{"title":"Crystallographic complexity partition analysis","authors":"W. Hornfeck","doi":"10.1515/zkri-2021-2062","DOIUrl":null,"url":null,"abstract":"Abstract We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.","PeriodicalId":48676,"journal":{"name":"Zeitschrift Fur Kristallographie-Crystalline Materials","volume":"237 1","pages":"127 - 134"},"PeriodicalIF":0.9000,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift Fur Kristallographie-Crystalline Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1515/zkri-2021-2062","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CRYSTALLOGRAPHY","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.
期刊介绍：
Zeitschrift für Kristallographie – Crystalline Materials was founded in 1877 by Paul von Groth and is today one of the world’s oldest scientific journals. It offers a place for researchers to present results of their theoretical experimental crystallographic studies. The journal presents significant results on structures and on properties of organic/inorganic substances with crystalline character, periodically ordered, modulated or quasicrystalline on static and dynamic phenomena applying the various methods of diffraction, spectroscopy and microscopy.
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