The role of hydrogen bonding in the incommensurate modulation of myo-inositol camphor ketal

myo-Inositol-2,3-D-camphor ketal crystallizes as an incommensurate structure with the C2(0σ2½) superspace group symmetry [σ2 = 0.1486 (3) at 100 K]. The bornane and myo-inositol moieties aggregate in distinct layers extending parallel to (001). The myo-inositol rings are connected by a complex hydrogen-bonding network extending in two dimensions, which is disordered in the basic structure and (mostly) ordered in the actual modulated structure. The domains of definition of the H atoms in internal space were derived by chemical reasoning and modeled with crenel functions. By tracing the hydrogen bonding, distinct chains, which are periodic in the [100] direction, are identified. These chains possess one of two possible orientations with respect to the hydrogen bonding. The incommensurate modulation is characterized by a non-periodic succession of the two chain orientations in the [010] direction. On heating, the σ2-component of the modulation wave vector decreases from σ2 = 0.1486 (3) at 100 K to σ2 = 0.1405 (6) at 430 K, which means that the periodicity of the modulation wave increases. No order–disorder phase transition was evidenced up to the melting point (with decomposition).

Spectroscopic and Crystal-Chemical Features of Sodalite-Group Minerals from Gem Lazurite Deposits

Five samples of differently colored sodalite-group minerals from gem lazurite deposits were studied by means of electron microprobe and wet chemical analyses, infrared, Raman, electron spin resonance (ESR) and UV-Visible spectroscopy, and X-ray diffraction. Various extra-framework components (SO42−, S2− and Cl− anions, S3•−, S2•− and SO3•− radical anions, H2O, CO2, COS, cis- as well as trans- or gauche-S4 neutral molecules have been identified. It is shown that S3•− and S4 are the main blue and purple chromophores, respectively, whereas the S2•− yellow chromophore and SO3•− blue chromophore play a subordinate role. X-ray diffraction patterns of all samples of sodalite-group minerals from lazurite deposits studied in this work contain superstructure reflections which indicate different kinds of incommensurate modulation of the structures.

Magic-angle semimetals

Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

Structure solution of incommensurately modulated La6MnSb15

La6MnSb15 is synthesized from the constituent elements in quartz ampoules at 973 K. Crucial for the quality of the obtained single-crystals was a slow cooling rate of 2 K h−1. The crystal structure of La6MnSb15 was investigated via single-crystal X-ray diffraction experiments, leading to the observation of superstructure reflections as described in the literature. Two crystals, with refined compositions of La6MnSb15 (1) and La6MnSb14.66(1) (2) were obtained from different batches, yet both showed an orthorhombic body centered unit cell as well as additional reflections at q1 = (0,0,0.258(1)) for crystal (1) and q1 = (0,0,0.244(1)) for crystal (2). The structure could be solved and refined in superspace group Immm(00γ)000 (71.1.12.1), leading to a concise structural model. Due to γ not being exactly 1/4, an incommensurate modulation is present in the presented compounds. In order to describe the structural influence of the modulation in 3D, different approximants were chosen and the differences compared. Additionally, the temperature dependence of the electrical resistivity was investigated, indicating a metallic behavior of the title compound. This result is in line with the retro-theoretical investigation in the literature that counts excess electrons when using the Zintl–Klemm–Busmann concept. 121Sb Mößbauer-spectroscopic investigations at 78 K show a broad signal with an average isomeric shift of δ ∼ −10 mm s−1, in line with a negatively charged Sb species. The massive line broadening can be explained by the large number of crystallographic antimony sites in the basic structure and the approximant.

Incommensurately Modulated Crystal Structure and Photoluminescence Properties of Eu2O3- and P2O5-Doped Ca2SiO4 Phosphor

We prepared four types of Eu2O3- and P2O5-doped Ca2SiO4 phosphors with different phase compositions but identical chemical composition, the chemical formula of which was (Ca1.950Eu3+0.013☐0.037)(Si0.940P0.060)O4 (☐ denotes vacancies in Ca sites). One of the phosphors was composed exclusively of the incommensurate (IC) phase with superspace group Pnma(0β0)00s and basic unit-cell dimensions of a = 0.68004(2) nm, b = 0.54481(2) nm, and c = 0.93956(3) nm (Z = 4). The crystal structure was made up of four types of β-Ca2SiO4-related layers with an interlayer. The incommensurate modulation with wavelength of 4.110 × b was induced by the long-range stacking order of these layers. When increasing the relative amount of the IC-phase with respect to the coexisting β-phase, the red light emission intensity, under excitation at 394 nm, steadily decreased to reach the minimum, at which the specimen was composed exclusively of the IC-phase. The coordination environments of Eu3+ ion in the crystal structures of β- and IC-phases might be closely related to the photoluminescence intensities of the phosphors.

Incommensurately modulated crystal structure of flamite – natural analogue of \alpha _{\rm H}^{\prime}-Ca2SiO4

Crystal structures of unquenchable high-temperature polymorphs of Ca2SiO4, important in cement chemistry, have eluded single-crystal X-ray analysis. However, the problem may be addressed by studying chemically stabilized Ca2SiO4 polymorphs at ambient temperature. Here an incommensurately modulated crystal structure of flamite [Pnma(0β0)00s, q = 0.2728 (2)b*, a = 6.8588 (2) Å, b = 5.4301 (2) Å, c = 9.4052 (3) Å] is described. It is a mineral analogue of orthorhombic \alpha _{\rm H}^{\prime}-Ca2SiO4 (stable between 1160 and 1425°C), naturally stabilized by substitution with phosphorus. The incommensurate modulation results from wave-like displacement of cation sites accompanied by tilting of (Si,P)O4 tetrahedra and variation of the Na/(Ca + Na + K) ratio along the modulation period. The studied sample from Hatrurim Basin (Negev Desert, Israel) with composition (Ca1.75K0.12Na0.12)1.99(Si0.74P0.26)1.00O4 also demonstrates pseudomerohedral cyclic twinning around the a axis, which results from pseudohexagonal topology of the crystal structure and complicates the indexing of X-ray diffraction data.

Twinning and incommensurate modulation in baumoite, Ba0.5[(UO2)3O8Mo2(OH)3](H2O)~3, the first natural Ba uranyl molybdate

ABSTRACTBaumoite, Ba0.5[(UO2)3O8Mo2(OH)3](H2O)~3, is a new mineral found near Radium Hill, South Australia, where it occurs in a granite matrix associated with baryte, metatorbernite, phurcalite and kaolinite. Baumoite forms thin crusts of yellow to orange–yellow tabular to prismatic crystals. The mineral is translucent with a vitreous lustre and pale yellow streak. Crystals are brittle, the fracture is uneven and show one excellent cleavage. The Mohs hardness is ~2½. The calculated density is 4.61 g/cm3. Optically, baumoite crystals are biaxial (–), with α = 1.716(4), β = 1.761(4), γ = 1.767(4) (white light); and 2Vcalc= 42.2°. Electron microprobe analyses gave the empirical formula Ba0.87Ca0.03Al0.04U2.97Mo2.02P0.03O22H11.99, based on 22 O atoms per formula unit. The eight strongest lines in the powder X-ray diffraction pattern are [dobsÅ (I) (hkl)]: 9.175(39)(12${\bar 1}$), 7.450(100)(020), 3.554(20)(221), 3.365(31)(004, 202), 3.255(31)(123, 30${\bar 2}$), 3.209(28)(12${\bar 4}$), 3.067(33)(30${\bar 3}$, 222, 32${\bar 2}$) and 2.977(20)(142). Single-crystal X-ray studies (R1= 5.85% for 1892 main reflections) indicate that baumoite is monoclinic, superspace groupX2/m(a0g)0swithX= (0,½,0,½), with unit-cell parameters:a= 9.8337(3),b= 15.0436(5),c= 14.2055(6) Å, β = 108.978(3)°,V= 1987.25(13) Å3andZ= 4. The crystal structure is twinned and incommensurately modulated and is based upon sheets of U6+and Mo6+polyhedra of unique topology. Four independent cationic sites partially occupied by Ba atoms are located between the sheets, together with H2O molecules.