Kuniaki Kihara

The crystal structure of low melanophlogite

Abstract The crystal structure of the low temperature form of natural melanophlogite, 46SiO2 · 6M14 · 2M12 (M14 = N2, CO2; M12 = CH4, N2), was determined using single-crystal X-ray diffraction data at room temperature. The structure is tetragonal with space group P42/nbc and unit cell a = 26.818(2) and c = 13.365(1) Å, which is the (2 × 2 × 1) superstructure of high-temperature cubic melanophlogite and includes four formula units. The structure with 335 variable parameters including anisotropic temperature factors (or atomic displacement factors) was refined to R = 0.0288 for 2706 observed reflections. The main silica framework consists of nearly regular SiO4 tetrahedra forming large internal voids represented by distorted tetrakaidecahedra and pentagondodecahedra, which accommodate CO2 or N2 and CH4 or N2 guest molecules, respectively. This low temperature form is a displacive variant of the cubic high-temperature form. The mean bond length is 1.588(4) Å for Si-O, and the bond angles for Si-O-Si are distributed over a large range from about 145 to 171° with a mean value of 159.4(3)°. The thermal vibrations of Si are nearly isotropic with amplitudes approximately equal to the average mean square displacement of 0.0119(4) Å2. The thermal vibrations of the O atoms are highly anisotropic with a wide range of mean square displacements. There is a positive correlation between the Si-O-Si bond angles and the mean-square displacements of the O atoms.

High-order thermal-motion tensor analyses of tridymite

Two least-squares methods based on the Gram-Charlier expansion and the Edgeworth expansion were applied to a test structure to examine their usefulness in analysing multimodal density distribution of atoms. The Gram-Charlier expansion was more successful to reproduce the test structure than the Edgeworth expansion. The least-squares method based on the Gram-Charlier expansion was applied to the high temperature forms of tridymite to analyse density distribution of Ο atoms. The obtained density distribution of Ο was concave and nearly concentric at both 693 and 733 Κ (hexagonal), but clearly bimodal, at 493 Κ (orthorhombic), with the mean positions of low densities.

Structural analysis of AgxCu1−xI (0≤x≤0.5) by solid 63Cu NMR and X-ray diffraction methods

Abstract 63 Cu NMR and X-ray diffraction methods have been used to investigate the temperature dependence of the nuclear chemical shifts and the diffraction patterns, respectively, for mixed crystal Ag x Cu 1− x I (0 x T d CuI 4 3− and O h CuI 6 5− species, as obtained by the finite perturbation theory in an ab initio Gaussian 94 program using double-ζ basis set for Cu and I atoms. In the case of the nonlinear temperature dependence of the shift, we introduce the shift model as proposed by Negita and coworkers: The shift is also due to the cation which moves to the qausi-stable interstitial octahedral sites.

Lattice dynamical calculations of anisotropic temperature factors of atoms in quartz, and the structure of β-quartz

Temperature factors for oxygen and silicon atoms in β-quartz were calculated on a Born-von Karman lattice dynamical model of an ordered structure. The calculated thermal ellipsoids were in excellent agreements with those of the previous structure refinements of the order model, for both magnitudes and orientations of the principal axes. The temperature factors are contributed mainly by the soft optic modes in Γ-M and the lowest-lying acoustic modes along Γ-A, which are also strongly temperature-dependent. The cusp-shaped temperature dependence of mean square displacements, 〈u2〉, of oxygen atom, observed previously around the α-β transition, are resulted from the softening of these modes. The temperature-dependent modes in Γ-A were also found to cause diffuse scattering extending along ±c* of the fourth hexagon of the hk0 reciprocal lattice plane. The negative expansion known in β-quartz were interpreted in terms of asymmetrical forces exerting on oxygen atoms in Si-O-Si bending modes. In β-quartz, librational motions of oxygen atoms around Si-Si lines with large amplitudes, whose center is just on the β-position of high symmetry, must be possible under the condition that bending tetrahedral O-Si-O angles is energetically more favourable than compressing or stretching Si-O bonds.

Disorder and successive structure transitions in the tridymite forms of SiO2

Disorder models of oxygen positions in P63/ mmc, C2221 and P212121 tridymites were given in applying geometrical and lattice dynamical calculations. Sixmembered rings of rigid SiO4 units are all collapsed in these forms; with silicon atoms fixed, SiO4 units can take six different orientations in forming tridymite frameworks in both the P63/mmc and C2221 forms, and three orientations in the P212121 form. Atomic distances and angles obtained from the distance least-squares method are about equal for the three forms: 〈Si-O〉 (mean Si-O) = 1.611 Å, 〈O-O〉 = 2.629 Å, and 〈Si-O-Si〉 = 147°. Domain formation models are given for the three forms.The tridymite framework structures may possibly undergo lattice vibrations with low frequencies in two kinds of pair-wise rotational modes of SiO4 units joined by the apical oxygen atoms, at the Γ-point: one is around 〈100〉 (or 〈210〉 for the hexagonal case), and the other is around 〈010〉. As temperature approaches the hexagonal-orthorhombic transition from below, the rotational mode around 〈100〉 remarkably softens at the Γ-point. The behavior of the atoms at the hexagonal-orthorhombic transition is explained in terms of a coupled softening of the two rotational modes of neighboring local domains in different orientations.

Refinements of Ag3AsSe3 based on high-order thermal-motion tensors

Ag3AsSe3; rhombohedral, R3c, ahci = 11.299(2), cheiI = 8.759(3) Ä, c/α = 0.7752, Ζ = 6, is composed of the trigonal pyramids of AsSe3 and Ag atoms, which weakly link the AsSe3 groups. High-order thermal-motion tensor analyses of Ag3AsSe3, based on the Gram-Charlier expansion, have shown that the density distribution of Ag is well expressed by a combination of the first-, the secondand the third-order tensors. The density distribution of Ag is unimodal but strongly distorted from that expected for harmonic vibrations: it occupies a platy region, and tails off long toward three neighboring interstitial sites, each of which is located at about equal distances from the three nearest Ag atoms. The thermal vibrations of other atoms are of much smaller amplitudes than those of Ag, and can be well approximated by harmonic motions.

An application of the Patterson method to the determination of the structures composed of two kinds of layers with approximately equal thickness

The Patterson method is applied to the determination of the structures composed of two kinds of layers with approximately equal thickness. The order of two different layers is easily determined by getting a set of the numbers of pairs for the same kind layers separated by every numbers in a unit cell. Examples in the system Bi—Te, Se and S, for instance, BiTe, Bi4(S, Se>3 and BieSea are given.