Free energy calculations solid-state defects

In order to be able to calculate the concentrations of point defects at thermodynamic equilibrium, it is necessary to know the change in free energy of the crystal which accompanies the formation of point defects, since the equilibrium is determined by the minimization of the free energy when the pressure, the temperature, and the other independent thermodynamic variables are given. A theoretical calculation of the free energy of formation of defects is still one of the most difficult problems in solid state physics and chemistry. The methods of calculation for each group of materials - metals, covalent crystals, ionic crystals - are all very... 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

Knowledge of the concentration of defects and molar disturbance enthalpies would permit calculation of the actual free energy of the solid, and also the chemical potential. These can be measured by using either solution calorimetry or differential scanning calorimetry. An example of the excess energy was given as 20-30 kj mol-i in mechanically activated quartz. Different types of reactions demand different defect types. For example, Boldyrev et al. [25] state a classification and provide examples for solid reactions with different mechanisms and necessary solid alterations. Often, reaction rates in solids depend strongly on the mass transport of matter. Lidi-ard [26] and Schmalzried [27] each provide reviews on transport properties in mechanically treated solids. The increased amount of defects allows a faster transport of ions and atoms in the solid structure. 

---