SeaFreeze

V0.9.2

The SeaFreeze package allows to compute the thermodynamic and elastic properties of water and ice polymorphs (Ih, II, III, V and VI) in the 0-2300 MPa and 220-500K range. It is based on the evaluation of Gibbs Local Basis Functions parametrization (https://github.com/jmichaelb/LocalBasisFunction) for each phase, constructed to reproduce thermodynamic measurments. 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).

Getting Started

Installing

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

Running SeaFreeze

This section provide basic example on how to run SeaFreeze. It is using pseudo code, so synthax will change depdending on the version used.

Inputs

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

out=SeaFreeze(PT,'material')

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

'material' defines which ice or water 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)
• '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)

Outputs

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

Quantity	Symbol in SeaFreeze	Unit (SI)
Gibbs Energy	G	J/kg
Entropy	S	J/K/kg
Internal Energy	U	J/kg
Enthalpy	H	J/kg
Helmholtz free energy	A	J/kg
Density	rho	kg/m^3
Specific heat capacity at constant pressure	Cp	J/kg/K
Specific heat capacity at constant volume	Cv	J/kg/K
Isothermal bulk modulus	Kt	MPa
Pressure derivative of the Isothermal bulk modulus	Kp	-
Isoentropic bulk modulus	Ks	MPa
Thermal expansivity	alpha	/K
Shear modulus	shear	MPa
P wave velocity	Vp	m/s
S wave velocity	Vs	m/s
Bulk sound speed	vel	m/s

NaN values returned when out of parametrization boundaries.

Example

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

Single point input

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 input

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 input

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]

Important remarks

Water representation

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 incorect melting curves. 'water2' (Brown 2018) and 'water_IAPWS95' (IAPWS95) parametrization are provided for HP extention (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.

Range of validity

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:

References

• 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

Authors

• Baptiste Journaux - 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
• Erica Clinton - University of Washington, Earth and Space Sciences Department, Seattle, USA

Change log

Changes since 0.9.0

• SeaFreeze GUI available
• 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.

Planned updates

• ice VII and X
• NaCl and MgSO4 aqueous solutions
• NH_3 aqueous solutions
• NaCl bearing solids (Halite and hydrohalite)

License

This project is licensed under the MIT License :

Copyright (c) 2019, B. Journaux

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files, to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Acknowledgments

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.