Calculation of Vibrational Spectra and Thermodynamic Functions of a Natural Zinc Silicate – Willemite

Abstract

<p>A zinc silicate is in a great demand in modern technology due to its fluorescent, optical and catalytic properties. However, its thermodynamic properties have been studied not sufficiently, and they are focused primarily in the geological and geochemical sciences. An attempt to calculate for a natural zinc silicate willemite (Zn<sub>2</sub>SiO<sub>4</sub>) its crystal structure, vibrational properties, phonon states and thermodynamic functions was made in this work. The force constants and vibrational states of the mineral have been calculated in this paper by a combination of the methods of quantum-chemical calculations (MOPAC) with semi-empirical method PM5 and the theory of crystal lattice dynamics (LADY program) with valence force field potential model. Theoretical infrared and Raman spectra of the mineral were simulated on the base of calculated vibrational states. A good agreement between the experimental and theoretical vibrational spectra of the mineral has been achieved. After that the Brillouin zone scanning of the mineral crystal structure was made which is necessary to obtain the information about the whole phonon spectrum in the lattice. Density-of-state function was determined by summation over all the phonon states and used for determination of energetics of the crystal. The values of the basic thermodynamic functions for willemite (heat capacity, entropy and change of enthalpy) over the range of (10-298.15) K have been obtained. The standard values of these functions are: <em>C</em><sub>p</sub>(298.15) = 126 J/(mol•K) (PM5 calculation) and 122.5 J/(mol•K) (LADY calculation), S°(298.15) = 133.4 J/(mol•K) (LADY calculation), and H°(298.15)–H°(0) = 21494 J/mol (PM5 calculation). The calculated heat capacity values are in satisfactory agreement with known experimental data.</p>