  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
