SIMULATING THE EFFECT OF TEMPERATURE AND PRESSURE ON CRYSTAL STRUCTURES

SIMULATING THE EFFECT OF TEMPERATURE AND PRESSURE ON CRYSTAL STRUCTURES 

When discussing energy minimization no explicit mention of temperature was made. The majority of such studies are simulated at absolute zero or at an effective room temperature, depending on how the interatomic potentials were derived. In many cases this is sufficient to reproduce a crystal structure within the limits of the accuracy of the 

Inclusion of a uniform external pressure into an energy minimization is relatively trivial since this only requires the addition of the term pV to the internal energy, which is normally calculated, to make the objective quantity the enthalpy. However, the problem becomes more difficult when considering the cases of uni- or bi-axial stress. 

There have been many other examples of the introduction of pressure into static lattice energy minimization calculations, particularly for silicates. For example, there has been a detailed study of the effect of pressure on a-quartz using a range of different models (de Boer et al. 1996). Beyond the consideration of structural trends, this work also evaluated the pressure dependence of some physical properties as well. In particular 

Within the silicate field, Parker and co-workers (Parker and Price 1989 Tschaufeser and Parker 1995) have used free energy minimization with success for modelling thermal expansion. Their approach is based on the assumption that the dominant effect of temperature is on the unit cell dimensions, rather than the internal fractional co-ordinates. If this is the case then it becomes feasible to numerically determine the strain derivatives of the free energy by finite differences as there are at most six components to evaluate and for many materials, with symmetry taken into account, there may be considerably less than this. 

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