First find of a potentially new mineral, Na-dominant at M 2-site eudialyte analogue: crystal structure and significance as a marker of ultraagpaitic environment

A potentially new mineral, M2Na-dominant analogue of eudialyte from the Khibiny alkaline massif, was investigated using the methods of electron probe microanalysis, X-ray diffraction, and IR spectroscopy. The crystal structure was refined to R = 5.7% in the anisotropic approximation of atomic displacements using 2577 independent reflections with F > 3(F). The unit-cell parameters are: a = 14.277(1), c = 30.400(1) Å, V = 5328.7(1) Å3; the space group is R-3m. The idealized formula of the mineral is (Z = 3): Na14Ca6Zr3[Na2(Fe,Mn)][Si26O72](OH)2(H2O1.0Cl0.6S2-0.5)(OH,H2O)2.5. Distribution of cations in the M2 micro-region is established: Fe in the flat-square coordination, Mn in the square pyramid and Na in the seven-vertex polyhedron. A comparative analysis of crystal chemical features of eudialyte М2Na-analogue samples from the Khibiny-Lovozero alkaline complex and Ilimaussaq alkaline pluton, Greenland is given. The mechanism of blocky isomorphism with the replacement of IVFe2+ with VIINa in the M2 micro-region is discussed. IR spectra of the М2Na-dominant eudialyte analogue are given: essentially hydrated sample (Na,H3O,H2O)15Ca6Zr3[Na2Fe][Si26O72](OH)2Cl∙2H2O from Ilimaussaq, less hydrated М2Zr-bearing sample (Na,H3O)13(Ca4Mn2)Zr3(Na2Zr)[Si26O72](OH)2Cl∙H2O from Lovozero and low-hydrated sample Na14Ca6Zr3[Na2(Fe,Mn)][Si26O72](OH)2Cl(OH,H2O)3 from Khibiny studied in this work.

A new tetragonal structure type for Li2B2C

The ternary dilithium diboron carbide, Li2B2C (tetragonal, space groupP\overline{4}m2,tP10), crystallizes as a new structure type and consists of structural fragments which are typical for structures of elemental lithium and boron or binary borocarbide B13C2. The symmetries of the occupied sites are .m. and 2mm. for the B and C atoms, and \overline{4}m2 and 2mm. for the Li atoms. The coordination polyhedra around the Li atoms are cuboctahedra and 15-vertex distorted pseudo-Frank–Kasper polyhedra. The environment of the B atom is a ten-vertex polyhedron. The nearest neighbours of the C atom are two B atoms, and this group is surrounded by a deformed cuboctahedron with one centred lateral facet. Electronic structure calculations using the TB–LMTO–ASA method reveal strong B...C and B...B interactions.

The Ce2Li0.39Ni1.61Si2structure as a new derivative of the AlB2family

A new quaternary dicerium lithium/nickel disilicide, Ce2Li0.39Ni1.61Si2, crystallizes as a new structure type of intermetallic compounds closely related to the AlB2family. The crystal–chemical interrelationships between parent AlB2-type, BaLiSi, ZrBeSi and the title compound are discussed using the Bärnighausen formalism. Two Ce atoms occupy sites of 3m. symmetry. The remainder,i.e.Ni, mixed Ni/Li and Si atoms, occupy sites of \overline{6}m2 symmetry. The environment of the Ce atom is an 18-vertex polyhedron and the Ni, Ni/Li and Si atoms are enclosed in tricapped trigonal prisms. The title structure can be assigned to class No. 10 (trigonal prism and its derivatives) according to the Krypyakevich classification scheme [Krypyakevich (1977). InStructure Types of Intermetallic Compounds. Moscow: Nauka]. The electronic structure of the title compound was calculated using the tight-binding linear muffin-tin orbital method in the atomic spheres approximation (TB-LMTO-ASA). Metallic bonding is dominant in this compound. The strongest interactions are Ni—Si and Ce—Si.

The New Ternary Silicide ErCo3Si2

The new ternary silicide ErCo3Si2 adopts the ErRh3Si2 structure type (space group Imma, Pearson code oI24, Z = 4, a = 6:950(1), b = 9:020(2), c = 5:230(1) Å, R1 = 0:0565, wR2 = 0:0355, 253 F2 values, 23 variables). It is a deformation derivative of the CeCo3B2 structure type. The coordination of the Er atom shows a normal 20- vertex polyhedron [Er(Si6Co12Er2)]. The two similar coordination polyhedra of Co are a distorted icosahedron [Co(Si4Co4Er4)], and a distorted icosahedron with one capped face [Co(Si4Co5Er4)]. The Si atom is surrounded by the polyhedron [Si(Co6Si2Er3)]

Tm2.22Co6Sn20and TmLi2Co6Sn20stannides as disordered derivatives of the Cr23C6structure type

A new ternary dithulium hexacobalt icosastannide, Tm2.22Co6Sn20, and a new quaternary thulium dilithium hexacobalt icosastannide, TmLi2Co6Sn20, crystallize as disordered variants of the binary cubic Cr23C6structure type (cF116). 48 Sn atoms occupy sites ofm.m2 symmetry, 32 Sn atoms sites of .3msymmetry, 24 Co atoms sites of 4m.msymmetry, eight Li (or Tm in the case of the ternary phase) atoms sites of \overline{4} 3m symmetry and four Tm atoms sites of m \overline{3} m symmetry. The environment of one Tm atom is an 18-vertex polyhedron and that of the second Tm (or Li) atom is a 16-vertex polyhedron. Tetragonal antiprismatic coordination is observed for the Co atoms. Two Sn atoms are enclosed in a heavily deformed bicapped hexagonal prism and a monocapped hexagonal prism, respectively, and the environment of the third Sn atom is a 12-vertex polyhedron. The electronic structures of both title compounds were calculated using the tight-binding linear muffin-tin orbital method in the atomic spheres approximation (TB–LMTO–ASA). Metallic bonding is dominant in these compounds, but the presence of Sn—Sn covalent dumbbells is also observed.

Crystal and electronic structures of La2LiGe6−x(x= 0.21) and La2LiGe4Si2

The synthesis and characterization of a new ternary dilanthanum lithium hexagermanide, La2LiGe6−x(x= 0.21), belonging to the Pr2LiGe6structure type, and a quaternary dilanthanum lithium tetragermanium disilicide, La2LiGe4Si2, which crystallizes as an ordered variant of this type, are reported. In both structures, Li is on a site ofmmmsymmetry. All other atoms are on sites ofm2msymmetry. These structures are new representatives of a homologous linear structure series based on structural fragments of the AlB2, CaF2and ZrSi2structure types. The observed 17-vertex polyhedra are typical for La atoms and the environment of the Li atom is cubic. Two Ge atoms are enclosed in a tetragonal prism with one added atom (nine-vertex polyhedron). The trigonal prismatic coordination is typical for Ge or Si atoms. The metallic nature of the bonding is indicated by the interatomic distances and electronic structure calculations.

GENERALIZING MONOTONICITY: ON RECOGNIZING SPECIAL CLASSES OF POLYGONS AND POLYHEDRA

A simple polyhedron is weakly-monotonic in direction [Formula: see text] provided that the intersection of the polyhedron and any plane with normal [Formula: see text] is simply-connected (i.e. empty, a point, a line-segment or a simple polygon). Furthermore, if the intersection is a convex set, then the polyhedron is said to be weakly-monotonic in the convex sense. Toussaint10 introduced these types of polyhedra as generalizations of the 2-dimensional notion of monotonicity. We study the following recognition problems: Given a simple n-vertex polyhedron in 3-dimensions, we present an O(n log n) time algorithm to determine if there exists a direction [Formula: see text] such that when sweeping over the polyhedron with a plane in direction [Formula: see text], the cross-section (or intersection) is a convex set. If we allow multiple convex polygons in the cross-section as opposed to a single convex polygon, then we provide a linear-time recognition algorithm. For simply-connected cross-sections (i.e. the cross-section is empty, a point, a line-segment or a simple polygon), we derive an O(n2) time recognition algorithm to determine if a direction [Formula: see text] exists. We then study variations of monotonicity in 2-dimensions, i.e. for simple polygons. Given a simple n-vertex polygon P, we can determine whether or not a line ℓ can be swept over P in a continuous manner but with varying direction, such that any position of ℓ intersects P in at most two edges. We study two variants of the problem: one where the line is allowed to sweep over a portion of the polygon multiple times and one where it can sweep any portion of the polygon only once. Although the latter problem is slightly more complicated than the former since the line movements are restricted, our solutions to both problems run in O(n2) time.

Polyhedral organoiridaazaborane chemistry. The preparation of the eleven-vertex nido compound [9-Cl-8-(η5-C5Me5)-nido-8,7-IrNHB9H10] and its characterization by single-crystal X-ray diffraction analysis and nuclear magnetic resonance spectroscopy

Reaction between nido-6-HNB9H11 (from[9-(MeNC)-arachno-6-HNB9H11] and [(η5-C5Me5).IrCl2]2 in the presence of N,N,N’,N’-tetramethylnaphthalene-1,8-diamine) gives [9-Cl-8-(η5-C5Me5)-nido-8,7-IrNHB9H10] as a yellow crystalline solid in 40% yield. Crystals are triclinic, space group P1, Z = 2, with a = 825.5(1), b = 986.4(2), c = 1 158.7(2) pm, α = 95.12(1), β = 91.00(1), γ = 111.90(1)°. The molecular structure is based on an open-faced nido {IrNB9} eleven-vertex polyhedron with the iridium and nitrogen atoms in adjacent positions in the open face. Nuclear magnetic single and multiple resonance spectroscopy assigns the cluster 11B and 1H resonances, and suggests strong electronic similarities to the sulphur-containing analogue [9-Cl-8-(η5-C5Me5)-nido-8,7-IrSB9H10].