Add library of solidus parameterizations selectable via melting_dir parameter

[planetmariana]

Feature description

This issue covers a script that provides a collection of commonly used solidus parameterizations from the literature. The goal is to allow users to easily select different melting curves by modifying the parameter melting_dir. Providing a centralized list of parameterizations would make it easier to test different melting curves and compare their impact on PROTEUS simulations.

Preferred solution

Create a script that contains several solidus parameterizations from the literature. The script would generate the appropriate melting curves and will save them in FWL_DATA/interior_lookup_tables/Melting_curves and link them to the melting_dir parameter in the configuration file.

Each option in melting_dir would correspond to a predefined set of solidus/liquidus relations, allowing the user to switch between parameterizations.

Additional information

This feature originates from the implementation of an fO₂-dependent solidus used in a project based on Lin et al, 2024. The function describing this solidus takes the target fO₂ and the pressure–temperature (P–T) range as input parameters, allowing the melting curve to be generated dynamically for different redox conditions. Generalizing this approach would allow additional parameterizations (e.g., Earth-like mantle, reduced/oxidized compositions, or other experimental fits) to be included in a consistent framework.

Relevant people

@nichollsh @maraattia @timlichtenberg

[maraattia]

Some feedback from the PALEOS side, since the EoS tables depend on the solidus/liquidus.

On the preferred solution

The idea of centralizing solidus/liquidus parameterizations in a single script sounds great. One thing to keep in mind: it would be helpful if each parameterization exposes a consistent interface (e.g., T_solidus(P) and T_liquidus(P) callables, or simply writes out the same two-column P [Pa] T [K] format currently used) so that downstream tools can consume them without special-casing.

Implications for PALEOS tables

The PALEOS MgSiO₃ lookup tables for PROTEUS (Zenodo) use the solidus and liquidus files only to set global temperature bounds: min(T_solidus) for the liquid table and max(T_liquidus) for the solid table. This means the tables need to be generated once for the solidus/liquidus pair with the maximal P–T extent, so that they cover the domain required by all available parameterizations. I will determine the appropriate bounds from the current set of curves now (@planetmariana can you direct me to where I can find all of them please?), but if new parameterizations are added in the future with a larger P–T footprint, the tables will need to be regenerated using the notebook at utils/mgsio3_tables_proteus.ipynb. It has a single user-input cell where the boundary files and grid parameters can be swapped in.

Solidus–liquidus relation

Worth noting for the collection: a well-behaved solidus parameterization from Stixrude (2014) relates the solidus to the liquidus via

$$T_\mathrm{solidus} = \frac{T_\mathrm{liquidus}}{1 - \ln\phi_\mathrm{c}}$$

where $\phi_\mathrm{c} = 0.79$ is the rheological transition melt fraction (giving a factor of roughly $1/(1 - \ln 0.79) \approx 0.8$). This is a multiplicative scaling that preserves the shape of the melting curve, which is arguably more physical than a constant offset (e.g., the current 600 K shift between solidus and liquidus, which becomes negligible at high P where both curves reach tens of thousands of K). Might be worth including as one of the available options.

[planetmariana]

Thanks for the information @maraattia. So far I have collected the following parametrizations from the literature. Some of them provide both the solidus and liquidus, while others only include one of them. For those cases, I plan to generate the missing curve using the relation you mentioned from Stixrude (2014) . Then once the melting_dir parameter is called, it will generate and use those tables.

If I am missing any important parametrizations, please let me know :)

Reference	Solidus	Liquidus
Andrault et al. (2011)	X	X
Monteux et al. (2016)	X	X
Lin et al. (2024)	X
Hirschmann (2020)	X	X
Katz et al. (2003)	X	X
Stixrude (2014)	X
Fei et al. (2021)		X
Belonoshko et al. (2005)		X
Fiquet et al. (2010)		X