Equation of State (EOS) Library
MAGRATHEA includes a comprehensive set of Equations of State (EOS) for solid, liquid, and gaseous planetary materials.
This page describes all EOS entries defined in EOSlist.cpp, with their variable names, references, and notes.
Default EOS Set
These are the default EOSs used by the standard phase diagrams (Fe_default, Si_default, water_default, and gas_default).
Fe_hcp3 — Epsilon (hcp) iron, Dorogokupets et al. (2017, Scientific Reports). Default solid core EOS.
Fe_liquid — Liquid iron, Dorogokupets et al. (2017). Default molten core EOS.
Si_Pv — Perovskite (Bridgmanite) MgSiO₃, Oganov & Ono (2004, Nature). Default mantle EOS.
Si_PPv_Sakai — Post‑Perovskite MgSiO₃, Sakai et al. (2016, Scientific Reports). Default deep mantle EOS.
Si_Liquid_Wolf — Liquid MgSiO₃, Wolf & Bower (2018). Default silicate melt EOS.
Water_IAPWS — Liquid water, Wagner & Prub (2022, JPCRD). Default low‑pressure hydrosphere EOS.
Water_Brown — Supercritical water, Brown (2018, Fluid Phase Equilibria). Default high‑temperature fluid EOS.
IceVI_Bezacier, IceVII_Bezacier, IceX — High‑pressure ice polymorphs, Bezacier et al. (2014), Fei et al. (1993). Default ices.
Gas — Adiabatic ideal gas, default atmospheric EOS.
Gas_iso — Isothermal ideal gas, used for fixed‑temperature atmospheres.
Iron EOS
Fe_liquid, Dorogokupets et al. 2017 — Liquid Fe, primary melt EOS.
Fe_liquid2, Anderson & Ahrens 1994 — Alternate liquid Fe fit.
Fe_bcc, Dorogokupets et al. 2017 — α‑Fe (bcc).
Fe_fcc, Dorogokupets et al. 2017 — γ‑Fe (fcc).
Fe_hcp, Smith et al. 2018 — ε‑Fe (hcp), solid core EOS.
Fe_hcp2, Bouchet et al. 2013 — Alternate ε‑Fe model.
Fe_hcp3, Dorogokupets et al. 2017 — Default solid Fe EOS.
Fe_7Si, Wicks et al. 2018 — Fe‑7wt%Si alloy.
Fe_15Si, Wicks et al. 2018 — Fe‑15wt%Si alloy.
Fe_Seager, Seager et al. 2007 — Tabulated Fe EOS.
Fe_Dummy — Placeholder Fe EOS.
Silicate and Mantle EOS
Si_liquid, Mosenfelder et al. 2009 — Liquid MgSiO₃.
Si_Liquid_Wolf, Wolf & Bower 2018 — Default silicate melt (RTpress form).
Fo, Wds, Rwd, Akm, Dorogokupets et al. 2015 — Olivine, Wadsleyite, Ringwoodite, Akimotoite.
Fo_Sotin, En, Mw, Sotin et al. 2007 — Simplified mantle phases.
Si_Pv, Oganov & Ono 2004 — Perovskite (Bridgmanite).
Si_Pv_Shim, Shim & Duffy 2000 — Alternate perovskite.
Pv_Doro, Dorogokupets et al. 2015 — Bridgmanite variant.
Si_PPv_Sakai, Sakai et al. 2016 — Default post‑perovskite.
Si_PPv, Oganov & Ono 2004 — Alternate post‑perovskite.
PPv_Doro, Dorogokupets et al. 2015 — Post‑perovskite variant.
Si_PREM, Stacey & Davis 2008 — Tabulated PREM silicate.
Si_BM2fit, Zeng 2016 — Simplified PREM extrapolation.
Si_Seager, Seager et al. 2007 — Tabulated silicate.
Si_Dummy — Placeholder silicate EOS.
Extended Silicate Library (Stixrude & Lithgow‑Bertelloni 2011)
Covers mineral families used for complex mantle models.
Anorthite, Spinel, Fayalite, Fe_Wadsleyite, Fe_Ringwoodite, Enstatite, Ferrosilite, Diopside, Hedenbergite, HP_clinopyroxene, Mg_Akimotoite, Fe_Akimotoite, Pyrope, Mg_Majorite, Almandine, Grossular, Quartz, Coesite, Stishovite, Seifertite, Fe_Post_Perovskite, Fe_Perovskite, HP_Clinoferrosilite, Periclase, Wustite, Kyanite, Nepheline — All use Vinet EOS fits from Stixrude & Lithgow‑Bertelloni (2011).
Water, Ice, and Hydrosphere EOS
Water_SF, Bollengier et al. 2019 — SeaFreeze table.
Water_IAPWS, Wagner & Prub 2022 — IAPWS R6‑95 water.
Water_ExoPlex, unknown source — ExoPlex liquid water.
Water, Valencia et al. 2007 — Simplified water EOS.
Water_Brown, Brown 2018 — Supercritical water.
Water_sc_Mazevet, Mazevet et al. 2019 — A&A 621, high‑T plasma water.
IceIh_SF, IceII_SF, IceIII_SF, IceV_SF, IceVI_SF, Journaux et al. 2020 — Tabulated ice phases.
IceIh, Feistel & Wagner 2006 — Solid ice Ih.
IceIh_ExoPlex, ExoPlex variant.
IceVI_ExoPlex, Bezacier et al. 2014 — Ice VI.
IceVI_Bezacier, Bezacier et al. 2014 — Default ice VI EOS.
IceVII_Bezacier, Bezacier et al. 2014 — Default ice VII EOS.
IceVII_FFH2004, Frank, Fei & Hu 2004 — Ice VII, Vinet fit.
IceVII_FFH2004fit/BM/T, FFH2004 variations.
IceVII_Fei, Fei et al. 1993 — Ice VII model with melt curve.
IceVIIp, IceVII, IceVII (Grande) — Alternate high‑pressure ice fits.
IceX, Grande — Default high‑P ice.
IceX_HS, Hermann & Schwerdtfeger 2011 — PRL fit.
Ice_Seager, Seager et al. 2007 — Tabulated ice.
H2O_AQUA, Haldemann et al. 2022 — AQUA tabulated EOS.
H2O_SeaFreeze, Journaux et al. 2020 — Combined water/ice table.
Ice_Dummy, Placeholder EOS.
IceZeng2013FFH/FMNR, Zeng 2013 — Modified Zeng ice fits.
Atmosphere and Gas EOS
Gas — Ideal adiabatic gas (default).
Gas_iso — Isothermal ideal gas.
vdW_H2, vdW_He, vdW_H2O, vdW_CH4, vdW_NH3, vdW_CO2 — Van der Waals EOS for major planetary gases.
watervapor — Ideal water vapor.
Water_Vap_IAPWS — IAPWS vapor EOS.
Gas_hhe — H/He mixture, Chabrier & Debras (2021).
Carbon and Carbides
Graph, Seager et al. 2007 — Graphite, Birch‑Murnaghan EOS.
Diam, Benedict et al. 2018 — Diamond, Vinet EOS.
BC8, Benedict et al. 2018 — BC8 carbon polymorph.
SiC_B3_Vinet, SiC_B1_Vinet, Miozzi et al. 2018 — Silicon carbide polymorphs.
Calibration and Miscellaneous Metals
Gold_BM3, Heinz & Jeanloz 1983 — Gold calibration EOS (BM3).
Gold, Matsui et al. 2010 — Alternate gold fit.
Plat, Matsui et al. 2009 — Platinum standard.
EOS Parameter Schema
Each EOS uses a numerical parameter list {{index, value}}, where key fields include:
Index |
Parameter |
Meaning |
|---|---|---|
1 |
V₀ |
Molar volume (cm³/mol) |
2 |
K₀ |
Bulk modulus (GPa) |
3 |
K₀′ |
Pressure derivative |
5 |
M |
Molar mass (g/mol) |
7 |
Θ₀ |
Debye/Einstein temperature (K) |
8–11 |
γ parameters |
Grüneisen model coefficients |
14 |
n |
Atoms per formula unit |
16–19 |
α parameters |
Thermal expansion coefficients |
20–22 |
cₚ coefficients |
Heat capacity model |
23 |
Debye flag |
+Debye, −Einstein |
33–34 |
Van der Waals a,b |
Gas constants |
Full definitions appear in the top comments of EOSlist.cpp.
Implementation Notes
All EOS return pressure–density–temperature relations compatible with the hydrostatic solver.
Most solids use Birch–Murnaghan (BM3) or Vinet forms with Debye/Einstein thermal corrections.
Liquids may use RTpress or tabulated equations.
Atmosphere and gas EOS use ideal or van der Waals forms.
Tabulated EOS load from the
./tabulated/directory.Units: pressure in GPa, density in g cm⁻³, temperature in K.
This document summarizes all EOS definitions contained in EOSlist.cpp.