Data Mining Approach to Ab-Initio Prediction of Crystal Structure
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Data Mining Approach to Ab-Initio Prediction of Crystal Structure Dane Morgan, Gerbrand Ceder Department of Materials Science and Engineering, Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA Stefano Curtarolo Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708 ABSTRACT Predicting crystal structure is one of the most fundamental problems in materials science and a key early step in computational materials design. Ab initio simulation methods are a powerful tool for predicting crystal structure, but are too slow to explore the extremely large space of possible structures for new alloys. Here we describe ongoing work on a novel method (Data Mining of Quantum Calculations, or DMQC) that applies data mining techniques to existing ab initio data in order to increase the efficiency of crystal structure prediction for new alloys. We find about a factor of three speedup in ab intio prediction of crystal structures using DMQC as compared to naïve random guessing. This study represents an extension of work done by Curtarolo, et al. [1] to a larger library of data. INTRODUCTION Predicting the stable crystal structures for new alloys is a challenging problem, and only a few paths lead to practical solutions. One important class of techniques, generally called structure maps [2], clusters known crystal structures based on properties of the alloying elements. The crystal structure of new alloys can then be predicted by looking at known structures in the relevant clusters. These methods have recently been shown to be quite accurate [3], but are severely limited by requiring very large amounts of data to map out well-defined clusters. Other approaches predict the relative stability of different structures using total energy models. These approaches are limited by the very large space of possible structures and presence of many local minimum, making direct optimization to find the minimum energy very difficult. By using coarse-grained Hamiltonians that can be evaluated very quickly (for example, empirical rules and potentials [4] or cluster expansions [5]) it is often possible to optimize structures over some portion of the possible structural space. However, these coarse-grained models can be difficult to construct, are often inaccurate, and usually cannot explore the whole structure space to obtain a global minimum. Problems of model construction and accuracy can be largely overcome by avoiding coarse graining and using a full ab initio Hamiltonian to calculate the energies. Unfortunately, ab initio methods can only examine a very limited number of candidate structures because of computational limitations. Directly optimizing the energy over all of the space of possible structures with full ab initio simulations is not possible, and ground state searches have been limited to very restricted structure subsets [6]. For ab
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initio prediction the problem is to find a list of candidate structures that is as short as possible, but still likely to con
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