Quantifying multi-point ordering in alloys

Abstract

A central problem in multicomponent lattice systems is to systematically quantify multi-point ordering. Ordering in such systems is often described in terms of pair correlations, even though this is not sufficient when three-point and higher-order interactions are significant. Current models and parameters for multi-point ordering are often only applicable for very specific cases and/or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this work, a multi-point cluster order parameter is introduced to quantify arbitrary multi-point ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multi-point chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined within and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on alloy nanocage stability are discussed. It is demonstrated that approximating multi-point order parameters from combinations of low-order correlations is not sufficient in cases where multi-point energetics are significant. Conclusions about the formation mechanisms of nanocages may change significantly when using common low-order approximations.