Molecular assembly indices of mineral heteropolyanions: some abiotic molecules are as complex as large biomolecules.

Molecular assembly indices, which measure the number of unique sequential steps theoretically required to construct a three-dimensional molecule from its constituent atomic bonds, have been proposed as potential biosignatures. A central hypothesis of assembly theory is that any molecule with an assembly index ≥15 found in significant local concentrations represents an unambiguous sign of life. We show that abiotic molecule-like heteropolyanions, which assemble in aqueous solution as precursors to some mineral crystals, range in molecular assembly indices from 2 for H2CO3 or Si(OH)4 groups to as large as 21 for the most complex known molecule-like subunits in the rare minerals ewingite and ilmajokite. Therefore, values of molecular assembly indices ≥15 do not represent unambiguous biosignatures.

The AM-4 Family of Layered Titanosilicates: Single-Crystal-to-Single-Crystal Transformation, Synthesis and Ionic Conductivity.

Flexible crystal() structures, which exhibit() single-crystal()-to-single-crystal() (SCSC) transformations(), are attracting attention() in many applied aspects: magnetic() switches, catalysis, ferroelectrics and sorption. Acid treatment() for titanosilicate material() AM-4 and natural() compounds with the same structures led to SCSC transformation() by loss() Na+, Li+ and Zn2+ cations with large structural() changes (20% of the unit()-cell() volume()). The conservation() of crystallinity through complex() transformation() is possible due() to the formation() of a strong hydrogen bonding() system(). The mechanism() of transformation() has been characterized using single-crystal() X-ray() diffraction analysis(), powder() diffraction, Rietvield refinement, Raman spectroscopy and electron microscopy. The low migration() energy() of cations in the considered materials() is confirmed using bond()-valence and density() functional() theory() calculations, and the ion conductivity of the AM-4 family's materials() has been experimentally verified.

One of Nature's Puzzles Is Assembled: Analog of the Earth's Most Complex Mineral, Ewingite, Synthesized in a Laboratory.

Through the combination of low-temperature hydrothermal synthesis and room-temperature evaporation, a synthetic phase similar in composition and crystal structure to the Earth's most complex mineral, ewingite, was obtained. The crystal structures of both natural and synthetic compounds are based on supertetrahedral uranyl-carbonate nanoclusters that are arranged according to the cubic body-centered lattice principle. The structure and composition of the uranyl carbonate nanocluster were refined using the data on synthetic material. Although the stability of natural ewingite is higher (according to visual observation and experimental studies), the synthetic phase can be regarded as a primary and/or metastable reaction product which further re-crystallizes into a more stable form under environmental conditions.

The role of local heteropolyhedral substitutions in the stoichiometry, topological characteristics and ion-migration paths in the eudialyte-related structures: a quantitative analysis.

Topological analysis of the heteropolyhedral MT framework (where M and T are octahedral and tetrahedral cations, respectively) in the eudialyte-type structure and its derivatives was performed based on a natural tiling analysis of the 3D cation. To analyze the migration paths of sodium cations in these structures, the Voronoi method was used. The parental eudialyte-type MT framework is formed by isolated ZO6 octahedra, six-membered [M(1)6O24] rings of edge-sharing M(1)O6 octahedra, and two kinds of rings of tetrahedra, [Si3O9] and [Si9O27]. Different occupancies of M(2), M(3) and M(4) sites with variable coordination numbers by the additional Q, T* and M* cations, respectively, result in 12 different types of the MT framework. Based on the results of natural tilings calculations as well as theoretical analysis of migration paths, it is found that Na+ ions can migrate through six- and seven-membered rings, while all other rings are too small for the migration. In eight types of MT frameworks, Na+-ion migration and diffusion is possible at ambient temperature and pressure, while in four other types cages are connected by narrow windows and, as a result, the Na+ diffusion in them is complicated at ambient conditions because of the window diameter, but may be possible either at higher temperatures or under mild geological conditions for long periods of time.

Expanding the Averievite Family, (MX)Cu5O2(T5+O4)2 (T5+ = P, V; M = K, Rb, Cs, Cu; X = Cl, Br): Synthesis and Single-Crystal X-ray Diffraction Study.

Averievite-type compounds with the general formula (MX)[Cu5O2(TO4)], where M = alkali metal, X = halogen and T = P, V, have been synthesized by crystallization from gases and structurally characterized for six different compositions: 1 (M = Cs; X = Cl; T = P), 2 (M = Cs; X = Cl; T = V), 3 (M = Rb; X = Cl; T = P), 4 (M = K; X = Br; T = P), 5 (M = K; X = Cl; T = P) and 6 (M = Cu; X = Cl; T = V). The crystal structures of the compounds are based upon the same structural unit, the layer consisting of a kagome lattice of Cu2+ ions and are composed from corner-sharing (OCu4) anion-centered tetrahedra. Each tetrahedron shares common corners with three neighboring tetrahedra, forming hexagonal rings, linked into the two-dimensional [O2Cu5]6+ sheets parallel to (001). The layers are interlinked by (T5+O4) tetrahedra (T5+ = V, P) attached to the bases of the oxocentered tetrahedra in a "face-to-face" manner. The resulting electroneutral 3D framework {[O2Cu5](T5+O4)2}0 possesses channels occupied by monovalent metal cations M+ and halide ions X-. The halide ions are located at the centers of the hexagonal rings of the kagome nets, whereas the metal cations are in the interlayer space. There are at least four different structure types of the averievite-type compounds: the P-3m1 archetype, the 2 × 2 × 1 superstructure with the P-3 space group, the monoclinically distorted 1 × 1 × 2 superstructure with the C2/c symmetry and the low-temperature P21/c superstructure with a doubled unit cell relative to the high-temperature archetype. The formation of a particular structure type is controlled by the interplay of the chemical composition and temperature. Changing the chemical composition may lead to modification of the structure type, which opens up the possibility to tune the geometrical parameters of the kagome net of Cu2+ ions.

Embedding parallelohedra into primitive cubic networks and structural automata description.

The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists. The question of how many ways the embedding of a parallelohedron can be constructed is answered. For each parallelohedron, the deterministic finite automaton is developed which models the growth of the crystalline structure with the same combinatorial type as the given parallelohedron.

Polyoxometalate clusters in minerals: review and complexity analysis.

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+6O51]7-), bouazzerite and whitecapsite ([M3+3Fe7(AsO4)9O8-;n(OH)n]), putnisite ([Cr3+8(OH)16(CO3)8]8-), and ewingite ([(UO2)24(CO3)30O4(OH)12(H2O)8]32-) 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.

Producing highly complicated materials. Nature does it better.

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.

The Fedorov-Groth law revisited: complexity analysis using mineralogical data.

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.

Extraordinary structural complexity of ilmajokite: a multilevel hierarchical framework structure of natural origin.

The crystal structure of ilmajokite, a rare Na-K-Ba-Ce-titanosilicate from the Khibiny mountains, Kola peninsula, Russia, has been solved using single-crystal X-ray diffraction data. The crystal structure is based on a 3D titanosilicate framework consisting of trigonal prismatic titanosilicate (TPTS) clusters centered by Ce3+ in [9]-coordination. Four adjacent TPTS clusters are linked into four-membered rings within the (010) plane and connected via ribbons parallel to 101. The ribbons are organized into layers parallel to (010) and modulated along the a axis with a modulation wavelength of csinß = 32.91 Šand an amplitude of ∼b/2 = 13.89 Å. The layers are linked by additional silicate tetrahedra. Na+, K+, Ba2+ and H2O groups occur in the framework cavities and have different occupancies and coordination environments. The crystal structure of ilmajokite can be separated into eight hierarchical levels: atoms, coordination polyhedra, TPTS clusters, rings, ribbons, layers, the framework and the whole structure. The information-based analysis allows estimation of the complexity of the structure as 8.468 bits per atom and 11990.129 bits per cell. According to this analysis, ilmajokite is the third-most complex mineral known to date after ewingite and morrisonite, and is the most complex mineral framework structure, comparable in complexity to paulingite-(Ca) (11 590.532 bits per cell).

Chemically Induced Polytypic Phase Transitions in the Mg[(UO2)(TO4)2(H2O)](H2O)4 (T = S, Se) System.

Chemically induced polytypic phase transitions have been observed during experimental investigations of crystallization in the mixed uranyl sulfate-selenate Mg[(UO2)(TO4)2(H2O)](H2O)4 (T = S, Se) system. Three different structure types form in the system, depending upon the Se:S ratio in the initial aqueous solution. The phases with the Se/(Se + S) ratios (in mol %) in the ranges 0-9, 16-47, and 58-100 crystallize in the space groups P21, Pmn21, and P21/c, respectively. The structures of the phases are based upon the same type of uranyl-based sulfate/selenate chains that, through hydrogen bonds, are linked into pseudolayers of the same topological type. The layers are linked into three-dimensional structures via interlayer Mg-centered octahedra. The three structure types contain the same layers but with different stacking sequences that can be conveniently described as belonging to the 1M, 2O, and 2M polytypic modifications. The Se-for-S substitution demonstrates a strong selectivity with preferential incorporation of Se into less tightly bonded T1 site. The larger ionic radius of Se6+ relative to S6+ induces rotation of (T1O4) tetrahedra in the adjacent layers and reconstruction of the structure types. From the information-theoretic viewpoint, the intermediate Pmn21 structure type is more complex than the monoclinic end-member structure types.

High pressure phase transitions of paracelsian BaAl2Si2O8.

Three new polymorphs of aluminosilicate paracelsian, BaAl2Si2O8, have been discovered using synchrotron-based in situ high-pressure single crystal X-ray diffraction. The first isosymmetric phase transition (from paracelsian-I to paracelsian-II) occurs between 3 and 6 GPa. The phase transition is associated with the formation of pentacoordinated Al3+ and Si4+ ions, which occurs in a stepwise fashion by sequential formation of Al-O and Si-O bonds additional to those in AlO4 and SiO4 tetrahedra, respectively. The next phase transition occurs between 25 and 28 GPa and is accompanied by the symmetry change from monoclinic (P21/c) to orthorhombic (Pna21). The structure of paracelsian-III consists of SiO6 octahedra, AlO6 octahedra and distorted AlO4 tetrahedra, i.e. the transition is reconstructive and associated with the changes of Si4+ and Al3+ coordination, which show rather complex behaviour with the general tendency towards increasing coordination numbers. The third phase transition is observed between 28 and 32 GPa and results in the symmetry decreasing from Pna21 to Pn. The transition has a displacive character. In the course of the phase transformation pathway up to 32 GPa, the structure of polymorphs becomes denser: paracelsian-II is based upon elements of cubic and hexagonal close-packing arrangements of large O2- and Ba2+ ions, whereas, in the crystal structure of paracelsian-III and IV, this arrangement corresponds to 9-layer closest-packing with the layer sequence ABACACBCB.

Functionality in metal-organic framework minerals: proton conductivity, stability and potential for polymorphism.

Rare metal-organic framework (MOF) minerals stepanovite and zhemchuzhnikovite can exhibit properties comparable to known oxalate MOF proton conductors, including high proton conductivity over a range of relative humidities at 25 °C, and retention of the framework structure upon thermal dehydration. They also have high thermodynamic stability, with a pronounced stabilizing effect of substituting aluminium for iron, illustrating a simple design to access stable, highly proton-conductive MOFs without using complex organic ligands.

High-temperature Fe oxidation coupled with redistribution of framework cations in lobanovite, K2Na(Fe2+4Mg2Na)Ti2(Si4O12)2O2(OH)4 - the first titanosilicate case.

The high-temperature (HT) behaviour of lobanovite, K2Na(Fe2+4Mg2Na)Ti2(Si4O12)2O2(OH)4, was studied using in situ powder X-ray diffraction in the temperature range 25-1000°C and ex situ single-crystal X-ray diffraction of 17 crystals quenched from different temperatures. HT iron oxidation associated with dehydroxylation starts at 450°C, similar to other ferrous-hydroxy-rich heterophyllosilicates such as astrophyllite and bafertisite. A prominent feature of lobanovite HT crystal chemistry is the redistribution of Fe and Mg+Mn cations over the M(2), M(3), M(4) sites of the octahedral (O) layer that accompanies iron oxidation and dehydroxylation. This HT redistribution of cations has not been observed in titanosilicates until now, and seems to be triggered by the need to maintain bond strengths at the apical oxygen atom of the TiO5 pyramid in the heteropolyhedral (H) layer during oxidation-dehydroxylation. Comparison of the HT behaviour of lobanovite with five-coordinated Ti and astrophyllite with six-coordinated Ti shows that the geometry of the Ti polyhedron plays a key role in the HT behaviour of heterophyllosilicates. The thermal expansion, geometrical changes and redistribution of site occupancies which occur in lobanovite under increasing temperature are reported. A brief discussion is given of minerals in which the cation ordering (usually for Fe and Mg) occurs together with iron oxidation-dehydroxylation at elevated temperatures: micas, amphiboles and tourmalines. Now this list is expanded by the inclusion of titanosilicate minerals.

Rb2CaCu6(PO4)4O2, a novel oxophosphate with a shchurovskyite-type topology: synthesis, structure, magnetic properties and crystal chemistry of rubidium copper phosphates.

Single crystals of Rb2CaCu6(PO4)4O2 were synthesized by a hydrothermal method in the multicomponent system CuCl2-Ca(OH)2-RbCl-B2O3-Rb3PO4. The synthesis was carried out in the temperature range from 690 to 700 K and at the general pressure of 480-500 atm [1 atm = 101.325 kPa] from the mixture in the molar ratio 2CuO:CaO:Rb2O:B2O3:P2O5. The crystals studied by single-crystal X-ray analysis were found to be monoclinic, space group C2, a = 16.8913 (4), b = 5.6406 (1), c = 8.3591 (3) Å, ß = 93.919 (3)°, V = 794.57 (4) Å3. The crystal structure of Rb2CaCu6(PO4)4O2 is similar to that of shchurovskyite and dmisokolovite and is based upon a heteropolyhedral open framework formed by polar layers of copper polyhedra linked via isolated PO4 tetrahedra. The presence of well-isolated 2D heteropolyhedral layers in the title compound suggests low-dimensional magnetic behavior which is masked, however, by the fierce competition between multiple ferromagnetic and antiferromagnetic exchange interactions. At TC = 25 K, Rb2CaCu6(PO4)4O2 reaches a magnetically ordered state with large residual magnetization.

On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. An ideal crystal is a regular or multi-regular system, that is, a Delone set, which is the orbit of a single point or finitely many points under a crystallographic group of isometries. The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set X to be a regular or multi-regular system. One of the main goals is to estimate the regularity radius \hat{\rho}_d for Delone sets X in terms of the radius R of the largest `empty ball' for X. The celebrated `local criterion for regular systems' provides an upper bound for \hat{\rho_d} for any d. Better upper bounds are known for d ≤ 3. The present article establishes the lower bound \hat{\rho_d}\geq 2dR for all d, which is linear in d. The best previously known lower bound had been \hat{\rho}_d\geq 4R for d ≥ 2. The proof of the new lower bound is accomplished through explicit constructions of Delone sets with mutually equivalent (2dR - ℇ)-clusters, which are not regular systems. The two- and three-dimensional constructions are illustrated by examples. In addition to its fundamental importance, the obtained result is also relevant for the understanding of geometrical conditions of the formation of ordered and disordered arrangements in polytypic materials.

ℇ-RbCuCl3, a new polymorph of rubidium copper trichloride: synthesis, structure and structural complexity.

A novel polymorph of RbCuCl3 (rubidium copper trichloride), denoted ℇ-RbCuCl3, has been prepared by chemical vapour transport (CVT) from a mixture of CuO, CuCl2, SeO2 and RbCl. The new polymorph crystallizes in the orthorhombic space group C2221. The crystal structure is based on an octahedral framework of the 4H perovskite type. The Rb+ and Cl- ions form a four-layer closest-packing array with an ABCB sequence. The Cu2+ cations reside in octahedral cavities with a typical [4 + 2]-Jahn-Teller-distorted coordination, forming four short and two long Cu-Cl bonds. ℇ-RbCuCl3 is the most structurally complex and most dense among all currently known RbCuCl3 polymorphs, which allows us to suggest that it is a high-pressure phase, which is unstable under ambient conditions.

The first lead cobalt phosphite, PbCo2(HPO3)3.

Single crystals of a new lead cobalt phosphite, PbCo2(HPO3)3, have been synthesized using mild hydrothermal techniques and characterized by X-ray diffraction analysis, SQUID magnetic measurements, IR spectroscopy, UV/vis spectroscopy, thermogravimetric analysis, and scanning electron microscopy. PbCo2(HPO3)3 crystallizes in the non-centrosymmetric (NCS) R3m space group, a = 5.3145(15) Å, c = 25.494(7) Å, V = 623.6(4) Å3. The crystal structure of PbCo2(HPO3)3 is based upon 2D heteropolyhedral blocks built up from Co2O9 octahedral dimers and HPO3 pseudo-tetrahedra. Lead cations reside in the interlayer space of the structure. Here, the NCS character results reasonably from the cooperative Pb2+ lone electron pair arrangements, by analogy to the centrosymmetric compound (NH4)2Co2(HPO3)3 with similar but disordered blocks. A local twisting of specific HPO3 groups arises due to unreasonably short HH contacts between two phosphite oxoanions. In terms of the magnetic behavior, the new PbCo2(HPO3)3 phase demonstrates weak antiferromagnetic interactions inside the Co2O9 dimers between cobalt ions as expected from the phosphite µ-O bridges.

Xenon in Rigid Oxide Frameworks: Structure, Bonding and Explosive Properties of Layered Perovskite K4Xe3O12.

The tendency of high-valence xenon to form consolidated oxide structures is herein supported by the study of K4Xe3O12, the first example of a layered xenon perovskite. Xenon seems to be the only nontransition element that can adopt single-cation oxide perovskite frameworks. At the same time, peculiarities of electronic structure of xenon impose specific features on the bonding within a perovskite structure. Weak supramolecular interactions known as aerogen bonds are the linkers that maintain structural integrity of perovskite slabs in K4Xe3O12. The occurrence of aerogen bonding can provide an insight into the explosive properties of K4Xe3O12: the weakness of supramolecular interactions allows consideration of them as possible trigger bonds responsible for the detonation sensitivity of layered xenon perovskite.

Minerals with metal-organic framework structures.

Metal-organic frameworks (MOFs) are an increasingly important family of advanced materials based on open, nanometer-scale metal-organic architectures, whose design and synthesis are based on the directed assembly of carefully designed subunits. We now demonstrate an unexpected link between mineralogy and MOF chemistry by discovering that the rare organic minerals stepanovite and zhemchuzhnikovite exhibit structures found in well-established magnetic and proton-conducting metal oxalate MOFs. Structures of stepanovite and zhemchuzhnikovite, exhibiting almost nanometer-wide and guest-filled apertures and channels, respectively, change the perspective of MOFs as exclusively artificial materials and represent, so far, unique examples of open framework architectures in organic minerals.