A knowledge of thermal expansion at high temperature and high pressure is important when modelling the equation of the state of the Earth's interior. It is a necessary parameter for solving many materials science problems and is critical for understanding the nature of residual stress in materials. Thermal expansion has been related to other thermodynamic parameters through Grüneisen rules. It is a factor in the equations describing many important properties of solids.

In this research project funded by the Army Research Office, a semi-empirical, quasi-harmonic lattice dynamic model, its extension to high temperatures and high pressures and the roles of thermal defects are applied to understand the thermal expansion of minerals and materials. The following examples illustrate recent work for MgO and diamond. Related work is listed in the references.

Thermal expansion of MgO, periclase, is approximated by contributions from a quasi-harmonic perfect crystal and its equlibrium high temperature/pressure defects. We demonstrated that the influence of thermal defects on high pressure thermal expansion is very small and may be neglected at lower mantle conditions. Following that, a simple relationship has been obtained between high pressure thermal expansion and the thermal expansion of a quasi-harmonic perfect crystal at zero pressure. Our estimation of MgO thermal expansion at the core-mantle boundary is 9.36x10^-6/K.

Figure 1. The temperature dependence of thermal expansion of MgO at zero pressure and several high pressures calculated with our model.

Figure 2. Comparison of our model at 135 GPa (pressure at the core-mantle boundary) with earlier studies.

Thermal expansion is of both practical and theoretical importance and it together with specific heat is essential for predicting a thermodynamic equation of state. We utilize a semi-empirical quasi-harmonic model to evaluate available data for diamond. The model allows us to predict the thermal properties of the metastable diamond polymorph to 3000K. The approach consisting of a simplified frequency spectrum with several Einstein terms provides a convenient mathematical method where a minimum of empirical parameters represent the thermal property.

Figure 1. Predicted and experimental lattice parameters of diamond as a function of temperature.

Figure 2. Predicted and experimental thermal expansion of diamond over an extended temperature range.

Figure 3. Predicted and experimental isochoric specific heat of diamond.

Figure 4. Recommended values and calculations of the thermal expansion of diamond.

Figure 5. The temperature dependence of the Grüneisen parameter of diamond.

References

Wang, K. and R.R. Reeber (1996): Thermal expansion of alkali halides at high pressure: NaCl as an example, Physics and Chemistry of Minerals, (in press).

Wang, K. and R.R. Reeber (1996): A model for evaluating and predicting high temperature thermal expansion, Journal Materials Research, (in press).

Wang, K. and R.R. Reeber (1996): Thermal expansion of copper, High Temperature and Materials Sciences, (in press).

Reeber, R.R. and K. Wang (1996): Thermal expansion, molar volume and specific heat of diamond from 0 to 3000K, Journal Electronic Materials, 25, 63-67.

Reeber, R.R. and K. Wang (1996): Thermal expansion and lattice parameter of Group IV semiconductors, Materials Chemistry and Physics, (in press).

Reeber, R.R. and K. Wang (1996): Thermal Expansion of beta-SiC, GaP and InP, Proceedings of the Materials Research Society Fall Meeting, 1995(in press).

Wang, K. and R.R. Reeber (1995): A simplified model for Predicting High Pressure Thermal Expansion of MgO, Geophysical Research Letters, 22, 1297-1300.

Wang, K. and R.R. Reeber (1995): High temperature thermal expansion of alkali halides, Journal of Physics and Chemistry of Solids, 56, 895-900.

Wang, K. and R.R. Reeber (1995): Thermal Expansion of caesium halides with the CsCl structure, Journal of Applied Crystallography, 28, 306-313.

Reeber, R.R. , K. Goessel, and K. Wang (1995): Thermal expansion and molar volume of MgO, periclase, from 5 to 3000K, European Journal of Mineralogy, 7, 1039-1047.

Wang, K. and R.R. Reeber (1994): Thermal defects and thermal expansion of ionic crystals at high temperatures, physica status solidi, 146, 621-627.

Comments? Please send email to

Kai Wang, kai_wang@ncsu.edu

or

R. R. Reeber, robert_reeber@ncsu.edu

J.A. Rial, jar@wave.gphys.unc.edu

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