Path integral Monte Carlo simulations of silicates

The study and analysis of materials properties of crystalline silicates are important since these systems are used in many industrial processes and they occur also in many natural rocks. Many interesting effects have been found by experimental techniques at temperatures well below the Debye temperature. In this temperature range quantum effects like zero point motions and corresponding delocalizations of atoms are important which have to be taken into account in serious theoretical studies. Usually this is done by lattice dynamics theories, in the framework of the harmonic or quasiharmonic approximation. However, both near secondorder structural phase transitions and quite generally at higher temperatures the accuracy of this approach is sometimes uncertain, 1 and methods that work at all conditions would be desirable. Path integral Monte Carlo ~PIMC! simulations 2 enable us to analyze the crystal low-temperature thermal properties. In principle, this method yields exact quantum-statistical averages ~apart from statistical errors! and reduces to classical statistical averages at high temperatures. In general, the agreement with experimental data is better compared to classical computations. For b-cristobalite it turns out that even at temperatures as high as 600 K only with PIMC a good agreement with experimental findings is obtained. The negative thermal expansion in b-quartz, however, may be explained by a classical modeling. The outline of this paper now is as follows: in Sec. II we define the models that are studied, in Sec. III we briefly review the PIMC technique, while Sec. IV describes our results in detail. We conclude in Sec. V with a brief summary.