Phase equilibrium resource hub

A great many resources are now available on all aspects of phase equilibrium modelling. Here we collect links and references to resources for calculating geological phase equilibria. We will add to it over time. Please contact us with corrections, suggested additions to the list, and reports of broken links.

Theoretical background

General background

An excellent place to start is the Teaching Phase Equilibria website provided by the Science Education Resource Center at Carleton College (SERC).

See also this list of some of our favourite textbooks, papers and online resources, providing a fairly general overview of the subject in its various aspects. The topics covered include:

  • expressing the thermodynamic properties of a phase in an equation of state
  • theoretical underpinnings of phase equilibrium
  • geological phase relations
  • use of phase diagrams to describe phase equilibria in a way that can be helpfully related to observations
  • calculating geological phase equilibria and phase diagrams.

Some perspectives

Here we discuss some themes that we find interesting, particularly those arising from the Discussion Group. Discussion Group questions often concern the HPx-eos, but we are also interested in more general aspects of phase equilibrium modelling. We will add more discussion themes over time.

Ask us more questions via this website or the discussion group!

Modelling packages

THERMOCALC and the HPx-eos

Our own THERMOCALC software and HPx-eos.

The HPx-eos are the set of thermodynamic models that contain the information we need to predict geological phase relations. They must be used via calculation software of some sort. They are native to THERMOCALC, but can be used via alternative software such as Perple_X and Theriak/Domino. However:

  • we do not guarantee that they have been implemented correctly outside THERMOCALC
  • in other software, it may be harder to identify the families of HPx-eos that can be used together.

THERMOCALC can be used to calculate a variety of equilibrium phase diagrams, perform multiple-reaction thermobarometry, and obtain thermodynamic information from the HPx-eos and the Holland & Powell dataset. It is not possible to use any other thermodynamic datasets or models in THERMOCALC.


The Perple_X software package (e.g. Connolly, 2009, Am J Sci 290 524-541) allows the user to calculate phase diagrams and obtain thermodynamic data on phases and stable phase assemblages. It implements many different thermodynamic datasets and models for phases, including our own HPx-eos.


The Theriak/Domino software package (de Capitani & Petrakakis, 2010, Am Mineral 95 1006-1016) allows the user to calculate phase diagrams and obtain thermodynamic data on phases and stable phase assemblages. It implements our HPx-eos.


MELTS (e.g. Asimow & Ghiorso, 1998, Am Mineral 83 1127-1131) is a package for phase equilibrium modelling in magmatic systems, including fractional crystallisation calculations. MELTS is both a calculation program and a set of thermodynamic models, or x-eos (originating in Ghiorso & Sack, 1995, Contrib Mineral Petrol 119 197-212), for describing the phase relations.


The ENKI (Enabling KNowledge Integration) project seeks to provide a universal environment for developing and using both thermodynamic models such as the HPx-eos, and fluid dynamical models for geodynamics calculations. Within the development phase of the ENKI project, we will aim to ensure that the HPx-eos are fully and correctly implemented in it. We may ultimately provide many of our methods through ENKI.

Web forums and user groups

There has been a vigorous Perple_X Discussion Group for many years (moving from Yahoo! to Nov-Dec 2019), which, among other things, has discussed aspects of modelling with the HPx-eos.

There are also forums for users of Theriak/Domino and MELTS.

We are introducing a THERMOCALC Discussion Group. It will be primarily focused on use of the HPx-eos via THERMOCALC, and on the details of the HPx-eos themselves. You are welcome to ask questions about results that you’ve obtained by using the HPx-eos in a program other than THERMOCALC. However, please check first that your question hasn’t already been answered on the forum associated with that software – inevitably there will be themes that overlap between the various discussion groups.

Help! My results make no sense

Try checking that:

Puzzle pieces: from a jigsaw puzzle based on Transience II (Peony) 2019 by Cai Guo-Qiang, currently on display at the National Gallery of Victoria.
  • Phase equilibrium modelling is appropriate for your rock. Is the assemblage likely to be at equilibrium on the lengthscale that you are considering? Some microstructurally complex rocks may be interpreted from an equilibrium perspective but this requires detailed analysis and thought. It is typically not a pseudosection problem, but might require the use of µ-µ diagrams, as in White et al (2008).
  • The calculation has been set up appropriately. What is the best choice of the independent variables in the problem (the usual P, T and bulk composition may not be appropriate)? Is the estimate of bulk composition a representative one?
  • The HPx-eos you are using are appropriate for the phase assemblages and compositions you observe
  • Phases have not been omitted from the calculations that should be present
  • You are aware of any quirks of the HPx-eos that you are using
  • You are not asking for too much precision from the HPx-eos. We hope HPx-eos will accurately predict the main phases present and their approximate modal proportions. The phase compositions may not be predicted well. It is not realistic to expect that the predicted site occupancies will be accurate.

If none of this is helpful or you are still unsure, you may find that a similar problem has been solved on one of the user forums, or you could ask a question yourself.

What have we missed?

Please contact us with corrections, suggested additions to the list above, and reports of broken links.