Volume 233, Issue 3-4

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(TO 4 )ϕ] layers (M=Fe, Mg, Mn, Ni, Zn, Co; T=P, As; ϕ=OH, H 2 O) 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.

Electron diffraction tomography is a powerful emerging method for the structure characterization of materials available only as sub-micrometric grains. This technique can in fact deliver complete 3D information from a single crystal of few hundreds or few tens of nanometers, allowing the analysis of polyphasic or polytypic mixtures that generally cannot be fully addressed by X-ray methods. In this paper, we report and discuss three mineralogy-related study cases where electron diffraction tomography was the only way for achieving a proper description of the sample, by the identification and the structure determination of all the phases or all the polytypes within. We also show how electron diffraction tomography and dynamical refinement can be combined for finding accurate atomic positions and localizing hydrogen atoms at room conditions. Finally, we stress the future potential of this method in the fields of mineralogy and experimental petrology, where till now many samples cannot be properly described because nanocrystalline, polyphasic or disordered. Electron diffraction tomography can be used for detecting unexpected or unknown phases in high-pressure synthetic yields or for the characterization of fine rocks formed under extreme conditions, like impactites or meteorites. Eventually, this method allows the structure characterization of single domains that are ordered only at the scale of few cell repetitions, and therefore it makes possible investigating those materials at the borderline between crystalline and amorphous matter and delivers crucial and unique elements for the understanding of the first stages of solid matter organization.

A significant number of non-molecular crystal structures can be described as derivative structures of sphere packings, with variable degrees of distortion. The undistorted sphere packing model with all the cavities completely occupied is the aristotype, from which an idealized model of the real structure can be obtained as a substitution, undistorted hettotype. The real structure can then be seen as a distorted derivative of the substitution hettotype. In this article we revive the symbolism introduced by Zoltai and Stout to describe the substitution hettotypes and compare these with the corresponding real structures. In most cases, the distortions are small or even negligible. For some structures, a significant departure from the substitution hettotype is observed, which however does not prevent to adopt the same description as a unifying scheme.

The titanium-silicate (TS) block is the main structural unit in the 45 seidozerite-supergroup minerals; it consists of a central O (O=Octahedral) sheet and two adjacent H (H=Heteropolyhedral) sheets where Si 2 O 7 groups occur in the H sheets. The three HOH sheets of the TS block form a three-layered close packing of cations with an ABC repeat; mean cation–cation distances are 3.41 Å. Minerals of the seidozerite supergroup are divided into four groups based on the content of Ti and topology and stereochemistry of the TS block: in rinkite, bafertisite, lamprophyllite and murmanite groups, Ti (+Nb+Zr+Fe 3+ +Mg+Mn)=1, 2, 3 and 4 apfu, respectively. All TS-block structures consist either solely of TS blocks or of two types of block: the TS block and an I (intermediate) block that comprises atoms between two TS blocks. The TS block propagates close packing of cations into the I block. There are two types of close-packed layers of cations in the I block: (I) a layer of Na + and P 5+ with mean cation–cation distances of 3.41 Å and (II) a layer of Ba 2+ (+K + , Sr 2+ and Na + ) with mean cation–cation distances of 4.73 Å. The general topology of the TS block is independent of the topology and chemical composition of the I block. However direct interaction between TS and I blocks takes place in the crystal structures of jinshajiangite, bobshannonite, bafertisite, hejtmanite, delindeite and cámaraite. Interaction of Ba atoms in the I block and F (+O) atoms of the TS block results in doubling of the minimal translations, 2 t 1 and 2 t 2 , and a concomitant change in symmetry of the structure from primitive to C -centered.

The uranyl mineral swamboite has been redefined to swamboite-(Nd) and its structure has been solved and refined as a commensurate structure in six-dimensional superspace. The structure is monoclinic, superspace group P 2 1 /m ( a 1, b 1, g 1)00(− a 1, b 1, g 1)00 ( a 2,0, g 2)0 s , cell parameters a =6.6560(3), b =6.9881(5), c =8.8059(6), c=11.3361(16) Å, β=102.591(5)°, modulation wave-vectors q 1 =1/3 1/3 0; q 2 =−1/3 1/3 0; q 3 =1/2 0 1/2. The structure was refined from 8717 reflections to a final R =0.0610. The model includes modulation both of atomic positions and displacement parameters, as well as occupancy waves. The structure is based upon uranyl-silicate sheets of uranophane topology alternating with an interlayer of partly occupied Nd 3+ sites and H 2 O molecules. The strong (3+3) dimensional modulation of the structure originates from the distribution of the Nd-dominated sites and further accommodation of the suitable geometry within the sheets and charge distribution within the structure. The separation distances between the corresponding occupied Nd sites are rationals of the super-cell vectors corresponding to the modulation vectors of the structure. The case of swamboite-(Nd) is the first example of a modulated structure within the oxysalts of U 6+ .

Single crystals of two novel uranyl sulfates and two novel uranyl selenates with protonated cyclen and 3-aminotropane molecules, ((C 8 H 24 N 4 )[(UO 2 ) 3 (SO 4 ) 5 ](H 2 O) 3 ( I ), (C 8 H 24 N 4 )(H 5 O 2 )(H 3 O)[(UO 2 ) 4 (SeO 4 ) 7 (H 2 O)](H 2 O) 6.6 ( II ), (C 8 H 18 N 2 )(H 5 O 2 )(H 3 O)[(UO 2 ) 3 (SO 4 ) 5 (H 2 O)](H 2 O) 0.5 ( III ), and (C 8 H 18 N 2 )(H 5 O 2 )(H 3 O)[(UO 2 ) 3 (SeO 4 ) 5 (H 2 O)](H 2 O) 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.

The crystal structure of the mineral stützite, a relatively common silver telluride, was solved using intensity data collected using a crystal from the cotype material from the May Day mine, La Plata District, CO (USA). The study revealed that the structure is hexagonal, space group P 6̅, with cell parameters: a =13.454(2), c =8.459(1) Å and V =1326.0(5) Å 3 . The refinement of an anisotropic model led to an R index of 0.0421 for 1950 independent reflections. In the crystal structure of stützite there are eight independent Te sites and eight Ag sites with Z =7. Only Ag5, Ag6, Ag7 and Ag8 form classic metal-anion polyhedra: Ag8 is in linear coordination, Ag5 and Ag6 are triangularly coordinated, whereas Ag7 is in tetrahedral coordination. The case for Ag1, Ag2, Ag3 and Ag4 is more complicated as there are Ag–Ag contacts beside the typical bonds with the chalcogen. These positions correspond to low coordination (two, three and four) sites, in agreement with the silver preference for such environments. d 10 silver ion distribution has been evidenced by means of a combination of a Gram-Charlier development of the atomic displacement factors and a split model. A discussion on the possible existence of different polytypes in stützite-like compounds and on the use of the non-harmonic approach based upon a Gram-Charlier development of the atomic displacement factors for the determination of disordered structures is also presented.

The Pb–Ag–Sb sulfide roshchinite, Cu 0.09 Ag 1.04 Pb 0.65 Sb 2.82 As 0.37 S 6.08 , is a lillianite homologue N=4 with a complex incommensurate superstructure in the 8.46 Å direction of the orthorhombic crystal lattice with a 19.0804(1) Å, b 8.4591(2) Å and c 12.9451(3) Å, superspace group Pbcn (0 σ 2 0)00 s , q =0.41458(3) b* . A structure solution and refinement in (3+1) superspace, based on 10,019 observed reflections and 437 refined parameters was terminated at R obs (wR) equal to 7.27 (8.07)% using satellites up to second order; R obs is 4.82 for main reflections only. The Pb atoms in trigonal coordination prisms on planes of unit-cell twinning are semiperiodically replaced by antimony. The marginal columns of (311) PbS slabs of the Sb–Ag based structure which is based on PbS-like topology contain Sb, Ag(Cu) and mixed Ag/Sb sites in a complicated sequence. Central portions of the slabs are occupied by Sb–S crankshaft chains, best exposed on the (100) PbS planes, which run diagonally across the slabs. In these planes, in their majority the chains display Sb 3 S 4 form and two opposing orientations, zig-zagging along the [010] direction. Every six chains, a parallel configuration of two chains occurs, but occasionally this interval is reduced to five chains. This, together with related compositional changes in the Pb– and Ag–Sb column, explains the one-dimensionally incommensurate character of roshchinite. Modestly elevated contents of As replacing Sb are the probable reason of modulation and non-commensurability in roshchinite.

The crystal structure of Cu-bearing zinkenite from Saint-Pons (Alpes Maritimes department, France), having idealized chemical composition Cu 0.7 Pb 9.7 Sb 21.3 S 42 , has been studied. It has a pronounced hexagonal sub-cell, with unit-cell parameters a =22.1219(11), c =4.3207(3) Å, V =1831.2(2) Å 3 , space group P 6 3 , Z =1. The sub-cell crystal structure was refined to R 1 =0.072 on the basis of 3905 reflections with F o >4σ( F o ) and 133 refined parameters. It can be described as formed by one kind of rod, with walls of columns of (Pb/Sb)-centered polyhedra flanking both the rods and the sites located along the 6 3 screw axis. Minor Cu is hosted in the tetrahedral voids between the rods and the walls of polyhedra. Alternatively, the crystal structure of zinkenite can be described as formed by trigonal rods, delimited by lone electron-pair micelles, and tunnels hosting (Pb/Sb) atoms. The occurrence of weak superstructure reflections points to a triclinic unit cell with parameters a =38.271(2), b =22.1219(13), c =8.6475(5) Å, α=89.931(3), β=90.030(3), γ=89.957(3)°, V =7323.6(7) Å 3 , space group P 1, Z =4. The twin laws making the twin lattice hexagonal have been taken into account and the crystal structure has been solved and refined. Notwithstanding the very low R 1 value ( R 1 =0.038 on the basis of 22563 reflections with F o >4σ( F o ) and 1194 refined parameters), several shortcomings, mainly due to the low diffraction quality of the available crystals, allow only the description of the main structural features of the superstructure of zinkenite, indicating the correctness of the triclinic model hypothesized by previous authors.

The crystal structure of semseyite, Pb 9 Sb 8 S 21 was successfully refined using a single-crystal specimen from Wolfsberg, Harz, Germany, having chemical composition (EPMA) Pb 9.01(1) Sb 8.00(3) S 21.05(5) . The structure belongs to the monoclinic C 2/ c space group ( a =13.6267(10) Å, b =11.9742(9) Å, c =24.5891(18) Å, β =105.997(3)°, V =3856.8(5) Å 3 , Z =4, D c =6.048 g/cm 3 ). Crystal structure refinement with all atoms refined anisotropically converged to R 1 =4.64% (I>2σ(I)). The crystal structure is built of two subunits (A and B) showing TlSbS 2 -like topology. Each of them stacks parallel to (001), and c /2 in thickness. Two cation sites (Pb1 and Sb5) located at central part of the subunit, show mixed occupancy behavior as 95% Pb and 5% Sb at the Pb5 site, and 95% Sb and 5% Pb at the Sb1 site, respectively. Each of subunits are related by unit cell-level twinning mechanism “tropochemical cell twinning” with the TlSbS 2 -like subunits alternatively parallel to (1 1 −4) and (−1 1 4) planes.