Thermodynamic properties of the phases of H2O
Project description
SeaFreeze
V0.9.4
The SeaFreeze package allows to compute the thermodynamic and elastic properties of water and ice polymorphs (Ih, III, V, VI and ice VII/ice X) in the 0100 GPa and 220  10000K range, with the study of icy worlds and their ocean in mind. It is based on the evaluation of Gibbs Local Basis Functions parametrization (https://github.com/jmichaelb/LocalBasisFunction) for each phase. The formalism is described in more details in Brown (2018), Journaux et al. (2019), and in the liquid water Gibbs parametrization by Bollengier, Brown, and Shaw (2019).
Installation
This package will install SeaFreeze, LBFTD, and MLBspline and their dependencies.
Run the following command to install
pip install SeaFreeze
To upgrade to the latest version, use
pip install upgrade SeaFreeze
seafreeze.seafreeze
: calculating thermodynamic and elastic properties of a phase of water
Usage
The main function of SeaFreeze is seafreeze.seafreeze
, which has the following parameters:
PT
: the pressure (MPa) and temperature (K) conditions at which the thermodynamic quantities should be calculated  note that these are required units, as conversions are built into several calculations This parameter can have one of the following formats: a 1dimensional numpy array of tuples with one or more scattered (P,T) tuples
 a numpy array with 2 nested numpy arrays, the first with pressures and the second with temperatures  each inner array must be sorted from low to high values a grid will be constructed from the P and T arrays such that each row of the output will correspond to a pressure and each column to a temperature
phase
: indicates the phase of H₂O. Supported phases are 'Ih'  from Feistel and Wagner, 2006
 'II'  from Journaux et al., 2019
 'III'  from Journaux et al., 2019
 'V'  from Journaux et al., 2019
 'VI'  from Journaux et al., 2019
 'VII_X_French' for ice VII and ice X (French and Redmer 2015)
 'water1'  extends to 500 K and 2300 MPa; from Bollengier et al. 2019
 'water2'  extends to 100 GPa; from Brown 2018
 'water_IAPWS95'  LBF representation of IAPWS 95; from Wagner and Pruß, 2002
The output of the function is an object with properties corresponding to the following thermodynamic quantities (all but the last three are from lbftd):
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^{1} 
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 parameterization boundaries.
Example
import numpy as np
from seafreeze import seafreeze as sf
# list supported phases
sf.phases.keys()
# evaluate thermodynamics for ice VI at 900 MPa and 255 K
PT = np.empty((1,), dtype='object')
PT[0] = (900, 255)
out = sf.seafreeze(PT, 'VI')
# view a couple of the calculated thermodynamic quantities at this P and T
out.rho # density
out.Vp # compressional wave velocity
# evaluate thermodynamics for water at three separate PT conditions
PT = np.empty((3,), dtype='object')
PT[0] = (441.0858, 313.95)
PT[1] = (478.7415, 313.96)
PT[2] = (444.8285, 313.78)
out = sf.seafreeze(PT, 'water1')
# values for output fields correspond positionally to (P,T) tuples
out.H # enthalpy
# evaluate ice V thermodynamics at pressures 400500 MPa and temperatures 240250 K
P = np.arange(400, 501, 2)
T = np.arange(240, 250.1, 0.5)
PT = np.array([P, T], dtype='object')
out = sf.seafreeze(PT, 'V')
# rows in output correspond to pressures; columns to temperatures
out.A # Helmholtz energy
out.shear # shear modulus
seafreeze.whichphase
: determining the stable phase of water
Usage
Seafreeze also includes a function to determine which of the supported phases is stable
under the given pressure and temperature conditions.
The function whichphase
has a single parameter, PT
,
which requires the same format as in the seafreeze
function.
The output of the function is a Numpy array
with an integer indicating the phase number corresponding to the PT
input. The phase number 0 means
liquid water, phase number 1 means ice Ih, phase number 3 means ice III, etc. Points outside the range
of all phases will return numpy.nan
.
 for a list of scattered (P,T) conditions, each value corresponds to the same index in the input
 for a grid of PT conditions, each row corresponds to a pressure and each column to a temperature from the input.
seafreeze.phasenum2phase
can be used to map output phase numbers to a phase.
Each item in this dictionary has the phase number as its key and the phase as the value.
Example
import numpy as np
from seafreeze import seafreeze as sf
# determine the phase of water at 900 MPa and 255 K
PT = np.empty((1,), dtype=object)
PT[0] = (900, 255)
out = sf.whichphase(PT)
# map to a phase using phasenum2phase
sf.phasenum2phase[out[0]]
# determine phase for three separate (P,T) conditions
PT = np.empty((3,), dtype=object)
PT[0] = (100, 200)
PT[1] = (400, 250)
PT[2] = (1000, 300)
out = sf.whichphase(PT)
# show phase for each (P,T)
[(PT, sf.phasenum2phase[pn]) for (PT, pn) in zip(PT, out)]
# find the likely phases at pressures 05 MPa and temperatures 240300 K
P = np.arange(0, 5, 0.1)
T = np.arange(240, 300)
PT = np.array([P, T])
out = sf.whichphase(PT)
Important remarks
Water representation
The ices Gibbs parameterizations are optimized to be used with 'water1' Gibbs LBF from Bollengier et al. (2019), specially for phase equilibrium calculation. Using other water parameterization wil lead to incorrect 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 200355 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 ice VII and ice X representation extend to 1TPa (1e6 MPa) and 2000K.
References
 Bollengier, Brown and Shaw (2019) J. Chem. Phys. 151, 054501; doi: 10.1063/1.5097179
 Brown (2018) Fluid Phase Equilibria 463, pp. 1831
 Feistel and Wagner (2006), J. Phys. Chem. Ref. Data 35, pp. 10211047
 Journaux et al., (2019), in review in JGR: Planets (available on ArXiv)
 Wagner and Pruss (2002), J. Phys. Chem. Ref. Data 31, pp. 387535
 French and Redmer (2015), Physical Review B 91, 014308
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
 Marshall J. Styczinski  Blue Marble Space Institute of Science, Seattle, USA
 Tyler Gordon  University of Washington, Department of Astronomy, Seattle, USA
Change log
Changes since 0.9.0
0.9.4
: Adjusted python readme syntax and package authorship info0.9.3
: add ice VII and ice X from French and Redmer (2015). LocalBasisFunction spline interpretation software integrated into SeaFreeze Python package. Adjusted packaging to work better with pip0.9.2.post2
:whichphase
returnsnumpy.nan
if PT is outside the regime of all phases0.9.2
: add ice II to the representation.0.9.1
: addwhichphase
function
Changes from 0.8
 rename function get_phase_thermodynamics to seafreeze
 reverse order of PT and phase in function signature
 remove a layer of nesting (
seafreeze.seafreeze
rather thanseafreeze.seafreeze.seafreeze
)
License
SeaFreeze is licensed under the GPL3 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.
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 (08NAI50021).
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.
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