Application of canonical augmentation to the atomic substitution problem
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866910865467375616 |
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| author | Prayogo, Genki I. Tirelli, Andrea Utimula, Keishu Hongo, Kenta Maezono, Ryo Nakano, Kousuke |
| author_facet | Prayogo, Genki I. Tirelli, Andrea Utimula, Keishu Hongo, Kenta Maezono, Ryo Nakano, Kousuke |
| contents | A common approach for studying a solid solution or disordered system within a periodic ab-initio framework is to create a supercell in which a certain amount of target elements is substituted with other ones. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from the large number of substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. A straightforward solution would be to classify them after determining all possible patterns, but it is redundant and practically unfeasible. Therefore, to alleviate this drawback, we developed a new formalism based on the {\it canonical augmentation}, and successfully applied it to the atomic substitution problem. Our developed \verb|python| software package, which is called \textsc{SHRY} (\underline{S}uite for \underline{H}igh-th\underline{r}oughput generation of models with atomic substitutions implemented by p\underline{y}thon), enables us to pick up only symmetry-inequivalent structures from the vast number of candidates very efficiently. We demonstrate that the computational time required by our algorithm to find $N$ symmetry-inequivalent structures scales {\it linearly} with $N$ up to $\sim 10^9$. This is the best scaling for such problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_13409 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Application of canonical augmentation to the atomic substitution problem Prayogo, Genki I. Tirelli, Andrea Utimula, Keishu Hongo, Kenta Maezono, Ryo Nakano, Kousuke Materials Science Software Engineering Computational Physics A common approach for studying a solid solution or disordered system within a periodic ab-initio framework is to create a supercell in which a certain amount of target elements is substituted with other ones. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from the large number of substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. A straightforward solution would be to classify them after determining all possible patterns, but it is redundant and practically unfeasible. Therefore, to alleviate this drawback, we developed a new formalism based on the {\it canonical augmentation}, and successfully applied it to the atomic substitution problem. Our developed \verb|python| software package, which is called \textsc{SHRY} (\underline{S}uite for \underline{H}igh-th\underline{r}oughput generation of models with atomic substitutions implemented by p\underline{y}thon), enables us to pick up only symmetry-inequivalent structures from the vast number of candidates very efficiently. We demonstrate that the computational time required by our algorithm to find $N$ symmetry-inequivalent structures scales {\it linearly} with $N$ up to $\sim 10^9$. This is the best scaling for such problems. |
| title | Application of canonical augmentation to the atomic substitution problem |
| topic | Materials Science Software Engineering Computational Physics |
| url | https://arxiv.org/abs/2111.13409 |