Monte Carlo simulation of equilibrium L1_0 ordering in FePt nanoparticles

TL;DR

This study uses Monte Carlo simulations to analyze how equilibrium L1_0 ordering in FePt nanoparticles varies with temperature and size, revealing size-dependent transition behavior and suggesting kinetic factors limit ordering.

Contribution

It provides the first-principles derived mixing potentials and models the size-dependent equilibrium ordering in FePt nanoparticles, highlighting the role of kinetics in experimental observations.

Findings

Bulk order-disorder temperature matches experimental data within 4%.

Nanoparticles show a smooth decrease in order parameter with temperature, no sharp transition.

Predicted high order parameter at 600°C for 3.5nm particles, indicating kinetic limitations in experiments.

Abstract

First, second and third nearest neighbor mixing potentials for FePt alloys, were calculated from first principles using a Connolly-Williams approach. Using the mixing potentials obtained in this manner, the dependency of equilibrium L1_0 ordering on temperature was studied for bulk and for a spherical nanoparticle with 3.5nm 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 (1572K). 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 3.5nm diameter particles in configurational equilibrium at 600 C (a typical annealing temperature for promoting L1_0 ordering) have an L1_0 order parameter of 0.83 (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