Lattice Dynamics of Crystals of the Calcite Structure II. Dispersion Curves and Phonon Densities

Abstract

Phonon dispersion curves of the external and internal modes of trigonal CaCO, have been calculated for some directions in the Brillouin zone. The one-phonon density, the two-phonon density, and the specific heat havc also been determined. The results are compared \\ ith available experimental data on the specific heat and the two-phonon absorption spectrum. The frequencies of the external modes have been calculated neglecting the internal degrees of freedom of the complex ions CO; -, using a shell model which takes the short range interaction of nearest neighbours, the Coulomb interaction, and the polarizability of the complex ions into account. The variation of the frequencies of the internal modes with wave vector y has been determined by considering only the coupling of the transition dipoles of the complex ions. For this purpose the dipole-dipole interaction formalism normally used a t wave vector y = 0 to calculate the Davydov splitting of the internal modes is extended t o wave vectors ly] $; 0.Fur den trigonalen Kristall CaCO, wurden fur einige Richtungen in der Brillouin-Zone die Dispersionszweige der auBeren und inneren Schwingungen berechnet. AuBerdem wurde die Einphononendichte, die Zweiphononendichte und die spezifische Warme bestimmt. Die Ergebnisse werden mit experimentellen Werten der spezifischen Warme und des Zweiphononen-Absorptionsspektrunis verglichen. Bei der Berechnung der Frequenzen der h B eren Schwingungen werden die inneren Schwingnngsfreiheitsgrade der Komplexionen COYnicht berucksichtigt. Die Frequenzen werden im Rahmen eines Schalenmodells berechnet, welches die Nahkraft-Wechselwirkung nachster Nachbam,., die Coulombwechselwirkang und die Polarisierbarkeit der Komplexionen enthalt. Die Anderung der Frequenzen der inneren Schwingungen mit dem Wellenvektor y wird bestimmt, indem nur die Wechselwirkung der Ubergangsdipole der Komplexionen berucksichtigt wird. Hierzu wird der Formalismus dieser Wechselwirkung, welcher beim Wellenvektor y = 0 zur Berechnung der Davydov-Aafspaltung dcr inneren Schwingungen benutzt wird, auf Welleiivektoren lyl $= 0 rrweitert.

Raman spectroscopic studies of carbonates part I: High-pressure and high-temperature behaviour of calcite, magnesite, dolomite and aragonite

“…From IR studies, a v2 internal mode of Ag symmetry should lie in this frequency range (Couture 1947;White 1974), and we propose that the 880 cm-1 peak is the second dolomite Ag mode corresponding to a silent A2g of calcite. The lowest frequency A2g mode of calcite was measured at 172 cm-1 by inelastic neutron scattering, and calculated at 210 cm-1 for calcite and 287 cm -1 for magnesite (Cowley and Pant 1973;Plihal 1973;Plihal and Schaak 1970). We have not observed the analogue of this mode in dolomite.…”

Lattice dynamics and elasticity of SrCO3

“…In this context, most of the important carbonates such as calcite, CaCO 3 , dolomite, CaMg(CO 3 ) 2 , and magnesite, MgCO 3 , and their respective polymorphs have been extensively studied (Reeder, 1983;Luth, 1999). Consequently, the CaCO 3 polymorphs calcite and aragonite are by far the most studied carbonates with respect to their lattice dynamics and phase transitions at high pressure and temperature (Dove et al, 1992;Singh et al, 1987;Plihal & Schaack, 1970;Plihal, 1973;Ye et al, 2012;Lin & Liu, 1997a;Arapan & Ahuja, 2010;Fiquet et al, 1994). These studies are facilitated by the ubiquity of large calcite crystals of excellent quality.…”

Relative importance of the T-5 and T-7 terms in spin-lattice relaxation time

“…This value of463 K does not correspond to the upper limit of the transverse ,acoustical phonon branch given in ref. [14]. Considering the phonon density curve of CaCo3, the best fit is given by :…”