3 - Lattice Energy and Free Energy Minimization Techniques

Abstract

This chapter focuses on the use of energy minimization techniques to model the crystal structures of inorganic solids. It is both desirable and possible to go beyond lattice energy minimization where no account is taken of temperature to perform free energy minimization which allows simulating crystal structures over a wide range of temperatures and pressures. Free energy minimization is a powerful tool for modeling a wide range of crystal properties including structure and elasticity. When applying this approach to larger and more complex systems special attention always needs to be paid to the reliability of the potential model. The atomistic approach to modeling the crystal structure and properties involves the definition of interatomic potential functions to simulate the forces acting between ions. There are two principal methods by which potential parameters may be obtained: empirical fitting and direct calculation. Empirical fitting is essentially the reverse of the lattice simulation methods. The structural and lattice properties are used to determine the potential by requiring that the potential reproduces these properties. Directly calculated potentials can be obtained for any interatomic distance or relative atomic configuration, but care must be taken that environmental factors are taken into account correctly.