# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for
# the Earth and Planetary Sciences
# Copyright (C) 2012 - 2021 by the BurnMan team, released under the GNU
# GPL v2 or later.
from . import equation_of_state as eos
import warnings
import numpy as np
def volume(pressure, V_0, K_0, Kprime_0):
return V_0 * np.power(1.0 + (pressure * Kprime_0 / K_0), -1.0 / Kprime_0)
def pressure(volume, V_0, K_0, Kprime_0):
return K_0 / Kprime_0 * (np.power(volume / V_0, -Kprime_0) - 1.0)
def bulk_modulus(pressure, K_0, Kprime_0):
return K_0 + pressure * Kprime_0
def energy(volume, E_0, V_0, K_0, Kprime_0):
Vrel = volume / V_0
return E_0 + K_0 * V_0 * (
np.power(Vrel, 1.0 - Kprime_0) / (Kprime_0 * (Kprime_0 - 1))
+ Vrel / Kprime_0
- 1.0 / (Kprime_0 - 1.0)
)
def intVdP(pressure, V_0, K_0, Kprime_0):
return (
V_0
* K_0
* ((np.power(1.0 + (pressure * Kprime_0 / K_0), 1.0 - (1.0 / Kprime_0))) - 1.0)
/ (Kprime_0 - 1.0)
)
[docs]class Murnaghan(eos.EquationOfState):
"""
Base class for the isothermal Murnaghan equation of state,
as described in :cite:`Murnaghan1944`.
"""
[docs] def volume(self, pressure, temperature, params):
"""
Returns volume :math:`[m^3]` as a function of pressure :math:`[Pa]`.
"""
return volume(pressure, params["V_0"], params["K_0"], params["Kprime_0"])
[docs] def pressure(self, temperature, volume, params):
return pressure(volume, params["V_0"], params["K_0"], params["Kprime_0"])
[docs] def isothermal_bulk_modulus(self, pressure, temperature, volume, params):
"""
Returns isothermal bulk modulus :math:`K_T` :math:`[Pa]`
as a function of pressure :math:`[Pa]`,
temperature :math:`[K]` and volume :math:`[m^3]`.
"""
return bulk_modulus(pressure, params["K_0"], params["Kprime_0"])
[docs] def adiabatic_bulk_modulus(self, pressure, temperature, volume, params):
"""
Returns adiabatic bulk modulus :math:`K_s` of the mineral. :math:`[Pa]`.
"""
return bulk_modulus(pressure, params["K_0"], params["Kprime_0"])
[docs] def shear_modulus(self, pressure, temperature, volume, params):
"""
Returns shear modulus :math:`G` of the mineral. :math:`[Pa]`
Currently not included in the Murnghan EOS, so omitted.
"""
return 0.0
[docs] def entropy(self, pressure, temperature, volume, params):
"""
Returns the molar entropy :math:`\mathcal{S}` of the mineral.
:math:`[J/K/mol]`
"""
return 0.0
[docs] def molar_internal_energy(self, pressure, temperature, volume, params):
"""
Returns the internal energy :math:`\mathcal{E}` of the mineral.
:math:`[J/mol]`
"""
return energy(
volume, params["E_0"], params["V_0"], params["K_0"], params["Kprime_0"]
)
[docs] def gibbs_free_energy(self, pressure, temperature, volume, params):
"""
Returns the Gibbs free energy :math:`\mathcal{G}` of the mineral.
:math:`[J/mol]`
"""
# G = E + PV
return (
self.molar_internal_energy(pressure, temperature, volume, params)
+ volume * pressure
)
[docs] def molar_heat_capacity_v(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects,
return a very large number. :math:`[J/K/mol]`
"""
return 1.0e99
[docs] def molar_heat_capacity_p(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects,
return a very large number. :math:`[J/K/mol]`
"""
return 1.0e99
[docs] def thermal_expansivity(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects,
return zero. :math:`[1/K]`
"""
return 0.0
[docs] def grueneisen_parameter(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects,
return zero. :math:`[unitless]`
"""
return 0.0
[docs] def validate_parameters(self, params):
"""
Check for existence and validity of the parameters
"""
if "E_0" not in params:
params["E_0"] = 0.0
if "P_0" not in params:
params["P_0"] = 0.0
# G is not included in the Murnaghan EOS so we shall set them to NaN's
if "G_0" not in params:
params["G_0"] = float("nan")
if "Gprime_0" not in params:
params["Gprime_0"] = float("nan")
# check that all the required keys are in the dictionary
expected_keys = ["V_0", "K_0", "Kprime_0"]
for k in expected_keys:
if k not in params:
raise KeyError("params object missing parameter : " + k)
# now check that the values are reasonable. I mostly just
# made up these values from experience, and we are only
# raising a warning. Better way to do this? [IR]
if params["V_0"] < 1.0e-7 or params["V_0"] > 1.0e-3:
warnings.warn("Unusual value for V_0", stacklevel=2)
if params["K_0"] < 1.0e9 or params["K_0"] > 1.0e13:
warnings.warn("Unusual value for K_0", stacklevel=2)
if params["Kprime_0"] < -5.0 or params["Kprime_0"] > 30.0:
warnings.warn("Unusual value for Kprime_0", stacklevel=2)