Heat capacity (Cp) of the melt and H2O dissolved

[Gabriel Girela]

Hello,

I am using alphaMELTS 2 with the rhyoliteMELTS 1.1.0 to make some numerical simulations. I wanted to know if (and how) the Cp of the melt phase is calculated, and how it takes into account the Cp of H2O dissolved. Checking on the papers I found that for the melt, the Cp is calculated by Lange & Navrosky (1992) model, but I don't know if this had being updated since to add the Cp of the water (for example, with the model of Bouhifd et al. (2006)).

Thank you very much!

[Paula]

The H2O model in rhyolite-MELTS 1.1.0 is the old one, same as rhyolite-MELTS 1.0.2 and the original MELTS model. How the thermodynamic properties of the H2O dissolved in the melt, including the Cp contribution, are calculated is described in the last paragraph of Ghiorso & Sack (1995):

Thermodynamic properties of the H20 component in molten silicate liquids are modeled following the method of Nicholls (1980; Ghiorso et al. 1983). We adopt his value for the reference state entropy (152.63 J/mol-K) and optimize a value of the reference enthalpy (-279.992 kJ/mol) to satisfy best the experimental data on water solubility discussed above. We modify Nicholls' (1980) function for the volume integral contribution to the molar Gibbs energy of dissolved H20 by subtracting the Gibbs energy of supercritical water tabulated by Robie et al. (1978) and adding the identical quantity from Berman (1988, see previous paragraphs). This insures the thermodynamic properties of the H20 component of Table AI are internally consistent with those of the supercritical fluid.

However, unless you are trying to model the granite ternary minimum you should probably be using rhyolite-MELTS 1.2.0, which includes the updated water solubility model (Ghiorso & Gualda, 2015). See the MELTS decision tree:

https://melts.ofm-research.org/MELTS-decision-tree.html

Paula

[Gabriel Girela]

Thank you very much for your response. I was also checking on the mineral phases' Cp, and I don't quite get the same results using Berman (1985) model, most probably because this model accounts for the end members solid solutions. How is it computed for, for example, a "plagioclase1" with a not end-member albite composition? Meaning that it is not pure NaAlSi3O8, but this is the predominant composition.

Thank you very much!

[Paula]

It depends how you are calculating Cp for the Berman model. Are you taking the Cp expressions from Berman & Brown (1985)? There are a couple of sources of discrepancy:

• 
  For albite you need to accounting for Al-Si order / disorder. The approach used is described on page 498 of Berman (1988) and encoded in the albite.c file that is part of the MELTS source code.
• Pure phases that include 2nd order transitions, such as the silica polymorphs, have slightly different Landau contributions to Cp in Berman (1988), as compared to Berman & Brown (1985). The correction is implied by, but not discussed in, Berman (1988), and is also not mentioned in the MELTS papers.

The solution properties of feldspar in MELTS are taken from Elkins and Grove, Ternary feldspar experiments and thermodynamic models, American Mineralogist 75, 544-559 and encoded in feldspar.c. The expressions from that give the Gibbs Free Energy of mixing (G_mix). The Cp of mixing is Cp_mix = - T ∂²G_mix/∂T²

However, for feldspar and most of the other solution phases in MELTS models, the Cp_mix term is zero. See the following and the code for more details:

• 
  https://magmasource.caltech.edu/forum/index.php/topic,85.0.html
• https://melts.ofm-research.org/CORBA_CTserver/Webservices/CTserverPLWS.html

If you want to view the MELTS source code you should sign up for GitLab (gitlab.com) and write to Mark Ghiorso (ghiorso@ofm-research.org) with your GitLab username to request access.