{"title":"在两个相似晶面之间构建共同超级晶胞的确定性方法。","authors":"Weon-Gyu Lee, Jung-Hoon Lee","doi":"10.1002/smtd.202400579","DOIUrl":null,"url":null,"abstract":"<p>Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector–eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with <i>O</i>(log <i>N</i><sub>max</sub>) time complexity, where <i>N</i><sub>max</sub> is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (<span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <msubsup>\n <mi>N</mi>\n <mi>max</mi>\n <mn>4</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n <annotation>$O(N_{\\mathrm{max}}^4)$</annotation>\n </semantics></math>). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.</p>","PeriodicalId":229,"journal":{"name":"Small Methods","volume":"8 12","pages":""},"PeriodicalIF":9.1000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces\",\"authors\":\"Weon-Gyu Lee, Jung-Hoon Lee\",\"doi\":\"10.1002/smtd.202400579\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector–eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with <i>O</i>(log <i>N</i><sub>max</sub>) time complexity, where <i>N</i><sub>max</sub> is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>O</mi>\\n <mo>(</mo>\\n <msubsup>\\n <mi>N</mi>\\n <mi>max</mi>\\n <mn>4</mn>\\n </msubsup>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$O(N_{\\\\mathrm{max}}^4)$</annotation>\\n </semantics></math>). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.</p>\",\"PeriodicalId\":229,\"journal\":{\"name\":\"Small Methods\",\"volume\":\"8 12\",\"pages\":\"\"},\"PeriodicalIF\":9.1000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Small Methods\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/smtd.202400579\",\"RegionNum\":2,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Small Methods","FirstCategoryId":"88","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/smtd.202400579","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
摘要
这里提出了一种确定性算法,无需扫描所有可能的情况,就能在两个相似的晶体表面之间构建一个共同的超级晶胞。利用复平面,二维晶格被定义为二维复向量。然后,两个表面之间的关系就变成了特征向量-特征值关系,其中一个算子对应于一个变换矩阵。研究表明,该变换矩阵可直接由两个给定晶体表面的晶格参数和旋转角度确定,时间复杂度为 O(log Nmax),其中 Nmax 是重复矩阵元素的最大索引。这一过程比传统的蛮力法(O ( N max 4 ) $O(N_{mathrm{max}}^4)$)快得多。通过在 Python 代码中实现该方法,成功生成了实验性二维异质结构及其摩尔纹,并发现了尚未报道的新摩尔纹。根据密度泛函理论(DFT)计算,一些新的摩尔纹有望与实验观察到的摩尔纹一样稳定。综上所述,相信该方法可作为一种有用的工具广泛应用于设计具有有趣特性的新型异质结构。
A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces
Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector–eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with O(log Nmax) time complexity, where Nmax is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.
Small MethodsMaterials Science-General Materials Science
CiteScore
17.40
自引率
1.60%
发文量
347
期刊介绍:
Small Methods is a multidisciplinary journal that publishes groundbreaking research on methods relevant to nano- and microscale research. It welcomes contributions from the fields of materials science, biomedical science, chemistry, and physics, showcasing the latest advancements in experimental techniques.
With a notable 2022 Impact Factor of 12.4 (Journal Citation Reports, Clarivate Analytics, 2023), Small Methods is recognized for its significant impact on the scientific community.
The online ISSN for Small Methods is 2366-9608.