def check_mgd_shim_duffy_kenichi():
"""
Attemmpts to recreate Shim Duffy Kenichi (2002)
"""
plt.close()
# Create gold material from Table 1
gold = burnman.Mineral()
gold.params = {
'name': 'gold',
'V_0': 10.22e-6,
'K_0': 167.0e9,
'Kprime_0': 5.0,
'G_0': 0.0e9,
'Gprime_0': 0.0,
'molar_mass': .196966,
'n': 1.0,
'Debye_0': 170.,
'grueneisen_0': 2.97, # this does better with gr = 2.93. Why?
'q_0': 1.0
}
gold.set_method('mgd3')
# Total pressures, pulled from Table 2
ref_pressures = [
np.array([
0., 3.55, 7.55, 12.06, 17.16, 22.91, 29.42, 36.77, 45.11, 54.56,
65.29, 77.50, 91.42, 107.32, 125.51, 146.38, 170.38, 198.07
])
]
ref_pressures.append(
np.array([
4.99, 8.53, 12.53, 17.04, 22.13, 27.88, 34.38, 41.73, 50.06, 59.50,
70.22, 82.43, 96.33, 112.22, 130.40, 151.25, 175.24, 202.90
]))
ref_pressures.append(
np.array([
12.14, 15.69, 19.68, 24.19, 29.28, 35.03, 41.53, 48.88, 57.20,
66.64, 77.37, 89.57, 103.47, 119.35, 137.53, 158.38, 182.36, 210.02
]))
ref_pressures.append(
np.array([
19.30, 22.84, 26.84, 31.35, 36.44, 42.19, 48.68, 56.03, 64.35,
73.80, 84.52, 96.72, 110.62, 126.50, 144.68, 165.53, 189.51, 217.17
]))
eos = mgd.MGD3()
pressures = np.empty_like(ref_pressures)
ref_dv = np.linspace(0.0, 0.34, len(pressures[0]))
ref_volumes = (1 - ref_dv) * gold.params['V_0']
T = np.array([300., 1000., 2000., 3000.])
for t in range(len(pressures)):
for i in range(len(pressures[t])):
pressures[t][i] = eos.pressure(T[t], ref_volumes[i], gold.params)
plt.plot(ref_dv, (pressures[t] / 1.e9 - ref_pressures[t]))
plt.ylim(-1, 1)
plt.ylabel("Difference in pressure (GPa)")
plt.xlabel("1-dV/V")
plt.title("Comparing with Shim, Duffy, and Kenichi (2002)")
plt.show()
def check_mgd_fei_mao_shu_hu():
"""
Benchmark agains Fei Mao Shu Hu (1991)
"""
mgfeo = burnman.Mineral()
mgfeo.params = {
'name': 'MgFeO',
'V_0': 11.657e-6,
'K_0': 157.0e9,
'Kprime_0': 4.0,
'G_0': 0.0e9,
'Gprime_0': 0.0,
'molar_mass': .196966,
'n': 2.0,
'Debye_0': 500.,
'grueneisen_0': 1.50,
'q_0': 1.1
}
mgfeo.set_method('mgd3')
# pulled from table 1
temperatures = np.array([
300, 300, 483, 483, 483, 590, 593, 593, 593, 700, 600, 500, 650, 600,
600, 650, 700, 737, 727, 673, 600, 543, 565, 585, 600, 628, 654, 745,
768, 747, 726, 700, 676
])
volumes = np.array([
77.418, 72.327, 74.427, 73.655, 72.595, 74.1, 73.834, 73.101, 70.845,
73.024, 72.630, 68.644, 72.969, 72.324, 71.857, 72.128, 73.283, 73.337,
72.963, 71.969, 69.894, 67.430, 67.607, 67.737, 68.204, 68.518, 68.955,
70.777, 72.921, 72.476, 72.152, 71.858, 71.473
])
# change from cubic angstroms per unit cell to cubic meters per mol of
# molecules.
volumes = volumes / 1.e30 * 6.022141e23 / 4.0
ref_pressures = np.array([
0.0, 12.23, 7.77, 9.69, 12.54, 9.21, 9.90, 11.83, 18.35, 12.68, 13.15,
25.16, 12.53, 14.01, 15.34, 14.86, 11.99, 12.08, 13.03, 15.46, 21.44,
29.98, 29.41, 29.05, 27.36, 26.38, 24.97, 19.49, 13.39, 14.48, 15.27,
15.95, 16.94
])
ref_pressures = ref_pressures
pressures = np.empty_like(volumes)
eos = mgd.MGD3()
for i in range(len(temperatures)):
pressures[i] = eos.pressure(temperatures[i], volumes[i], mgfeo.params)
plt.scatter(temperatures, (pressures / 1.e9 - ref_pressures))
plt.ylim(-1, 1)
plt.title("Comparing with Fei, Mao, Shu, and Hu (1991)")
plt.xlabel("Temperature (K) at various volumes")
plt.ylabel("Difference in total pressure (GPa)")
plt.show()
def check_birch_murnaghan():
"""
Recreates Stixrude and Lithgow-Bertelloni (2005) Figure 1,
bulk and shear modulus without thermal corrections
"""
plt.close()
# make a test mineral
test_mineral = burnman.Mineral()
test_mineral.params = {
'name': 'test',
'V_0': 6.844e-6,
'K_0': 259.0e9,
'Kprime_0': 4.0,
'G_0': 175.0e9,
'Gprime_0': 1.7,
'molar_mass': .0,
}
test_mineral.set_method('bm3')
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('../../burnman/data/input_figures/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 calc_velocities(ref_rho, K_0, K_prime, G_0, G_prime):
rock = burnman.Mineral()
rock.params['V_0'] = 10.e-6
rock.params['molar_mass'] = ref_rho * rock.params['V_0']
rock.params['K_0'] = K_0
rock.params['Kprime_0'] = K_prime
rock.params['G_0'] = G_0
rock.params['Gprime_0'] = G_prime
rock.set_method('bm3')
temperature = np.empty_like(seis_p)
mat_rho, mat_vphi, mat_vs = \
rock.evaluate(['density', 'v_phi', 'v_s'], seis_p, temperature)
return mat_rho, mat_vphi, mat_vs
def check_birch_murnaghan_4th():
"""
Recreates the formulation of the 4th order Birch-Murnaghan EOS as in
Ahmad and Alkammash, 2012; Figure 1.
"""
plt.close()
# make a test mineral
test_mineral = burnman.Mineral()
test_mineral.params = {
'name': 'test',
'V_0': 10.e-6,
'K_0': 72.7e9,
'Kprime_0': 4.14,
'Kprime_prime_0': -0.0484e-9,
}
test_mineral.set_method('bm4')
pressure = np.linspace(0., 90.e9, 20)
volume = np.empty_like(pressure)
# calculate its static properties
for i in range(len(pressure)):
volume[i] = bm4.volume_fourth_order(
pressure[i], test_mineral.params) / test_mineral.params.get('V_0')
# compare with figure 1
plt.plot(pressure / 1.e9, volume)
fig1 = mpimg.imread('../../burnman/data/input_figures/Ahmad.png')
plt.imshow(fig1, extent=[0., 90., .65, 1.], aspect='auto')
plt.plot(pressure / 1.e9,
volume,
marker='o',
color='r',
linestyle='',
label='BM4')
plt.legend(loc='lower left')
plt.xlim(0., 90.)
plt.ylim(.65, 1.)
plt.xlabel("Volume/V0")
plt.ylabel("Pressure (GPa)")
plt.title("Comparing with Figure 1 of Ahmad et al., (2012)")
plt.show()
def check_slb_fig3():
"""
Benchmark grueneisen parameter against figure 3 of Stixrude and Lithgow-Bertelloni (2005b)
"""
perovskite = burnman.Mineral()
perovskite.params = {
'name': 'perovksite',
'V_0': molar_volume_from_unit_cell_volume(168.27, 4.),
'grueneisen_0': 1.63,
'q_0': 1.7
}
volume = np.linspace(0.6, 1.0, 100)
grueneisen_slb = np.empty_like(volume)
grueneisen_mgd = np.empty_like(volume)
q_slb = np.empty_like(volume)
q_mgd = np.empty_like(volume)
slb_eos = slb.SLB2()
mgd_eos = mgd.MGD2()
# calculate its thermal properties
for i in range(len(volume)):
# call with dummy pressure and temperatures, they do not change it
grueneisen_slb[i] = slb_eos.grueneisen_parameter(
0., 0., volume[i] * perovskite.params['V_0'], perovskite.params)
grueneisen_mgd[i] = mgd_eos.grueneisen_parameter(
0., 0., volume[i] * perovskite.params['V_0'], perovskite.params)
q_slb[i] = slb_eos.volume_dependent_q(1. / volume[i],
perovskite.params)
q_mgd[i] = perovskite.params['q_0']
# compare with figure 7
fig1 = mpimg.imread('../../burnman/data/input_figures/slb_fig3.png')
plt.imshow(fig1, extent=[0.6, 1.0, 0.35, 2.0], aspect='auto')
plt.plot(volume, grueneisen_slb, 'g+', volume, grueneisen_mgd, 'b+')
plt.plot(volume, q_slb, 'g+', volume, q_mgd, 'b+')
plt.xlim(0.6, 1.0)
plt.ylim(0.35, 2.0)
plt.ylabel("Grueneisen parameter")
plt.xlabel("Relative Volume V/V0")
plt.title(
"Comparing with Figure 3 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
def check_vinet():
"""
Recreates Dewaele et al., 2006, Figure 1, fitting a Vinet EOS to Fe data
"""
plt.close()
# make a test mineral
test_mineral = burnman.Mineral()
test_mineral.params = {
'name': 'test',
'V_0': 6.75e-6,
'K_0': 163.4e9,
'Kprime_0': 5.38,
}
test_mineral.set_method('vinet')
pressure = np.linspace(17.7e9, 300.e9, 20)
volume = np.empty_like(pressure)
# calculate its static properties
for i in range(len(pressure)):
volume[i] = vinet.volume(pressure[i], test_mineral.params)
# compare with figure 1
plt.plot(pressure / 1.e9, volume / 6.02e-7)
fig1 = mpimg.imread('../../burnman/data/input_figures/Dewaele.png')
plt.imshow(fig1, extent=[0., 300., 6.8, 11.8], aspect='auto')
plt.plot(pressure / 1.e9,
volume / 6.02e-7,
marker='o',
color='r',
linestyle='',
label='Vinet Fit')
plt.legend(loc='lower left')
plt.xlim(0., 300.)
plt.ylim(6.8, 11.8)
plt.ylabel("Volume (Angstroms^3/atom")
plt.xlabel("Pressure (GPa)")
plt.title("Comparing with Figure 1 of Dewaele et al., (2006)")
plt.show()
from contrib.CHRU2014.helper_solid_solution import HelperSolidSolution
import contrib.CHRU2014.colors as colors
if __name__ == "__main__":
fig = plt.figure(dpi=100, figsize=(12, 6))
prop = {'size': 12}
plt.rc('text', usetex=True)
plt.rcParams['text.latex.preamble'] = r'\usepackage{relsize}'
dashstyle2 = (7, 3)
dashstyle3 = (3, 2)
method = 'slb2'
# define the minerals from table 6.3
mg_perovskite = burnman.Mineral()
mg_perovskite.params = {
'name': 'Mg perovskite',
'molar_mass': 0.1004,
'V_0': 24.43e-6,
'K_0': 253.0e9,
'Kprime_0': 3.9,
'G_0': 172.9e9,
'Gprime_0': 1.56,
'n': 5.0,
'Debye_0': 1100.,
'grueneisen_0': 1.40,
'q_0': 1.40,
'eta_s_0': 2.6
}
mg_perovskite.set_method('slb2')
def check_slb_fig7():
"""
Calculates all values for forsterite and benchmarks with figure 7 from Stixrude and Lithgow-Bertelloni (2005)
"""
forsterite = burnman.Mineral()
forsterite.params = {'name': 'forsterite',
'V_0': 43.60e-6,
'K_0': 128.0e9,
'Kprime_0': 4.2,
'G_0': 82.0e9,
'Gprime_0': 1.4,
'n': 7.0,
'molar_mass': .140695,
'Debye_0': 809.,
'grueneisen_0': .99,
'q_0': 2.1,
'eta_s_0': 2.4}
forsterite.set_method('slb3')
temperature = np.linspace(0., 2000., 200)
volume = np.empty_like(temperature)
bulk_modulus = np.empty_like(temperature)
shear_modulus = np.empty_like(temperature)
heat_capacity = np.empty_like(temperature)
pressure = 1.0e5
forsterite.set_state(pressure, 300.)
Ks_0 = forsterite.adiabatic_bulk_modulus
# calculate its thermal properties
for i in range(len(temperature)):
forsterite.set_state(pressure, temperature[i])
volume[i] = forsterite.molar_volume / forsterite.params['V_0']
bulk_modulus[i] = forsterite.adiabatic_bulk_modulus / Ks_0
shear_modulus[i] = forsterite.shear_modulus / forsterite.params['G_0']
heat_capacity[i] = forsterite.heat_capacity_p / forsterite.params['n']
# compare with figure 7
fig1 = mpimg.imread('../../burnman/data/input_figures/slb_fig7_vol.png')
plt.imshow(fig1, extent=[0, 2200, 0.99, 1.08], aspect='auto')
plt.plot(temperature, volume, 'g+')
plt.ylim(0.99, 1.08)
plt.xlim(0, 2200)
plt.xlabel("Temperature (K)")
plt.ylabel("Relative Volume V/V0")
plt.title(
"Comparing with Figure 7 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
fig1 = mpimg.imread('../../burnman/data/input_figures/slb_fig7_Cp.png')
plt.imshow(fig1, extent=[0, 2200, 0., 70.], aspect='auto')
plt.plot(temperature, heat_capacity, 'g+')
plt.ylim(0, 70)
plt.xlim(0, 2200)
plt.xlabel("Temperature (K)")
plt.ylabel("Heat Capacity Cp")
plt.title(
"Comparing with adiabatic_bulk_modulus7 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
fig1 = mpimg.imread('../../burnman/data/input_figures/slb_fig7_K.png')
plt.imshow(fig1, extent=[0, 2200, 0.6, 1.02], aspect='auto')
plt.plot(temperature, bulk_modulus, 'g+')
plt.ylim(0.6, 1.02)
plt.xlim(0, 2200)
plt.xlabel("Temperature (K)")
plt.ylabel("Relative Bulk Modulus K/K0")
plt.title(
"Comparing with Figure 7 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
fig1 = mpimg.imread('../../burnman/data/input_figures/slb_fig7_G.png')
plt.imshow(fig1, extent=[0, 2200, 0.6, 1.02], aspect='auto')
plt.plot(temperature, shear_modulus, 'g+')
plt.ylim(0.6, 1.02)
plt.xlim(0, 2200)
plt.xlabel("Temperature (K)")
plt.ylabel("Relative Shear Modulus G/G0")
plt.title(
"Comparing with Figure 7 of Stixrude and Lithgow-Bertelloni (2005)")
plt.show()
def check_slb_fig7_txt():
"""
Calculates all values for forsterite and benchmarks with values from Stixrude and Lithgow-Bertelloni (personal communication)
"""
forsterite = burnman.Mineral()
forsterite.params = {'name': 'forsterite',
'V_0': 43.603e-6,
'K_0': 127.955e9,
'Kprime_0': 4.232,
'G_0': 81.6e9,
'Gprime_0': 1.4,
'molar_mass': .140695,
'n': 7.0,
'Debye_0': 809.183,
'grueneisen_0': .993,
'q_0': 2.093,
'F_0': -1.1406e5,
'eta_s_0': 2.364}
forsterite.set_method('slb3')
data = np.loadtxt(
"../../burnman/data/input_minphys/slb_fig7.txt", skiprows=2)
temperature = np.array(data[:, 2])
pressure = np.array(data[:, 0])
rho = np.array(data[:, 3])
rho_comp = np.empty_like(rho)
Kt = np.array(data[:, 4])
Kt_comp = np.empty_like(Kt)
Ks = np.array(data[:, 5])
Ks_comp = np.empty_like(Ks)
G = np.array(data[:, 6])
G_comp = np.empty_like(G)
VB = np.array(data[:, 7])
VB_comp = np.empty_like(VB)
VS = np.array(data[:, 8])
VS_comp = np.empty_like(VS)
VP = np.array(data[:, 9])
VP_comp = np.empty_like(VP)
vol = np.array(data[:, 10])
vol_comp = np.empty_like(vol)
alpha = np.array(data[:, 11])
alpha_comp = np.empty_like(alpha)
Cp = np.array(data[:, 12])
Cp_comp = np.empty_like(Cp)
gr = np.array(data[:, 13])
gr_comp = np.empty_like(gr)
gibbs = np.array(data[:, 14])
gibbs_comp = np.empty_like(gibbs)
entropy = np.array(data[:, 15])
entropy_comp = np.empty_like(gibbs)
enthalpy = np.array(data[:, 16])
enthalpy_comp = np.empty_like(gibbs)
for i in range(len(temperature)):
forsterite.set_state(pressure[i], temperature[i])
rho_comp[i] = 100. * (forsterite.density / 1000. - rho[i]) / rho[i]
Kt_comp[i] = 100. * (
forsterite.isothermal_bulk_modulus / 1.e9 - Kt[i]) / Kt[i]
Ks_comp[i] = 100. * (
forsterite.adiabatic_bulk_modulus / 1.e9 - Ks[i]) / Ks[i]
G_comp[i] = 100. * (forsterite.shear_modulus / 1.e9 - G[i]) / G[i]
VB_comp[i] = 100. * (forsterite.v_phi / 1000. - VB[i]) / VB[i]
VS_comp[i] = 100. * (forsterite.v_s / 1000. - VS[i]) / VS[i]
VP_comp[i] = 100. * (forsterite.v_p / 1000. - VP[i]) / VP[i]
vol_comp[i] = 100. * (forsterite.molar_volume * 1.e6 - vol[i]) / vol[i]
alpha_comp[i] = 100. * (
forsterite.thermal_expansivity / 1.e-5 - alpha[i]) / (alpha[-1])
Cp_comp[i] = 100. * (forsterite.heat_capacity_p /
forsterite.params['molar_mass'] / 1000. - Cp[i]) / (Cp[-1])
gr_comp[i] = (forsterite.grueneisen_parameter - gr[i]) / gr[i]
gibbs_comp[i] = 100. * (
forsterite.molar_gibbs / 1.e6 - gibbs[i]) / gibbs[i]
entropy_comp[i] = 100. * (
forsterite.molar_entropy - entropy[i]) / (entropy[i] if entropy[i] != 0. else 1.)
enthalpy_comp[i] = 100. * (
forsterite.molar_enthalpy / 1.e6 - enthalpy[i]) / (enthalpy[i] if enthalpy[i] != 0. else 1.)
plt.plot(temperature, rho_comp, label=r'$\rho$')
plt.plot(temperature, Kt_comp, label=r'$K_S$')
plt.plot(temperature, Ks_comp, label=r'$K_T$')
plt.plot(temperature, G_comp, label=r'$G$')
plt.plot(temperature, VS_comp, label=r'$V_S$')
plt.plot(temperature, VP_comp, label=r'$V_P$')
plt.plot(temperature, VB_comp, label=r'$V_\phi$')
plt.plot(temperature, vol_comp, label=r'$V$')
plt.plot(temperature, alpha_comp, label=r'$\alpha$')
plt.plot(temperature, Cp_comp, label=r'$c_P$')
plt.plot(temperature, gr_comp, label=r'$\gamma$')
plt.plot(temperature, gibbs_comp, label=r'Gibbs')
plt.plot(temperature, enthalpy_comp, label=r'Enthalpy')
plt.plot(temperature, entropy_comp, label=r'Entropy')
plt.xlim([0, 2750])
plt.ylim([-0.001, 0.001])
plt.xticks([0, 800, 1600, 2200])
plt.xlabel("Temperature (K)")
plt.ylabel("Percent Difference from HeFESTo")
plt.legend(loc="center right")
# plt.savefig("output_figures/benchmark1.pdf")
plt.show()
if __name__ == "__main__":
# 1) Fitting shear modulus and its derivative to shear wave velocity data
print(
'1) Fitting shear modulus and its derivative to shear wave velocity data\n'
)
# First, read in the data from file and convert to SI units.
PTp_data = np.loadtxt(
'../burnman/data/input_minphys/Murakami_perovskite.txt')
PTp_data[:, 0] = PTp_data[:, 0] * 1.e9
PTp_data[:, 2] = PTp_data[:, 2] * 1.e3
# Make the test mineral
mg_perovskite_test = burnman.Mineral()
mg_perovskite_test.params = {
'V_0': 24.45e-6,
'K_0': 281.e9,
'Kprime_0': 4.1,
'molar_mass': .10,
'G_0': 200.e9,
'Gprime_0': 2.
}
def best_fit():
return burnman.tools.fit_PTp_data(mineral=mg_perovskite_test,
flags='shear_wave_velocity',
fit_params=['G_0', 'Gprime_0'],
data=PTp_data,
verbose=False)
def check_slb_fig7_txt():
"""
Calculates all values for forsterite and benchmarks with values from Stixrude and Lithgow-Bertelloni (personal communication)
"""
forsterite = burnman.Mineral()
forsterite.params = {
'name': 'forsterite',
'V_0': 43.603e-6,
'K_0': 127.955e9,
'Kprime_0': 4.232,
'G_0': 81.6e9,
'Gprime_0': 1.4,
'molar_mass': .140695,
'n': 7.0,
'Debye_0': 809.183,
'grueneisen_0': .993,
'q_0': 2.093,
'eta_s_0': 2.364
}
forsterite.set_method('slb3')
data = np.loadtxt("slb_benchmark.txt", skiprows=1)
temperature = np.array(data[:, 2])
pressure = np.array(data[:, 0])
rho = np.array(data[:, 3])
frho = np.empty_like(rho)
rho_comp = np.empty_like(rho)
Kt = np.array(data[:, 4])
fKt = np.empty_like(Kt)
Kt_comp = np.empty_like(Kt)
Ks = np.array(data[:, 5])
fKs = np.empty_like(Ks)
Ks_comp = np.empty_like(Ks)
G = np.array(data[:, 6])
fG = np.empty_like(G)
G_comp = np.empty_like(G)
VB = np.array(data[:, 7])
fVB = np.empty_like(VB)
VB_comp = np.empty_like(VB)
VS = np.array(data[:, 8])
fVS = np.empty_like(VS)
VS_comp = np.empty_like(VS)
VP = np.array(data[:, 9])
fVP = np.empty_like(VP)
VP_comp = np.empty_like(VP)
vol = np.array(data[:, 10])
fvol = np.empty_like(vol)
vol_comp = np.empty_like(vol)
alpha = np.array(data[:, 11])
falpha = np.empty_like(alpha)
alpha_comp = np.empty_like(alpha)
Cp = np.array(data[:, 12])
fCp = np.empty_like(Cp)
Cp_comp = np.empty_like(Cp)
gr = np.array(data[:, 13])
gr_comp = np.empty_like(gr)
for i in range(len(temperature)):
forsterite.set_state(pressure[i], temperature[i])
rho_comp[i] = 100. * (forsterite.density / 1000. - rho[i]) / rho[i]
Kt_comp[i] = 100. * (forsterite.isothermal_bulk_modulus / 1.e9 -
Kt[i]) / Kt[i]
Ks_comp[i] = 100. * (forsterite.adiabatic_bulk_modulus / 1.e9 -
Ks[i]) / Ks[i]
G_comp[i] = 100. * (forsterite.shear_modulus / 1.e9 - G[i]) / G[i]
VB_comp[i] = 100. * (forsterite.v_phi / 1000. - VB[i]) / VB[i]
VS_comp[i] = 100. * (forsterite.v_s / 1000. - VS[i]) / VS[i]
VP_comp[i] = 100. * (forsterite.v_p / 1000. - VP[i]) / VP[i]
vol_comp[i] = 100. * (forsterite.molar_volume * 1.e6 - vol[i]) / vol[i]
alpha_comp[i] = 100. * (forsterite.thermal_expansivity / 1.e-5 -
alpha[i]) / (alpha[-1])
Cp_comp[i] = 100. * (forsterite.molar_heat_capacity_p /
forsterite.params['molar_mass'] / 1000. -
Cp[i]) / (Cp[-1])
gr_comp[i] = (forsterite.grueneisen_parameter - gr[i]) / gr[i]
plt.plot(temperature, rho_comp, label=r'$\rho$')
plt.plot(temperature, Kt_comp, label=r'$K_S$')
plt.plot(temperature, Ks_comp, label=r'$K_T$')
plt.plot(temperature, G_comp, label=r'$G$')
plt.plot(temperature, VS_comp, label=r'$V_S$')
plt.plot(temperature, VP_comp, label=r'$V_P$')
plt.plot(temperature, VB_comp, label=r'$V_\phi$')
plt.plot(temperature, vol_comp, label=r'$V$')
plt.plot(temperature, alpha_comp, label=r'$\alpha$')
plt.plot(temperature, Cp_comp, label=r'$c_P$')
plt.plot(temperature, gr_comp, label=r'$\gamma$')
plt.xlim([0, 2200])
plt.ylim([-0.002, 0.002])
plt.yticks([-0.002, -0.001, 0, 0.001, 0.002])
plt.xticks([0, 800, 1600, 2200])
plt.xlabel("Temperature (K)")
plt.ylabel("Difference (\%)")
plt.legend(loc="lower center", prop=prop, ncol=4)
if "RUNNING_TESTS" not in globals():
plt.savefig("benchmark1.pdf", bbox_inches='tight')
plt.show()
def make_orthorhombic_mineral_from_parameters(x):
f_order = 3
Pth_order = 2
constants = np.zeros((6, 6, f_order+1, Pth_order+1))
san_carlos_params = {'name': 'San Carlos olivine',
'formula': formula,
'equation_of_state': 'slb3',
'F_0': 0.0,
'V_0': V_0_guess, # we overwrite this in a second
'K_0': 1.263e+11, # Abramson et al. 1997
'Kprime_0': 4.28, # Abramson et al. 1997
'Debye_0': fo.params['Debye_0']*0.9 + fa.params['Debye_0']*0.1, #
'grueneisen_0': 0.99282, # Fo in SLB2011
'q_0': 2.10672, # Fo in SLB2011
'G_0': 81.6e9,
'Gprime_0': 1.46257,
'eta_s_0': 2.29972,
'n': 7.,
'molar_mass': formula_mass}
san_carlos_property_modifiers = [['linear', {'delta_E': 0.0,
'delta_S': 26.76*0.1 - 2.*burnman.constants.gas_constant*(0.1*np.log(0.1) + 0.9*np.log(0.9)),
'delta_V': 0.0}]]
ol = burnman.Mineral(params=san_carlos_params,
property_modifiers=san_carlos_property_modifiers)
# Overwrite some properties
ol.params['V_0'] = x[0]*V_0_guess # Abramson et al. 1997
ol.params['K_0'] = x[1]*1.263e+11 # Abramson et al. 1997
ol.params['Kprime_0'] = x[2]*4.28 # Abramson et al. 1997
#ol.params['Debye_0'] = x[3]*809.1703 # Fo in SLB2011 strong tendency to 0
ol.params['grueneisen_0'] = x[3]*0.99282 # Fo in SLB2011
ol.params['q_0'] = x[4]*2.10672 # Fo in SLB2011
# Next, each of the eight independent elastic tensor component get their turn.
# We arbitrarily choose S[2,3] as the ninth component, which is determined by the others.
i = 5
for (p, q) in ((1, 1),
(2, 2),
(3, 3),
(4, 4),
(5, 5),
(6, 6),
(1, 2),
(1, 3)):
for (m, n) in ((1, 0),
(2, 0),
(3, 0)):
constants[p-1, q-1, m, n] = x[i]
constants[q-1, p-1, m, n] = x[i]
i += 1
for (m, n) in ((0, 1),
(1, 1),
(2, 1),
(3, 1)):
constants[p-1, q-1, m, n] = x[i]*1.e-11
constants[q-1, p-1, m, n] = x[i]*1.e-11
i += 1
for (m, n) in ((0, 2),):
constants[p-1, q-1, m, n] = x[i]*1.e-22
constants[q-1, p-1, m, n] = x[i]*1.e-22
i += 1
assert i == 69 # 40 parameters
# Fill the values for the dependent element c[2,3]
constants[1,2,1,0] = (1. - np.sum(constants[:3,:3,1,0])) / 2.
constants[1,2,2:,0] = - np.sum(constants[:3,:3,2:,0], axis=(0, 1)) / 2.
constants[1,2,:,1:] = - np.sum(constants[:3,:3,:,1:], axis=(0, 1)) / 2.
# And for c[3,2]
constants[2,1,:,:] = constants[1,2,:,:]
cell_lengths = cell_lengths_0_guess*np.cbrt(ol.params['V_0']/V_0_guess)
ol_cell_parameters = np.array([cell_lengths[0],
cell_lengths[1],
cell_lengths[2],
90, 90, 90])
m = AnisotropicMineral(ol, ol_cell_parameters, constants)
return m
'formula': forsterite_formula,
'equation_of_state': 'slb3',
'F_0': -2055403.0,
'V_0': 4.3603e-05,
'K_0': 1.279555e+11,
'Kprime_0': 4.21796,
'Debye_0': 809.1703,
'grueneisen_0': 0.99282,
'q_0': 2.10672,
'G_0': 81599990000.0,
'Gprime_0': 1.46257,
'eta_s_0': 2.29972,
'n': sum(forsterite_formula.values()),
'molar_mass': formula_mass(forsterite_formula)}
forsterite = burnman.Mineral(params=forsterite_params)
"""
BurnMan also contains the Stixrude and Lithgow-Bertelloni (2011)
dataset, so we can also create an object corresponding to this mineral
directly.
"""
forsterite = SLB_2011.forsterite()
"""
In petrology, we are often interested in phases for which we have little
experimental or theoretical information.
One common example is when we want to approximate the properties
of an ordered phase relative to its disordered counterparts.
