Temperature and particle size dependence of equilibrium order parameter of FePt

TL;DR

This study investigates how temperature and particle size influence the equilibrium L1_0 order parameter in FePt alloys, revealing size-dependent inflection points and suggesting kinetic factors limit ordering in small nanoparticles.

Contribution

It provides a first-principles based analysis of size and temperature effects on FePt ordering, combining Monte Carlo and analytical methods to predict equilibrium states in nanoparticles.

Findings

Order parameter decreases with decreasing particle size.

Inflection points in order parameter occur below bulk transition temperature.

Small nanoparticles at typical annealing temperatures have high but not maximal order.

Abstract

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