# Source code for burnman.eos.birch_murnaghan

from __future__ import absolute_import
# 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.

import scipy.optimize as opt
from . import equation_of_state as eos
from ..tools import bracket
import warnings

def bulk_modulus(volume, params):
"""
compute the bulk modulus as per the third order
birch-murnaghan equation of state.  Returns bulk
modulus in the same units as the reference bulk
modulus.  Pressure must be in :math:[Pa].
"""

x = params['V_0'] / volume
f = 0.5 * (pow(x, 2. / 3.) - 1.0)

K = pow(1. + 2. * f, 5. / 2.) * (params['K_0'] + (3. * params['K_0'] * params['Kprime_0'] -
5 * params['K_0']) * f + 27. / 2. * (params['K_0'] * params['Kprime_0'] - 4. * params['K_0']) * f * f)
return K

def birch_murnaghan(x, params):
"""
equation for the third order birch-murnaghan equation of state, returns
pressure in the same units that are supplied for the reference bulk
modulus (params['K_0'])
"""

return 3. * params['K_0'] / 2. * (pow(x, 7. / 3.) - pow(x, 5. / 3.)) \
* (1. - .75 * (4. - params['Kprime_0']) * (pow(x, 2. / 3.) - 1.)) + params['P_0']

def volume(pressure, params):
"""
Get the birch-murnaghan volume at a reference temperature for a given
pressure :math:[Pa]. Returns molar volume in :math:[m^3]
"""

func = lambda x: birch_murnaghan(params['V_0'] / x, params) - pressure
try:
sol = bracket(func, params['V_0'], 1.e-2 * params['V_0'])
except:
raise ValueError(
'Cannot find a volume, perhaps you are outside of the range of validity for the equation of state?')
return opt.brentq(func, sol[0], sol[1])

def shear_modulus_second_order(volume, params):
"""
Get the birch murnaghan shear modulus at a reference temperature, for a
given volume.  Returns shear modulus in :math:[Pa] (the same units as in
params['G_0']).  This uses a second order finite strain expansion
"""

x = params['V_0'] / volume
G = params['G_0'] * pow(x, 5. / 3.) * (
1. - 0.5 * (pow(x, 2. / 3.) - 1.) * (5. - 3. * params['Gprime_0'] * params['K_0'] / params['G_0']))
return G

def shear_modulus_third_order(volume, params):
"""
Get the birch murnaghan shear modulus at a reference temperature, for a
given volume.  Returns shear modulus in :math:[Pa] (the same units as in
params['G_0']).  This uses a third order finite strain expansion
"""

x = params['V_0'] / volume
f = 0.5 * (pow(x, 2. / 3.) - 1.0)
G = pow((1. + 2. * f), 5. / 2.) * (params['G_0'] + (3. * params['K_0'] * params['Gprime_0'] - 5. * params['G_0']) * f + (
6. * params['K_0'] * params['Gprime_0'] - 24. * params['K_0'] - 14. * params['G_0'] + 9. / 2. * params['K_0'] * params['Kprime_0']) * f * f)
return G

[docs]class BirchMurnaghanBase(eos.EquationOfState):

"""
Base class for the isothermal Birch Murnaghan equation of state.  This is third order in strain, and
has no temperature dependence.  However, the shear modulus is sometimes fit to a second order
function, so if this is the case, you should use that.  For more see :class:burnman.birch_murnaghan.BM2 and :class:burnman.birch_murnaghan.BM3.
"""

[docs]    def volume(self, pressure, temperature, params):
"""
Returns volume :math:[m^3] as a function of pressure :math:[Pa].
"""
return volume(pressure, params)

[docs]    def pressure(self, temperature, volume, params):
return birch_murnaghan(params['V_0'] / volume, params)

[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(volume, params)

[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(volume, params)

[docs]    def shear_modulus(self, pressure, temperature, volume, params):
"""
Returns shear modulus :math:G of the mineral. :math:[Pa]
"""
if(self.order == 2):
return shear_modulus_second_order(volume, params)
elif(self.order == 3):
return shear_modulus_third_order(volume, params)

[docs]    def heat_capacity_v(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects, simply return a very large number. :math:[J/K/mol]
"""
return 1.e99

[docs]    def heat_capacity_p(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects, simply return a very large number. :math:[J/K/mol]
"""
return 1.e99

[docs]    def thermal_expansivity(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects, simply return zero. :math:[1/K]
"""
return 0.

[docs]    def grueneisen_parameter(self, pressure, temperature, volume, params):
"""
Since this equation of state does not contain temperature effects, simply return zero. :math:[unitless]
"""
return 0.

[docs]    def validate_parameters(self, params):
"""
Check for existence and validity of the parameters
"""

if 'P_0' not in params:
params['P_0'] = 0.

# If G and Gprime are not included this is presumably deliberate,
# as we can model density and bulk modulus just fine without them,
# so just add them to the dictionary as nans
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', 'G_0', 'Gprime_0']
for k in expected_keys:
if k not in params:
raise KeyError('params object missing parameter : ' + k)

# Finally, check that the values are reasonable.
if params['P_0'] < 0.:
warnings.warn('Unusual value for P_0', stacklevel=2)
if params['V_0'] < 1.e-7 or params['V_0'] > 1.e-3:
warnings.warn('Unusual value for V_0', stacklevel=2)
if params['K_0'] < 1.e9 or params['K_0'] > 1.e13:
warnings.warn('Unusual value for K_0', stacklevel=2)
if params['Kprime_0'] < 0. or params['Kprime_0'] > 10.:
warnings.warn('Unusual value for Kprime_0', stacklevel=2)
if params['G_0'] < 0.0 or params['G_0'] > 1.e13:
warnings.warn('Unusual value for G_0', stacklevel=2)
if params['Gprime_0'] < -5. or params['Gprime_0'] > 10.:
warnings.warn('Unusual value for Gprime_0', stacklevel=2)

class BM3(BirchMurnaghanBase):

"""
Third order Birch Murnaghan isothermal equation of state.
This uses the third order expansion for shear modulus.
"""

def __init__(self):
self.order = 3

class BM2(BirchMurnaghanBase):

"""
Third order Birch Murnaghan isothermal equation of state.
This uses the third order expansion for shear modulus.
"""

def __init__(self):
self.order = 2