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In this study, galeite, Na15(SO4)5ClF4 and schairerite, Na21(SO4)7ClF6 were investigated via in situ single-crystal X-ray diffraction in the temperature range of 300–750 K. Galeite and schairerite are trigonal, P31m, a = 12.1903(2), c = 13.9454(2) Å, V = 1794.69(6) Å3, and Z = 3 (R1 = 0.0273, 300 K) for galeite and a = 12.1859(3), c = 19.3080(6) Å, V = 2483.04(14) Å3, and Z = 3 (R1 = 0.0334, 300 K) for schairerite. The crystal structures of galeite and schairerite are based upon frameworks consisting of alternating face- and corner-sharing fluorine- and chlorine-centered octahedra. Galeite and schairerite can be attributed to 5H (galeite) and 7H (schairerite) antiperovskite polytypes, respectively. It was observed that schairerite undergoes at least one reversible phase transition before it starts to lose its crystallinity at 750 K. This phase transition occurs in the temperature range of 550–600 K. The high-temperature modification of schairerite is trigonal, with the centrosymmetric space group P-3m1 and the unit-cell parameters a = 7.0714(2), c = 19.5972(7) Å, V = 848.66(6) Å3, and Z = 1. Galeite is stable up to 600 K. The crystal structures of minerals expand anisotropically, and, in both cases, the strongest thermal expansion was parallel to the modules of face-sharing anion-centered octahedra. The structural complexity analysis showed that galeite is complex (695.175 bits/cell) and that the LT-modification of schairerite is very complex (1064.990 bits/cell), whereas its HT-modification is intermediate in complexity (256.755 bits/cell). The complexities of LT- and HT-polymorphs of schairerite are consistent with the general observations regarding structures with positional disorder: complexity decreases with increasing temperature, and simpler polymorphs have lower physical density. [ABSTRACT FROM AUTHOR]

The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth's history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth's continental crust, initiation of plate tectonics and the Great Oxidation event. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Single crystals of two novel uranyl sulfates and two novel uranyl selenates with protonated cyclen and 3-aminotropane molecules, ((C8H24N4)[(UO2)3(SO4)5](H2O)3 (I), (C8H24N4)(H5O2)(H3O)[(UO2)4(SeO4)7(H2O)](H2O)6.6 (II), (C8H18N2)(H5O2)(H3O)[(UO2)3(SO4)5(H2O)](H2O)0.5 (III), and (C8H18N2)(H5O2)(H3O)[(UO2)3(SeO4)5 (H2O)](H2O)2 (IV) have been prepared by isothermal evaporation from aqueous solutions and structurally characterized. Uranyl-containing 2D units have been investigated using topological approach and information-based complexity measures demonstrating that complex topologies form more rare than their simplest counterparts, which is a response of the crystal structure to changes of chemical conditions within the system. [ABSTRACT FROM AUTHOR]

Single crystals of four novel uranyl selenate and selenite-selenate oxysalts with protonated ethylamine molecules, (C 2 H 8 N) 2 [(UO 2 )(SeO 4 ) 2 (H 2 O)](H 2 O) ( I ), (C 2 H 8 N) 3 [(UO 2 )(SeO 4 ) 2 (HSeO 4 )] ( II ), (C 2 H 8 N)[(UO 2 )(SeO 4 )(HSeO 3 )] ( III ), and (C 2 H 8 N)(H 3 O)[(UO 2 )(SeO 4 ) 2 (H 2 O)] ( IV ) have been prepared by isothermal evaporation from aqueous solutions. Uranyl-containing 1D and 2D units have been investigated using topological approach and information-based complexity measurements that demonstrate the evolution of structural units and the increase of topological complexity with the decrease of H 2 O content. [ABSTRACT FROM AUTHOR]

The review is devoted to the start-of-the-art of the description, interpretation and classification of crystal structures in mineralogy. Among methods, the focus is on the atomic packings (including both anion and cation arrays), coordination polyhedra (both cation- and anion-centred), the concept of fundamental building blocks and related ideas, the use of networks, graphs and tilings (space partitions). The basic concepts under discussion in modern structural mineralogy include structure hierarchy (specification and compositional hierarchies are considered separately), modularity (representation of crystal structures as constructed from modules extracted from simple archetype structures) and complexity (with emphasis on static or informational and algorithmic complexities). Short historical notes are given for all of the topics considered. [ABSTRACT FROM PUBLISHER]

Modularity is an important construction principle of many inorganic crystal structures that has been used for the analysis of structural relations, classification, structure description and structure prediction. The principle of maximal simplicity for modular inorganic crystal structures can be formulated as follows: in a modular series of inorganic crystal structures, the most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. The latter can be quantitatively estimated using information-based structural complexity parameters. The principle is applied for the modular series based upon 0D (lovozerite family), 1D (biopyriboles) and 2D (spinelloids and kurchatovite family) modules. This principle is empirical and is valid for those cases only, where there are no factors that may lead to the destabilization of simplest structural arrangements. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). It can also be seen as an analogy of the principle of least action in physics. [ABSTRACT FROM AUTHOR]

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures. [ABSTRACT FROM AUTHOR]

The compound Na 2 CaPO 4 F has at least three polymorphic modifications: monoclinic α (also known as the natural mineral nacaphite), orthorhombic β and rhombohedral γ. All three polymorphs have antiperovskite-type structures belonging to either 2 H (α and β) or 15 R (γ) polytypes. The β-phase was synthesized using CaF 2 , NaF and Na 3 PO 4 as initial reagents at 800 ​°C. Its crystal structure is orthorhombic (Pnma, a ​= ​5.3542(1), b ​= ​7.0878(2), c ​= ​12.2560(3) Å, V ​= ​465.11(3) Å3, Z ​= ​4) and based upon the chains of fluorine-centered face-sharing octahedra running along [100]. Upon heating, the β form is stable up to 640 ​°C, when it melts and, in the temperature range of 640–800 ​°C, the γ form crystallizes. Its crystal structure (rhombohedral, R 3 ¯ m , a ​= ​7.0272(3), c ​= ​40.609(2) Å, V ​= ​1736.66(18) Å3, Z ​= ​15) consists of framework based upon pentamers of face-sharing [F(Na,Ca) 6 ] octahedra connected to each other through common Na vertices. The strongest thermal expansion for both modifications is parallel to the modules of face-sharing anion-centered octahedra, whereas it is almost isotropic within the plane perpendicular to the modules. The information-theoretic structural complexity analysis points out to the possible metastable character of the β-polymorph. The proposed stability row of the Na 2 CaPO 4 F phases under ambient conditions corresponds to the following sequence: α ​> ​γ ​> ​β. This agrees well with the relations among their structural complexities, degrees of order, physical and information densities. The sequence of phase transitions α → β → γ proceeds via transitional metastable β-phase. The α → β transition is reversible and of the order-disorder type with the conservation of structural topology, whereas the β → γ transition is reconstructive and irreversible. The latter transition is associated with the transformation of the antiperovskite 2 H polytype into the 15 R polytype. The β-Na 2 CaPO 4 F transforms into γ-Na 2 CaPO 4 F in the temperature range 640–720 ​°C. The transition is not direct and involves melting of the initial phase and its re-crystallization. The crystal structure of γ-Na 2 CaPO 4 F is based on pentamers of face-sharing octahedra connected with each other through common Na1 vertices (instead of chains observed in other polymorphs). [Display omitted] • The possible metastable character of the β-polymorph is discussed on the base of the information-theoretic structural complexity analysis. • The α → β transition is reversible and has the order-disorder type, the β → γ transition is reconstructive and irreversible; • Thermal expansion of all three Na 2 CaPO 4 F polymorphs is anisotropic and has the same general features. [ABSTRACT FROM AUTHOR]