[Show abstract][Hide abstract] ABSTRACT: Predicting and characterizing the crystal structure of materials is a key problem in materials research and development. It is typically addressed with highly accurate quantum mechanical computations on a small set of candidate structures, or with empirical rules that have been extracted from a large amount of experimental information, but have limited predictive power. In this Letter, we transfer the concept of heuristic rule extraction to a large library of ab initio calculated information, and we demonstrate that this can be developed into a tool for crystal structure prediction.
Full-text · Article · Oct 2003 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: 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 A 3 B 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.
[Show abstract][Hide abstract] ABSTRACT: The ability to predict the crystal structure of a material, given its constituent atoms, is one of the most fundamental problems in materials research. Knowledge of the crystal structure is essential to predict or rationalize properties of the material, from mechanical behavior, to optical and electronic properties. Despite its importance, the structure problem remains unsolved and most crystal structure determinations are performed after synthesis, by experimental means. While first principles computations can be used to predict with high accuracy a structural energy, ground state searches are usually limited to calculating the energy of a small number of pre-defined structures. Hence it is difficult to make predictions for completely novel and unknown systems. In order to drastically improve the capability of predicting the ground states of intermetallic alloys, we present an algorithm that can rank a relatively large number of trial structures in terms of the probability that they are ground states. First principles predictions can then be performed on the most likely candidates. With each first principles calculation, the candidate list is improved. This technique makes it possible to predict intermetallic ground states with ˜90% accuracy using only ˜20 first principles calculations. Unlike previous methods, this approach is not limited to super structures of a given lattice type and extends relatively easily to multi-component systems.