Face-sharing Tetrahedra Research Articles

Atomically precise inorganic helices with a programmable irrational twist.

Helicity in solids often arises from the precise ordering of cooperative intra- and intermolecular interactions unique to natural, organic or molecular systems. This exclusivity limited the realization of helicity and its ensuing properties in dense inorganic solids. Here we report that Ga atoms in GaSeI, a representative III-VI-VII one-dimensional (1D) van der Waals crystal, manifest the rare Boerdijk-Coxeter helix motif. This motif is a non-repeating geometric pattern characterized by 1D face-sharing tetrahedra whose adjacent vertices are rotated by an irrational angle. Using InSeI and GaSeI, we show that the modularity of 1D van der Waals lattices accommodates the systematic twisting of a periodic tetrahelix with a 41 screw axis in InSeI to an infinitely extending Boerdijk-Coxeter helix in GaSeI. GaSeI crystals are non-centrosymmetric, optically active and exfoliable to a single chain. These results present a materials platform towards understanding the origin and physical manifestation of aperiodic helicity in low-dimensional solids.

The crystal structures and magnetic properties of YbMg0.75In1.25 and Yb6Mg6.41In5.59

Abstract The quasi-binary system YbMg2-YbIn2 was studied around the equiatomic composition. In contrast to the ordered rare earth (RE) phases REMgIn (ZrNiAl type), ytterbium forms phases with different structures and pronounced Mg/In mixing (M sites). The structures of YbMg0.75In1.25 (CaLiSn type, P3m1, a = 501.95(7), c = 1087.3(2) pm, wR2 = 0.0490, 790 F 2 values, 32 variables) and Yb6Mg6.41In5.59 (Yb6Ir5Ga7 type, P63/mcm, a = 1060.77(14), c = 970.27(16) pm, wR2 = 0.0484, 701 F 2 values, 26 variables) were refined from single-crystal X-ray diffractometer data. YbMg0.75In1.25 is an AlB2 superstructure with a tripling of the subcell. The magnesium and indium atoms form three differently puckered layers of M 6 hexagons. The Yb6Mg6.41In5.59 structure is derived from the hexagonal Laves phase YbMg2 (MgZn2 type, P63/mmc). A klassengleiche symmetry reduction leads to four crystallographically independent M sites for the rows of corner- and face-sharing tetrahedra which allow a composition close to the equiatomic one. The M–M distances in both structures cover the broad range from 289 to 331 pm, comparable to the sums of the covalent radii. Temperature dependent magnetic susceptibility studies of the polycrystalline YbMg0.75In1.25 and Yb12Mg13In11 samples indicate Pauli paramagnetism with room temperature values of 2.8(1) × 10−3 emu mol−1 (YbMg0.75In1.25) and 5.2(1) × 10−3 emu mol−1 (Yb12Mg13In11).

Stuffed Rare-Earth Garnets.

We report the synthesis and magnetic characterization of stuffed rare-earth gallium garnets, RE3+xGa5-xO12 (RE = Lu, Yb, Er, Dy, Gd), for x up to 0.5. The excess rare-earth ions partly fill the octahedral sites normally fully occupied by Ga3+, forming disordered pairs of corner-shared face-sharing magnetic tetrahedra. The Curie-Weiss constants and observed effective moments per rare-earth are smaller than are seen for the unstuffed gallium garnets. No significant change in the field-dependent magnetization is observed but missing entropy is seen when integrating the heat capacity down to 0.5 K.

Modular Principle for Complex Disordered Tetrahedral Frameworks in Quenched High-Pressure Phases of Phosphorus Oxide Nitrides.

The crystal structures of the new phosphorus oxide nitrides P40 O31 N46 and P74 O59 N84 , which were synthesized from amorphous phosphorus oxide nitride imide, exhibit complex frameworks built up from P(O,N)4 tetrahedra. The latter form various chain-like building units with various degrees of branching. These modular units can be combined and arranged in different ways, which leads to closely related structures and several disordered configurations in each compound. As the material was obtained by high-pressure high-temperature synthesis, the disorder is most likely a consequence of quenching a high-pressure phase with P(O,N)5 trigonal bipyramids. Under ambient conditions, P atoms are expected to relax by moving to the centers of the face-sharing tetrahedra that constitute the bipyramid. Diffraction patterns acquired with microfocused synchrotron radiation reveal that domains of both compounds are intergrown with H3 P8 O8 N9 , whose tetrahedral framework represents a cutout of the structures of both P40 O31 N46 and P74 O59 N84 . Powder diffraction patterns do not indicate any further phases.

Mg2MnGa3 – An orthorhombically distorted superstructure variant of the hexagonal Laves phase MgZn2

Abstract The Laves phase Mg2MnGa3 was synthesized from the elements by arc-melting and subsequent annealing in a silica ampoule at T = 670 K. The structure of Mg2MnGa3 was refined from single-crystal X-ray diffractometer data: URe2 type, Cmcm, a = 543.24(1), b = 869.59(3), c = 858.58(2) pm, wR2 = 0.0556, 273 F 2 values and 24 variables. The manganese and gallium atoms form a three-dimensional network of corner- and face-sharing MnGa3 tetrahedra that derive as a ternary ordering variant from the hexagonal Laves phase MgZn2. The structures of the distortion and coloring variants, i.e., MgZn2, URe2, Mg2Cu3Si and Mg2MnGa3 are discussed on the basis of a Bärnighausen tree. The electronic structure calculation data indicate that in addition to the metallic type of bonding an additional covalent interaction appears between the Ga–Ga and Mn–Ga atoms.

Mechanistic Origin of Superionic Lithium Diffusion in Anion-Disordered Li6PS5 X Argyrodites.

The rational development of fast-ion-conducting solid electrolytes for all-solid-state lithium-ion batteries requires understanding the key structural and chemical principles that give some materials their exceptional ionic conductivities. For the lithium argyrodites Li6PS5X (X = Cl, Br, or I), the choice of the halide, X, strongly affects the ionic conductivity, giving room-temperature ionic conductivities for X = {Cl,Br} that are ×103 higher than for X = I. This variation has been attributed to differing degrees of S/X anion disorder. For X = {Cl,Br}, the S/X anions are substitutionally disordered, while for X = I, the anion substructure is fully ordered. To better understand the role of substitutional anion disorder in enabling fast lithium-ion transport, we have performed a first-principles molecular dynamics study of Li6PS5I and Li6PS5Cl with varying amounts of S/X anion-site disorder. By considering the S/X anions as a tetrahedrally close-packed substructure, we identify three partially occupied lithium sites that define a contiguous three-dimensional network of face-sharing tetrahedra. The active lithium-ion diffusion pathways within this network are found to depend on the S/X anion configuration. For anion-disordered systems, the active site–site pathways give a percolating three-dimensional diffusion network; whereas for anion-ordered systems, critical site–site pathways are inactive, giving a disconnected diffusion network with lithium motion restricted to local orbits around S positions. Analysis of the lithium substructure and dynamics in terms of the lithium coordination around each sulfur site highlights a mechanistic link between substitutional anion disorder and lithium disorder. In anion-ordered systems, the lithium ions are pseudo-ordered, with preferential 6-fold coordination of sulfur sites. Long-ranged lithium diffusion would disrupt this SLi6 pseudo-ordering, and is, therefore, disfavored. In anion-disordered systems, the pseudo-ordered 6-fold S–Li coordination is frustrated because of Li–Li Coulombic repulsion. Lithium positions become disordered, giving a range of S–Li coordination environments. Long-ranged lithium diffusion is now possible with no net change in S–Li coordination numbers. This gives rise to superionic lithium transport in the anion-disordered systems, effected by a concerted string-like diffusion mechanism.

Osmium and magnesium: structural segregation in the rare earth-rich intermetallics RE 4OsMg (RE=La–Nd, Sm) and RE 9 TMg4 (RE=Gd, Tb)

Abstract Ternary rare earth metal-rich intermetallic phases containing osmium and magnesium were obtained by induction melting of the elements in sealed niobium ampoules under argon followed by annealing in muffle furnaces. The large rare earth elements form the series of Gd4RhIn-type (F4̅3m) intermetallics RE 4OsMg with RE = La–Nd and Sm, while the smaller rare earth metals gadolinium and terbium form the Y9CoMg4-type (P63/mmc) phases Gd9OsMg4 and Tb9OsMg4. All samples were characterized by X-ray powder diffraction (Guinier technique). The structures of Ce4Os0.973Mg1.027 (a = 1406.54(7) pm, wR2 = 0.0478), Nd4Os0.978Mg1.022 (a = 1402.00(7) pm, wR2 = 0.0463), Sm4Os0.920Mg1.080 (a = 1387.33(5) pm, wR2 = 0.0378) and Gd9OsMg4 (a = 971.01(5), c = 980.43(5) pm, wR2 = 0.0494) were refined from single-crystal X-ray diffractometer data. The three RE 4OsMg phases show small degrees of Os/Mg mixing, as is frequently observed for Rh/In in Gd4RhIn-type intermetallics. The basic building units in both structures are osmium-centered RE 6 trigonal prisms that are condensed with empty RE 6 octahedra. The magnesium atoms in both types build Mg4 tetrahedra. The latter are isolated (312 pm Mg–Mg in Ce4OsMg) and incorporated within the three-dimensional network of prisms and octahedra in the RE 4OsMg phases while one observes rows of corner- and face-sharing tetrahedra in Gd9OsMg4 (305 and 314 pm Mg–Mg). In both structure types direct Os–Mg bonding is not observed.

Crystallization and arrest mechanisms of model colloids.

We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong interactions. Arrested states are characterized by the formation of networks of face-sharing tetrahedra that can be detected by a local common neighbor analysis.

Lithium Argyrodites with Phosphorus and Arsenic: Order and Disorder of Lithium Atoms, Crystal Chemistry, and Phase Transitions

Crystal chemical data of high- (HT) and low-temperature (LT) modifications of lithium argyrodites with the compositions Li(7)PCh(6) (Ch=S, Se), Li(6)PCh(5)X (X=Cl, Br, I), Li(6)AsS(5)Br, and Li(6)AsCh(5)I (Ch=S, Se) based on single-crystal, powder X-ray (113 K<T<503 K) and neutron measurements (5 K<T<293 K) are presented. In the HT modifications, the Li atoms are strongly disordered over a fraction of the available tetrahedral holes, whereas in the LT modifications they occupy ordered crystallographic positions with a pronounced site preference that is analysed on a crystal chemical basis. The Ch/X partial structures remain nearly unchanged upon the reversible phase transitions. Crystal chemical and crystallographic relations between HT and LT modifications based on the Frank-Kasper model of tetrahedral close packing are discussed. X-ray single-crystal data for HT-Li(6)PS(5)I show the electron density of the disordered Li to be smeared out over an extended region preferably inside face-sharing double tetrahedra. A series of temperature-dependent powder neutron data for Li(6)PS(5)I gives clear evidence for an HT/LT phase transition at approximately 175 K with an ordering of the Li atoms in different polyhedra with coordination numbers between three and four.

A new rare earth disilicate (REE2Si2O7; REE = Dy, Tm, Lu; type-L): Evidence for non-quenchable 10 GPa polymorph with silicon in fivefold trigonal bipyramidal coordination?

A new structure type (L) is reported for disilicates of the middle and heavy rare earth elements (REE) quenched from 10 GPa, 1600-1700 °C. Crystal data are: triclinic, space group P1̅ , Z = 6; Dy2Si2O7: a = 6.5971(3), b = 6.6504(2), c = 18.0582(6) Å, α = 83.791(2), β = 88.653(2), γ = 88.498(2)°, V = 787.2 Å3, and Dx = 6.242 g/cm3; Tm2Si2O7: a = 6.5499(2), b = 6.5876(2), c = 17.8916(7) Å, α = 83.828(1), β = 88.368(1), γ = 88.152(2)°, V = 766.9 Å3, and Dx = 6.574 g/cm3; Lu2Si2O7: a = 6.5240(2), b = 6.5553(2), c = 17.7909(6) Å, α = 83.977(2), β = 88.074(2), γ = 87.846(2)°, V = 755.8 Å3, and Dx = 6.830 g/cm3. The type-L structure comprises linear trisilicate [Si3O10]8- and orthosilicate [SiO4]4- ions cross linked by REE3+ in one sevenfold and five eightfold coordinated positions (to 3.0 Å), and is assembled from alternating (001) strips of the type-B structure of REE2Si2O7 and a sheared structure containing structural elements found in the type-B structure but with Si distributed with 50% occupancy over two face-sharing tetrahedra. The geometry of these half-occupied tetrahedra is consistent with decomposition of a SiO5 trigonal bipyramid during quenching of the pressure.

On the structure of Li3Ti2(PO4)3

The structure of the Nasicon-type phase Li3Ti2(PO4)3, obtained by chemical lithiation of LiTi2(PO4)3, has been characterised using neutron diffraction for the long range structure and 7Li NMR for more local information. The lithium atoms were precisely located from the neutron diffraction data, using nuclear difference Fourier maps. The lithium ions, which were known to be in the large M2 cavity, occupy two M3 and M′3 subsites (distorted tetrahedra) with occupation factors of 2/3 and 1/3, respectively. From these two intermediate sites, it was shown that the diffusion pathway between two M1 sites in these Nasicon-type structures consists of a set of seven face-sharing tetrahedra. A variable temperature 7Li MAS NMR study showed a set of signals due to a distribution of environments for a given Li+ ion, in terms of occupied or vacant M3/M′3 sites in its vicinity. Elevation of the temperature to 353 K leads to a reversible exchange of these signals, due to fast hopping of Li between the two sites within a given M2 cavity.

Cobalt Lithium Orthoborate, LiCoBO3

The title compound has been synthesized by a solid-state reaction. Its structure is isotypic with those of LiMgBO3, LiMnBO3 and LiZnBO3. CoII occupies statistically two close positions within the CoO5 trigonal bipyramids. These polyhedra share edges to form chains running along the [\overline{1}01] axis and are linked together, via corner sharing, by BO3 planar groups. The Li atoms occupy statistically the center of two face-sharing tetrahedra. Such pairs of tetrahedra share edges to form chains running along the c axis.

On the origin of second-peak splitting in the static structure factor of metallic glasses

It is proposed that the splitting of the second peak of the total static structure factor, S(k), of many metallic glasses is essentially the same feature as the indentation at kσ = (9/2)π in the function (sin k σ + α−1 sin kασ), caused by the coincidence of the fourth minimum of the second term with the third maximum of the first term when α ≈ 5/3. Together with the strong-weak relation of the split peak components of S(k), this feature indicates the splitting to be direct evidence for face-sharing of regular tetrahedra (α = 2√2/3) dominating the topological short range order; increasing the number of face-sharing tetrahedra in local structural units indeed increases the amount of peak splitting in S(k); a dense random packing of well defined identical structural units (DRPSU), with neighbouring units linked together by a shared icosahedron, is described in detail. The packing fraction in a homogeneous, isotropic 1078-atom model is 0.67, after static relaxation under a two-body Lennard-Jones potential.

(C6H5)4P][Cu3I4]—The First Compound with a Helical Chain of Face‐Sharing Tetrahedra as a Structural Element

Face-sharing tetrahedra arranged in a helix (idealized form shown below) mark the structure of the iodocuprate 1, which was obtained from Ph4PI, I2, and Cu. Five Cu positions were identified at room temperature; at lower temperatures only three (slow cooling) or four (rapid cooling) are occupied.

Rectilinear rods of face-sharing tetrahedra and the structure ofβ-Mn

Rectilinear rods of face-sharing tetrahedra and the structure of<i>β</i>-Mn

Rectilinear rods of face-sharing tetrahedra and the structure of β-Mn

Rectilinear rods of face-sharing tetrahedra and the structure of β-Mn

Crystal structure and electrical conductivity of the “one-dimensional solid electrolyte N, N-dimethylmorpholinium pentaiodotetraargentate

The new solid electrolyte N, N-dimethylmorpholinium pentaiodotetraargentate, [(CH 3)N(CH 2) 2-(CH 2) 2O]Ag 4I 5 (DMMAg 4I 5), has a crystal structure which allows the Ag + ions to move effectively in only one dimension. The channels for this motion result from the sharing of opposite faces of icosahedra, having iodides at their centers, forming infinite chains of icosahedra along thea axis. The joining of the icosahedra forms three more face-sharing tetrahedra at each junction, or a total of 23 tetrahedra per eight Ag + ions, which are distributed non-uniformly over the tetrahedral sites. The limited number of pathways for the Ag + ion diffusion leads to a low average conductivity, 1 × 10 −4 Ω −1 cm −1 and a high activation enthalpy, 0.35 eV. Crystals of DMMAg 4I 5 belong to space groupP2 12 12 1 (D 4 2) witha = 13.167(4), b = 23.437(3), c = 12.758(3)A˚; the unit cell contains eight formula units. The structure of dimethylmorpholinium iodide (DMMI) confirms the chair model for the DMM + ion. Crystals of DMMI belong to space groupP2 1m(C 2 2h), witha = 8.861(4), b = 8.020(2), c = 6.685(2)A˚, β = 101.07(3)°; each unit cell contains two formula units.

Some Helical Structures Generated by Reflexions

There has recently been a revival of interest in the helical structure built up as a column of face-sharing tetrahedra, because of possible applications in structural crystallography (Nelson 1983). This structure and its analogues in spaces of different dimensions are investigated here. It is shown that the only crystallographic cases are the structures in one- and two-dimensional space. For three and higher dimensional space the structures are all non-crystallographic. For the physically important case of three dimensions, this result is implicit in an early discussion by Coxeter (1969). Results obtained here include explicit formulae for the positions of all vertices of the simplexes for dimensions n = 1-4 and a demonstration that, for arbitrary n, the ratio of the translation component of the screw to the edge of the simplex is {6/ n(n+ I)(n+ 2)}1/2

Structural characterisation of [Au10Cl3(PCy2Ph)6](NO3)(Cy = cyclohexyl) and the development of a structural principle for high nuclearity gold clusters

[Au10Cl3(PCy2Ph)6](CO3) which has been synthesised in low yield from Au(NO3)(PCy2Ph) and NaBH4 has a toroidal geometry based on a hexagonal ring of edge- and face-sharing tetrahedra which share a common central vertex.

Spectroscopic investigation on the presence of OH in natural barrerite and in its collapsed phases

Barrerite, a zeolite with a stilbite-type framework, transforms on heating at 200–380° C and at 380–450° C into two new phases, called barrerite B and D respectively. After a few days barrerite B rehydrates to barrerite C. In the B and C heat-collapsed phases the aluminosilicate framework is interrupted by the statistical breaking of an oxygen bridge, giving rise to two partially occupied face-sharing tetrahedra. Near infrared (NIR) diffuse reflectance spectra show the absence of hydroxyls in natural barrerite and the presence of hydroxyls in its heat-collapsed phases. These results confirm the hypothesis that the fourth vertex of the tetrahedra generated from the breaking of the oxygen bridge is a hydroxyl. The presence of OH-bands in phase D suggests for this phase, as in the B and C phases, the presence of interrupted oxygen bridges.