Shin-ichi Iwai

Structural analysis of anodic alumina films

Abstract Structures of amorphous anodic alumina films have been investigated by the X-ray radial distrubution function and the correlation method. The amorphous anodic alumina films are considered to contain AlO5 coordination polyhedra as well as AlO4 tetrahedra and AlO6 octahedra. Two types of conformation are taken into account by the correlation method; one (model A) is the conformation in which the above coordination polyhedra are arranged in a similar way to that found in the crystalline modifications of γ-Al2O3 within a short range of r A and the other (model B) is the conformation in which coordination polyhedra are randomly arranged. The final model formed by mixing these two conformations (model A and B) in 1 : 1 ratio describes quantitatively the observed scattering intensity curves of the amorphous anodic alumina films.

Structure of barium chlorapatite

BasCl(PO4) 3, hexagonal, P63/m, a = 10.284 (2), c = 7.651 (3) A, Z = 2. The crystals were grown by hydrothermal reaction of BaCI2.2H20 and K2HPO 4 at 473 K. Refinements were carried out by the full-matrix least-squares method to R = 0.034 and R w = 0.039 with 810 independent reflexion data. Comparisons with the structures of other chlorapatites are presented. Introduction. Chlorapatites, MsCI(PO4) 3 (M = Ca, Ba, Sr, Mn, Cd, etc.), belong to the apatite group of compounds. The crystal structures have been investigated for CasCI(PO4) 3 (Mackie, EUiott & Young, 1972), CdsCI(PO4) 3 (Sudarsanan, Young & Donnay, 1973), SrsCI(PO4) 3 (Sudarsanan & Young, 1974) and Mn5Cl0.9OH0.1(PO4) 3 (Engel, Pretzsch, Gramlich & Baur, 1975) by X-ray diffraction. All these apatites have the space group P63/m, except CasCI(PO4) 3 which crystallizes in P2~/b. The locations of the CIions are not the same among these crystals. The anion occupies the special position 2(b) (0,0,0) in Sr5CI(PO4) 3, and 2(a) (0,0,1⁄4) in Cd5CI(PO4) 3 and MnsCl0.9OH0.t(PO4) 3. In CasCI(PO4)3, it lies at 4(e) (0,0,z) with z = 0.06, giving a similar atomic configuration to that of SrsCI(PO4) 3. As part of a study of the apatite group compounds, single crystals of BasCI(PO4) 3 were synthesized by a hydrothermal reaction and the crystal structure was refined. The structure is in principle the same as that of SrsCI(PO4)3. Single crystals of barium chlorapatite were prepared by hydrothermal reaction of BaC12.2H20 and K2HPO 4. 0.05 mol of BaC12.2H20 and 0.03 mol of K2HPO 4 in 50 ml of distilled water were heated at 473 K for 2 weeks. Single cv./stals of barium chlorapatites grew at pH 5-6 with BaHPO 4. The crystals obtained were colourless, transparent hexagonal prisms 0 .1-0 .3 mm in length and 0 .03-0.1 mm in diameter. The infrared spectrum of BasCI(PO4) 3 was recorded in the range 4000 to 400 cm -~, but the OH stretching band was not observed. This indicates that C1 is not replaced by OH in the crystal. 0567-7408/79/102382-03501.00 Weissenberg photographs showed Laue symmetry 6/m and the systematic absences 001 for l odd. The possible space groups are, therefore, P63/m (centrosymmetric) and P63 (noncentrosymmetric). P6a/m was employed in the structure refinement, since all the apatite group compounds known to date belong to this space group. Intensities were measured on an automated fourcircle diffractometer (Philips PW 1100/20), with graphite-monochromated Mo Kt~ radiation, by the 20-o3 scan technique with a scan speed of 4 ° min -~ in 09, using a crystal 0.15 mm in length and 0.06 mm in diameter. 810 independent reflexion data IF o > 3a(Fo)] were obtained within the range 20 _< 80 °. Intensities were corrected for Lorentz and polarization factors. Absorption corrections (p = 14.868 mm -1 for Mo KCt) were made with the program A CACA (Wuensch & Prewitt, 1965). The refinement was started from the parameters of cadmium hydroxyapatite, CdsOH(PO4) 3 (Hata, Okada, Iwai, Akao & Aoki, 1978), and the position of CI was determined in the difference Fourier syntheses. The calculation with the full-matrix least-squares program LINUS (Coppens & Hamilton, 1970) converged to the residual R = ~ [IFol IFcl~/~ IFol = 0-034 and the weighted residual R,. = ~ w(IFol -IFcl)2/~ WlFo 12 = 0.039 with anisotropic temperature factors. The weighting scheme employed was that of Hughes, with w = 1 if F , < Fomax, and w = Fomax/F o if Table 1. Final positional parameters (x 104) and isotropic thermalparameters (x 104) for BasCI(PO4) 3

Structure reinvestigation of the high-temperature form of K2SO4

The crystal structure of the high-temperature form of K2SO 4 was redetermined from three-dimensional X-ray diffractometer data at 1073 K and refined to an R value of 0.086 for 66 observed reflexions. The structure belongs to the hexagonal space group P63/mmc, with a = 5.947 (2), c = 8.375 (3) A, Z = 2, and D x = 2.26 Mg m -3. The SO 2- tetrahedron has two orientations with one of the apices of the SO 2- tetrahedron pointing statistically in opposite directions along the c axis. The net entropy change, AS = 5.02 J mol -t K -t at the phase-transition point (860 K), was explained successfully by the configurational change of the SO 2tetrahedron in the low- and high-temperature forms. The SO 2- tetrahedron is approximately undistorted with a corrected mean S-O distance of 1.43 A. Two crystallographieally independent K atoms are coordinated by 9 and 13 O atoms with mean K-O distances of 3.20 and 3.3 7 A, respectively.

Phase transition of potassium sulfate, K2SO4 (III); thermodynamical and phenomenological study

The orthorhombic-hexagonal phase transition of K2SO4 has been investigated by measurements of the temperature dependencies of the specific heat, expansion, and X-ray intensity of superstructure reflections, correlated with the structural point of view.The values of the net enthalpy and entropy changes are ΔH=4.28 KJ/mol and ΔS=4.98 J/mol·K at the phase transition temperature (587°C), respectively. The thermal expansion along the c axis shows strong anisotropic character above about 300°C and exhibits a very large discontinuous increase at 587°C, whereas those along the a and b axes increase linearly and exhibit small discontinuous decreases at 587°C. The X-ray intensity of superstructure reflections in the low-temperature form gradually decrease with increasing temperature, and come to extinction at 587°C, exhibiting a discontinuity.The observed entropy change and pressure dependence of the phase transition temperature were explained successfully by the use of results of the structural analysis and measured physical properties. The temperature dependencies of the spontaneous strain, X-ray intensity of superstructure reflection, and birefringence were consistently described by introducing a transition parameter on the basis of an instability at the M point in the Brillouin zone of the hexagonal phase.

Gas Flame Heating Equipment Providing up to 2300°C for an X‐Ray Diffractometer

Gas‐flame heating equipment for a single crystal x‐ray diffractometer has been designed and constructed for the study of materials in the molten state up to 2300°C. An application of this equipment to structural investigation of molten platinum is discussed. Radial distribution functions were computed and analyzed employing the diffracted intensities.

Structural analysis of molten V2O5

The structure of molten V2O5 has been investigated using a radial distribution function based on X-ray scattered intensity data collected at 750 °C; analysis was by the correlation method. The average V—O distance of 1.75 A in the melt is shorter than that of 1.82 A in the crystal and the coordination number of 3.9 in the melt is smaller than that of 5.0 in the crystal. The most probable model for molten V2O5 is similar to the crystal structure of P2O5 or SiO2. Each VO4 tetrahedron is surrounded by three VO4 tetrahedra and the V—V distance of 3.44 A is almost equal to twice the V—O distance. The estimated density of the model assuming the cristoballite-like structure is 2.4 g cm–3, while the measured density is 2.15 g cm–3.

Phase transition of potassium sulfate, K2SO4 (II); dielectric constant and electrical conductivity

The phase transition of K2SO4 has been investigated by measurements of the dielectric constant and electrical conductivity, correlated with the structural point of view. Using single crystals, the temperature dependences of the dielectric constants and electrical conductivities were measured at frequencies of 0.3, 1, 3, and 5 MHz in the temperature range from 20° to 640 °C.Within this range, the dielectric constant does not reach a maximum, but near the phase-transition temperature at 587° C, the dielectric constant along the c axis shows a larger discontinuity than those along the a and b axes. The temperature dependence of the dielectric constant is consistent with the disordered structure of the high temperature form. Based on the parabolic increase of the dielectric constant in the temperature range from 582° to 587° C, it is likely that the phase transition propagates through an intermediate state.The electrical conductivity coefficients of K2SO4 increase with increasing temperature, exhibiting semiconducting character above the phase-transition temperature. In the high-temperature form, the electrical conductivity along the a axis exceeds that along the c axis. Since the electrical conductivity of K2SO4 is mainly ionic in character, the migration of K+ ions makes a major contribution to the conduction process.

Structural analysis of the amorphous sodium salt and aluminium hydroxide salt of sucrose sulphate

The structure of the amorphous sodium salt and aluminium hydroxide salt of sucrose sulphate has been investigated using the radical distribution function together with the correlation method based on X-ray scattering intensity data. The most likely model for the short-range arrangements in the sodium salt and the aluminium hydroxide salt of sucrose sulphate is similar to that found in the crystal structure of potassium sucrose sulphate. Each sulphur atom is tetrahedrally surrounded by oxygen atoms at an average distance of 1.50 A, while each sodium atom is octahedrally surrounded by oxygen atoms at a distance of 2.42 A. The nearest-neighbouring Na—S distance is found to be r= 3.63 A. Each aluminium atom is octahedrally surrounded by oxygen atoms at a distance r= 1.90 A and two AlO6 octahedra share an edge to form a dimer. The Al—Al distance of 2.88 A is slightly longer than the octahedral edge (O—O) distance of 2.69 A. Each dimer is probably surrounded by four SO4 groups and the independent Al—S distances are 3.44 and 4.37 A.

Optimal design of linear control systems by an interactive optimization method

Abstract When designing linear control systems, one of the most difficult problems is that the designer almost has no theoretical basis for the determination of proper parameters in order to obtain a system with desired specifications. Poles and directions of eigenvectors in the pole assignment method or weighting matrices of the quadratic criterion function in the optimal regulator method are such parameters. The designer has to determine them by trial-and-error using computer simulation. The purpose of this paper is to propose an approach to helping determine proper parameters in linear control system design by the state space methods. In the case where the desired specifications are not given explicitly, the approach applies an interactive optimization method called the Interactive Simplex method to search the most suitable parameters directly in the parameter space. But, if the specifications are given explicitly, the design problem can be formulated as a multiobjective optimization problem. In this case, weights which indicate relative importance of different specifications are introduced and the Interactive Simplex method is applied in the weight space to indirectly find the most appropriate parameters. The approach is implemented as part of a CAD system. The designer has only to make pairwise comparisons of response curves which are shown on a graphics display terminal in order to obtain the most preferred control system. Two illustrative examples are demonstrated to indicate the efficiency of the approach.

Structural analysis of molten K2SO4

The structure of molten K2SO4 has been investigated using the radial distribution function together with the correlation method based on X-ray scattering intensity data collected at ≈ 1150°C. The SO4 tetrahedron which exists in the crystalline state of K2SO4 is shown to be preserved in the molten state. The most likely model for the short-range arrangement is that of four near-neighbour potassium atoms situated around the SO4 tetrahedron. One of the four potassium atoms practically occupies the corner-site and the others occupy the edge-sites. The nearest-neighbour K–O and K–S distance are r= 2.80 and 3.38 A, respectively. The most likely model for the long-range arrangement is about thirteen K2SO4 units situated around one K2SO4 unit with an average inter-unit distance of 7.0 A.