The discovery of the diffraction of X‐rays on crystals opened up a new era in our understanding of nature, leading to a multitude of striking discoveries about the structures and functions of matter ...on the atomic and molecular scales. Over the last hundred years, about 150 000 of inorganic crystal structures have been elucidated and visualized. The advent of new technologies, such as area detectors and synchrotron radiation, led to the solution of structures of unprecedented complexity. However, the very notion of structural complexity of crystals still lacks an unambiguous quantitative definition. In this Minireview we use information theory to characterize complexity of inorganic structures in terms of their information content.
Cause and complexity: Analysis of inorganic crystal structures using information‐based complexity measures indicates that structural complexity is generated by the assembly of nanoscale building blocks, modularity induced by complex chemical compositions, and the formation of superlattices as a result of local atomic ordering or displacive phase transitions.
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The information-entropy measures of the complexity of nets are proposed that take into consideration both the vertices and edges of nets. The parameters quantify the amount of Shannon information per ...element (vertex or edge) and per the translationally independent parts of the nets. The nets can be classified according to their complexity into very simple (0-20 bit per cell), simple (20-100 bit per cell), intermediate (100-500 bit per cell), complex (500-1000 bit per cell), and very complex (>1000 bit per cell). The information entropies for 1936 3D nets were calculated and analysed, showing that the simplest (information-poor) nets possess the lowest transitivities. The majority of the most common nets in metal-organic frameworks (MOFs) are the simplest nets within their respective categories (
i.e.
among the nets with the same coordination of vertices). Since the information is directly related to entropy, which is understood as a statistical parameter, the preference of the simplest nets in MOFs is at least in part governed by their low information contents and high configurational entropies.
The information-entropy measures of the complexity of 3D nets indicate that the most common nets in metal-organic frameworks (MOFs) are usually the simplest and highest-entropy nets within the respective category.
Through the years, mineralogical studies have produced a tremendous amount of data on the atomic arrangement and mineral properties. Quite often, structural analysis has led to elucidate the role ...played by minor components, giving interesting insights into the physico-chemical conditions of mineral crystallization and allowing the description of unpredictable structures that represented a body of knowledge critical for assessing their technological potentialities. Using such a rich database, containing many basic acquisitions, further steps became appropriate and possible, into the directions of more advanced knowledge frontiers. Some of these frontiers assume the name of modularity, complexity, aperiodicity, and matter organization at not conventional levels, and will be discussed in this review.
Using a statistical approach, it is demonstrated that the complexity of a crystal structure measured as the Shannon information per atom Krivovichev (2012). Acta Cryst. A68, 393–398 represents a ...negative contribution to the configurational entropy of a crystalline solid. This conclusion is in full accordance with the general agreement that information and entropy are reciprocal variables. It also agrees well with the understanding that complex structures possess lower entropies relative to their simpler counterparts. The obtained equation is consistent with the Landauer principle and points out that the information encoded in a crystal structure has a physical nature.
Structural complexity measured as the Shannon information per atom represents a negative contribution to the configurational entropy of a crystalline solid.
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Most research on polyoxometalates (POMs) has been devoted to synthetic compounds. However, recent mineralogical discoveries of POMs in mineral structures demonstrate their importance in geochemical ...systems. In total, 15 different types of POM nanoscale‐size clusters in minerals are described herein, which occur in 42 different mineral species. The topological diversity of POM clusters in minerals is rather restricted compared to the multitude of moieties reported for synthetic compounds, but the lists of synthetic and natural POMs do not overlap completely. The metal–oxo clusters in the crystal structures of the vanarsite‐group minerals (As3+V4+2V5+10As5+6O517−), bouazzerite and whitecapsite (M3+3Fe7(AsO4)9O8–;n(OH)n), putnisite (Cr3+8(OH)16(CO3)88−), and ewingite ((UO2)24(CO3)30O4(OH)12(H2O)832−) contain metal–oxo clusters that have no close chemical or topological analogues in synthetic chemistry. The interesting feature of the POM cluster topologies in minerals is the presence of unusual coordination of metal atoms enforced by the topological restraints imposed upon the cluster geometry (the cubic coordination of Fe3+ and Ti4+ ions in arsmirandite and lehmannite, respectively, and the trigonal prismatic coordination of Fe3+ in bouazzerite and whitecapsite). Complexity analysis indicates that ewingite and morrisonite are the first and the second most structurally complex minerals known so far. The formation of nanoscale clusters can be viewed as one of the leading mechanisms of generating structural complexity in both minerals and synthetic inorganic crystalline compounds. The discovery of POM minerals is one of the specific landmarks of descriptive mineralogy and mineralogical crystallography of our time.
This article reviews current progress in the investigations of polyoxometalate clusters in minerals.
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The Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. ...Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.
Using mineralogical data, it is demonstrated that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov–Groth law.
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Structural Chemistry of Inorganic Actinide Compounds is a collection of 13 reviews on structural and coordination chemistry of actinide compounds. Within the last decade, these compounds have ...attracted considerable attention because of their importance for radioactive waste management, catalysis, ion-exchange and absorption applications, etc. Synthetic and natural actinide compounds are also of great environmental concern as they form as a result of alteration of spent nuclear fuel and radioactive waste under Earth surface conditions, during burn-up of nuclear fuel in reactors, represent oxidation products of uranium miles and mine tailings, etc. The actinide compounds are also of considerable interest to material scientists due to the unique electronic properties of actinides that give rise to interesting physical properties controlled by the structural architecture of respective compounds. The book provides both general overview and review of recent developments in the field, including such emergent topics as nanomaterials and nanoparticles and their relevance to the transfer of actinides under environmental conditions. * Covers over 2,000 actinide compounds including materials, minerals and coordination polymers * Summarizes recent achievements in the field * Some chapters reveal (secret) advances made by the Soviet Union during the 'Cold war'.
The chemical and structural diversity of minerals containing sulfur as an essential mineral-forming element has been analyzed in terms of the concept of mineral systems and the information-based ...structural and chemical complexity parameters. The study employs data for 1118 sulfur mineral species approved by the International Mineralogical Association. All known sulfur minerals belong to nine mineral systems, with the number of essential components ranging from one to nine. The chemical and structural complexity of S minerals correlate with each other; that is, on average, chemical complexification results in structural complexification. The minerals with S–O bonds (sulfates and sulfites) are more complex than those without S–O bonds (sulfides and sulfosalts). However, the most complex sulfur mineral known so far is incomsartorite, Tl6Pb144As246S516, a sulfosalt. The complexity-generating mechanism in sulfides and sulfosalts is the complex combination of different modules excised from parent PbS or SnS archetypes with the subsequent formation of superstructures. The drivers for structural complexity in sulfates are more diverse and, in addition to modular construction and superstructures, also include a high hydration state, the presence of polyatomic clusters, and framework complexity. The most complex Martian minerals are most probably halotrichite-group minerals. The chemical and structural complexity increases with the passage of geological time with the formation of the most complex sulfosalts at Lengenbach (Swiss Alps) triggered by life (activity of sulfur-reducing bacteria).
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