First-Principle Studies of the Vibrational Properties of Carbonates under Pressure

Using the density functional theory with the hybrid functional B3LYP and the basis of localized orbitals of the CRYSTAL17 program code, the dependences of the wavenumbers of normal long-wave nu vibrations on the P(GPa) pressure nu(cm(-1)) = nu(0) + (dv/dP)center dot P + (d(2)v/dP(2))center dot P and structural parameters R(angstrom) (R: a, b, c, RM-O, RC-O): nu(cm(-1)) = nu(0) + (dv/dR) - (R - R-0) were calculated. Calculations were made for crystals with the structure of calcite (MgCO3, ZnCO3, CdCO3), dolomite (CaMg(CO3)(2), CdMg(CO3)(2), CaZn(CO3)(2)) and aragonite (SrCO3, BaCO3, PbCO3). A comparison with the experimental data showed that the derivatives can be used to determine the P pressures, a, b, c lattice constants and the RM-O metal-oxygen, and the RC-O carbon-oxygen interatomic distances from the known Delta nu shifts. It was found that, with the increasing pressure, the lattice constants and distances R decrease, and the wavenumbers increase with velocities the more, the higher the nu(0) is. The exceptions were individual low-frequency lattice modes and out-of-plane vibrations of the v(2)-type carbonate ion, for which the dependences are either nonlinear or have negative dv/dP (positive dv/dR) derivatives. The reason for this lies in the properties of chemical bonding and the nature of atomic displacements during these vibrations, which cause a decrease in RM-O and an increase in RC-O.

Automated summary

By using density functional theory with the B3LYP hybrid functional and CRYSTAL17 program code, the relationships between the wavenumbers of normal long-wave nu vibrations and pressure and structural parameters were calculated for various crystals. The study found that with increasing pressure, lattice constants and distances decrease, while wavenumbers increase with higher nu(0).