We have discovered an algebraic error in the silicate melt x-eos published in two of our papers and previously available through this website:
- Holland et al (2018), which we made available as the “igneous set” of x-eos.
- Tomlinson & Holland (2021), a variant of the Holland et al (2018) set which focused on improving calculations in anhydrous peridotitic systems.
The nature and implications of the error are discussed in: Green et al (2025), Corrigendum to: “Melting of Peridotites through to Granites: A Simple Thermodynamic Model in the System KNCFMASHTOCr”, and “A Thermodynamic Model for the Subsolidus Evolution and Melting of Peridotite”, Journal of Petrology, submitted.
Replacement “igneous set” x-eos
For the Holland et al (2018) “igneous set”, we have corrected and recalibrated the melt x-eos (many thanks to TJBH for his very hard work on this). In the process, we took the opportunity to update all of the x-eos for mineral phases to the latest versions, making the anhydrous mineral x-eos and the version of the Holland & Powell (2011) dataset consistent with those in our new alkaline to subalkaline igneous x-eos in Weller et al (2024).
The replacement x-eos (Green et al, 2025, corrected from Holland et al, 2018) will shortly (by 10th January?) be available in MAGEMin. They are documented on this website, and will soon (end of January?) be available for THERMOCALC 3.51 and above. There is currently no replacement for the Tomlinson & Holland (2021) x-eos, due to ongoing model development in anhydrous peridotitic systems.
Implications for calculations
Fortunately, as far as we’ve been able to tell (see Green et al, 2025, for more details), the error in the melt x-eos doesn’t seem to affect calculations with the former “igneous set” beyond a typical model uncertainty, as estimated in various ways:
- Weller et al (2024) and Green et al (2016) estimate that the 1 sigma uncertainty in pseudosection boundaries is typically around +/- 1 kbar or +/- 50ºC for non-accessory phases.
- In subalkaline systems, calculations with the replacement “igneous set” can be compared with the alkaline to subalkaline x-eos used in Weller et al (2024). In this comparison, the mineral x-eos and the key subalkaline calibration constraints are identical in both cases, but the melt x-eos have different structures, allowing the Weller et al (2024) melt x-eos to reproduce experiments in alkaline systems. The difference between these calculations suggests a scale for uncertainty, arising from the non-unique choice of structure and parameterization in melt x-eos in subalkaline systems.
- Since 2018 we have introduced several changes to x-eos in the downloadable “igneous set”. In particular, we changed the ternary feldspar x-eos from the Holland & Powell (2003) model to the Holland et al (2021) model, reflecting our changing understanding of the best way to represent the energetics of the feldspar lattice and fit experimental data in the ternary system. A scale for the uncertainties is provided by the effect of such updates to the mineral x-eos.
Nevertheless, please let us know if you see any dramatic changes in calculations after switching to the corrected model. We will pass on new information that we learn from users via this blog and the Discussion Group.
The HPx-eos and THERMOCALC 