There was a disagreement of chemical formulae between the formula derived from structure determination (CuBi₅S₈) [Ohmasa, M. and Nowacki, W. (1973) Zeits. Krist., 137, pp. 422–432] and the one from synthetic studies (CuBi₃S₈). In order to clarify the origin of the disagreement, the crystal structure of the compound has been reinvestigated. It was found that some of the Bi atoms are partly substituted by Cu, and that the obtained chemical formula is Cu_1.57Bi_4.57S₈. When the number of S is fixed to five, the new formula can also be expressed as Cu_0.98Bi_2.86S₅, and is approximately identical with CuBi₃S₅. The amount of substitution found in Cu_2+xBi_6−xS₉ (x=1.21) [Ohmasa, M. (1973) Neues Jahrb. Miner. Monatsh., pp. 227–233] was also reexamined for comparison.
Both structures consist of two kinds of slabs, and the substitution between Bi and Cu was found in the slab II. Since these elements have quite different properties, the substitution found in these compounds is quite unique. The chemical formulae of the fundamental structures, which are ideal structures having no substitution between Bi and Cu, are different from the apparent formulae given in the synthetic studies, and the discrepancies are compensated by substitution, Cu for Bi. The formula CuBi₅S₈ obtained in the previous study corresponds to that of the fundamental structure.

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Electrostatic energies of olivine, modified spinel and spinel with M₂SiO₄ stoichiometry (M=Ni, Mg, Co, Fe and Mn) and those of their constituent ions were calculated by the method of Bertaut, to obtain better understanding on each polymorph; the stability relations under high pressures and the effect of ionic size on the electrostatic stability.
Stability relations of these polymorphs can be explained on the basis of proposed criteria; minerals with high repulsive energy and “simple” energetics only can survive under high pressures, where the “simple” energetics means that the electrostatic energies of constituent ions do not differ greatly from each other. Olivine does not have high repulsive energy, but involves a complex energetics. It cannot, therefore, survive under high pressures. Instability of modified spinel under very high pressures can be explained also in terms of its complex energetics. Spinel has high repulsive energy and does not involve a complex energetics. It is, therefore, stable under high pressures.
Electrostatic energies plotted against ionic radius ratio r_M⁄r_Si reveal the effect of ionic size on crystal energetics as follows : Electrostatic energies of M ion, O ion and the whole crystal become higher, whereas that of Si ion becomes lower with an increase of ionic radius ratio. Electrostatic energy of Mg₂SiO₄ olivine is slightly different from the trend of those of transition metal olivines. A rapid increase in electrostatic instability of olivine structure is observed at the ionic radius of Mn.

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The frequencies of the k=0 vibrational spectra and the elastic constants of diopside have been calculated based on the modified Urey-Bradley force field. The vibrational spectra have been assigned from theoretical vibrational modes and each mode has been characterized by the contribution of force constants to potential energy. The elastic constants of diopside are grouped into three types; the first are attributable mainly to the cation polyhedra, the second to the silica chain and the third to their mixtures.

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