Abstract
The information content of a crystal structure as conceived by information theory has recently proved an intriguing approach to calculate the complexity of a crystal structure within a consistent concept. Given the relatively young nature of the field, theory development is still at the core of ongoing research efforts. This work provides an update to the current theory, enabling the complexity analysis of crystal structures with partial occupancies as frequently found in disordered systems. To encourage wider application and further theory development, the updated formulas are incorporated into crystIT (crystal structure and information theory), an open-source Python-based program that allows for calculating various complexity measures of crystal structures based on a standardized *.cif file.
Highlights
The definition of complexity is a challenging and fascinating subject, touching different scientific disciplines such as economics, informatics, biology, mathematics and chemistry
Krivovichev (2014) performed a database analysis based on crystallographic data as available in the Inorganic Crystal Structure Database
In order to provide a different research angle, and to show the big-data analysis capabilities of crystIT, we here focus on the development of complexity with time, using the full Crystallography Open Database (COD; http:// www.crystallography.net/cod/; Grazulis et al, 2009) as input
Summary
The definition of complexity is a challenging and fascinating subject, touching different scientific disciplines such as economics, informatics, biology, mathematics and chemistry. Baur et al (1983) defined topological and crystallographic parsimony indices of crystal structures, and more recently, the number of atoms per reduced unit cell was used as a measure to classify various metallic alloys (Dshemuchadse & Steurer, 2015). Such practical concepts seem suitable for assessing structure complexity within certain material subclasses, but exhibit drawbacks related to a limited discriminating character between simple crystal structures and when one is interested in comparable measures across different material classes. Krivovichev (2014) applied the concept of Shannon entropy to crystalline materials, evaluating the information content of a crystal structure. An intuitive understanding between crystal structure, information content and complexity is fostered by applying crystIT to selected research examples
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