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Nefedovite, Na5Ca4(PO4)4F, has been investigated by in situ high-temperature powder (30–690 °C) and single crystal (27–827 °C) X-ray diffraction and Raman spectroscopy. Nefedovite is tetragonal, space group I-4, a = 11.6560(2), c = 5.4062(2) Å, V = 734.50(2) Å3 (R1 = 0.0149). Nefedovite is a 1D antiperovskite, since its crystal structure contains chains of corner-sharing anion-centered [FCa4Na2]9+ octahedra. The chains are parallel to the c direction. Nefedovite is stable up to 727 °C and undergoes a displacive phase transition in the temperature range 277–327 °C. With increasing temperature, the PO4 tetrahedra in the crystal structure of nefedovite gradually rotate around the imaginary fourfold inversion axes aligning the O2…O3 edge parallel to [110], which ultimately leads to the appearance of the mirror plane perpendicular to the c direction and the change of space group from I-4 (82) to I4/m (87). The crystal structure of nefedovite expands strongly anisotropically with the direction of the maximum thermal expansion oriented perpendicular to the chains of anion-centered octahedra. The information-based structural complexity analysis demonstrates that both low- and high-temperature modifications of nefedovite are structurally simple with the IG,total value less than 100 bits per unit cell. The structural complexity decreases along the phase transition, which is typical for displacive phase transitions. [ABSTRACT FROM AUTHOR]

The crystal structure of Pb10(PO4)6O, the proposed matrix for the potential room-temperature superconductor LK-99, Pb10−xCux(PO4)6O (x = 0.9–1.0), has been reinvestigated via single-crystal X-ray diffraction using crystals prepared by Merker and Wondratschek (Z. Anorg. Allg. Chem. 1960, 306, 25–29). The crystal structure is trigonal, P 3 ¯ , a = 9.8109(6), c = 14.8403(12) Å, V = 1237.06(15), R1 = 0.0413 using 3456 unique observed reflections. The crystal structure of Pb10(PO4)6O is a superstructure with regard to the 'standard' P63/m apatite structure type. The doubling of the c parameter is induced through the ordering of the split sites of 'additional' O' atoms within the structure channels running parallel to the c axis and centered at (00z). The O' atoms form short bonds to the Pb1 atoms, resulting in splitting the Pb1 site into two, Pb1A and Pb1B. The structural distortions are further transmitted to the Pb phosphate framework formed by four Pb2 sites and PO4 groups. The structure data previously reported by Krivovichev and Burns (Z. Kristallogr. 2003, 218, 357–365) may either correspond to the Pb10(PO4)6Ox(OH)2−2x (x ~ 0.4) member of the Pb10(PO4)6O—Pb10(PO4)6(OH)2 solid solution series, or to the high-temperature polymorph of Pb10(PO4)6O (with the phase with doubled c parameter being the low-temperature polymorph). [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

The crystal structure of manganotychite has been refined using the holotype specimen from the Alluaiv Mountain, Lovozero massif, Kola peninsula, Russia. The mineral is cubic, Fd 3 ¯ , a = 14.0015(3) Å, V = 2744.88(18) Å3, Z = 8, R1 = 0.020 for 388 independently observed reflections. Manganotychite is isotypic to tychite and ferrotychite. Its crystal structure is based upon a three-dimensional infinite framework formed by condensation of MnO6 octahedra and CO3 groups by sharing common O atoms. The sulfate groups and Na+ cations reside in the cavities of the octahedral-triangular metal-carbonate framework. In terms of symmetry and basic construction of the octahedral-triangular framework, the crystal structure of manganotychite is identical to that of northupite, Na3Mg(CO3)2Cl. The transition northupite → tychite can be described as a result of the multiatomic 2Cl− → (SO4)2− substitution, where both chlorine and sulfate ions are the extra-framework constituents. However, the positions occupied by sulfate groups and chlorine ions correspond to different octahedral cavities within the skeletons of Na atoms. The crystal structure of northupite can be considered as an interpenetration of two frameworks: anionic [Mg(CO3)2]2− octahedral-triangular framework and cationic [ClNa3]2− framework with the antipyrochlore topology. Both manganotychite and northupite structure types can be described as a modification of the crystal structure of diamond (or the dia net) via the following steps: (i) replacement of a vertex of the dia net by an M4 tetrahedron (no symmetry reduction); (ii) attachment of (CO3) triangles to the triangular faces of the M4 tetrahedra (accompanied by the Fd 3 ¯ m → Fd 3 ¯ symmetry reduction); (iii) filling voids of the resulting framework by Na+ cations (no symmetry reduction); and (iv) filling voids of the Na skeleton by either sulfate groups (in tychite-type structures) or chlorine atoms (in northupite). As a result, the information-based structural complexity of manganotychite and northupite exceeds that of the dia net. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The crystal structure of sergeysmirnovite, MgZn2(PO4)2·4H2O (orthorhombic, Pnma, a = 10.6286(4), b = 18.3700(6), c = 5.02060(15) Å, V = 980.26(6) Å3, Z = 4), a new member of the hopeite group of minerals, was determined and refined to R1 = 0.030 using crystals from the Këster mineral deposit in Sakha-Yakutia, Russia. Similar to other members of the hopeite group, the crystal structure of sergeysmirnovite is based upon [Zn(PO4)]– layers interlinked via interstitial [MO2(H2O)4]2– octahedra, where M = Mg2+. The layers are parallel to the (010) plane. Within the layer, the ZnO4 tetrahedra share common corners to form chains running along [001]. Sergeysmirnovite is a dimorph of reaphookhillite, a mineral from the Reaphook Hill zinc deposit in South Australia. The relations between sergeysmirnovite and reaphookhillite are the same as those between hopeite and parahopeite. Topological and structural complexity analysis using information theory shows that the hopeite (sergeysmirnovite) structure type is more complex, both structurally and topologically, than the parahopeite (reaphookhillite) structure type. Such complexity relations contradict the general observation that more complex polymorphs possess higher physical density and higher stability, since parahopeite is denser than hopeite. It could be hypothesized that hopeite is metastable under ambient conditions and separated from parahopeite by a structural and topological reconstruction that requires an essential energy barrier that is difficult to overcome. [ABSTRACT FROM AUTHOR]

The new mineral vasilseverginite, ideally Cu9O4(AsO4)2(SO4)2, was found in the Arsenatnaya fumarole at the second scoria cone of the Northern Breakthrough of the Great Tolbachik Fissure Eruption, Tolbachik volcano, Kamchatka, Russia. It is associated with tenorite, lammerite, stranskiite, lammerite-β, langbeinite, dolerophanite, sanidine, hematite, and gahnite. Vasilseverginite occurs as prismatic crystals up to 0.02 × 0.02 × 0.06 mm3 combined in groups or interrupted crusts up to 1 × 2 cm2 in area and up to 0.1 mm thick. It is transparent, bright green, with vitreous luster. Dcalc is 4.41 g⋅cm–3. Vasilseverginite is optically biaxial (–), α 1.816(5), β 1.870(5), γ 1.897(5), estimated 2V is 30(15)°. Chemical composition (wt%, electron-microprobe) is: CuO 64.03, ZnO 0.79, Fe2O3 0.25, P2O5 0.05, As2O5 20.83, SO3 14.92, total 100.87. The empirical formula calculated on O = 20 apfu is C u 8.78 Z n 0.11 F e 0.03 3 + Σ 8.92 A s 1.98 P 0.01 S 2.03 O 20 $\left(\mathrm{Cu}_{8.78} \mathrm{Zn}_{0.11} \mathrm{Fe}_{0.03}^{3+}\right)_{\Sigma 8.92} \mathrm{As}_{1.98} \mathrm{P}_{0.01} \mathrm{~S}_{2.03} \mathrm{O}_{20}$. Vasilseverginite is monoclinic, P21/n, a = 8.1131(4), b = 9.9182(4), c = 11.0225(5) Å, β = 110.855(2)°, V = 828.84(6) Å3, and Z = 2. The strongest reflections in the powder XRD pattern [d,Å(I)(hkl)] are: 7.13(41)(101̅), 5.99(70)(110, 111̅), 5.260(100)(101), 4.642(46)(111), 3.140(31)(031̅), 2.821(35)(023̅), 2.784(38)(132̅, 032̅), 2.597(35)(204̅), and 2.556(50) (231̅, 212). The crystal structure, solved using single-crystal X‑ray diffraction data, R1 = 0.025, is based upon complex [O4Cu9]10+ layers parallel to (101̅) that are composed of edge- and corner-sharing (OCu4) tetrahedra. The topology is unprecedented in inorganic structural chemistry. The crystal structure can be considered a hybrid of the structures of popovite Cu5O2(AsO4)2 and dolerophanite Cu2O(SO4) according to the scheme Cu9O4(AsO4)2(SO4)2 = Cu5O2(AsO4)2 + 2Cu2O(SO4). The chemical hybridization does not result in a significant increase in chemical complexity of vasilseverginite compared to the sum of those of popovite and dolerophanite, whereas the structural hybridization leads to the doubling of structural information per unit cell. The mineral is named in memory of the outstanding Russian mineralogist, geologist, and chemist Vasiliy Mikhailovich Severgin (1765–1826). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

[Display omitted] • the review of structural diversity of antiperovskites includes more than 280 compounds. • the review covers a wide range of chemical compounds, including oxides, halogenides, nitrides, etc. • 45 topological types of antiperovskite units are considered and analysed. • the topological principles of antiperovskite constructions are formulated. • topological complexity analysis is performed using the information-theory methods. The overview of more than 280 antiperovskites as compounds based upon the units formed by condensation of XA 6 anion-centered octahedra (X = anion; A = cation) shows that there are forty-five topologically different types of antiperovskite structures, including eighteen frameworks, fourteen layers, six chains and seven finite clusters. The XA 6 octahedra may polymerize by sharing common corners, edges and faces. One A atom may be shared by no more than six XA 6 octahedra, whereas one A-A edge may be shared by no more than three octahedra. The average connectivity of an octahedron in the unit, < s >, defined as the average number of octahedra linked to a single octahedron in the complex, correlates positively with the X:A ratio. The information-based analysis of topological complexity of antiperovskite units shows that most antiperovskites are rather simple from the structural point of view with the most complex units being the layers present in the crystal structures of A 4 [N 8 O 3 A 47 ](A'N 4) 12 (A = Ca, Sr; A' = Mo, W). The information-based complexity parameters correlate with the number k' of symmetrically independent octahedra in the antiperovskite unit: the higher the value of k' , the more complex is the unit. From the chemical point of view, the review covers oxides, suboxides, oxysalts, nitrides, subnitrides, and complex halogenides. [ABSTRACT FROM AUTHOR]

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, β = 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. [ABSTRACT FROM AUTHOR]

Philipsburgite, Cu5Zn((As,P)O4)2(OH)6·H2O, from the Middle Pit, Gold Hill Mine, Tooele Co., Utah, USA, was studied by single-crystal X-ray diffraction and scanning electron microscopy. The empirical formula of the studied sample is (Cu4.69Zn1.23)(As0.86P0.18O4)2(OH)5.61·H2O, which agrees well with the previous reports on the mineral. Philipsburgite is monoclinic, P21/c, a = 12.385(6), b = 9.261(4), c = 10.770(5) Å, β = 97.10(1)o, V = 1225.7(9) Å3 (at 100 K), and Z = 4. The crystal structure was refined to R1 = 0.046 for 2563 unique observed reflections with |Fo| ≥ 4σF. The crystal structure of philipsburgite is isotypic to that of kipushite and can be considered as a complex three-dimensional framework consisting of two types of layers stacked parallel to the a-axis. The A-type layer is formed by the edge-sharing Jahn-Teller-distorted Cuφ6 octahedra [φ = O2−, (OH)−, H2O]. Two adjacent octahedral layers are linked via (As2O4) tetrahedra. The B-type layer is built by corner-sharing (ZnO4) and (As1O4) tetrahedra and is formed by the four- and eight-membered tetrahedral rings. The A:B ratio of the A and B layers is equal to 2:1. The hydrogen bonding network in philipsburgite is rather complex and consists of two- and three-center hydrogen bonds. The As1 site accommodates ca. 18% of P and is a preferable position for the P substitution in philipsburgite. The observed selectivity of the As1 site for P may indicate that, for the intermediate compositions with the P:As ratios close to 1:1, there is a fully ordered species with P prevalent at the As1 site and As prevalent at the As2 site. The intermediate composition would, therefore, be Cu5Zn(AsO4)(PO4)(OH)6·H2O and such a mineral can be considered as a separate species, according to the rules of the International Mineralogical Association (IMA). Philipsburgite should be considered as structurally complex with the Shannon information contents of 4.954 bits/atom and 614.320 bits/cell. The obvious reason for the structural complexity of the mineral is its modularity, i.e., the presence of two structurally distinct modules, the octahedral-tetrahedral (A) and tetrahedral (B) layers. [ABSTRACT FROM AUTHOR]

Kurchatovite and clinokurchatovite, both of ideal composition CaMgB2O5, from the type localities (Solongo, Buryatia, Russia, and Sayak-IV, Kazakhstan, respectively) have been studied using electron microprobe and single-crystal X-ray diffraction methods. The empirical formulae of the samples are Ca1.01Mg0.87Mn0.11Fe2+0.02B1.99O5 and Ca0.94Mg0.91Fe2+0.10Mn0.04B2.01O5 for kurchatovite and clinokurchatovite, respectively. The crystal structures of the two minerals are similar and based upon two-dimensional blocks arranged parallel to the c axis in kurchatovite and parallel to the a axis in clinokurchatovite. The blocks are built up from diborate B2O5 groups, and Ca2+ and Mg2+ cations in seven- and six-fold coordination, respectively. Detailed analysis of geometrical parameters of the adjacent blocks reveals that symmetrically different diborate groups have different degrees of conformation in terms of the δ angles between the planes of two BO3 triangles sharing a common O atom, featuring two discrete sets of the δ values of ca. 55° (B' blocks) and 34° (B" blocks). The stacking of the blocks in clinokurchatovite can be presented as ...(+B')(+B")(+B')(+B")... or [(+B')(+B")], whereas in kurchatovite it is more complex and corresponds to the sequence ...(+B')(+B")(+B')(-B')(-B")(-B')(+B')(+B")(+B')(-B')(-B")(-B')... or [(+B')(+B")(+B')(-B')(-B")(-B')]. The B':B" ratios for clinokurchatovite and kurchatovite are 1:1 and 2:1, respectively. According to this description, the two minerals cannot be considered as polytypes and their mutual relationship corresponds to the term modular polymorphs. From the viewpoint of information-based measures of structural complexity, clinokurchatovite (IG = 4.170 bits/atom and IG, total = 300.235 bits/cell) is structurally simpler than kurchatovite (IG = 4.755 bits/atom and IG, total = 1027.056 bits/cell). The high structural complexity of kurchatovite can be inferred from the modular character of its structure. The analysis of structural combinatorics in terms of the modular approach allows to construct the whole family of theoretically possible "kurchatovite"-type structures that bear the same structural features common for kurchatovite and clinokurchatovite. However, the crystal structures of the latter minerals are the simplest and are the only ones that have been observed in nature. The absence of other possible structures is remarkable and can be explained by either the maximum-entropy of the least-action fundamental principles. [ABSTRACT FROM AUTHOR]

A novel polymorph of RbCuCl3 (rubidium copper trichloride), denoted ϵ‐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. ϵ‐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. [ABSTRACT FROM AUTHOR]

Complexity is one of the important characteristics of crystal structures, which can be measured as the amount of Shannon information per atom or per unit cell. Since complexity may arise due to combination of different factors, herein we suggest a method of ladder diagrams for the analysis of contributions to structural complexity from different crystal-chemical phenomena (topological complexity, superstructures, modularity, hydration state, etc.). The group of minerals and inorganic compounds based upon the batagayite-type [M(TO4)Ï•] layers (M = Fe, Mg, Mn, Ni, Zn, Co; T = P, As; Ï• = OH, H2O) is used as an example. It is demonstrated that the method allows for the quantitative estimates of various contributions to the complexity of the whole structure. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) is used to determine positions of H atoms and to investigate hydrogen bonding in the crystal structures of two polymorphs of Cu3(AsO4)(OH)3: clinoclase and gilmarite. Hydrogen bonds in clinoclase involve interactions between hydroxyl groups and O atoms of arsenate tetrahedra, whereas the crystal structure of gilmarite features OH···OH bonding, which is rather uncommon in copper hydroxy-oxysalts. Information-based parameters of structural complexity for clinoclase and gilmarite show that the former is more complex (IG,total = 213.212 bits/cell) than the latter (IG,total = 53.303 bits/cell), which indirectly points out that gilmarite is metastable. This suggestion is supported by the lower density of gilmarite (4.264 g/cm3) compared to that of clinoclase (4.397 g/cm3). The hypothesis of metastable character of gilmarite is in agreement with the Goldsmith's simplexity principle and the Ostwald-Volmer rule. [ABSTRACT FROM AUTHOR]

The system B2O3-Al2O3-SiO2 (BAS) includes two ternary phases occurring naturally, boromullite, Al9BSi2O19, and boralsilite, Al16B6Si2O37, as well as synthetic compounds structurally related to mullite. The new mineral vránaite, a third naturally occurring anhydrous ternary BAS phase, is found with albite and K-feldspar as a breakdown product of spodumene in the elbaite-subtype Manjaka granitic pegmatite, Sahatany Valley, Madagascar. Boralsilite also occurs in this association, although separately from vránaite; both minerals form rare aggregates of subparallel prisms up to 100 µm long. Optically, vránaite is biaxial (-), nα = 1.607(1), nβ = 1.634(1), nγ = 1.637(1) (white light), 2Vx(calc) = 36.4°, X ≈ c; Y ≈ a; Z = b. An averaged analysis by EMP and LA-ICP-MS (Li, Be) gives (wt%) SiO2 20.24, B2O3 11.73, Al2O3 64.77, BeO 1.03, MnO 0.01, FeO 0.13, Li2O 1.40, Sum 99.31. Raman spectroscopy in the 3000-4000 cm-1 region rules out the presence of significant OH or H2O. Vránaite is monoclinic, space group I2/m, a = 10.3832(12), b = 5.6682(7), c = 10.8228(12) Å, β = 90.106(11)°; V = 636.97(13) ų, Z = 1. In the structure [R1 = 0.0416 for 550 Fo > 4σFo], chains of AlO6 octahedra run parallel to [010] and are cross-linked by Si2O7 disilicate groups, BO3 triangles, and clusters of AlO4 and two AlO5 polyhedra. Two Al positions with fivefold coordination, Al4 and Al5, are too close to one another to be occupied simultaneously; their refined site-occupancy factors are 54% and 20% occupancy, respectively. Al5 is fivefold-coordinated Al when the Al9 site and both O9 sites are occupied, a situation giving a reasonable structure model as it explains why occupancies of the Al5 and O9 sites are almost equal. Bond valence calculations for the Al4 site suggest Li is likely to be sited here, whereas Be is most probably at the Al5 site. One of the nine O sites is only 20% occupied; this O9 site completes the coordination of the Al5 site and is located at the fourth corner of what could be a partially occupied BO4 tetrahedron, in which case the B site is shifted out of the plane of the BO3 triangle. However, this shift remains an inference as we have no evidence for a split position of the B atom. If all sites were filled (Al4 and Al5 to 50%), the formula becomes Al16B4Si4O38, close to Li1.08Be0.47Fe0.02Al14.65B3.89Si3.88O36.62 calculated from the analyses assuming cations sum to 24. The compatibility index based on the Gladstone-Dale relationship is 0.001 ("superior"). Assemblages with vránaite and boralsilite are inferred to represent initial reaction products of a residual liquid rich in Li, Be, Na, K, and B during a pressure and chemical quench, but at low H2O activities due to early melt contamination by carbonate in the host rocks. The two BAS phases are interpreted to have crystallized metastably in lieu of dumortierite in accordance with Ostwald Step Rule, possibly first as "boron mullite," then as monoclinic phases. The presence of such metastable phases is suggestive that pegmatites crystallize, at least partially, by disequilibrium processes, with significant undercooling, and at high viscosities, which limit diffusion rates. [ABSTRACT FROM AUTHOR]

The chemical diversity and complexity of tellurium minerals were analyzed using the concept of mineral systems and Shannon informational entropy. The study employed data for 176 Te mineral species known today. Tellurium minerals belong to six mineral systems in the range of one-to-six species-defining elements. For 176 tellurium minerals, only 36 chemical elements act as essential species-defining constituents. The numbers of minerals of main elements are calculated as follows (the number of mineral species is given in parentheses): O (89), H (48), Cu (48), Pb (43), Bi (31), S (29), Ag (20), Fe (20), Pd (16), Cl (13), and Zn (11). In accordance with their chemistry, all Te minerals are classified into five types of mineral systems: tellurium, oxides, tellurides and intermetalides, tellurites, and tellurates. A statistical analysis showed positive relationships between the chemical, structural, and crystallochemical complexities and the number of essential species-defining elements in a mineral. A positive statistically significant relationship between chemical and structural complexities was established. It is shown that oxygen-free and oxygen-bearing Te minerals differ sharply from each other in terms of chemical and structural complexity, with the first group of minerals being simpler than the second group. The oxygen-free Te minerals (tellurium, tellurides, and intermetallides) are formed under reducing conditions with the participation of hydrothermal solutions. The most structurally complex oxygen-bearing Te minerals originate either from chemical weathering and the oxidation of ore deposits or from volcanic exhalations (Nabokoite). [ABSTRACT FROM AUTHOR]

Single crystals of the novel boroarsenate (K,Na)2[As2B12O24][B3O3(OH)3] (I) were obtained using the borax flux method. The crystal structure of I was found to be triclinic, P-1, a = 8.414(5), b = 10.173(6), c = 15.90(1) Å, α = 79.56(1), β = 78.68(1), γ = 70.91(1), V = 1251(1) Å3, Z = 2. The crystal structure of I is based upon the novel [AsB6O12]− microporous boroarsenate framework formed by B and As coordination polyhedra. This framework can be subdivided into borate units that are interlinked by AsO4 tetrahedra. In the case of I, the borate substructure is a chain consisting of triborate rings, ☐2Δ, formed by two (BO3) triangles and one (BO4) tetrahedron connected through shared common oxygen atoms. The chains are extended along [0 1 ¯ 1] and are interlinked by (AsO4) tetrahedra in the [011] direction. As a result, the framework has large channels parallel to [100], having an effective diameter of 4.2 × 5.6 Å2. The channels contain occluded electroneutral ring triborate complexes, [B3O3(OH)3]0, formed by three (BO2(OH−))− triangles sharing common O atoms, as well as K+ and Na+ cations. The triborate [B3O3(OH)3]0 units correspond to similar clusters found in the crystal structure of the α-form of metaboric acid, HBO2. According to information-based complexity calculations, the crystal structure of I should be described as complex, with IG = 5.781 bits/atom and IG,total = 625.950 bits/cell. Teruggite, Ca4Mg[B6As(OH)6O11]2(H2O)14, the only known boroarsenate of natural origin, has almost twice as much information per unit cell, with IG,total = 1201.992 bits/cell. The observed difference in structural complexity between I and teruggite is the consequence of their chemistry (hydration state) and different formation conditions. [ABSTRACT FROM AUTHOR]

Chemical diversity of minerals containing selenium as an essential 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 123 Se mineral species approved by the International Mineralogical Association as of 25 May 2019. All known selenium minerals belong to seven mineral systems with the number of essential components ranging from one to seven. According to their chemical features, the minerals are subdivided into five groups: Native selenium, oxides, selenides, selenites, and selenates. Statistical analysis shows that there are strong and positive correlations between the chemical and structural complexities (measured as amounts of Shannon information per atom and per formula or unit cell) and the number of different chemical elements in a mineral. Analysis of relations between chemical and structural complexities provides strong evidence that there is an overall trend of increasing structural complexity with the increasing chemical complexity. The average structural complexity for Se minerals is equal to 2.4(1) bits per atom and 101(17) bits per unit cell. The chemical and structural complexities of O-free and O-bearing Se minerals are drastically different with the first group being simpler and the second group more complex. The O-free Se minerals (selenides and native Se) are primary minerals; their formation requires reducing conditions and is due to hydrothermal activity. The O-bearing Se minerals (oxides and oxysalts) form in near-surface environment, including oxidation zones of mineral deposits, evaporites and volcanic fumaroles. From the structural viewpoint, the five most complex Se minerals are marthozite, Cu(UO2)3(SeO3)2O2·8H2O (744.5 bits/cell); mandarinoite, Fe2(SeO3)3·6H2O (640.000 bits/cell); carlosruizite, K6Na4Na6Mg10(SeO4)12(IO3)12·12H2O (629.273 bits/cell); prewittite, KPb1.5ZnCu6O2(SeO3)2Cl10 (498.1 bits/cell); and nicksobolevite, Cu7(SeO3)2O2Cl6 (420.168 bits/cell). The mechanisms responsible for the high structural complexity of these minerals are high hydration states (marthozite and mandarinoite), high topological complexity (marthozite, mandarinoite, carlosruizite, nicksobolevite), high chemical complexity (prewittite and carlosruizite), and the presence of relatively large clusters of atoms (carlosruizite and nicksobolevite). In most cases, selenium itself does not play the crucial role in determining structural complexity (there are structural analogues or close species of marthozite, mandarinoite, and carlosruizite that do not contain Se), except for selenite chlorides, where stability of crystal structures is adjusted by the existence of attractive Se–Cl closed-shell interactions impossible for sulfates or phosphates. Most structurally complex Se minerals originate either from relatively low-temperature hydrothermal environments (as marthozite, mandarinoite, and carlosruizite) or from mild (500–700 °C) anhydrous gaseous environments of volcanic fumaroles (prewittite, nicksobolevite). [ABSTRACT FROM AUTHOR]

The crystal structure of a novel natural uranyl sulfate, Ca(UO2)6(SO4)2O2(OH)6·12H2O (CaUS), has been determined using data collected under ambient conditions at the Swiss–Norwegian beamline BM01 of the European Synchrotron Research Facility (ESRF). The compound is monoclinic, P21/c, a = 11.931(2), b = 14.246(6), c = 20.873(4) Å, β = 102.768(15), V = 3460.1(18) Å3, and R1 = 0.172 for 3805 unique observed reflections. The crystal structure contains six symmetrically independent U6+ atoms forming (UO7) pentagonal bipyramids that share O...O edges to form hexamers oriented parallel to the (010) plane and extended along [1–20]. The hexamers are linked via (SO4) groups to form [(UO2)6(SO4)2O2(OH)6(H2O)4]2− chains running along the c-axis. The adjacent chains are arranged into sheets parallel to (010). The Ca2+ ions are coordinated by seven O atoms, and are located in between the sheets, providing their linkage into a three-dimensional structure. The crystal structure of CaUS is closely related to that of uranopilite, (UO2)6(SO4)O2(OH)6·14H2O, which is also based upon uranyl sulfate chains consisting of hexameric units formed by the polymerization of six (UO7) pentagonal bipyramids. However, in uranopilite, each (SO4) tetrahedron shares its four O atoms with (UO7) bipyramids, whereas in CaUS, each sulfate group is linked to three uranyl ions only, and has one O atom (O16) linked to the Ca2+ cation. The chains are also different in the U:S ratio, which is equal to 6:1 for uranopilite and 3:1 for CaUS. The information-based structural complexity parameters for CaUS were calculated taking into account H atoms show that the crystal structure of this phase should be described as very complex, possessing 6.304 bits/atom and 1991.995 bits/cell. The high structural complexity of CaUS can be explained by the high topological complexity of the uranyl sulfate chain based upon uranyl hydroxo/oxo hexamers and the high hydration character of the phase. [ABSTRACT FROM AUTHOR]

A sample of uranyl carbonate mineral andersonite, Na2Ca[(UO2)(CO3)3]·5−6H2O, originating from the Cane Springs Canyon, San Juan Co., UT, USA was studied using single-crystal and powder X-ray diffraction at various temperatures. Andersonite is trigonal, R−3m, a = 17.8448(4), c = 23.6688(6) Å, V = 6527.3(3) Å3, Z = 18, R1 = 0.018. Low-temperature SCXRD determined the positions of H atoms and disordered H2O molecules, arranged within the zeolite-like channels. The results of high-temperature PXRD experiments revealed that the structure of andersonite is stable up to 100 °C; afterwards, it loses crystallinity due to release of H2O molecules. Taking into account the well-defined presence of H2O molecules forming channels' walls that to the total of five molecules p.f.u., we suggest that the formula of andersonite is Na2Ca[(UO2)(CO3)3]·(5+x)H2O, where x ≤ 1. The thermal behavior of andersonite is essentially anisotropic with the lowest values of the main thermal expansion coefficients in the direction perpendicular to the channels (plane (001)), while the maximal expansion is observed along the c axis—in the direction of channels. The thermal expansion around 80 °C within the (001) plane becomes negative due to the total release of "zeolitic" H2O molecules. The information-based structural complexity parameters of andersonite were calculated after the removal of all the disordered atoms, leaving only the predominantly occupied sites, and show that the crystal structure of the mineral should be described as complex, possessing 4.535 bits/atom and 961.477 bits/cell, which is comparative to the values for another very common natural uranyl carbonate, liebigite. [ABSTRACT FROM AUTHOR]

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. A 68, 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. [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]

The crystal structure of magnesian halotrichite has been refined for two samples collected as white efflorescences from the surface of geothermal fields associated with the Koshelevsky (sample VK4-09) and Centralny Semyachik (sample SC2-20) volcanoes (both Kamchatka peninsula, Russia). Halotrichite and its Mg-rich varieties are common products of the acid leaching of rocks, both volcanic and technogenic. The crystal structures of two halotrichite crystals were refined in the P21/n space group (vs. P21/c used previously) with the unit-cell parameters a = 6.1947(2)/6.1963(5) Å, b = 24.2966(8)/24.2821(14) Å, c = 21.0593(8)/21.063(2) Å, β = 96.512(4)/96.563(9) º, V = 3149.2(2)/3148.3(5) Å3, Z = 4 to R1 = 0.055 and 0.067 for 5673 and 3936 reflections with I > 2σI reflections, respectively. The crystal structure consists of isolated Al(H2O)6 octahedra, SO4 tetrahedra, H2O molecules and [X(SO4)(H2O)5]0 clusters (X = Fe, Mg). The chemical analyses of both samples show their enrichment of Mg at the Fe2+ site. The analysis of geometrical parameters of the crystal structures of halotrichite and its Mg-analogue pickeringite suggests that the localization of O atoms carried out in this work is more accurate and the single-crystal X-ray diffraction data for the first time allowed localization of hydrogen atom positions. The refined number of H2O molecules agrees with the ideal chemical formula. The crystal structure complexity of halotrichite is estimated as IG, total = 2305 bits/cell, which belongs to the family of very complex mineral structures. The contribution of hydrogen bonding system plays a significant role in the overall bonding scheme and the overall complexity of the crystal structure, increasing the Shannon information amount more than twice from IG, total(noH) = 988 bits/cell (no hydrogen atoms) to IG, total = 2305 bits/cell (all atoms including hydrogen). The comparative distribution of halotrichite relative to other Fe-Al hydrated sulfates from the standpoint of structural complexity is considered. [ABSTRACT FROM AUTHOR]

Thermal expansion of Ba silicates with tetrahedrally coordinated Si atoms in the temperature range of 25–1100 °C had been studied by high-temperature X-ray powder diffraction. The volume thermal expansion coefficients (TECs) are in the range 41–50×10 −6 °C −1 with an average value of 〈 α V 〉 = 45 × 10 − 6 ° C − 1 . In the structures with chain and layered silicate anions, thermal expansion is anisotropic: the direction of maximal TEC is parallel to the extension of the zweier chains of silicate tetrahedra, which are strained owing to the interactions with Ba 2+ . The strain is released during thermal expansion due to the increasing effective size of Ba 2+ induced by thermal vibrations. Information-theoretic analysis of the structural and topological complexities of Ba silicates indicates that their structural complexity is a function of the topological complexity of their silicate anions. The latter displays a non-linear behaviour with increasing SiO 2 content (=the increasing degree of polymerization and increasing dimensionality): it starts from simple topologies, reaches a maximum at topologies of intermediate complexity, and ends up at simple topologies again. The specificity of the interactions of Ba 2+ with the silicate anions results in higher complexity of high-temperature α -BaSi 2 O 5 compared to that of low-temperature β -BaSi 2 O 5 . This uncommon behaviour may be explained by the vibrational advantages provided by flatter and more complex silicate layers in the α -phase, which overcome negative differences in configurational entropies of the two modifications apparent in the differences of their structural Shannon information. [ABSTRACT FROM AUTHOR]

High-temperature phase transition of synthetic kogarkoite, Na 3 SO 4 F, has been studied by high-temperature X-ray powder and single-crystal diffraction. The temperature of the phase transition can be estimated as 112.5±12.5 °C. The low-temperature phase, α-Na 3 SO 4 F, at 293 K, is monoclinic, P 2 1 / m , a= 18.065(3), b= 6.958(1), c= 11.446(1) Å , β= 107.711(1)°, Z =12. The structure contains thirteen symmetrically independent Na sites with coordination numbers varying from 6 to 8, and six independent S sites. The high-temperature β-phase at 423 K is rhombohedral, R- 3 m , a= 6.94(1), c= 24.58(4) Å, Z =9. The crystal structure of both polymorphs of Na 3 SO 4 F can be described as a 9 R antiperovskite polytype based upon triplets of face-sharing [FNa 6 ] octahedra linked into a three-dimensional framework by sharing corners. In the α-modification, the SO 4 tetrahedra are completely ordered and located in the framework cavities. In the β-modification, there are only two symmetrically independent Na atoms in the structure. The main difference between the structures of the α- and β-phases is the degree of ordering of the SO 4 tetrahedra: in the α-modification, they are completely ordered, whereas, in the β-modification, the complete disorder is observed, which is manifested in a number of low-occupied O sites around fully occupied S sites. The phase transition is therefore has an order–disorder character and is associated with the decrease of structural complexity measured as an information content per unit cell [577.528 bits for the low- (α) and 154.830 bits for the high- (β) temperature modifications]. [ABSTRACT FROM AUTHOR]

Beryllium borates are mostly water-free, with the natural mineral berborite, Be 2 (BO 3)(OH)‧H 2 O, being the only known exception. A sample of berborite from the Vevja quarry, Tvedalen, Larvik, Norway was studied by single-crystal X-ray diffraction, variable temperature 1H nuclear magnetic resonance (NMR), and infrared (IR) spectroscopy. The crystal structure is the trigonal 1 T -polytype with space group P 321 and is based on electroneutral [BeØ 2 (BΔO 3)]-layers formed by BeO 3 Ø-tetrahedra and BΔO 3 -triangles. Due to statistical occupancy of the Ø-ligand by hydroxyl groups (50%) and water molecules (50%), berborite-1 T and its related polytypes are characterized by complex systems of hydrogen bonds. Accurate analysis shows that in the structure of berborite there are two independent systems of hydrogen bonds involving mobile protons. Lowering of temperature results in the complete stabilization of protons at the critical "freezing-point" of 243 K. The crystal chemistry and complexity of layered beryllium borates are discussed. Despite the broad structural diversity of these compounds, their crystal structures are classified as simple (20–100 bits per unit cell) or intermediately complex (100–500 bits per unit cell). The complexity of berborite polytypes increases in accordance with the quantity of layers from 29.038 (1 T) to 78.077 (2 H), which is in good agreement with the negative contribution of complexity to the configurational entropy. • A sample of was studied by SCXRD, variable temperature 1H NMR, and IR spectroscopy. • In the berborite structure there are two substantially independent systems of hydrogen bonds involving mobile protons. • The crystal chemistry and complexity of layered beryllium borates are discussed. [ABSTRACT FROM AUTHOR]

We report the crystal structures of four synthetic members of the variscite group (space group type Pbca) and of bonacinaite, the first naturally occurring scandium arsenate member of the metavariscite group. All structures were determined using single-crystal X-ray intensity data. The following members were all synthesised under either mild hydrothermal conditions or by wet-chemical methods (<90°C). CrAsO4⋅2H2O (deep green): a = 8.894(2), b = 9.946(2), c = 10.206(2) Å and V = 902.8(3) Å3; R1 = 2.14%. Tl3+PO4⋅2H2O (colourless): a = 10.2848(7), b = 8.8578(6), c = 10.3637(7) Å and V = 944.14(11) Å3 (data at –173°C); R1 = 2.56%. MnSeO4⋅2H2O (pale pink): a = 10.441(2), b = 9.2410(18), c = 10.552(2) Å and V = 1018.1(3) Å3; R1 = 2.19%. A different method of preparation of MnSeO4⋅2H2O yielded crystals with very similar unit-cell parameters, a = 10.4353(5), b = 9.2420(5) and c = 10.5349(6) Å; R1 = 2.25%. CdSeO4⋅2H2O (colourless) has a = 10.481(1), b = 9.416(1), c = 10.755(1) Å and V = 1061.4(2) Å3; R1 = 1.53%. The thermal behaviour of the two selenate members was studied by a combination of DSC and TG, supplemented by PXRD. Bonacinaite (IMA2018-056), metavariscite-type natural (Sc,Al)(As,P)O4⋅2H2O (ideally ScAsO4⋅2H2O), crystallises in the space group P21/n, with a = 5.533(1), b = 10.409(2), c = 9.036(2) Å, β = 91.94(3)° and V = 520.11(18) Å3; R1 = 3.66%. The structural formula, supported by chemical analysis, is (Sc0.807(1)Al0.193)(As0.767(7)P0.233)O4⋅2H2O. All structures are based on frameworks built by corner-sharing of TO4 tetrahedra (T = P5+, As5+ or Se6+) with MO4(H2O)2 (M = Mn2+, Cd2+, Cr3+, Sc3+ or Tl3+) octahedra. The flexible frameworks are reinforced by partly bifurcated, strong to weak hydrogen bonds. The crystal chemistry of all known synthetic and natural members of the variscite and metavariscite groups is discussed and compared, and the relative stabilities are evaluated. With the aid of the COMPSTRU program (Bilbao Crystallographic Server), a quantitative comparison of the crystal structures in both groups is given. Calculations of the structural and topological complexity reveal that the metavariscite structure type is structurally and topologically simpler than that of variscite. It is suggested that metavariscite and phosphosiderite are metastable kinetically stabilised phases, in contrast to thermodynamically stable variscite and strengite, respectively. The 3D frameworks of the members of both groups have been shown to be potential electrode materials for rechargeable Li ion batteries. [ABSTRACT FROM AUTHOR]

The discovery of natural minerals provided methodology for the targeted synthesis of a novel type of polyoxocuprate clusters, [ M ⊂Cu 12 O 8 (AsO 4) 8 ] q- (M = Ti(IV), Bi(III)), with a cubooctahedral arrangement of Cu2+ cations. [Display omitted] • a new class of polyoxocuprate clusters has been prepared using mineralogical information. • a targeted synthesis of new compounds with cubooctahedral arrangement of Cu2+ cations. • the new materials can be considered as inclusion-in-salt compounds. • crystallization from gaseous phase provides a new access to polyoxometalates. A novel type of polyoxocuprate (POCu) clusters, [ M ⊂Cu 12 O 8 (AsO 4) 8 ] q- (M = Ti(IV), Bi(III)), with a cubooctahedral arrangement of Cu2+ cations, have been prepared by chemical vapor transport reactions (CVT) using the methodology inspired by mineralogical discoveries at volcanic fumaroles of the Tolbachik volcano (Kamchatka peninsula, Russia). Three new compounds, Na 21 Cl 6 F[TiF 6 ][TiCu 12 O 8 (AsO 4) 8 ] (1), Na 18 Cl 6 [TiCu 12 O 8 (AsO 4) 8 ] (2), and Na 18 Cl 5 [BiCu 12 O 8 (AsO 4) 8 ] (3), prepared under low-vacuum conditions, contain the {[ M ⊂Cu 12 O 8 ](AsO 4) 8 } (M = Ti4+, Fe3+) clusters with a Keggin-ion-like cubooctahedral arrangement of Cu2+ cations encapsulating M n+ cations strikingly similar to the {[Pd 13 O 8 ]L 8 ] q- polyoxoanions observed in polyoxopalladates. The packing modes of clusters in different structures are different, with the structures of 1 and 3 based upon cubic-close-packing and hexagonal-close-packing arrangements, respectively. The packing of clusters in 2 is rather complex that results in its extreme structural complexity with the amount of Shannon structural information per unit cell exceeding 3000 bits. In the title compounds, the POCu clusters are embedded into salt matrices and therefore can be considered as an inverse analogue of salt-inclusion compounds, i.e., as inclusion-in-salt compounds. The successful synthesis of new types of POCu clusters using the CVT techniques opens up a new synthetic pathway for the exploration of polyoxocuprates with promising interesting structures and physical properties. [ABSTRACT FROM AUTHOR]