The calculation of the activity of SiO2/TiO2

[chengkaide]

Recently I have read the paper about the application of Ti-in-zircon thermometry.

Paper title: Application of Ti-in-zircon thermometry to granite studies: problems and possible solutions

So I want to calculate the activity of SiO2 and the activity of TiO2 with the rhyolite-MELTS.

The paper shows the rhyolite-MELTS can calculate the affinity value. Although I open the melt.out with the melts for excel, I can not find the affinity.

If anyone has done this job before, I hope you can tell me your solution. Thank you very much

[asimow]

First, let's be careful: "activity" and "affinity" are not the same, and MELTS can calculate both, so let's go over the difference.

Affinity -- in an equilibrated assemblage, where the system chemical potentials are well-defined, there is a hyperplane that is tangent to the free-energy surfaces of all the phases that coexist in the equilibrium assemblage. The affinity of a phase is then the vertical distance, in energy units, between this tangent hyperplane and the corresponding parallel hyperplane that is tangent to the free energy surface of that phase. So, if the phase is part of the equilibrium assemblage its affinity is zero. If a phase is under-saturated (not present and no tendency for it to appear), its affinity is a positive number ... the larger its value, the further the phase is from stability. If a phase is over-saturated (meaning the current assemblage is metastable and this phase needs to be added to the assemblage in order to work towards the global minimum equilibrium state), its affinity is a negative number. So, you need affinities if you are interested in whether some solid phases are going to appear or not.

Activity -- for any component of a phase, the chemical potential is mu = mu0 + RTln(a), where mu0 is a standard state value defined by the properties of the phase at the P, T of interest when its composition is purely the component of interest, R is the gas constant, T is absolute temperature, and a is the activity. So, it expresses the (usually) decrease in chemical potential of a component in a solution as the solution is diluted with other components. You need activities to ask about the thermodynamic properties of component in a solution, such as silicate melt.

Now, for the particular cases of SiO2 and TiO2, it is easy to confuse these because quartz and rutile are pure phases. Therefore the affinity of quartz or rutile is zero when the activity of SiO2 or TiO2 is one. And so more generally it seems that the affinity of quartz is (mu0_quartz - mu_SiO2) = ââ,¬â€œRTln(a_SiO2) and the affinity of rutile is (mu0_rutile - mu_TiO2) = -RTln(a_TiO2). But this is wrong. The correct equation for activity is (mu0_SiO2_liquid - mu_SiO2) = ââ,¬â€œRTln(a_SiO2), so these are different if the standard state chemical potential of quartz is not equal to the standard state chemical potential of silica liquid, i.e if you are not exactly at the melting point of quartz.

So, the rhyoliteMELTS GUI displays phase affinities in the bottom panel of the rhyoliteMELTS GUI, but don't use these for this purpose.

Now, you're right that this information is not in melts.out. But it is in melts_liquid.tbl, which has entries for "activity SiO2" and "activity TiO2".

[chengkaide]

Thanks a lot.
I know the difference between affinity and activity.
There is an equation that can transform affinity to activity.
a(TiO2)=e^(-A(TiO2)/R*T)
Anyway, thank you very much for your answer.

[Paula]

You are right that in the paper and also in Ghiorso and Gualda (2013), which is cited, it is a(TiO₂)^{liquid-rutile} that they are estimating i.e. everything is referenced to the standard state of rutile. a(TiO₂)^{liquid-rutile} is independent of the liquid standard state and is related to affinity of rutile as you mention in your reply.

It turns out that there is a mistake in the standard state of TiO₂ in the liquid in rhyolite-MELTS (inherited in the MELTS liquid from The Oxide Handbook [Samsonov 1982] where T_fus is listed as 1870 K when it should be 1870 ^oC). Fortunately this doesn't affect the logic of the Ti-in-zircon paper as mu0(TiO₂)^liquid ends up cancelling out. It does mean that the activity of TiO₂ in the rhyolite-MELTS output file may be slightly off but the mu(TiO₂)^liquid should be fine. The chemical potentials were calibrated on a wide range of mineral-liquid constraints for natural composition liquids.

Note that in pMELTS the standard state of TiO₂, and some of the other end members in the liquid, are deliberately tweaked by adjusting S_fus so that the model behaves better in the compositional range of interest (i.e. for partial melting of peridotite and mafic pyroxenite). So the melting point of rutile is not reproduced there either, but this time by design. Likewise the melting point of quartz is not matched in rhyolite-MELTS because the standard state properties of the solid quartz and sanidine are adjusted in order to reproduce the granite ternary minimum. There's no such thing as a free lunch!

I think Ghiorso and Gualda (2013) used MELTS-batch (which is the MELTS implementation used in the Magma Chamber Simulator package). It can be used to output mu(TiO₂)^liquid and mu(TiO₂)^rutile in a relatively automated way. You could also try MELTS for Excel, which does record the affinities, though the traffic on the MELTS for Excel server is quite heavy at the moment with more people working from home than normal. Or you can take the affinities displayed in the bottom panel of the graphical user interface.

Alternatively, alphaMELTS for MATLAB/Python can be used for this calculation, and alphaMELTS 2 will be able to do it soon (just a bit hectic at the moment so I haven't had time to hook up the "thermodynamic output file" option).

Paula

[chengkaide]

Thanks for your reply.
I will try the procedure as your advice.
If there's progress, I'll show it.