| Summary: | 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 <i>ν</i> vibrations on the <i>P</i>(GPa) pressure <i>ν</i>(cm<sup>−1</sup>) = <i>ν</i><sub>0</sub> + (<i>dv</i>/<i>dP</i>)·<i>P</i> + (<i>d</i><sup>2</sup><i>v</i>/<i>dP</i><sup>2</sup>)·<i>P</i> and structural parameters <i>R</i>(Å) (<i>R</i>: <i>a</i>, <i>b</i>, <i>c</i>, <i>R</i><sub>M-O</sub>, <i>R</i><sub>C-O</sub>): <i>ν</i>(cm<sup>−1</sup>) = <i>ν</i><sub>0</sub> + (<i>dv</i>/<i>dR</i>) − (<i>R</i> − <i>R</i><sub>0</sub>) were calculated. Calculations were made for crystals with the structure of calcite (MgCO<sub>3</sub>, ZnCO<sub>3</sub>, CdCO<sub>3</sub>), dolomite (CaMg(CO<sub>3</sub>)<sub>2</sub>, CdMg(CO<sub>3</sub>)<sub>2</sub>, CaZn(CO<sub>3</sub>)<sub>2</sub>) and aragonite (SrCO<sub>3</sub>, BaCO<sub>3</sub>, PbCO<sub>3</sub>). A comparison with the experimental data showed that the derivatives can be used to determine the <i>P</i> pressures, <i>a</i>, <i>b</i>, <i>c</i> lattice constants and the <i>R</i><sub>M-O</sub> metal-oxygen, and the <i>R</i><sub>C-O</sub> carbon-oxygen interatomic distances from the known Δ<i>ν</i> shifts. It was found that, with the increasing pressure, the lattice constants and distances <i>R</i> decrease, and the wavenumbers increase with velocities the more, the higher the <i>ν</i><sub>0</sub> is. The exceptions were individual low-frequency lattice modes and out-of-plane vibrations of the <i>v</i><sub>2</sub>-type carbonate ion, for which the dependences are either nonlinear or have negative <i>dv/dP</i> (positive <i>dv</i>/<i>dR</i>) 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 <i>R</i><sub>M-O</sub> and an increase in <i>R</i><sub>C-O</sub>.
|
|---|