Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids
A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampl...
| Main Authors: | , , , , , |
|---|---|
| Format: | Journal Article |
| Published: |
Institute of Physics Publishing Ltd.
2013
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/35925 |
| _version_ | 1848754627697180672 |
|---|---|
| author | D'Arco, P. Mustapha, S. Ferrabone, M. Noël, Y. De La Pierre, Marco Dovesi, R. |
| author_facet | D'Arco, P. Mustapha, S. Ferrabone, M. Noël, Y. De La Pierre, Marco Dovesi, R. |
| author_sort | D'Arco, P. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4. |
| first_indexed | 2025-11-14T08:43:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-35925 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:43:25Z |
| publishDate | 2013 |
| publisher | Institute of Physics Publishing Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-359252019-02-19T05:35:34Z Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids D'Arco, P. Mustapha, S. Ferrabone, M. Noël, Y. De La Pierre, Marco Dovesi, R. mechanical & thermal Condensed matter: structural A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4. 2013 Journal Article http://hdl.handle.net/20.500.11937/35925 10.1088/0953-8984/25/35/355401 Institute of Physics Publishing Ltd. fulltext |
| spellingShingle | mechanical & thermal Condensed matter: structural D'Arco, P. Mustapha, S. Ferrabone, M. Noël, Y. De La Pierre, Marco Dovesi, R. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title | Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title_full | Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title_fullStr | Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title_full_unstemmed | Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title_short | Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| title_sort | symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids |
| topic | mechanical & thermal Condensed matter: structural |
| url | http://hdl.handle.net/20.500.11937/35925 |