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First, second and third nearest neighbor pair mixing potentials forequiatomic FePt alloys were calculated from first principles by theConnolly-Williams method within the canonical cluster expansion formalism.Using the mixing potentials obtained in this manner, the dependency ofequilibrium L1_0 ordering on temperature was studied for bulk and for(approximately) spherical nanoparticles ranging in size from 2.5 to 6nm. Theorder parameter was calculated using Monte Carlo simulation and the analyticalring approximation. For nanoparticles of finite size, the (long range) orderparameter changed continuously from unity to zero with increasing temperature.Rather than a discontinuity indicative of a phase transition, we obtained aninflection point in the order as a function of temperature. This inflectionpoint occurred at a temperature below the bulk phase transition temperature anddecreased as the particle size decreased. Our calculations predict that 3.5nmdiameter particles in configurational equilibrium at 600 C (a typical annealingtemperature for promoting L1_0 ordering) have an L1_0 order parameter ofapproximately 0.84 (compared to a maximum possible value equal to unity).According to our investigations, the experimental absence of (relatively) highL1_0 order in 3.5nm diameter nanoparticles annealed at 600 C or below isprimarily a problem of kinetics rather than equilibriu

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