Hi,
I am trying to understand/confirm how rhyolite-Melts calculates liquid, mineral and system density but have not been able to build up a complete picture from the details given in the literature and have not be able to obtain a copy of Lange and Carmichael (1990).
If I follow correctly the density each oxide component of the liquid is calculated based on the EOS: V = a + b(T-Tr) + c(P-Pr) + D(T-Tr)(P-Pr) + e(P-Pr)^2. This gives the molar volume which can be divided by the molar weight to get the density of each component, which can then be combined based on the mass percentage to get the liquid density.
Are the mineral densities calculated in the same way? Or are they determined based on a reference density and the co-efficient of thermal expansion?
Thanks in advance for any help!
For the liquid, the calculation of volume (and hence density) is equivalent to what you describe. Constants a, b, c and d in your expression are calculated for the liquid end members from Lange & Carmichael and e is from comparison with the Birch-Murnaghan equation. This is described and tabulated in the Appendix to Ghiorso & Sack 1995.
For the solid end members the expression is taken from Berman 1988 (equation 5). In your notation it would be: V = a + b(T-Tr) + c(P-Pr) + d(T-Tr)^2 + e(P-Pr)^2
In addition some of the solid solutions, e.g. pyroxenes, have non-ideal volumes of mixing that are detailed in the individual papers describing the solution models. The references are linked in the the pinned forum post (https://magmasource.caltech.edu/forum/index.php/topic,85.0.html) but I imagine that's a lot more weeds than you want to get into.
Many thanks Paula!