The Holland-Powell (2011) expression for the thermal pressure employs an Einstein function:
with ξ0 being the same as in the thermal expansion equation of Kroll et al. (2012) and is a constant calculated from the Einstein temperature θE.
Careful reading of Holland and Powell (2011) and comparison of equations, reveals that their thermal-pressure model is actually based on using a single Einstein oscillator to define the isochoric heat capacity CV, keeping the Einstein temperature the ratio γ/V constant (Kroll et al., 2012). It is thus a q-compromise model.
The difference between the Holland and Powell (2011) and Einstein oscillator models is in the parameterisation. Holland and Powell (2011) use the thermal expansion coefficient at reference conditions α0 and this allows the thermal pressure, as shown above, to be written in terms of the parameters α0K00 and without an explicit expression for the heat capacity or using the thermal Grüneisen parameter γ. These are effectively 'hidden' in the two brackets in the expression ofr Pth which are the integral of γCv from the reference temperature to T.
This thermal-pressure model has the properties that the product αK becomes constant at high temperatures while it decreases to zero at low temperatures. This means that both the bulk modulus K0T and the thermal expansion become constant at low temperatures, and both have an approximately linear variation with temperature above θE. The exact expressions for thermal expansion and bulk modulus as a function of temperature depend on the choice of isothermal equation of state, but at Tref and zero pressure α = α0 (Holland and Powell, 2011).
This model successfully fits the P-V-T data of diamond (Angel et al, 2015a), and both the P-V-T and bulk moduli data collected at both high P and at high T of grossular garnet (Milani et al., 2017). However, this model does not fit the P-V-T data of all materials, because it has the built-in property of a q-compromise EoS that the bulk modulus does not vary along an isochor (Kroll et al., 2012; Angel et al., 2017b).
The big advantage of reformulating the thermal pressure for an Einstein oscillator model in this way is that one can use the EoS for any volume units. It is not restricted to molar volumes. From version 7.6 of EosFit:
If you have an old .eos file, you can use the input utility to change the Natom to the correct value so as to get the heat capacities and adiabatic bulk moduli calculated correctly. EoS imported into EosFit 7.6 directly from the Thermocalc database have Natom and γ0 set correctly.