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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
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