Veniamin Polyakov has published the most on this topic. His papers are full of the equations that are needed to calculate whether there is a pressure dependence on isotope ratios. There are two main reasons why pressure might have an effect. The first, as stated below, is the molar volume isotope effect. This is important for light elements and for systems with water as discussed in a paper by Horita in Science about the pressure dependent fractionation between brucite and water. The second reason is that as pressure is increased, bonds stiffen and that bond stiffness does not occur in the same way to all crystals, melts, etc. Therefore, there is likely a pressure dependence in most systems where the bond stiffness between the two phases of interest is quite different. We discuss this in our paper — Shahar et al. 2016
Hope that helps!
Anat Shahar, Ph. D.
Carnegie Institution of Washington
5251 Broad Branch Road, NW
Washington, DC 20015
There are some ways this is an easy question and there are some ways it is not.
It is often a perfectly useful approximation to hold that hydrostatic pressure does not alter the distribution of stable isotopes in a system at equilibrium. This is not strictly true; one can write Gibbs free energy in terms of pressure and volume. If the molar volumes of two isotopologues are not equal, neither are their Gibbs free energies. In most cases, the change in molar volume that comes with isotopic substitution is so small that it is safely ignored. Hydrogen is almost sui generis in that the molar volume difference is not trivial with substitution, so it's not a safe bet to assume there's no difference.
If you are concerned about kinetic phenomena, there are circumstances where there is unquestionably a pressure effect. This is most obvious in biochemistry, where the catalytic capability of enzymes is a function of hydrostatic pressure. I haven't spent any real time thinking about whether fractional crystallization causes pressure-dependent isotopic fractionation, but I would not be surprised in the least if so. Someone here probably knows that kind of thing.
Department of Earth and Atmospheric Sciences
Bloomington IN 47405