Pawley et al. (1996) proposed a model that ensures that the thermal expansion becomes approximately constant at high temperatures:
Pawley et al. (1996) used 298K as a fixed reference temperature, but there is no need to do so. They also proposed a simplification with in which case the equation becomes:
This is sufficient to model low-resolution datasets, but maintains the saturation in thermal expansion at high temperatures. In order to accommodate this simplification in a simple manner which also allows the use of the more general equation, we modified the Pawley et al. (1996) equation to:
Note that the entire term of this equation is equal to the α1 coefficient used by Pawley et al. (1996). Thus, when α1 is fixed at zero the whole term
becomes equal to 10α0 and the simplified equation proposed by Pawley et al. (1996) and used in Holland & Powell (1998) is obtained. In the EoS module of CrysFML, the correct value of
is always calculated, so the returned values from the program will differ from those obtained by inserting the parameters in to the approximate equations for thermal expansion given by the previous authors. This equation cannot be used at low temperatures because below
the thermal expansion becomes negative and the volume is predicted to increase with decreasing temperature. If α1 = 0 this limiting temperature is 100K. Note also that, even when α1 = 0,
at Tref is not equal to α0.