# Source code for burnman.tools.chemistry

```
# 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.
# This module provides higher level chemistry-related functions.
from __future__ import absolute_import
import numpy as np
from scipy.optimize import fsolve
from .. import constants
# Import common lower level functions for backwards compatibility
from ..utils.chemistry import dictionarize_formula, formula_mass
from ..utils.chemistry import formula_to_string, site_occupancies_to_strings
[docs]def fugacity(standard_material, assemblage):
"""
Parameters
----------
standard_material: burnman.Material object
set_method and set_state should already have been used
material must have a formula as a dictionary parameter
assemblage: burnman.Composite object
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 = assemblage.chemical_potential([component_formula])[0]
fugacity = np.exp((chemical_potential - standard_material.gibbs)
/ (constants.gas_constant * assemblage.temperature))
return fugacity
[docs]def relative_fugacity(component_formula, assemblage, reference_assemblage):
"""
Parameters
----------
component_formula: dictionary
Chemical formula for which to compute the relative fugacity.
assemblage: burnman.Composite object
set_method and set_state should already have been used.
reference_assemblage: burnman.Composite object
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.
"""
chemical_potential = assemblage.chemical_potential([component_formula])[0]
reference_chemical_potential = reference_assemblage.chemical_potential([component_formula])[0]
relative_fugacity = np.exp((chemical_potential
- reference_chemical_potential)
/ (constants.gas_constant
* assemblage.temperature))
return relative_fugacity
[docs]def equilibrium_pressure(minerals, stoichiometry, temperature,
pressure_initial_guess=1.e5):
"""
Given a list of minerals, their reaction stoichiometries
and a temperature of interest, compute the
equilibrium pressure of the reaction.
Parameters
----------
minerals : list of minerals
List of minerals involved in the reaction.
stoichiometry : list of floats
Reaction stoichiometry for the minerals provided.
Reactants and products should have the opposite signs [mol]
temperature : float
Temperature of interest [K]
pressure_initial_guess : optional float
Initial pressure guess [Pa]
Returns
-------
pressure : float
The equilibrium pressure of the reaction [Pa]
"""
def eqm(P, T):
gibbs = 0.
for i, mineral in enumerate(minerals):
mineral.set_state(P[0], T)
gibbs = gibbs + mineral.gibbs * stoichiometry[i]
return gibbs
pressure = fsolve(eqm, [pressure_initial_guess], args=(temperature))[0]
return pressure
[docs]def equilibrium_temperature(minerals, stoichiometry, pressure, temperature_initial_guess=1000.):
"""
Given a list of minerals, their reaction stoichiometries
and a pressure of interest, compute the
equilibrium temperature of the reaction.
Parameters
----------
minerals : list of minerals
List of minerals involved in the reaction.
stoichiometry : list of floats
Reaction stoichiometry for the minerals provided.
Reactants and products should have the opposite signs [mol]
pressure : float
Pressure of interest [Pa]
temperature_initial_guess : optional float
Initial temperature guess [K]
Returns
-------
temperature : float
The equilibrium temperature of the reaction [K]
"""
def eqm(T, P):
gibbs = 0.
for i, mineral in enumerate(minerals):
mineral.set_state(P, T[0])
gibbs = gibbs + mineral.gibbs * stoichiometry[i]
return gibbs
temperature = fsolve(eqm, [temperature_initial_guess], args=(pressure))[0]
return temperature
[docs]def invariant_point(minerals_r1, stoichiometry_r1,
minerals_r2, stoichiometry_r2,
pressure_temperature_initial_guess=[1.e9, 1000.]):
"""
Given a list of minerals, their reaction stoichiometries
and a pressure of interest, compute the
equilibrium temperature of the reaction.
Parameters
----------
minerals : list of minerals
List of minerals involved in the reaction.
stoichiometry : list of floats
Reaction stoichiometry for the minerals provided.
Reactants and products should have the opposite signs [mol]
pressure : float
Pressure of interest [Pa]
temperature_initial_guess : optional float
Initial temperature guess [K]
Returns
-------
temperature : float
The equilibrium temperature of the reaction [K]
"""
def eqm(PT):
P, T = PT
gibbs_r1 = 0.
for i, mineral in enumerate(minerals_r1):
mineral.set_state(P, T)
gibbs_r1 = gibbs_r1 + mineral.gibbs * stoichiometry_r1[i]
gibbs_r2 = 0.
for i, mineral in enumerate(minerals_r2):
mineral.set_state(P, T)
gibbs_r2 = gibbs_r2 + mineral.gibbs * stoichiometry_r2[i]
return [gibbs_r1, gibbs_r2]
pressure, temperature = fsolve(eqm, pressure_temperature_initial_guess)
return pressure, temperature
[docs]def hugoniot(mineral, P_ref, T_ref, pressures, reference_mineral=None):
"""
Calculates the temperatures (and volumes) along a Hugoniot
as a function of pressure according to the Hugoniot equation
U2-U1 = 0.5*(p2 - p1)(V1 - V2) where U and V are the
internal energies and volumes (mass or molar) and U = F + TS
Parameters
----------
mineral : mineral
Mineral for which the Hugoniot is to be calculated.
P_ref : float
Reference pressure [Pa]
T_ref : float
Reference temperature [K]
pressures : numpy array of floats
Set of pressures [Pa] for which the Hugoniot temperature
and volume should be calculated
reference_mineral : mineral
Mineral which is stable at the reference conditions
Provides an alternative U_0 and V_0 when the reference
mineral transforms to the mineral of interest at some
(unspecified) pressure.
Returns
-------
temperatures : numpy array of floats
The Hugoniot temperatures at pressure
volumes : numpy array of floats
The Hugoniot volumes at pressure
"""
def Ediff(T, mineral, P, P_ref, U_ref, V_ref):
mineral.set_state(P, T[0])
U = mineral.helmholtz + T[0] * mineral.S
V = mineral.V
return (U - U_ref) - 0.5 * (P - P_ref) * (V_ref - V)
if reference_mineral is None:
reference_mineral = mineral
reference_mineral.set_state(P_ref, T_ref)
U_ref = reference_mineral.helmholtz + T_ref * reference_mineral.S
V_ref = reference_mineral.V
temperatures = np.empty_like(pressures)
volumes = np.empty_like(pressures)
for i, P in enumerate(pressures):
temperatures[i] = fsolve(
Ediff, [T_ref], args=(mineral, P, P_ref, U_ref, V_ref))[0]
volumes[i] = mineral.V
return temperatures, volumes
```