def check_mgd_shim_duffy_kenichi():
"""
Attemmpts to recreate Shim Duffy Kenichi (2002)
"""
plt.close()
#Create gold material from Table 1
gold = burnman.material()
gold.params = {
'name': 'gold',
'V_0': 10.22e-6,
'K_0': 167.0e9,
'Kprime_0': 5.0,
'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.material()
mgfeo.params = {
'name': 'MgFeO',
'V_0': 11.657e-6,
'K_0': 157.0e9,
'Kprime_0': 4.0,
'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.material()
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,
'n': 0.,
'Debye_0': 0.,
'grueneisen_0': 0.,
'q_0': 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('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 check_slb_fig3():
"""
Benchmark grueneisen parameter against figure 3 of Stixrude and Lithgow-Bertelloni (2005b)
"""
perovskite = burnman.material()
perovskite.params = {
'name': 'perovksite',
'V_0': burnman.tools.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('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_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.material()
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,
'n': 0.,
'Debye_0': 0.,
'grueneisen_0': 0.,
'q_0': 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('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 check_mgd_shim_duffy_kenichi():
"""
Attemmpts to recreate Shim Duffy Kenichi (2002)
"""
plt.close()
#Create gold material from Table 1
gold = burnman.material()
gold.params = {'name': 'gold',
'V_0': 10.22e-6,
'K_0': 167.0e9,
'Kprime_0': 5.0,
'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_slb_fig3():
"""
Benchmark grueneisen parameter against figure 3 of Stixrude and Lithgow-Bertelloni (2005b)
"""
perovskite= burnman.material()
perovskite.params = { 'name': 'perovksite',
'V_0': burnman.tools.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('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_mgd_fei_mao_shu_hu():
"""
Benchmark agains Fei Mao Shu Hu (1991)
"""
mgfeo = burnman.material()
mgfeo.params = { 'name': 'MgFeO',
'V_0': 11.657e-6,
'K_0': 157.0e9,
'Kprime_0': 4.0,
'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()
vs_l2 = [ (vs[i] - obs_vs[i])*(vs[i] - obs_vs[i]) for i in range(len(obs_vs)) ]
l2_error = sum(vs_l2)
return l2_error
mg_perovskite_data = np.loadtxt("Murakami_perovskite.txt")
obs_pressures = mg_perovskite_data[:,0]*1.e9
obs_vs = mg_perovskite_data[:,2]*1000.
pressures = np.linspace(25.e9, 135.e9, 100)
#make the mineral to fit
guess = [200.e9, 2.0]
mg_perovskite_test = burnman.material()
mg_perovskite_test.params['V_0'] = 24.45e-6
mg_perovskite_test.params['K_0'] = 281.e9
mg_perovskite_test.params['Kprime_0'] = 4.1
mg_perovskite_test.params['molar_mass'] = .10227
#first, do the second-order fit
mg_perovskite_test.set_method("bm2")
func = lambda x : error( x, mg_perovskite_test, obs_pressures, obs_vs)
sol = opt.fmin(func, guess)
print "2nd order fit: G = ", sol[0]/1.e9, "GPa\tG' = ", sol[1]
model_vs_2nd_order_correct = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
mg_perovskite_test.set_method("bm3")
model_vs_2nd_order_incorrect = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
#now do third-order fit
def check_slb_fig7():
"""
Calculates all values for forsterite and benchmarks with figure 7 from Stixrude and Lithgow-Bertelloni (2005)
"""
forsterite = burnman.material()
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,
'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('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('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('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('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.material()
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("input_minphys/slb_fig7.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.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, 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()
def check_slb_fig7_txt():
"""
Calculates all values for forsterite and benchmarks with values from Stixrude and Lithgow-Bertelloni (personal communication)
"""
forsterite = burnman.material()
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.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)
plt.savefig("benchmark1.pdf", bbox_inches='tight')
plt.show()
def check_slb_fig7():
"""
Calculates all values for forsterite and benchmarks with figure 7 from Stixrude and Lithgow-Bertelloni (2005)
"""
forsterite = burnman.material()
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,
'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('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('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('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('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()
import burnman.minerals_base as mb
import numpy as np
import colors
plt.figure(dpi=100, figsize=(12, 6))
prop = {'size': 12}
plt.rc('text', usetex=True)
plt.rcParams['text.latex.preamble'] = '\usepackage{relsize}'
dashstyle2 = (7, 3)
dashstyle3 = (3, 2)
method = 'slb2'
#define the minerals from table 6.3
mg_perovskite = burnman.material()
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')
import numpy as np
import colors
plt.figure(dpi=100,figsize=(12,6))
prop={'size':12}
plt.rc('text', usetex=True)
plt.rcParams['text.latex.preamble'] = '\usepackage{relsize}'
dashstyle2=(7,3)
dashstyle3=(3,2)
method = 'slb2'
#define the minerals from table 6.3
mg_perovskite = burnman.material()
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')
fe_perovskite = burnman.material()
