```
# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2015 by the BurnMan team, released under the GNU
# GPL v2 or later.
from __future__ import absolute_import
import numpy as np
from scipy.linalg import lu
from .processchemistry import *
from . import constants
from . import solidsolution
# This module computes chemical potentials (partial molar gibbs free
# energies) for an assemblage based on the Gibbs free energies and
# compositions of the individual phases.
# It can also calculate fugacities based on the gibbs free energies of the
# endmembers corresponding to chemical components.
# It can also calculate fugacities relative to other bulk compositions
[docs]def chemical_potentials(assemblage, component_formulae):
"""
The compositional space of the components does not have to be a
superset of the compositional space of the assemblage. Nor do they have to
compose an orthogonal basis.
The components must each be described by a linear mineral combination
The mineral compositions must be linearly independent
Parameters
----------
assemblage : list of classes
List of material classes
set_method and set_state should already have been used
the composition of the solid solutions should also have been set
component_formulae : list of dictionaries
List of chemical component formula dictionaries
No restriction on length
Returns
-------
component_potentials : array of floats
Array of chemical potentials of components
"""
# Split solid solutions into their respective endmembers
# Find the chemical potentials of all the endmembers
endmember_list = []
endmember_potentials = []
for mineral in assemblage:
if isinstance(mineral, solidsolution.SolidSolution):
for member in mineral.endmembers:
endmember_list.append(member[0])
for potential in mineral.partial_gibbs:
endmember_potentials.append(potential)
else:
endmember_list.append(mineral)
endmember_potentials.append(mineral.gibbs)
# Make an array of all the endmember formulae
endmember_formulae = [endmember.params['formula']
for endmember in endmember_list]
endmember_compositions, elements = compositional_array(endmember_formulae)
pl, u = lu(endmember_compositions, permute_l=True)
assert(min(np.dot(np.square(u), np.ones(shape=len(elements)))) > 1e-6), \
'Endmember compositions do not form an independent set of basis vectors'
# Make an array of component formulae with elements in the same order as
# the endmember array
component_compositions = ordered_compositional_array(
component_formulae, elements)
p = np.linalg.lstsq(endmember_compositions.T, component_compositions.T)
for idx, error in enumerate(p[1]):
assert (error < 1e-10), \
'Component %d not defined by prescribed assemblage' % (idx + 1)
# Create an array of endmember proportions which sum to each component
# composition
endmember_proportions = np.around(p[0], 10).T
# Calculate the chemical potential of each component
component_potentials = np.dot(endmember_proportions, endmember_potentials)
return component_potentials
[docs]def fugacity(standard_material, assemblage):
"""
Parameters
----------
standard_material: class
Material class
set_method and set_state should already have been used
material must have a formula as a dictionary parameter
assemblage: list of classes
List of material classes
set_method and set_state should already have been used
Returns
-------
fugacity : float
Value of the fugacity of the component with respect to
the standard material
"""
component_formula = standard_material.params['formula']
chemical_potential = chemical_potentials(
assemblage, [component_formula])[0]
fugacity = np.exp((chemical_potential - standard_material.gibbs) / (
constants.gas_constant * assemblage[0].temperature))
return fugacity
[docs]def relative_fugacity(standard_material, assemblage, reference_assemblage):
"""
Parameters
----------
standard_material: class
Material class
set_method and set_state should already have been used
material must have a formula as a dictionary parameter
assemblage: list of classes
List of material classes
set_method and set_state should already have been used
reference_assemblage: list of classes
List of material classes
set_method and set_state should already have been used
Returns
-------
relative_fugacity : float
Value of the fugacity of the component in the assemblage
with respect to the reference_assemblage
"""
component_formula = standard_material.params['formula']
chemical_potential = chemical_potentials(
assemblage, [component_formula])[0]
reference_chemical_potential = chemical_potentials(
reference_assemblage, [component_formula])[0]
relative_fugacity = np.exp((chemical_potential - reference_chemical_potential) / (
constants.gas_constant * assemblage[0].temperature))
return relative_fugacity
```