# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2017 by the BurnMan team, released under the GNU
# GPL v2 or later.
from __future__ import absolute_import
from __future__ import print_function
import numpy as np
import warnings
from .material import Material, material_property
from .mineral import Mineral
from . import averaging_schemes
from . import chemicalpotentials
from .solidsolution import SolidSolution
from .processchemistry import sum_formulae
def check_pairs(phases, fractions):
if len(fractions) < 1:
raise Exception('ERROR: we need at least one phase')
if len(phases) != len(fractions):
raise Exception(
'ERROR: different array lengths for phases and fractions')
total = sum(fractions)
if abs(total - 1.0) > 1e-10:
raise Exception(
'ERROR: list of molar fractions does not add up to one')
for p in phases:
if not isinstance(p, Mineral):
raise Exception(
'ERROR: object of type ''%s'' is not of type Mineral' % (type(p)))
# static composite of minerals/composites
[docs]class Composite(Material):
"""
Base class for a composite material.
The static phases can be minerals or materials,
meaning composite can be nested arbitrarily.
The fractions of the phases can be input
as either 'molar' or 'mass' during instantiation,
and modified (or initialised) after this point by
using set_fractions.
This class is available as ``burnman.Composite``.
"""
def __init__(self, phases, fractions=None, fraction_type='molar', name='Unnamed composite'):
"""
Create a composite using a list of phases and their fractions (adding to 1.0).
Parameters
----------
phases: list of :class:`burnman.Material`
list of phases.
fractions: list of floats
molar or mass fraction for each phase.
fraction_type: 'molar' or 'mass' (optional, 'molar' as standard)
specify whether molar or mass fractions are specified.
"""
Material.__init__(self)
assert(len(phases) > 0)
self.phases = phases
if fractions is not None:
self.set_fractions(fractions, fraction_type)
else:
self.molar_fractions = None
self.set_averaging_scheme('VoigtReussHill')
self.name=name
self.print_precision=4 # number of significant figures used by self.__str__
def __str__(self):
string='Composite: {0}'.format(self.name)
try:
string += '\n P, T: {0:.{sf}g} Pa, {1:.{sf}g} K'.format(self.pressure,
self.temperature,
sf=self.print_precision)
except:
pass
string+='\nPhase and endmember fractions:'
for phase, fraction in zip(*self.unroll()):
string+='\n {0}: {1:0.{sf}f}'.format(phase.name, fraction, sf=self.print_precision)
if isinstance(phase, SolidSolution):
for i in range(phase.n_endmembers):
string+='\n {0}: {1:0.{sf}f}'.format(phase.endmember_names[i],
phase.molar_fractions[i],
sf=self.print_precision)
return string
[docs] def set_fractions(self, fractions, fraction_type='molar'):
"""
Change the fractions of the phases of this Composite.
Resets cached properties
Parameters
----------
fractions: list of floats
molar or mass fraction for each phase.
fraction_type: 'molar' or 'mass'
specify whether molar or mass fractions are specified.
"""
assert(len(self.phases) == len(fractions))
try:
total = sum(fractions)
except TypeError:
raise Exception(
"Since v0.8, burnman.Composite takes an array of Materials, then an array of fractions")
for f in fractions:
assert (f >= -1e-12)
self.reset()
if abs(total - 1.0) > 1e-12:
warnings.warn(
"Warning: list of fractions does not add up to one but %g. Normalizing." % total)
corrected_fractions = [fr / total for fr in fractions]
fractions = corrected_fractions
if fraction_type == 'molar':
molar_fractions = fractions
elif fraction_type == 'mass':
molar_fractions = self._mass_to_molar_fractions(
self.phases, fractions)
else:
raise Exception(
"Fraction type not recognised. Please use 'molar' or mass")
# Set minimum value of a molar fraction at 0.0 (rather than -1.e-12)
self.molar_fractions = [max(0.0, fraction)
for fraction in molar_fractions]
[docs] def set_method(self, method):
"""
set the same equation of state method for all the phases in the composite
"""
for phase in self.phases:
phase.set_method(method)
# Clear the cache on resetting method
self.reset()
[docs] def set_averaging_scheme(self, averaging_scheme):
"""
Set the averaging scheme for the moduli in the composite.
Default is set to VoigtReussHill, when Composite is initialized.
"""
if type(averaging_scheme) == str:
self.averaging_scheme = getattr(
averaging_schemes, averaging_scheme)()
else:
self.averaging_scheme = averaging_scheme
# Clear the cache on resetting averaging scheme
self.reset()
[docs] def set_state(self, pressure, temperature):
"""
Update the material to the given pressure [Pa] and temperature [K].
"""
Material.set_state(self, pressure, temperature)
for phase in self.phases:
phase.set_state(pressure, temperature)
[docs] def debug_print(self, indent=""):
print("{0}Composite: {1}".format(indent, self.name))
indent += " "
if self.molar_fractions is None:
for i, phase in enumerate(self.phases):
phase.debug_print(indent + " ")
else:
for i, phase in enumerate(self.phases):
print("%s%g of" % (indent, self.molar_fractions[i]))
phase.debug_print(indent + " ")
[docs] def unroll(self):
if self.molar_fractions is None:
raise Exception(
"Unroll only works if the composite has defined fractions.")
phases = []
fractions = []
for i, phase in enumerate(self.phases):
p_mineral, p_fraction = phase.unroll()
check_pairs(p_mineral, p_fraction)
fractions.extend([f * self.molar_fractions[i] for f in p_fraction])
phases.extend(p_mineral)
return phases, fractions
[docs] def to_string(self):
"""
return the name of the composite
"""
return "{0}: {1}".format(self.__class__.__name__, self.name)
@material_property
def formula(self):
"""
Returns molar chemical formula of the composite
"""
return sum_formulae([ph.formula for ph in self.phases], self.molar_fractions)
@material_property
def molar_internal_energy(self):
"""
Returns molar internal energy of the mineral [J/mol]
Aliased with self.energy
"""
U = sum(phase.molar_internal_energy * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions))
return U
@material_property
def molar_gibbs(self):
"""
Returns molar Gibbs free energy of the composite [J/mol]
Aliased with self.gibbs
"""
G = sum(phase.molar_gibbs * molar_fraction for (phase, molar_fraction)
in zip(self.phases, self.molar_fractions))
return G
@material_property
def molar_helmholtz(self):
"""
Returns molar Helmholtz free energy of the mineral [J/mol]
Aliased with self.helmholtz
"""
F = sum(phase.molar_helmholtz * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions))
return F
@material_property
def molar_volume(self):
"""
Returns molar volume of the composite [m^3/mol]
Aliased with self.V
"""
volumes = np.array(
[phase.molar_volume * molar_fraction for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
return np.sum(volumes)
@material_property
def molar_mass(self):
"""
Returns molar mass of the composite [kg/mol]
"""
return sum([phase.molar_mass * molar_fraction for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
@material_property
def density(self):
"""
Compute the density of the composite based on the molar volumes and masses
Aliased with self.rho
"""
densities = np.array([phase.density for phase in self.phases])
volumes = np.array(
[phase.molar_volume * molar_fraction for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
return self.averaging_scheme.average_density(volumes, densities)
@material_property
def molar_entropy(self):
"""
Returns enthalpy of the mineral [J]
Aliased with self.S
"""
S = sum(phase.molar_entropy * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions))
return S
@material_property
def molar_enthalpy(self):
"""
Returns enthalpy of the mineral [J]
Aliased with self.H
"""
H = sum(phase.molar_enthalpy * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions))
return H
@material_property
def isothermal_bulk_modulus(self):
"""
Returns isothermal bulk modulus of the composite [Pa]
Aliased with self.K_T
"""
V_frac = np.array([phase.molar_volume * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
K_ph = np.array(
[phase.isothermal_bulk_modulus for phase in self.phases])
G_ph = np.array([phase.shear_modulus for phase in self.phases])
return self.averaging_scheme.average_bulk_moduli(V_frac, K_ph, G_ph)
@material_property
def adiabatic_bulk_modulus(self):
"""
Returns adiabatic bulk modulus of the mineral [Pa]
Aliased with self.K_S
"""
V_frac = np.array([phase.molar_volume * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
K_ph = np.array(
[phase.adiabatic_bulk_modulus for phase in self.phases])
G_ph = np.array([phase.shear_modulus for phase in self.phases])
return self.averaging_scheme.average_bulk_moduli(V_frac, K_ph, G_ph)
@material_property
def isothermal_compressibility(self):
"""
Returns isothermal compressibility of the composite (or inverse isothermal bulk modulus) [1/Pa]
Aliased with self.beta_T
"""
return 1. / self.isothermal_bulk_modulus
@material_property
def adiabatic_compressibility(self):
"""
Returns isothermal compressibility of the composite (or inverse isothermal bulk modulus) [1/Pa]
Aliased with self.beta_S
"""
return 1. / self.adiabatic_bulk_modulus
@material_property
def shear_modulus(self):
"""
Returns shear modulus of the mineral [Pa]
Aliased with self.G
"""
V_frac = np.array([phase.molar_volume * molar_fraction for (
phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
K_ph = np.array(
[phase.adiabatic_bulk_modulus for phase in self.phases])
G_ph = np.array([phase.shear_modulus for phase in self.phases])
return self.averaging_scheme.average_shear_moduli(V_frac, K_ph, G_ph)
@material_property
def p_wave_velocity(self):
"""
Returns P wave speed of the composite [m/s]
Aliased with self.v_p
"""
return np.sqrt((self.adiabatic_bulk_modulus + 4. / 3. *
self.shear_modulus) / self.density)
@material_property
def bulk_sound_velocity(self):
"""
Returns bulk sound speed of the composite [m/s]
Aliased with self.v_phi
"""
return np.sqrt(self.adiabatic_bulk_modulus / self.density)
@material_property
def shear_wave_velocity(self):
"""
Returns shear wave speed of the composite [m/s]
Aliased with self.v_s
"""
return np.sqrt(self.shear_modulus / self.density)
@material_property
def grueneisen_parameter(self):
"""
Returns grueneisen parameter of the composite [unitless]
Aliased with self.gr
"""
return self.thermal_expansivity * self.isothermal_bulk_modulus * self.molar_volume / self.molar_heat_capacity_v
@material_property
def thermal_expansivity(self):
"""
Returns thermal expansion coefficient of the composite [1/K]
Aliased with self.alpha
"""
volumes = np.array(
[phase.molar_volume * molar_fraction for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)])
alphas = np.array([phase.thermal_expansivity for phase in self.phases])
return self.averaging_scheme.average_thermal_expansivity(volumes, alphas)
@material_property
def molar_heat_capacity_v(self):
"""
Returns molar_heat capacity at constant volume of the composite [J/K/mol]
Aliased with self.C_v
"""
c_v = np.array([phase.molar_heat_capacity_v for phase in self.phases])
return self.averaging_scheme.average_heat_capacity_v(self.molar_fractions, c_v)
@material_property
def molar_heat_capacity_p(self):
"""
Returns molar heat capacity at constant pressure of the composite [J/K/mol]
Aliased with self.C_p
"""
c_p = np.array([phase.molar_heat_capacity_p for phase in self.phases])
return self.averaging_scheme.average_heat_capacity_p(self.molar_fractions, c_p)
def _mass_to_molar_fractions(self, phases, mass_fractions):
"""
Converts a set of mass fractions for phases into a set of molar fractions.
Parameters
----------
phases : list of :class:`burnman.Material`
The list of phases for which fractions should be converted.
mass_fractions : list of floats
The list of mass fractions of the input phases.
Returns
-------
molar_fractions : list of floats
The list of molar fractions corresponding to the input molar fractions
"""
total_moles = sum(
mass_fraction / phase.molar_mass for mass_fraction, phase in zip(mass_fractions, phases))
molar_fractions = [mass_fraction / (phase.molar_mass * total_moles)
for mass_fraction, phase in zip(mass_fractions, phases)]
return molar_fractions