Displacements Of Constituent Atoms Research Articles

Lattice Vibrations and Dispersion Relations near Conical Point in a Hexagonal Lattice

The dispersion relation of lattice vibrations in a hexagonal lattice is discussed on the basis of a simple model. It is found that there are the wavenumber-independent branches if only the nearest-neighbor interaction is taken into account. By taking the second-nearest-neighbor interaction into account, the origin of the appearance of the wavenumber-independent branches is clarified. At the reciprocal lattice point k = (1/3, 1/3, 0) of the hexagonal lattice, called the conical point, there are degenerate modes postulated from the symmetry, and the displacements of constituent atoms in them are concretely discussed.

Vibrational analysis of PbHPO4 and PbDPO4 crystals

AbstractLattice dynamics simulation of PbHPO4 and PbDPO4 crystals is performed in paraelectric phase within the semi‐empirical approach. The interpretation of experimental Raman spectra is done using the calculated density of states and the dispersion of mean square displacements of constituent atoms. The ferroelectric phase transition caused by proton–phonon and phonon–phonon interactions. The internal bending mode of PO4 tetrahedral groups may be treated as the probable candidate evoking the appearance of spontaneous polarisation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of grinding on the rate of oxidation of pyrite by oxygen in acid solutions

Solubility of pyrite (FeS 2) ground for different periods was investigated in acid solutions in air. In the initial dissolution, up to 50 h, the dissolution rate, r, was high, due to oxidized species such as FeSO 4 formed by grinding. After 50 h, the surface of pyrite was exposed and the dissolution rate decreased. The formation and dissolution of oxidized species were confirmed by X-ray photoelectron spectroscopy, XPS. From the dissolution rates of Fe and S species, r Fe and r S , for 50–200 h, it was found that pyrite dissolves nonstoichiometrically ( r S r Fe < 2 ) and that grinding promotes the dissolution of sulfur species leading to the stoichiometric dissolution ( r S r Fe = 2 ). The increase in r S can be explained by the displacement of S atoms in the crystal due to the grinding. The effective Debye-Waller parameter, B eff , depends on the displacement of constituent atoms in the crystal from their equilibrium positions and is measured from the diffraction intensities of X-rays. The parameter for S atoms in pyrite, B eff ( S), increased by one or two orders of magnitude with increasing grinding time, t G , while that for the pyrite, B eff ( FeS 2), did not change markedly. It was established that r S is closely related to B eff ( S). The phenomenon may be regarded as a type of mechanical activation.