Generating derivative structures at a fixed concentration

• Published in: Computational materials science Vol. 59; pp. 101 - 107
• Main Authors: Hart, Gus L.W., Nelson, Lance J., Forcade, Rodney W.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2012; Elsevier
• Subjects: Ag–Pt; Alloys; Cluster expansion; Condensed matter: structure, mechanical and thermal properties; Crystalline state (including molecular motions in solids); Derivative structures; Enumeration; Exact sciences and technology; Physics; Silver–platinum; Structure of solids and liquids; crystallography; Theory of crystal structure, crystal symmetry; calculations and modeling; Cluster expansion; Ag–Pt; Enumeration; Silver–platinum; Derivative structures; Alloys; Algorithms; Silver-platinum; Superstructure; Platinum alloys; Ag-Pt; Atomic structure; Silver alloys; Structural models
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2012.02.015

► An order-N algorithm for generating large derivative structures is developed. ► The algorithm is useful for bulk and surface alloys, oxides, hydrogen storage, etc. ► The algorithm extends previous work to much larger cases. We present an algorithm for generating derivative superstructures for large unit cells at a fixed concentration. The algorithm is useful when partial crystallographic information of an ordered phase is known. This work builds on the previous work of Hart and Forcade [Phys. Rev. B 77 224115, 2008; Phys. Rev. B 80 014120, 2009]. This extension of the original algorithm provides a mapping from atomic configurations to consecutive integers when only a subset (fixed concentration) of all possible configurations is under consideration. As in the earlier algorithm, this mapping results in a minimal hash table and perfect hash function that enables an efficient method for enumerating the configurations of large unit cells; the run time scales linearly with the number of symmetrically-distinct configurations. We demonstrate the algorithm for a proposed structure in the Ag–Pt system comprising 32 atoms, with stoichiometry 15:17, a configuration space of ∼400,000.