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).

Магнитные фазовые переходы в несоизмеримую магнитную структуру в соединении FeGe-=SUB=-2-=/SUB=-

A symmetry analysis of possible magnetic structures in an incommensurate magnetic phase in FeGe_2 compound, resulted from phase transitions from the paramagnetic phase, was performed based on a phenomenological consideration. It is shown that two possible approaches to a such an analysis, the first of which uses the magnetic representation of the space group, and the second one is based on the expansion of the magnetic moment in basis functions of irreducible representations of the space group of the paramagnetic phase, yield the same results. Space group irreducible representations are determined, according to which the transition to an incommensurate structure can occur. The set of these representations appears identical in both approaches. Ginzburg–Landau functionals for analyzing the transitions according to these representations are written. A renormalization group analysis of the second-order phase transitions from the paramagnetic state to the incommensurate magnetic structure is performed. It is shown that a helical magnetic structure can arise in the incommensurate phase as a result of two second-order phase transitions at the transitions temperature.

Crystal chemistry of K-rich nepheline in nephelinite from Hamada, Shimane Prefecture, Japan

K-rich nepheline with a structural formula of A2B6T14T24T34T44O32 (Z = 1) within melilite–olivine nephelinite from Hamada, Shimane Prefecture, Japan, was investigated to clarify its crystal structure and to determine cation distributions in the A and B structural positions of structural channels and tetrahedral T1–T4 sites. The chemical formula of a single-crystal sample was (Na5.437K2.248Mg0.034Ca0.031)Σ7.750(Si8.332Al7.445Fe3+0.158Ti0.009Cr0.005)Σ15.949O32, which results in 65.2, 27.8, 2.1, 3.2 and 1.6 mol.% NaAlSiO4, KAlSiO4, NaFe3+SiO4, □Si2O4 and □0.5(Ca,Mg)0.5AlSiO4 end-member components, respectively, where □ is a vacancy. X-ray diffraction data of a single crystal with dimensions of 0.28 mm × 0.15 mm × 0.05 mm measured at 296 K indicate the space group P63. In the structural refinement, the R1 factor was reduced to 3.69% by taking twinning by merohedry into the refinement. The refinement accounted for 77.7% of the absolute structure and 22.3% of the a and b axes reversed absolute structure. The atomic populations determined in the A and B positions were 1.834 K + 0.166 □ and 5.705 Na + 0.198 K + 0.031 Ca + 0.034 Mg, respectively, implying the substitution of K for Na in the B position. The a and c dimensions are a = 10.0270(3) and c = 8.4027(3) Å. The average <A–O> and <B–O> distances are 3.009 and 2.65 Å, respectively. The substitution of K for Na in the B channel results in increased volume and bond-length distortion of the BO8 polyhedra, which then reduces distortion of the AO9 polyhedra. The average T–O distances indicate that the T1 and T4 sites are essentially filled with Al, whereas the T2 and T3 are filled with Si. Despite the deviation of the O1 oxygen from the triad axis and the combination of K+ ions and vacancies in the hexagonal channels, an incommensurate structure was not observed in the X-ray diffraction data or using the electron diffraction technique.

Low-temperature behaviour of K2Sc[Si2O6]F: determination of the lock-in phase and its relationships with fresnoite- and melilite-type compounds

K2Sc[Si2O6]F exhibits, at room temperature, a (3 + 2)-dimensional incommensurately modulated structure [a= 8.9878 (1),c= 8.2694 (2) Å,V= 668.01 (2) Å3; superspace groupP42/mnm(α,α,0)000s(−α,α,0)0000] with modulation wavevectorsq1= 0.2982 (4)(a* +b*) andq2= 0.2982 (4)(−a* +b*). Its low-temperature behaviour has been studied by single-crystal X-ray diffraction. Down to 45 K, the irrational component α of the modulation wavevectors is quite constant varying from 0.2982 (4) (RT), through 0.2955 (8) (120 K), 0.297 (1) (90 K), 0.298 (1) (75 K), to 0.299 (1) (45 K). At 25 K it approaches the commensurate value of one-third [i.e.0.332 (3)]: thus indicating that the incommensurate–commensurate phase transition takes place between 45 K and 25 K. The commensurate lock-in phase of K2Sc[Si2O6]F has been solved and refined with a 3 × 3 × 1 supercell compared with the tetragonal incommensurately modulated structure stable at room temperature. This corresponds to a 3 × 1 × 3 supercell in the pseudo-orthorhombic monoclinic setting of the low-temperature structure, space groupP2/m, with lattice parametersa= 26.786 (3),b= 8.245 (2)c= 26.824 (3) Å, β = 90.00 (1)°. The structure is a mixed tetrahedral–octahedral framework composed of chains of [ScO4F2] octahedra that are interconnected by [Si4O12] rings with K atoms in fourfold to ninefold coordination. Distorted [ScO4F2] octahedra are connected to distorted Si tetrahedra to form octagonal arrangements closely resembling those observed in the incommensurate structure of fresnoite- and melilite-type compounds.

Could incommensurability in sulfosalts be more common than thought? The case of meneghinite, CuPb13Sb7S24

The structure of meneghinite (CuPb13Sb7S24), from the Bottino mine in the Apuan Alps (Italy), has been solved and refined as an incommensurate structure in four-dimensional superspace. The structure is orthorhombic, superspace groupPnma(0β0)00s, cell parametersa =24.0549 (3),b =4.1291 (6),c =11.3361 (16) Å, modulation vectorq= 0.5433 (4)b*. The structure was refined from 6604 reflections to a finalR= 0.0479. The model includes modulation of both atomic positions and displacement parameters, as well as occupational waves. The driving forces stabilizing the modulated structure of meneghinite are linked to the occupation modulation of Cu and some of the Pb atoms. As a consequence of the Cu/[] and Pb/Sb modulations, three- to sevenfold coordinations of theMcations (Pb/Sb) occur in different parts of the structure. The almost bimodal distribution of the occupation of Cu/[] and Pb/Sb atM5 conforms with the coupled substitution Sb3++ [] → Pb2++ Cu+, thus corroborating the hypothesis deduced previously for the incorporation of copper in the meneghinite structure. The very small departure (∼0.54versus0.50) from the commensurate value of the modulation raises the question of whether other sulfosalts considered superstructures have been properly described, and, in this light, if incommensurate modulation in sulfosalts could be much more common than thought.