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thermodynamic properties of the phases of H₂O

Project description



The SeaFreeze package allows computation of the thermodynamic and elastic properties of water and ice polymorphs Ih, III, V and VI in the 0-2300 MPa and 220-500 K range. It is based on the evaluation of Local Basis Functions for each phase. The formalism is described in more details in Brown (2018), Journaux et al. (2019), and in the liquid water Gibbs parameterization by Bollengier, Brown, and Shaw (2019).


This package will install uw-highP-geophysics-tools and its dependencies.

Run the following command to install

pip3 install SeaFreeze

To upgrade to the latest version, use

pip3 install --upgrade SeaFreeze

seafreeze.seafreeze: calculating thermodynamic and elastic properties of a phase of water


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 1-dimensional 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
    • '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/m3
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.


import numpy as np
import seafreeze as sf

# list supported phases

# evaluate thermodynamics for ice VI at 900 MPa and 255 K
PT = np.empty((1,), np.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,), np.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 400-500 MPa and temperatures 240-250 K
P = np.arange(400, 501, 2)
T = np.arange(240, 250.1, 0.5)
PT = np.array([P, T])
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


Seafreeze also includes a function to determine which of the supported phases is stable under the given pressure and temperature conditions. The function seafreeze.whichphase has a single parameter, PT, which requires the same format as in the seafreeze.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.


import numpy as np
import seafreeze as sf

# determine the phase of water at 900 MPa and 255 K
PT = np.empty((1,), np.object)
PT[0] = (900, 255)
out = sf.whichphase(PT)
# map to a phase using phasenum2phase

# determine phase for three separate (P,T) conditions
PT = np.empty((3,), np.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 0-5 MPa and temperatures 240-300 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 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).



  • Penny Espinoza - University of Washington, Earth and Space Sciences Department, Seattle, USA
  • 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

Change log

Changes since 0.9.0

  • 0.9.2: whichphase returns numpy.nan if PT is outside the regime of all phases
  • 0.9.1: add whichphase 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 than seafreeze.seafreeze.seafreeze)

Project details

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