V1.0

The SeaFreeze package allows to compute the thermodynamic and elastic properties of pure water, ice polymorphs (Ih, II, III, V VI and ice VII/ice X) up to 100 GPa and 10,000K and aqueous NaCl solution up to 8GPa and 2,000K. It is based on the evaluation of Gibbs Local Basis Functions parametrization (https://github.com/jmichaelb/LocalBasisFunction) for each phase, constructed to reproduce thermodynamic measurements. The formalism is described in more details in Journaux et al. (2020), and in the liquid water Gibbs parametrization by Bollengier, Brown, and Shaw (2019). Aqueous NaCl equation of state publication is in preparation.

Currently, the Python version is the most up to date. The Matlab version is still under beta for version 1.0.

Contact: bjournau (at) uw (dot) edu

Report to the README file for each version (Python or Matlab) for installing SeaFreeze.

This section provides basic examples on how to run SeaFreeze. It is using pseudocode, so syntax will change depending on the version used.

For Pure Water and ices

To run the SeaFreeze function for ices and pure water you need to provide pressure (MPa) and temperature (K) coordinates and a material input:

out=SeaFreeze(PT,'material')

For aqueous solutions

For obtaining properties aqueous solution of a given concentration in mol/kg, you need to provide pressure (MPa), temperature (K) and concentration coordinates (mol/kg):

out=SeaFreeze(PTm,'material')

For single properties

To improve computational efficiency, a list of specified thermodynamic variables can be calculated by specifying them as inputs to the SeaFreeze function:

out=SeaFreeze(PT,'material', 'G', 'rho')

PT is a structure (gridded output) or array (scatter output) containing pressure-temperature points (MPa and Kelvin).

• 'material' defines which ice, water, or solution to use. Possibilities:
• 'Ih' for ice Ih (Feistel and Wagner, 2006)
• 'II' for ice II (Journaux et al. 2020)
• 'III' for ice III (Journaux et al. 2020)
• 'V' for ice V (Journaux et al. 2020)
• 'VI' for ice VI (Journaux et al. 2020)
• 'VII_X_French' for ice VII and ice X (French and Redmer 2015)
• 'water1' for Bollengier et al. (2019) LBF extending to 500 K and 2300 MPa
• 'water2' for the modified EOS in Brown 2018 extending to 100 GPa and 10,000 K
• 'water_IAPWS95' for IAPWS95 water (Wagner and Pruss, 2002)
• 'aq_NaCl' for aqueous NaCl from JM Brown and B Journaux et al. (in prep.)

out is a structure containing all output quantities (SI units):

NaN values returned when out of parametrization boundaries.

An executable Matlab live script (Example_SeaFreeze.mlx) is provided allowing to run the following examples.

Single point for ice VI at 900 MPa and 255 K. This can be used to check returned thermodynamic properties values.

PT = {900,255};
out=SeaFreeze(PT,'VI')

Output :

out = 

  struct with fields:

      rho: 1.3561e+03
       Cp: 2.0054e+03
        G: 7.4677e+05
       Cv: 1.8762e+03
      vel: 3.6759e+03
       Kt: 1.7143e+04
       Ks: 1.8323e+04
       Kp: 6.2751
        S: -1.3827e+03
        U: -2.6951e+05
        H: 8.3090e+04
    alpha: 2.0020e-04
       Vp: 4.5490e+03
       Vs: 2.3207e+03
    shear: 7.3033e+03

Grid of points for ice V every 2 MPa from 400 to 500 MPa and every 0.5 K from 220 to 250 K

PT = {400:2:500,240:0.5:250};
out=SeaFreeze(PT,'V')

Output :

out = 

  struct with fields:

      rho: [51×21 double]
       Cp: [51×21 double]
        G: [51×21 double]
       Cv: [51×21 double]
      vel: [51×21 double]
       Kt: [51×21 double]
       Ks: [51×21 double]
       Kp: [51×21 double]
        S: [51×21 double]
        U: [51×21 double]
        H: [51×21 double]
    alpha: [51×21 double]
       Vp: [51×21 double]
       Vs: [51×21 double]
    shear: [51×21 double]

List of 3 points for liquid water at 300K and 200, 223 and 225 MPa

PT = ([200 300 ; 223 300 ; 225 300 ]);
out=SeaFreeze(PT,'water1')

out = 

  struct with fields:

      rho: [3×1 double]
       Cp: [3×1 double]
        G: [3×1 double]
       Cv: [3×1 double]
      vel: [3×1 double]
       Kt: [3×1 double]
       Ks: [3×1 double]
       Kp: [3×1 double]
        S: [3×1 double]
        U: [3×1 double]
        H: [3×1 double]
    alpha: [3×1 double]

Thermodynamic properties can be calculated for solutions of varying molality as well, where the input provides pressure (MPa), temperature (K), and molality (mol/kg) coordinates over a grid or list, or for a single point.

Single point for NaCl(aq) of 0.5 M at 900 MPa and 280 K:

PTm = {900, 280, 0.5};
out=SeaFreeze(PTm,'aq_NaCl')

Output :

out = 

  struct with fields:

           G: 7.7725e+05
           S: -143.0425
           U: 1.7738e+04
           H: 7.3720e+05
           A: 5.7790e+04
           F: 5.7790e+04
         rho: 1.2509e+03
          Cp: 3.7630e+03
          Cv: 3.3825e+03
          Kt: 7.7225e+03
          Ks: 8.5913e+03
          Kp: 5.7676
       alpha: 4.6921e-04
         vel: 2.6207e+03
          Va: 24.7939
         Cpa: 124.5329
         mus: 1.7721e+04
         muw: 1.4252e+04
          Vm: 24.3212
          Vw: 14.6032
         Cpm: 149.3719
         gam: 0.7631
         phi: 0.8174
         Vex: 0.2598
         Gex: -204.1910
          aw: 0.9854

Grid of points every 10 MPa from 0.1 to 1000 MPa, every 2 K from 240 to 501 K, and every 0.5 M from 1 to 6 mol/kg:

PTm = {0.1:10:1000.2,240:2:501,1:0.5:6}; 
out=SeaFreeze(PTm,'NaCl')

Output :

      out = 

  struct with fields:

           G: [101×131×11 double]
           S: [101×131×11 double]
           U: [101×131×11 double]
           H: [101×131×11 double]
           A: [101×131×11 double]
           F: [101×131×11 double]
         rho: [101×131×11 double]
          Cp: [101×131×11 double]
          Cv: [101×131×11 double]
          Kt: [101×131×11 double]
          Ks: [101×131×11 double]
          Kp: [101×131×11 double]
       alpha: [101×131×11 double]
         vel: [101×131×11 double]
          Va: [101×131×11 double]
         Cpa: [101×131×11 double]
         mus: [101×131×11 double]
         muw: [101×131×11 double]
          Vm: [101×131×11 double]
          Vw: [101×131×11 double]
         Cpm: [101×131×11 double]
         gam: [101×131×11 double]
         phi: [101×131×11 double]
         Vex: [101×131×11 double]
         Gex: [101×131×11 double]
          aw: [101×131×11 double]

The ices' Gibbs parametrizations are optimized to be used with 'water1' Gibbs LBF from Bollengier et al. (2019), specially for phase equilibrium calculation. Using other water parametrization wil lead to incorrect melting curves. 'water2' (Brown 2018) and 'water_IAPWS95' (IAPWS95) parametrization are provided for HP extension (up to 100 GPa) and comparison only. The authors recommend the use of 'water1' (Bollengier et al. 2019) for any application in the 200-355 K range and up to 2300 MPa.

A Gibbs energy representation of French and Redmer (2015) ice VII and X equation of state is provided for comparison only. It should not be used for melting point or solid-solid phase boundaries predictions.

SeaFreeze stability prediction is currently considered valid down to 130K, which correspond to the ice VI - ice XV transition. The ice Ih - II transition is potentially valid down to 73.4 K (ice Ih - ice XI transition).

The following figure shows the prediction of phase transitions from SeaFreeze (melting & solid-solid) and comparison with experimental data:

• Journaux et al. (2020) JGR Planets 125(1), e2019JE006176

• Bollengier, Brown and Shaw (2019) J. Chem. Phys. 151, 054501; doi: 10.1063/1.5097179
• Brown (2018) Fluid Phase Equilibria 463, pp. 18-31
• Feistel and Wagner (2006), J. Phys. Chem. Ref. Data 35, pp. 1021-1047
• Wagner and Pruss (2002), J. Phys. Chem. Ref. Data 31, pp. 387-535
• French and Redmer (2015), Physical Review B 91, 014308

• Baptiste Journaux (Lead) - University of Washington, Earth and Space Sciences Department, Seattle, USA
• J. Michael Brown - University of Washington, Earth and Space Sciences Department, Seattle, USA
• Penny Espinoza - University of Washington, Earth and Space Sciences Department, Seattle, USA
• Ula Jones - University of Washington, Earth and Space Sciences Department, Seattle, USA
• Erica Clinton - University of Washington, Earth and Space Sciences Department, Seattle, USA
• Tyler Gordon - University of Washington, Department of Astronomy, Seattle, USA

• 1.0: added NaCl aqueous solution EOS and concentration dependent thermodynamic variables. NaN returned for values outside the range of the representation.
• 0.9.4: add ice VII and ice X from French and Redmer (2015).
• SeaFreeze GUI available
• 0.9.4: Adjusted python readme syntax and package authorship info
• 0.9.3: LocalBasisFunction spline interpretation software integrated into SeaFreeze Python package. Adjusted packaging to work better with pip
• 0.9.2 patch1: added SF_WPD, SF_PhaseLines and SeaFreeze_version to the Matlab distribution.
• 0.9.2: add ice II to the representation.
• 0.9.1: add whichphase function to show which phase is stable at a PT coordinate.

• Ice VII and X available here as a beta
• NaCl aqueous solutions available here as a beta
• MgSO4, NasSO4 and MgCl2 aqueous solutions
• NH_3 aqueous solutions
• NaCl bearing solids (Halite and hydrohalite)

SeaFreeze is licensed under the GPL-3 License :

Copyright (c) 2019, B. Journaux

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, version 3.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.

THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

As of V1.0, SeaFreeze incorporates the mlbspline and lbftd packages originally developed by J. Michael Brown. Historical versions of these packages are no longer being updated and are available at https://github.com/jmichaelb/LocalBasisFunction.

This work was produced with the financial support provided by the NASA Postdoctoral Program fellowship, by the NASA Solar System Workings Grant 80NSSC17K0775 and by the Icy Worlds node of NASA's Astrobiology Institute (08-NAI5-0021).

Illustration montage uses pictures from NASA Galileo and Cassini spacecrafts (from top to bottom: Enceladus, Europa and Ganymede). Terrestrial sea ice picture use with the authorization of the author Rowan Romeyn.