Automatic construction, implementation and assessment of Pettifor maps

The ability to predict the crystal structure of a material, given its constituent atoms, is one of the most fundamental problems in materials research. There exist a number of empirical methods which make predictions by clustering existing experimental data, generally using a few simple physical parameters. Although Pettifor maps are perhaps the best known and most successful of these empirical methods, the implementation and assessment of Pettifor maps has not been formalized. Here we propose well-defined algorithms for transforming data from a standard materials crystal structure database into a Pettifor map, using the map to predict the crystal structure for a new system, and assessing the predictive accuracy of the map. We introduce the idea of a candidate crystal structure list, demonstrating that by predicting more than one candidate for a new system the utility of the maps can be enhanced. We assess the accuracy of the maps by testing predictive accuracy using a cross-validation technique on all AB and A₃B compounds in the CRYSTMET database. We show that for a new unknown alloy with a stable structure at the stoichiometry of the Pettifor map, a candidate list of five structures will contain the correct crystal structure for the alloy 86% of the time. The algorithms presented here can be used to automate Pettifor maps in materials crystal structure databases, making it possible for users to construct, apply and assess entirely new Pettifor maps quickly and easily.