Phys Chem Minerals (1993) 19:472-479 PlffSlCS [NHEM IIIY NMIIIEBJlS 9 Springer-Verlag 1993 Thermodynamic Properties of CaCO 3 Calcite and Aragonite: A Quasi-Harmonic Calculation M. CattP, A. Pavese 2'*, G.D. Price 3 1 Dipartimento di Chimica Fisica ed Elettrochimica, Universifft di Milano, via Golgi 19, 1-20133 Milano, Italy z Dipartimento di ScierLzeMineralogiche e Petrologiche, UniversitA di Torino, Via Valperga Caluso 37, 1-10137 Torino, Italy 3 Department of Geological Sciences, University College, London, UK Received June 1, 1992 / Revised, accepted September 28, 1992 Abstract. A quasi-harmonic model has been used to sim- ulate the thermodynamic behaviour of the CaCO3 poly- morphs, by equilibrating their crystal structures as a function of temperature so as to balance the sum of inner static and thermal pressures against the applied external pressure. The vibrational frequencies and elastic proper- ties needed have been computed using interatomic po- tentials based on two-body Born-type functions, with O- C- O angular terms to account for covalency inside the CO3 molecular ion. A good agreement with experi- mental data is generally shown by simulated heat capaci- ty and entropy, while the thermal expansion coefficient seems to be more difficult to reproduce. The results ob- tained for aragonite are less satisfactory than those of calcite, but they are improved by using a potential specif- ically optimized on properties of that phase itself. Introduction The application of chemical thermodynamics to the study of phase equilibria and reactions of mineral com- pounds is an important tool with which to understand phenomena occuring in the Earth's crust and mantle. In addition to direct calorimetric measurements, the thermodynamic properties of a mineral can also be de- rived from the spectrum of vibrational frequencies of its crystal lattice (including its dependence on pressure and temperature). These data are obtained either by spectroscopic experiments, or by theoretical calculations based on models for the atom-atom interaction energy (Catti 1986). The CaCO3 system shows an extensive polymorphism, which is not yet fully understood (Carl- son 1983; Goldsmith 1983; Speer 1983). The calcite and aragonite phases, however, have been studied by deriving thermodynamic data from spectroscopic measurements (SaIje and Viswanathan 1976). In this paper the full ther- * Present address: Dipartimento di Scienze della Terra (Sezione di Mineratogia), UniversitY, via Botticelli 23, 1-20133 Milano, Italy modynamic behaviour of those minerals is approached from the theoretical point of view by use of atomistic calculations, following a previous paper where the intera- tomic potential energy functions were obtained (Pavese et al. t992). Applications of empirically-optimized poten- tials in calcite have also been recently proposed for deriv- ing isotope fractionation coefficients (Dove et al. 1992). One of the aims of this work is to assess the reliability of the quasi-harmonic lattice-dynamical model to ac- count for the thermal properties of complex crystals such as calcite and aragonite. Further, the different potentials previously optimized have to be tested (a) with respect to their ability to reproduce thermodynamic behaviour, and (b) for their transferability between polymorphs. Interatomic Potentials The rigid-ion-model assumed for calcium carbonate crystals accounts for the O-O, Ca-O and C-O two- body potential energy by the Born formula eZzizj/r~j +Aijexp(-riJoO; where e is the electron charge, zi the charge of the i-th atom in e units, r~ the interatomic distance, A~j and Q~jthe coefficient and hardness parame- ter of the repulsive energy, respectively. A dispersive term -cij/r 6 is added in the O-O case only. The covalent, directional bonding in the CO3 molecular ion requires an additional angular term 1/2 ko(O-Oo) 2, where O is the actual O-C-O bond angle and Oo its equilibrium value of 120~ . Further, the potential energy of out-of- plane displacements of C within the CO3 group is ex- pressed by the function k~(1-cos 2~b) of the torsional angle q~ between the OCO' and OCO" planes. The atomic charge zo, the repulsive A~j, Q~j and har- monic angular ko, k o parameters were fitted to experi- mental structural data, elastic constants and IR and Ra- man vibrational frequencies (Pavese et al. 1992); Zc, was kept fixed at the formal value +2 e, while Zc=--Zc~ -3 zo. Working on calcite and aragonite the two sets of potential parameters RIM and RIMt, respectively, were obtained (Table 1). In the case of calcite, a shell