Vibration Spectra of Double K–Ca, K–Mg, and Na–Mg Carbonates under Pressure

Density functional theory methods with the B3LYP hybrid functional and the basis of a linear combination of localized atomic orbitals of the CRYSTAL17 program code were used to study the pressure dependences of the structural and vibrational properties of double carbonates K2Ca(CO3)2, K2Mg(CO3)2, and Na2Mg(CO3)2. The parameters of the Birch–Murnaghan equation of state of the third and second orders and the linear compression modulus are determined. A strong anisotropy is shown, when the compressibility along the c axis is 2–4 times greater than along the a axis. The C–O bonds are practically incompressible, and the Ca(Mg)–O and K(Na) –O distances change much faster with pressure. The frequencies and intensities of normal long-wavelength oscillations are calculated, from which the spectra of infrared absorption (IR) and Raman scattering (RS) are plotted by means of Gaussian broadening. It is shown that in the lattice region the band maxima are shifted towards the higher frequencies for carbonates with a lower atomic mass of the cation. In the region of intramolecular vibrations of atoms, the band formed by asymmetric stretching ν3 with a frequency of ~1420 cm–1 will dominate in IR, while the most intense band in RS spectra is provided by symmetric stretching ν1 with a frequency of ~1100 cm–1. As the pressure increases, the vibration frequencies increase according to a nearly linear law, and the Grüneisen mode parameters for lattice vibrations are much larger than for intramolecular vibrations. The ν3 modes have the highest rate of frequency increase with pressure, while the frequencies of out-of-plane deformations ν2 decrease with increasing pressure. The established frequency dependences in the IR and Raman spectra can be used to identify double carbonates under pressure.