Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 25, Issue 10, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0953-8984/25/10/105401
Keywords
-
Categories
Funding
- Compagnia di San Paolo (Progetti di Ricerca di Ateneo-Compagnia di San Paolo-2011-Linea 1A) [progetto ORTO11RRT5]
- CALSIMLAB under the French funds 'Investissements d'Avenir' [ANR-11-IDEX-0004-02]
Ask authors/readers for more resources
The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Polya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows analysis of the case where the colors are symmetry related, e. g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Polya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicographic ordering, which offers the advantage of avoiding the (computationally expensive) analysis and storage of all the possible configurations. When the number of colors increases, this strategy can be combined with the surjective resolution principle, which permits the efficient generation of SICs of a problem in vertical bar R vertical bar colors starting from the ones obtained for the (vertical bar R vertical bar - 1)-colors case. The whole scheme is documented by means of three examples: the abstract case of a square with C-4v symmetry and the real cases of the garnet and olivine mineral families.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available