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()