Re-examination of X-ray powder diffraction of todorokite from the Todoroki mine was carried out. We recognize that the diffraction peak of 19.3 Å shows the existence of long spacing in the direction of c axis. Calculated unit cell parameters are as follows, a=9.79 Å, b=2.86 Å, c=19.50Å.Todorokite from Urizukuri, Yamaguchi Prefecture also have 19.3Å diffraction peak. Such a long spacing may be common in todorokite structure.

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The crystal structure of lead chloride fluoride has been refined with three-dimensional X-ray diffraction data, and anharmonic potential parameters were determined. The crystal is tetragonal, P4/nmm, with a=4.1062(2), c=7.2264(9) Å, Z=2, D_x=7.13g/cm³, μ(Mo K α)=705.7cm^-1. All the ions showed anharmonicity in their thermal vibrations at room temperature. On the basis of the potentials calculated around Cl^- and F^- ions, it was found that the mobility of both Cl^- and F^- ions is larger within the (001) plane than along the c axis.

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Mössbauer spectra of helvine group have been measured at various temperatures. The quad-rupole splittings increase with lowering of the temperature; 0.369 mm/s at 321 K to 2.740 mm/s at 4.2 K (danalite from Hirako mine, Hiroshima Pref.), 0.243 mm/s at 290 K to 0.734 mm/s at 78 K (helvine from Yagisawa mine, Gunma Pref.). The widths at half height of the quadrupole doublets also increase with lowering of the temperature ; 0.455 mm/s at 321 K to 1.000 mm/s at 57 K (danalite from Hirako mine), 0.345 mm/s at 290 K to 0.654 mm/s at 78 K (helvine from Yagisawa mine). These phenomena are explained by the small splitting of the energy level between d_x²-y² and d_z² orbitals at the tetrahedral crystal field.

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The applications of infrared, far-infrared and Raman spectra to mineralogy are described. Problems of peak assignment are discussed by comparing the assignments determined by lattice dynamical calculations with those deduced from isotropic shifts. These assignments make it possible to predict the intracrystalline cation site preferences in olivine. The mode softening mechanism and the abnormal behaviuor o felastic constants near the α-β quartz transition temperature are explained by the contribution of potential energy terms to the potential energy. The emphasis is upon the nature of chemical bond in crystals. The effective charges deduced from thermochemical, spectroscopic and molecular orbital theories and accurate structure factors are compared with those determined by lattice dynamical calculations. The theoretical advances of the lattice dynamical calculation including the effect of the width of the atomic electron distribution provide us with a fundamental understanding of the chemical bond in silicates, because a wide range of physical properties is estimated by lattice dynamics.

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