Generating derivative structures from multilattices Algorithm.pdfVIP

PHYSICAL REVIEW B 80, 014120 2009 Generating derivative structures from multilattices: Algorithm and application to hcp alloys Gus L. W. Hart1 and Rodney W. Forcade2 1Department of Physics Astronomy, Brigham Young University, Provo, Utah 84602, USA 2Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA Received 10 April 2009; revised manuscript received 6 July 2009; published 31 July 2009 We present an algorithm for generating all derivative superstructures of a nonprimitive parent lattice. The algorithm has immediate application in important materials design problems such as modeling hexagonal- close-packed hcp alloys. Extending the work of Hart and Forcade Phys. Rev. B 77, 224115 2008 which applies only to Bravais lattices, this approach applies to arbitrary multilattices. The algorithm enumerates superlattices and atomic configurations using permutation groups rather than direct geometric comparisons. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The algorithm is very efficient; the run time scales linearly with the number of unique struc- tures found. We demonstrate the algorithm in the important case of hcp-derived superstructures. In the list of enumerated hexagonal-close-packed derivative superstructures, we predict several as-yet-unobserved structures as likely candidates for new intermetallic prototypes. DOI: 10.1103/PhysRevB.80.014120 PACS numbers: 61.50.Ah, 61.66.Dk, 61.90.d, 61.50.Nw