Statistical biases in the Cowley order parameter originating from broken homogeneity

What is it about?

The difference between two common definitions of the short-range order parameter in various ranges is discussed. It arises when they are applied to small systems, where the homogeneous bulk conditions are no longer valid. This is illustrated on the example of the order/disorder transitions in Au–Pd fcc bulk materials and nanoparticles. The thermodynamic equilibrium configurations of these systems are sampled using Metropolis Monte Carlo simulation in the canonical (NPT) ensemble.

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Why is it important?

We show that the application of the standard short-range order (SRO) parameter (derived under the assumption of homogeneous bulk systems) to finite systems (e.g. nanoparticles) may lead to significant statistical biases. Moreover, different definitions of the SRO parameter, which are otherwise equivalent in the bulk, yield different results when applied to nanoparticles.