Reference List

All equation-of-state parameter sets currently in the database, grouped by ice polymorph.

Ice Ih

Feistel, R. & Wagner, W. (2006). A new equation of state for H₂O ice Ih. J. Phys. Chem. Ref. Data, 35, 1021–1047.

H₂OFeistelWagnerIAPWS-2006 Gibbs energy EoS. Valid range: T ≤ 273.16 K, P ≲ 210 MPa (ice Ih stability).

Röttger, K., Endriss, A., Ihringer, J., Doyle, S. & Kuhs, W.F. (2012). Lattice constants and thermal expansion of H₂O and D₂O ice Ih between 10 and 265 K. Addendum. Acta Cryst. B, 68, 91.

DOI: 10.1107/S0108768111046908

H₂ORottgerPolynomialV_cell(T) = A₀ + A₃T³ + A₄T⁴ + … + A₇T⁷ [Å³]. P = 0 GPa only. Valid 10–265 K.

D₂ORottgerPolynomialV_cell(T) = A₀ + A₃T³ + A₄T⁴ + … + A₈T⁸ [Å³]. P = 0 GPa only. Valid 10–265 K. A₈ = 4.5747×10⁻¹⁸ (paper likely has a typo: "×10⁻¹" should be "×10⁻¹⁸").

Fortes, A.D. (2018). Accurate and precise lattice parameters of H₂O and D₂O ice Ih between 1.6 and 270 K from high-resolution time-of-flight neutron powder diffraction data. Acta Cryst. B, 74, 196–216.

DOI: 10.1107/S2052520618002159

H₂OFortesPowerExpα(T) = p·T^(q/T) + r·exp(s/T); V(T) = V₀·exp(∫₀ᵀ α dT'). P = 0 GPa only. Valid 1.6–270 K. Table 3.

D₂OFortesPowerExpα(T) = p·T^(q/T) + r·exp(s/T); V(T) = V₀·exp(∫₀ᵀ α dT'). P = 0 GPa only. Valid 1.6–270 K. Table 4.

Ice II

Journaux, B. et al. (2020). Holistic approach for studying planetary hydrospheres: Gibbs representation of ices thermodynamics, elasticity, and the water phase diagram to 2,300 MPa. J. Geophys. Res. Planets, 125, e2019JE006176.

DOI: 10.1029/2019JE006176

H₂OSeaFreezeGibbs energy (LBF) representation. Valid: ~0.20–0.45 GPa, 180–270 K.

Fortes, A.D., Wood, I.G., Alfredsson, M., Vočadlo, L. & Knight, K.S. (2005). The incompressibility and thermal expansivity of D₂O ice II determined by powder neutron diffraction. J. Appl. Cryst., 38, 612–618.

DOI: 10.1107/S0021889805014226

D₂OBM3Isothermal BM3 at 225 K. K₀′ = 6.0 fixed from ab initio (Fortes et al. 2003a). Fitted to 9 data points 0.25–0.45 GPa. BM3: P = (3K₀/2)(x^7/3 − x^5/3)(1 + 3/4(K₀′−4)(x^2/3−1)), x = V₀/V.

Ice III

DOI: 10.1029/2019JE006176

H₂OSeaFreezeGibbs energy (LBF) representation. Valid: ~0.29–0.45 GPa, 240–270 K.

Ice V

DOI: 10.1029/2019JE006176

H₂OSeaFreezeGibbs energy (LBF) representation. Valid: ~0.40–0.62 GPa, 210–280 K.

Ice VI

DOI: 10.1029/2019JE006176

H₂OSeaFreezeGibbs energy (LBF) representation. Valid: ~0.62–2.30 GPa, 130–450 K.

Bezacier, L. et al. (2014). Equations of state of ice VI and ice VII at high pressure and high temperature. J. Chem. Phys., 141, 104505.

DOI: 10.1063/1.4894421

H₂OBM3PVT BM2 fit (K₀′ fixed at 4). Valid ~1–2.6 GPa, 300–340 K. Table II. P = (3K₀/2)[(V₀(T)/V)^(7/3) − (V₀(T)/V)^(5/3)]; V₀(T) = V₀[1 + α₀(T − T_ref)].

Fortes, A.D. et al. (2012). The P–V–T equation of state of D₂O ice VI determined by neutron powder diffraction in the range 0 < P < 2.6 GPa and 120 < T < 330 K. J. Appl. Cryst., 45, 523–534.

DOI: 10.1107/S0021889812014847

D₂OMurnaghanMurnaghan PVT fit. Valid 0 < P < 2.6 GPa, 120 < T < 330 K. Table 4.

Ice VII

Bezacier, L. et al. (2014). Equations of state of ice VI and ice VII at high pressure and high temperature. J. Chem. Phys., 141, 104505.

DOI: 10.1063/1.4894421

H₂OBM3PVT BM2 fit (K₀′ fixed at 4). Valid ~2.7–10.1 GPa, 300–450 K. Table II. P = (3K₀/2)[(V₀(T)/V)^(7/3) − (V₀(T)/V)^(5/3)]; V₀(T) = V₀[1 + α₀(T − T_ref)].

Lai, X., Zhu, F., Zhang, D., Tkachev, S., Prakapenka, V. B., Chao, K.-H., & Chen, B. (2023). Thermal equation of state of ice-VII revisited by single-crystal X-ray diffraction. American Mineralogist, 108(8), 1530–1537.

DOI: 10.2138/am-2022-8554

H₂OBM3ThermalTable 1, Berman (1988) thermal BM3. Valid 3.5–78.2 GPa, 300–1000 K. SCXRD.

H₂OBM3Table 1, isothermal BM3 at 300 K (fitted V₀). Valid 3.5–78.2 GPa. SCXRD.

H₂OVinetTable 1, isothermal Vinet at 300 K (fitted V₀). Valid 3.5–78.2 GPa. SCXRD.

Klotz, S. et al. (2017). Bulk moduli and equations of state of ice VII and ice VIII. Phys. Rev. B, 95, 174111.

DOI: 10.1103/PhysRevB.95.174111

D₂OBM3Table III, BM3 fit. V₀ = 42.25 Å³ imposed at 298 K.

D₂OVinetTable III, Vinet (Rydberg-Vinet) fit. V₀ = 42.25 Å³ imposed at 298 K.

D₂OAP1Table III, Holzapfel AP1 fit. V₀ = 42.25 Å³ imposed at 298 K.

Sugimura, E. et al. (2010). Simultaneous high-pressure and high-temperature volume measurements of ice VII and its thermal equation of state. Phys. Rev. B, 82, 134103.

DOI: 10.1103/PhysRevB.82.134103

H₂OVinetAGTable II, This study. Vinet + Anderson-Grüneisen P-V-T EoS. Valid ~19–50 GPa, 430–880 K.

Somayazulu, M. et al. (2008). In situ high-pressure x-ray diffraction study of H₂O ice VII. J. Chem. Phys., 128, 064510.

DOI: 10.1063/1.2813890

H₂OVinetVinet fit, 3–48 GPa, RT. rXRD + SXRD.

Sugimura, E. et al. (2008). Compression of H₂O ice to 126 GPa and implications for hydrogen-bond symmetrization: Synchrotron x-ray diffraction measurements and density-functional calculations. Phys. Rev. B, 77, 214103.

DOI: 10.1103/PhysRevB.77.214103

H₂OVinetTable II, Experiment. Vinet EoS fit to synchrotron XRD data up to ~40 GPa at 300 K. V₀ fixed at ambient value.

Frank, M.R., Fei, Y. & Hu, J. (2004). Constraining the equation of state of fluid H₂O to 80 GPa using the melting curve, bulk modulus, and thermal expansivity of Ice VII. Geochim. Cosmochim. Acta, 68, 2781–2790.

DOI: 10.1016/j.gca.2003.12.007

H₂OBM3Table 3, BM3 fit at 300 K. Valid 6.57–60.52 GPa. V₀ is a fitted parameter (ice VII is nonquenchable).

H₂OBM3FrankPVTEqs. 4–5. α(P,T) = (a₀+a₁T)·(1+(K′/K)P)⁻η; V(P,T) = V_BM3(P,300K)·exp(∫₃₀₀ᵀ α dT). Valid 6.57–60.52 GPa, T ≥ 300 K (data collected on heating).

Loubeyre, P. et al. (1999). Modulated phases and proton centring in ice observed by X-ray diffraction up to 170 GPa. Nature, 397, 503–506.

DOI: 10.1038/17300

H₂OVinetVinet fit, 2–170 GPa, RT. V₀ fixed at ambient value. SCXRD.

Wolanin, E. et al. (1997). Equation of state of ice VII up to 106 GPa. Phys. Rev. B, 56, 5781.

DOI: 10.1103/PhysRevB.56.5781

H₂OBM3BM3 fit, ~5–106 GPa, RT. K₀ was fixed during fitting. PXRD.

H₂OVinetVinet fit, ~5–106 GPa, RT. K₀ was fixed during fitting. PXRD.

Fei, Y., Mao, H.-K. & Hemley, R.J. (1993). Thermal expansivity, bulk modulus, and melting curve of H₂O–ice VII to 20 GPa. J. Chem. Phys., 99, 5369–5373.

DOI: 10.1063/1.465980

H₂OBM3ThermalBM3 (isothermal, 300 K): P = (3K₀/2)(x⁷/³−x⁵/³)(1+(3/4)(K₀′−4)(x²/³−1)), x=V₀/V. PVT: V(P,T)=V(P,300K)·exp[∫α(P,T)dT], α(P,T)=α₀(T)(1+K′₀/K₀·P)^(−η), α₀(T)=a₀+a₁T; a₀=−3.9×10⁻⁴, a₁=1.5×10⁻⁶, η=0.9. Pressure-dependent α correction (η) not implemented; zero-pressure α₀(T) is used.

Hemley, R.J. et al. (1987). Static compression of H₂O-ice to 128 GPa. Nature, 330, 737–740.

DOI: 10.1038/330737a0

H₂OBM3BM3 (Jeanloz 1981 finite-strain form): P = (3K₀/2)(x⁷/³−x⁵/³)(1+(3/4)(K₀′−4)(x²/³−1)), x=V₀/V. V₀ extrapolated to zero pressure by linear least-squares fit using ice I density as reference. 4.3–128 GPa, RT.