Generation of Basis Vectors for Magnetic Structures and Displacement Modes
Increasing attention is being focused on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise such as the generation of too man...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Condensed Matter Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/3960145 |
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| author | Z. L. Davies A. S. Wills |
| author_facet | Z. L. Davies A. S. Wills |
| author_sort | Z. L. Davies |
| collection | DOAJ |
| description | Increasing attention is being focused on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary. |
| format | Article |
| id | doaj-art-f0576313dab6436f8b2aa6dff2bfee71 |
| institution | Kabale University |
| issn | 1687-8108 1687-8124 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Condensed Matter Physics |
| spelling | doaj-art-f0576313dab6436f8b2aa6dff2bfee712025-02-03T00:59:27ZengWileyAdvances in Condensed Matter Physics1687-81081687-81242016-01-01201610.1155/2016/39601453960145Generation of Basis Vectors for Magnetic Structures and Displacement ModesZ. L. Davies0A. S. Wills1Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UKDepartment of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UKIncreasing attention is being focused on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary.http://dx.doi.org/10.1155/2016/3960145 |
| spellingShingle | Z. L. Davies A. S. Wills Generation of Basis Vectors for Magnetic Structures and Displacement Modes Advances in Condensed Matter Physics |
| title | Generation of Basis Vectors for Magnetic Structures and Displacement Modes |
| title_full | Generation of Basis Vectors for Magnetic Structures and Displacement Modes |
| title_fullStr | Generation of Basis Vectors for Magnetic Structures and Displacement Modes |
| title_full_unstemmed | Generation of Basis Vectors for Magnetic Structures and Displacement Modes |
| title_short | Generation of Basis Vectors for Magnetic Structures and Displacement Modes |
| title_sort | generation of basis vectors for magnetic structures and displacement modes |
| url | http://dx.doi.org/10.1155/2016/3960145 |
| work_keys_str_mv | AT zldavies generationofbasisvectorsformagneticstructuresanddisplacementmodes AT aswills generationofbasisvectorsformagneticstructuresanddisplacementmodes |