A new x-eos for ternary feldspars

What’s new?

We have published new x-eos for plagioclase and alkali feldspars:

TJB Holland, ECR Green & R Powell (2021). A thermodynamic model for feldspars in KAlSi3O8-NaAlSi3O8-CaAl2Si2O8 for mineral equilibrium calculations. Journal of Metamorphic Geology, 1-14. DOI: 10.1111/jmg.12639

The preferred ternary feldspar x-eos in this paper is the 4TR model (the name is discussed below). This single x-eos replaces two previous x-eos: the Ibar1 and Cbar1 ternary feldspar x-eos of Holland & Powell (2003), Contributions to Mineralogy and Petrology, 145 492-501.

Additionally, we have introduced a binary x-eos to represent low albite with minor dissolved Ca. This can be used to model the peristerite gap in metabasites, where previously we used pure end-member albite.

Finding the feldspar x-eos in the axfiles

I have added the new (HGP21) feldspar x-eos to the downloadable axfiles, but have retained the older (HP03) x-eos for backwards-compatibility. I used the following phase names:

pl4trTernary feldspar, plagioclase-friendly variables.Replaces pli and plc. Same x-eos as k4tr.
k4trTernary feldspar, K-feldspar-friendly variables.Replaces ksp. Same x-eos as pl4tr
abcLow-albite with solid solution towards anorthite, for modelling the peristerite gap in metabasites.Previously modelled with the pure ab end-member.
pliIbar1 ternary feldspar, plagioclase-friendly variables.Replaced by pl4tr.
plc (“pl”)Cbar1 ternary feldspar, plagioclase-friendly variables.Replaced by pl4tr. Same x-eos as ksp. Called “pl” in older metabasite/metapelite axfiles.
kspCbar1 ternary feldspar, K-feldspar-friendly variables.Replaced by k4tr. Same x-eos as plc.

Note that pl4tr and k4tr are the same x-eos, and plc and ksp are the same x-eos. They are just expressed in terms of different compositional variables:

  • “Plagioclase-friendly variables” are {ca->xCa, k->xK}; these make it easy to eliminate K or Ca from the x-eos in THERMOCALC, which is often useful when modelling with plagioclase.
  • “K-feldspar-friendly variables” are {ca->xCa, na->xNa}; these make it easy to eliminate Na or Ca from the x-eos in THERMOCALC, which is often useful when modelling with K-feldspar.

Some of the names that I have chosen are cumbersome, although I hope that they are easy to distinguish. When using the x-eos, you might want to rename phases using the samecoding script. For example, you could rename pl4tr as pl by setting

samecoding pl4tr pl

and making sure that you have an xyzguess block for pl among your starting guesses.

Features of the new x-eos

The following are some of the key ideas discussed in the Holland et al (2021) paper:

The plagioclase solid solution is notorious for its structural complexity. However, calculations show that most of this structural complexity is not energetically significant in the context of petrological phase equilibrium modelling under geologically relevant conditions.

For example, Holland & Powell (2003) modelled the transition between albite-rich plagioclase in C1 symmetry, and anorthite-rich plagioclase with I1 symmetry. But key geological phase equilibria can be modelled successfully without including this transition in the plagioclase solid solution. This is convenient, especially given that:

  • As we now realise, the C1-I1 transition described by the plc and pli x-eos in the albite-anorthite binary cannot be extrapolated into the ternary system, as plc and pli attempted to do.
  • The development of the plc and pli x-eos was motivated by an interest in modelling the C1-I1 transition, rather than a wish to model most-stable petrological phase relations via pseudosection calculations. As a result, the x-eos that yielded the lower Gibbs energy for the assemblage was not necessarily the one that represented the correct symmetry for the plagioclase composition.

The only structural phenomenon that does have to be represented in plagioclase in order to fit the petrological data well is the partial ordering of Al and Si on the tetrahedral sites. The new ternary feldspar x-eos represents this by reducing the tetrahedral site entropy of mixing by a factor of 4: the “4TR” model. This is why I have used the names pl4tr (and k4tr) in the updated axfiles.

Erratum, Holland, Green & Powell (2021)

p.12. The ideal activity expression for anorthite (an) should include a normalisation constant of 16^(1/4). Thanks to Doug Tinkham for spotting this.