskii and W. H. Butler