def isothermal_bulk_modulus(self, pressure, temperature, volume, params):
"""
Returns isothermal bulk modulus at the pressure, temperature, and volume [Pa]
"""
debye_T = self.__debye_temperature(params['V_0'] / volume, params)
gr = self.grueneisen_parameter(pressure, temperature, volume, params)
E_th = debye.thermal_energy(
temperature, debye_T,
params['n']) #thermal energy at temperature T
E_th_ref = debye.thermal_energy(
300., debye_T,
params['n']) #thermal energy at reference temperature
C_v = debye.heat_capacity_v(
temperature, debye_T, params['n']) #heat capacity at temperature T
C_v_ref = debye.heat_capacity_v(
300., debye_T,
params['n']) #heat capacity at reference temperature
q = self.volume_dependent_q(params['V_0'] / volume, params)
K = bm.bulk_modulus(volume, params) \
+ (gr + 1.-q)* ( gr / volume ) * (E_th - E_th_ref) \
- ( pow(gr , 2.) / volume )*(C_v*temperature - C_v_ref*300.)
return K
def isothermal_bulk_modulus(self, pressure,temperature,volume, params):
"""
Returns isothermal bulk modulus [Pa] as a function of pressure [Pa],
temperature [K], and volume [m^3]. EQ B8
"""
K_T = bm.bulk_modulus(volume, params) + \
self.__thermal_bulk_modulus(temperature,volume, params) - \
self.__thermal_bulk_modulus(300.,volume, params) #EQB13
return K_T
def isothermal_bulk_modulus(self, pressure,temperature, volume, params):
"""
Returns isothermal bulk modulus at the pressure, temperature, and volume [Pa]
"""
debye_T = self.__debye_temperature(params['V_0']/volume, params)
gr = self.grueneisen_parameter(pressure, temperature, volume, params)
E_th = debye.thermal_energy(temperature, debye_T, params['n']) #thermal energy at temperature T
E_th_ref = debye.thermal_energy(300.,debye_T, params['n']) #thermal energy at reference temperature
C_v = debye.heat_capacity_v(temperature, debye_T, params['n']) #heat capacity at temperature T
C_v_ref = debye.heat_capacity_v(300.,debye_T, params['n']) #heat capacity at reference temperature
q = self.volume_dependent_q(params['V_0']/volume, params)
K = bm.bulk_modulus(volume, params) \
+ (gr + 1.-q)* ( gr / volume ) * (E_th - E_th_ref) \
- ( pow(gr , 2.) / volume )*(C_v*temperature - C_v_ref*300.)
return K
def check_birch_murnaghan():
plt.close()
#make a test mineral
test_mineral = material()
test_mineral.params ={'name':'test',
'ref_V': 6.844e-6,
'ref_K': 259.0e9,
'K_prime': 4.0,
'ref_mu': 175.0e9,
'mu_prime': 1.7,
'molar_mass': .0,
'n': 0.,
'ref_Debye': 0.,
'ref_grueneisen': 0.,
'q0': 0.}
pressure = np.linspace(0., 140.e9, 100)
volume = np.empty_like(pressure)
bulk_modulus = np.empty_like(pressure)
shear_modulus = np.empty_like(pressure)
#calculate its static properties
for i in range(len(pressure)):
volume[i] = bm.volume(pressure[i], test_mineral.params)
bulk_modulus[i] = bm.bulk_modulus(volume[i], test_mineral.params)
shear_modulus[i] = bm.shear_modulus_third_order(volume[i], test_mineral.params) #third order is used for the plot we are comparing against
#compare with figure 1
plt.plot(pressure/1.e9, bulk_modulus/1.e9, pressure/1.e9, shear_modulus/1.e9)
fig1 = mpimg.imread('data/slb_fig1.png')
plt.imshow(fig1, extent=[0,140,0,800], aspect='auto')
plt.plot(pressure/1.e9, bulk_modulus/1.e9, 'g+', pressure/1.e9, shear_modulus/1.e9, 'g+')
plt.ylim(0,800)
plt.xlim(0,140)
plt.xlabel("Pressure (GPa)")
plt.ylabel("Modulus (GPa)")
plt.title("Comparing with Figure 1 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
def isothermal_bulk_modulus(self, pressure, temperature, volume, params):
"""
Returns isothermal bulk modulus :math:`[Pa]`
"""
T_0 = params["T_0"]
debye_T = self.__debye_temperature(params["V_0"] / volume, params)
gr = self.grueneisen_parameter(pressure, temperature, volume, params)
E_th = debye.thermal_energy(temperature, debye_T, params["n"]) # thermal energy at temperature T
E_th_ref = debye.thermal_energy(T_0, debye_T, params["n"]) # thermal energy at reference temperature
C_v = debye.heat_capacity_v(temperature, debye_T, params["n"]) # heat capacity at temperature T
C_v_ref = debye.heat_capacity_v(T_0, debye_T, params["n"]) # heat capacity at reference temperature
q = self.volume_dependent_q(params["V_0"] / volume, params)
K = (
bm.bulk_modulus(volume, params)
+ (gr + 1.0 - q) * (gr / volume) * (E_th - E_th_ref)
- (pow(gr, 2.0) / volume) * (C_v * temperature - C_v_ref * T_0)
)
return K
def bulk_modulus(T,V, params):
K_T = bm.bulk_modulus(V, params) + \
thermal_bulk_modulus(T,V, params) - \
thermal_bulk_modulus(300.,V, params) #EQB13
return K_T
