Olivine Phase Loop¶
This notebook demonstrates calculation of the olivine liquid-solid
phase loop under the assumption that both phases behave as ideal
solutions.
The workflow is: - Use the coder module to generate endmember
properties of both solutions; the only thermodynamic properties that
are specified are the enthalpy and entropy of fusion - Use the
coder module to generate solid and liquid solution properties -
Import the generated code using the model module - Use the
equilibrate module to compute the liquid-solid phase loop - Plot
results
import numpy as np
import scipy as sp
import sympy as sym
import matplotlib.pyplot as plt
from thermoengine import model, equilibrate, coder
%matplotlib inline
Endmember properties¶
Write code into a working subdirectory
working_dir = "working"
!mkdir -p {working_dir}
%cd {working_dir}
/Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Equilibrate/working
Model generation function
def make_endmembers(module='none', name='none', formula='none', Hrefvalue=0.0, Srefvalue=0.0):
mdl = coder.StdStateModel()
T = mdl.get_symbol_for_t()
GPr,Href,Sref = sym.symbols('GPr Href Sref')
GPr = Href - T*Sref
params = [('Href', 'J', Href), ('Sref', 'J/K', Sref)]
mdl.add_expression_to_model(GPr, params)
mdl.set_module_name(module)
paramValues = {'Href':Hrefvalue, 'Sref':Srefvalue, 'T_r':298.15, 'P_r':1.0}
mdl.create_code_module(phase=name, formula=formula, params=paramValues,
module_type='calib', silent=True)
Forsterite Solid¶
make_endmembers(module='OlvSolid', name='Fo', formula='Mg(2)Si(1)O(4)', Hrefvalue=-100000.0, Srefvalue=0.0)
%cp OlvSolid.pyx endmembersolids.pyx
Fayalite Solid¶
make_endmembers(module='OlvSolid', name='Fa', formula='Fe(2)Si(1)O(4)', Hrefvalue=-100000.0, Srefvalue=0.0)
%cat OlvSolid.pyx >> endmembersolids.pyx
Forsterite Liquid¶
Fusion temperature is 2163 K, entropy is 57.2 J/K
make_endmembers(module='OlvLiquid', name='Fo', formula='Mg(2)Si(1)O(4)', Hrefvalue=-100000.0+57.2*2163.0, Srefvalue=57.2)
%cp OlvLiquid.pyx endmemberliquids.pyx
Fayalite Liquid¶
Fusion temperature is 1490 K, entropy is 59.9 J/K
make_endmembers(module='OlvLiquid', name='Fa', formula='Fe(2)Si(1)O(4)', Hrefvalue=-100000.0+59.9*1490.0, Srefvalue=59.9)
%cat OlvLiquid.pyx >> endmemberliquids.pyx
Solution Properties¶
Model generation function
def make_solution(module='none', name='none', endmembers=[]):
c = 2
mdl = coder.SimpleSolnModel(nc=c)
n = mdl.n
nT = mdl.nT
X = n/nT
T = mdl.get_symbol_for_t()
mu = mdl.mu
G_ss = (n.transpose()*mu)[0]
S_config,R = sym.symbols('S_config R')
S_config = 0
for i in range(0,c):
S_config += X[i]*sym.log(X[i])
S_config *= -R*nT
G_config = sym.simplify(-T*S_config)
G = G_ss + G_config
mdl.add_expression_to_model(G, [('dummy', 'none', sym.symbols('dummy'))])
mdl.module = module
mdl.formula_string = 'Mg[Mg]Fe[Fe]Si[Si]O4'
mdl.conversion_string = ['[0]=[Mg]', '[1]=[Fe]']
mdl.test_string = ['[0] > 0.0', '[1] > 0.0']
mdl.create_code_module(phase=name, params={'dummy':0.0, 'T_r':298.15, 'P_r':1.0},
endmembers=endmembers,
prefix="cy", module_type='calib', silent=True)
Solid solution¶
make_solution(module='OlvSolid', name='Olivine', endmembers=['Fo_OlvSolid', 'Fa_OlvSolid'])
%cat endmembersolids.pyx >> OlvSolid.pyx
Liquid solution¶
make_solution(module='OlvLiquid', name='Liquid', endmembers=['Fo_OlvLiquid', 'Fa_OlvLiquid'])
%cat endmemberliquids.pyx >> OlvLiquid.pyx
import OlvSolid
import OlvLiquid
%cd ..
/Users/ghiorso/anaconda3/lib/python3.7/site-packages/Cython/Compiler/Main.py:369: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Equilibrate/working/OlvSolid.pyx
tree = Parsing.p_module(s, pxd, full_module_name)
/Users/ghiorso/anaconda3/lib/python3.7/site-packages/Cython/Compiler/Main.py:369: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Equilibrate/working/OlvLiquid.pyx
tree = Parsing.p_module(s, pxd, full_module_name)
/Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Equilibrate
Set up phase loop calculation¶
modelDBsol = model.Database(database="CoderModule", calib='calib',
phase_tuple=('OlvSolid', {
'Ol':['Olivine','solution'],
'Fo':['Fo','pure'],
'Fa':['Fa','pure']
}))
modelDBliq = model.Database(database="CoderModule", calib='calib',
phase_tuple=('OlvLiquid', {
'Liq':['Liquid','solution'],
'Fo':['Fo','pure'],
'Fa':['Fa','pure']
}))
Solution phase code generated by the coder module does not yet provide information on solution species. Species are proxied by components.
Solution phase code generated by the coder module does not yet provide information on species properties. Species are proxied by components.
Solution phase code generated by the coder module does not yet provide information on solution species. Species are proxied by components.
Solution phase code generated by the coder module does not yet provide information on species properties. Species are proxied by components.
olivine = modelDBsol.get_phase("Ol")
liquid = modelDBliq.get_phase("Liq")
elm_sys = ['O','Mg','Si','Fe']
phs_sys = [liquid, olivine]
Compute the loop¶
xFoSol = [1.0]
xFoLiq = [1.0]
tC = [2163.0-273.15]
p = 1.0
for i in range(1,20):
XFo = 1.0 - i*0.05
XFa = 1.0 - XFo
blk_cmp = np.array([4.0*(XFo+XFa), 2.0*XFo, XFo+XFa, 2.0*XFa])
equil = equilibrate.Equilibrate(elm_sys, phs_sys)
t = 2163.0*XFo + 1490.0*XFa
state = equil.execute(t, p, bulk_comp=blk_cmp, debug=0, stats=True)
state.print_state()
tC.append(t-273.15)
xFoSol.append(state.compositions(phase_name='Olivine', units='mole_frac')[0])
xFoLiq.append(state.compositions(phase_name='Liquid', units='mole_frac')[0])
xFoSol.append(0.0)
xFoLiq.append(0.0)
tC.append(1490.0-273.15)
Add: Olivine
Quad (000) norm: 2.1104254762564e+00 Lin (016) step: 3.8779326997502e-01 func: -1.0402273326438e+05
Quad (001) norm: 3.2418611320216e-02 Lin (017) step: 1.7951470449315e+00 func: -1.0405375729263e+05
Quad (002) norm: 1.4763143793992e-02 Lin (010) step: 9.6932535179819e-01 func: -1.0405401325700e+05
Quad (003) norm: 4.0623266711652e-05 Lin (029) step: 9.9979197987555e-01 func: -1.0405401326837e+05
Quad (004) norm: 7.3677199507684e-09 Lin (039) step: 8.4138217960888e-01 func: -1.0405401326837e+05
Quad (005) norm: 1.1686594034085e-09 Lin (040) step: -7.3123984754483e-01 func: -1.0405401326837e+05
Minimal energy termination of quadratic loop.
T = 1856.20 °C, P = 0.1 MPa
Liquid moles: 0.361955 grams: 53.547
Fo form: Mg2SiO4 X: 0.8851 wt% SiO2 40.61
Fa form: Fe2SiO4 X: 0.1149 wt% FeO 11.16
wt% MgO 48.23
Olivine moles: 0.638045 grams: 90.300
Fo form: Mg2SiO4 X: 0.9868 wt% SiO2 42.45
Fa form: Fe2SiO4 X: 0.0132 wt% FeO 1.34
wt% MgO 56.20
Add: Olivine
Quad (000) norm: 2.0114451413753e+00 Lin (015) step: 3.9174467592009e-01 func: -1.0663613100463e+05
Quad (001) norm: 3.1142185393805e-02 Lin (032) step: 1.8317912801402e+00 func: -1.0670046985749e+05
Quad (002) norm: 1.5416604556166e-02 Lin (019) step: 9.6691766198867e-01 func: -1.0670104487450e+05
Quad (003) norm: 4.5064898567581e-05 Lin (028) step: 9.9975861375761e-01 func: -1.0670104490454e+05
Quad (004) norm: 9.6146541687342e-09 Lin (039) step: 8.5998149639898e-01 func: -1.0670104490454e+05
Quad (005) norm: 1.3462267133040e-09 Lin (039) step: 8.1909231079668e-01 func: -1.0670104490454e+05
Minimal energy termination of quadratic loop.
T = 1822.55 °C, P = 0.1 MPa
Liquid moles: 0.376308 grams: 58.172
Fo form: Mg2SiO4 X: 0.7798 wt% SiO2 38.87
Fa form: Fe2SiO4 X: 0.2202 wt% FeO 20.47
wt% MgO 40.66
Olivine moles: 0.623692 grams: 88.829
Fo form: Mg2SiO4 X: 0.9725 wt% SiO2 42.19
Fa form: Fe2SiO4 X: 0.0275 wt% FeO 2.77
wt% MgO 55.04
Add: Olivine
Quad (000) norm: 1.9106239644072e+00 Lin (016) step: 3.9582177358734e-01 func: -1.0863573839282e+05
Quad (001) norm: 3.0573320893983e-02 Lin (014) step: 1.8719312484472e+00 func: -1.0873576578541e+05
Quad (002) norm: 1.6092789244022e-02 Lin (014) step: 9.6415282496294e-01 func: -1.0873673638519e+05
Quad (003) norm: 5.1487274533657e-05 Lin (029) step: 9.9945717817509e-01 func: -1.0873673644510e+05
Quad (004) norm: 3.5575530590706e-09 Lin (038) step: 1.6519526824590e+00 func: -1.0873673644510e+05
Quad (005) norm: 2.3193563531757e-09 Lin (042) step: -3.6785150611398e-01 func: -1.0873673644510e+05
Minimal energy termination of quadratic loop.
T = 1788.90 °C, P = 0.1 MPa
Liquid moles: 0.391316 grams: 62.871
Fo form: Mg2SiO4 X: 0.6834 wt% SiO2 37.40
Fa form: Fe2SiO4 X: 0.3166 wt% FeO 28.31
wt% MgO 34.29
Olivine moles: 0.608684 grams: 87.285
Fo form: Mg2SiO4 X: 0.9571 wt% SiO2 41.90
Fa form: Fe2SiO4 X: 0.0429 wt% FeO 4.30
wt% MgO 53.80
Add: Olivine
Quad (000) norm: 1.8079136182821e+00 Lin (024) step: 4.0003822981413e-01 func: -1.1019554484785e+05
Quad (001) norm: 3.0787646794130e-02 Lin (016) step: 1.9160707731592e+00 func: -1.1033368599857e+05
Quad (002) norm: 1.6791400729548e-02 Lin (020) step: 9.6095788326558e-01 func: -1.1033514496278e+05
Quad (003) norm: 6.0794171941693e-05 Lin (024) step: 9.9954277934166e-01 func: -1.1033514506973e+05
Quad (004) norm: 9.9720374388972e-09 Lin (040) step: 4.9983406065890e-01 func: -1.1033514506973e+05
Quad (005) norm: 4.9876737609594e-09 Lin (047) step: -2.1334834772453e-02 func: -1.1033514506973e+05
Minimal energy termination of quadratic loop.
T = 1755.25 °C, P = 0.1 MPa
Liquid moles: 0.406994 grams: 67.643
Fo form: Mg2SiO4 X: 0.5956 wt% SiO2 36.15
Fa form: Fe2SiO4 X: 0.4044 wt% FeO 34.96
wt% MgO 28.89
Olivine moles: 0.593006 grams: 85.667
Fo form: Mg2SiO4 X: 0.9403 wt% SiO2 41.59
Fa form: Fe2SiO4 X: 0.0597 wt% FeO 5.94
wt% MgO 52.47
Add: Olivine
Quad (000) norm: 1.7032709372590e+00 Lin (014) step: 4.0441189414102e-01 func: -1.1139918109725e+05
Quad (001) norm: 3.1794373696592e-02 Lin (029) step: 1.9648182746974e+00 func: -1.1157786603177e+05
Quad (002) norm: 1.7512076248931e-02 Lin (021) step: 9.5724546055780e-01 func: -1.1157992569536e+05
Quad (003) norm: 7.4166851734302e-05 Lin (022) step: 9.9954766440304e-01 func: -1.1157992587561e+05
Quad (004) norm: 1.8561007700569e-08 Lin (038) step: 1.9941348560423e+00 func: -1.1157992587561e+05
Quad (005) norm: 1.8452144971921e-08 Lin (039) step: 1.3449506850978e+00 func: -1.1157992587561e+05
Minimal energy termination of quadratic loop.
T = 1721.60 °C, P = 0.1 MPa
Liquid moles: 0.423353 grams: 72.490
Fo form: Mg2SiO4 X: 0.5160 wt% SiO2 35.09
Fa form: Fe2SiO4 X: 0.4840 wt% FeO 40.62
wt% MgO 24.29
Olivine moles: 0.576647 grams: 83.975
Fo form: Mg2SiO4 X: 0.9218 wt% SiO2 41.26
Fa form: Fe2SiO4 X: 0.0782 wt% FeO 7.72
wt% MgO 51.03
Add: Olivine
Quad (000) norm: 1.5966604996323e+00 Lin (021) step: 4.0896682151642e-01 func: -1.1229597492575e+05
Quad (001) norm: 3.3531760786162e-02 Lin (038) step: 1.9999999695048e+00 func: -1.1251755736637e+05
Quad (002) norm: 1.8730262736856e-02 Lin (021) step: 9.5145608560682e-01 func: -1.1252036721908e+05
Quad (003) norm: 4.1909407472519e-05 Lin (026) step: 9.9978900144526e-01 func: -1.1252036728945e+05
Quad (004) norm: 9.2042603294142e-09 Lin (040) step: -4.4760217220127e-01 func: -1.1252036728945e+05
Quad (005) norm: 1.3324106387581e-08 Lin (040) step: 4.7007485184832e-01 func: -1.1252036728945e+05
Minimal energy termination of quadratic loop.
T = 1687.95 °C, P = 0.1 MPa
Liquid moles: 0.440402 grams: 77.409
Fo form: Mg2SiO4 X: 0.4440 wt% SiO2 34.18
Fa form: Fe2SiO4 X: 0.5560 wt% FeO 45.46
wt% MgO 20.36
Olivine moles: 0.559598 grams: 82.209
Fo form: Mg2SiO4 X: 0.9015 wt% SiO2 40.90
Fa form: Fe2SiO4 X: 0.0985 wt% FeO 9.64
wt% MgO 49.47
Add: Olivine
Quad (000) norm: 1.4880582357278e+00 Lin (012) step: 4.1373492082155e-01 func: -1.1291818273809e+05
Quad (001) norm: 3.5885647757584e-02 Lin (037) step: 1.9999999451233e+00 func: -1.1318463428273e+05
Quad (002) norm: 2.0995382584375e-02 Lin (013) step: 9.4673678156252e-01 func: -1.1318859383769e+05
Quad (003) norm: 1.2095598641376e-04 Lin (009) step: 1.0006930291438e+00 func: -1.1318859460434e+05
Quad (004) norm: 1.0234833107969e-07 Lin (032) step: 9.9640056598608e-01 func: -1.1318859460434e+05
Quad (005) norm: 3.6836719171515e-10 Lin (027) step: -1.0557282694161e+00 func: -1.1318859460434e+05
Minimal energy termination of quadratic loop.
T = 1654.30 °C, P = 0.1 MPa
Liquid moles: 0.458145 grams: 82.401
Fo form: Mg2SiO4 X: 0.3792 wt% SiO2 33.41
Fa form: Fe2SiO4 X: 0.6208 wt% FeO 49.60
wt% MgO 16.99
Olivine moles: 0.541855 grams: 80.372
Fo form: Mg2SiO4 X: 0.8790 wt% SiO2 40.51
Fa form: Fe2SiO4 X: 0.1210 wt% FeO 11.72
wt% MgO 47.77
Add: Olivine
Quad (000) norm: 1.3774563841416e+00 Lin (016) step: 4.1875957633954e-01 func: -1.1328816860212e+05
Quad (001) norm: 3.8714527790115e-02 Lin (037) step: 1.9999999507498e+00 func: -1.1360092303644e+05
Quad (002) norm: 2.3554754466832e-02 Lin (021) step: 9.4853093477755e-01 func: -1.1360670263280e+05
Quad (003) norm: 3.8209968150830e-04 Lin (017) step: 1.0016221307589e+00 func: -1.1360671021612e+05
Quad (004) norm: 9.3148899886895e-07 Lin (038) step: 9.8610154707078e-01 func: -1.1360671021613e+05
Quad (005) norm: 1.2944080631323e-08 Lin (040) step: 4.6997624564121e-01 func: -1.1360671021613e+05
Minimal energy termination of quadratic loop.
T = 1620.65 °C, P = 0.1 MPa
Liquid moles: 0.476580 grams: 87.461
Fo form: Mg2SiO4 X: 0.3211 wt% SiO2 32.74
Fa form: Fe2SiO4 X: 0.6789 wt% FeO 53.15
wt% MgO 14.11
Olivine moles: 0.523420 grams: 78.466
Fo form: Mg2SiO4 X: 0.8539 wt% SiO2 40.08
Fa form: Fe2SiO4 X: 0.1461 wt% FeO 14.00
wt% MgO 45.92
Add: Olivine
Quad (000) norm: 1.2648704862387e+00 Lin (014) step: 4.2409981494523e-01 func: -1.1342194473354e+05
Quad (001) norm: 4.1869525150838e-02 Lin (037) step: 1.9999999596761e+00 func: -1.1378169604333e+05
Quad (002) norm: 2.6613942137230e-02 Lin (019) step: 9.5579384524493e-01 func: -1.1379024996267e+05
Quad (003) norm: 7.9668730517902e-04 Lin (014) step: 1.0024585337351e+00 func: -1.1379027996411e+05
Quad (004) norm: 2.9607950072807e-06 Lin (032) step: 1.0007908725777e+00 func: -1.1379027996423e+05
Quad (005) norm: 2.3600833745774e-09 Lin (038) step: 1.7283434109660e+00 func: -1.1379027996423e+05
Minimal energy termination of quadratic loop.
T = 1587.00 °C, P = 0.1 MPa
Liquid moles: 0.495698 grams: 92.587
Fo form: Mg2SiO4 X: 0.2694 wt% SiO2 32.17
Fa form: Fe2SiO4 X: 0.7306 wt% FeO 56.20
wt% MgO 11.63
Olivine moles: 0.504302 grams: 76.494
Fo form: Mg2SiO4 X: 0.8258 wt% SiO2 39.61
Fa form: Fe2SiO4 X: 0.1742 wt% FeO 16.50
wt% MgO 43.89
Add: Olivine
Quad (000) norm: 1.1503493938843e+00 Lin (010) step: 4.2983715680788e-01 func: -1.1333111264439e+05
Quad (001) norm: 4.5202800591801e-02 Lin (037) step: 1.9999999484570e+00 func: -1.1373749443677e+05
Quad (002) norm: 3.0406944185969e-02 Lin (015) step: 9.6703569319832e-01 func: -1.1375011298796e+05
Quad (003) norm: 1.4006732752022e-03 Lin (015) step: 1.0033804526085e+00 func: -1.1375019792047e+05
Quad (004) norm: 6.4058759280046e-06 Lin (018) step: 9.9998379375210e-01 func: -1.1375019792108e+05
Quad (005) norm: 7.0408383870557e-11 Lin (028) step: 1.7770876763913e+00 func: -1.1375019792108e+05
Minimal energy termination of quadratic loop.
T = 1553.35 °C, P = 0.1 MPa
Liquid moles: 0.515485 grams: 97.774
Fo form: Mg2SiO4 X: 0.2236 wt% SiO2 31.68
Fa form: Fe2SiO4 X: 0.7764 wt% FeO 58.82
wt% MgO 9.50
Olivine moles: 0.484515 grams: 74.461
Fo form: Mg2SiO4 X: 0.7941 wt% SiO2 39.10
Fa form: Fe2SiO4 X: 0.2059 wt% FeO 19.25
wt% MgO 41.65
Add: Olivine
Quad (000) norm: 1.0339899082375e+00 Lin (016) step: 4.3608564888796e-01 func: -1.1302399689041e+05
Quad (001) norm: 4.8567089825116e-02 Lin (037) step: 1.9999999486317e+00 func: -1.1347515653818e+05
Quad (002) norm: 3.5170758113792e-02 Lin (016) step: 9.8102269403651e-01 func: -1.1349350833412e+05
Quad (003) norm: 2.2408633540299e-03 Lin (011) step: 1.0046605966100e+00 func: -1.1349371088887e+05
Quad (004) norm: 1.1680331732484e-05 Lin (019) step: 9.9995395647818e-01 func: -1.1349371089098e+05
Quad (005) norm: 4.5315777914587e-10 Lin (039) step: 1.4164078897546e+00 func: -1.1349371089098e+05
Minimal energy termination of quadratic loop.
T = 1519.70 °C, P = 0.1 MPa
Liquid moles: 0.535917 grams: 103.015
Fo form: Mg2SiO4 X: 0.1832 wt% SiO2 31.26
Fa form: Fe2SiO4 X: 0.8168 wt% FeO 61.06
wt% MgO 7.68
Olivine moles: 0.464083 grams: 72.375
Fo form: Mg2SiO4 X: 0.7581 wt% SiO2 38.53
Fa form: Fe2SiO4 X: 0.2419 wt% FeO 22.29
wt% MgO 39.19
Add: Olivine
Quad (000) norm: 9.1595877115216e-01 Lin (016) step: 4.4300754818810e-01 func: -1.1250631657962e+05
Quad (001) norm: 5.1809328381885e-02 Lin (037) step: 1.9999999486317e+00 func: -1.1299834763691e+05
Quad (002) norm: 4.1117061534466e-02 Lin (024) step: 9.9680566612166e-01 func: -1.1302449337895e+05
Quad (003) norm: 3.4076848385436e-03 Lin (020) step: 1.0066232763024e+00 func: -1.1302493065333e+05
Quad (004) norm: 2.0123925274523e-05 Lin (019) step: 9.9996011819525e-01 func: -1.1302493065956e+05
Quad (005) norm: 8.9683820119860e-10 Lin (040) step: 1.2909649445544e+00 func: -1.1302493065956e+05
Minimal energy termination of quadratic loop.
T = 1486.05 °C, P = 0.1 MPa
Liquid moles: 0.556960 grams: 108.302
Fo form: Mg2SiO4 X: 0.1478 wt% SiO2 30.90
Fa form: Fe2SiO4 X: 0.8522 wt% FeO 62.97
wt% MgO 6.13
Olivine moles: 0.443040 grams: 70.241
Fo form: Mg2SiO4 X: 0.7170 wt% SiO2 37.90
Fa form: Fe2SiO4 X: 0.2830 wt% FeO 25.65
wt% MgO 36.46
Add: Olivine
Quad (000) norm: 7.9652687717774e-01 Lin (013) step: 4.5083929279971e-01 func: -1.1178154576498e+05
Quad (001) norm: 5.4759990379579e-02 Lin (037) step: 1.9999999486317e+00 func: -1.1230772601811e+05
Quad (002) norm: 4.8408414712455e-02 Lin (019) step: 1.0134693868266e+00 func: -1.1234406869686e+05
Quad (003) norm: 5.0764193451215e-03 Lin (012) step: 1.0097330712646e+00 func: -1.1234495654607e+05
Quad (004) norm: 3.5796951091354e-05 Lin (027) step: 9.9996152538313e-01 func: -1.1234495656488e+05
Quad (005) norm: 2.3817893499710e-09 Lin (040) step: 1.9257054217066e-01 func: -1.1234495656488e+05
Minimal energy termination of quadratic loop.
T = 1452.40 °C, P = 0.1 MPa
Liquid moles: 0.578571 grams: 113.626
Fo form: Mg2SiO4 X: 0.1171 wt% SiO2 30.59
Fa form: Fe2SiO4 X: 0.8829 wt% FeO 64.60
wt% MgO 4.81
Olivine moles: 0.421429 grams: 68.071
Fo form: Mg2SiO4 X: 0.6698 wt% SiO2 37.20
Fa form: Fe2SiO4 X: 0.3302 wt% FeO 29.38
wt% MgO 33.42
Add: Olivine
Quad (000) norm: 6.7612492383195e-01 Lin (021) step: 4.5993569447173e-01 func: -1.1085100202990e+05
Quad (001) norm: 5.7217682254019e-02 Lin (037) step: 1.9999999486317e+00 func: -1.1140075998402e+05
Quad (002) norm: 5.7138211438038e-02 Lin (027) step: 1.0297538888655e+00 func: -1.1144986398854e+05
Quad (003) norm: 7.5762134765027e-03 Lin (013) step: 1.0147727341214e+00 func: -1.1145159773969e+05
Quad (004) norm: 7.1041544163877e-05 Lin (031) step: 9.9977449540369e-01 func: -1.1145159780779e+05
Quad (005) norm: 1.7571977345191e-08 Lin (039) step: 1.1827281053379e+00 func: -1.1145159780779e+05
Minimal energy termination of quadratic loop.
T = 1418.75 °C, P = 0.1 MPa
Liquid moles: 0.600695 grams: 118.976
Fo form: Mg2SiO4 X: 0.0906 wt% SiO2 30.34
Fa form: Fe2SiO4 X: 0.9094 wt% FeO 65.98
wt% MgO 3.69
Olivine moles: 0.399305 grams: 65.876
Fo form: Mg2SiO4 X: 0.6151 wt% SiO2 36.42
Fa form: Fe2SiO4 X: 0.3849 wt% FeO 33.53
wt% MgO 30.05
Add: Olivine
Quad (000) norm: 5.5543949202481e-01 Lin (021) step: 4.7085053128253e-01 func: -1.0971359206561e+05
Quad (001) norm: 5.8925356540378e-02 Lin (037) step: 1.9999999486317e+00 func: -1.1027108471228e+05
Quad (002) norm: 6.7305478732473e-02 Lin (013) step: 1.0435208574435e+00 func: -1.1033523428082e+05
Quad (003) norm: 1.1505030474154e-02 Lin (016) step: 1.0232335975700e+00 func: -1.1033853169246e+05
Quad (004) norm: 1.6369600248230e-04 Lin (021) step: 9.9973911783214e-01 func: -1.1033853201481e+05
Quad (005) norm: 5.5089535171400e-08 Lin (038) step: 1.0838690740601e+00 func: -1.1033853201481e+05
Minimal energy termination of quadratic loop.
T = 1385.10 °C, P = 0.1 MPa
Liquid moles: 0.623264 grams: 124.337
Fo form: Mg2SiO4 X: 0.0679 wt% SiO2 30.12
Fa form: Fe2SiO4 X: 0.9321 wt% FeO 67.14
wt% MgO 2.74
Olivine moles: 0.376736 grams: 63.669
Fo form: Mg2SiO4 X: 0.5513 wt% SiO2 35.55
Fa form: Fe2SiO4 X: 0.4487 wt% FeO 38.15
wt% MgO 26.29
Add: Olivine
Quad (000) norm: 4.3559312804386e-01 Lin (014) step: 4.8449627414159e-01 func: -1.0836493609787e+05
Quad (001) norm: 5.9529476050007e-02 Lin (037) step: 1.9999999486317e+00 func: -1.0890705815873e+05
Quad (002) norm: 7.8766975062179e-02 Lin (019) step: 1.0509975357788e+00 func: -1.0898730390469e+05
Quad (003) norm: 1.7891152136413e-02 Lin (017) step: 1.0382321492869e+00 func: -1.0899343676869e+05
Quad (004) norm: 4.2822065197050e-04 Lin (025) step: 9.9908284219637e-01 func: -1.0899343867446e+05
Quad (005) norm: 4.1366423993629e-07 Lin (035) step: 1.0540567761337e+00 func: -1.0899343867446e+05
Minimal energy termination of quadratic loop.
T = 1351.45 °C, P = 0.1 MPa
Liquid moles: 0.646198 grams: 129.694
Fo form: Mg2SiO4 X: 0.0487 wt% SiO2 29.94
Fa form: Fe2SiO4 X: 0.9513 wt% FeO 68.11
wt% MgO 1.96
Olivine moles: 0.353802 grams: 61.466
Fo form: Mg2SiO4 X: 0.4763 wt% SiO2 34.59
Fa form: Fe2SiO4 X: 0.5237 wt% FeO 43.31
wt% MgO 22.10
Add: Olivine
Quad (000) norm: 3.1852437204954e-01 Lin (013) step: 5.0249398225183e-01 func: -1.0679500499436e+05
Quad (001) norm: 5.8501068165817e-02 Lin (037) step: 1.9999999486317e+00 func: -1.0728856655177e+05
Quad (002) norm: 9.1131195096223e-02 Lin (019) step: 1.0458731597712e+00 func: -1.0738276874258e+05
Quad (003) norm: 2.8316580022175e-02 Lin (018) step: 1.0666690482862e+00 func: -1.0739383048254e+05
Quad (004) norm: 1.2011354132180e-03 Lin (020) step: 9.9659503150087e-01 func: -1.0739384283993e+05
Quad (005) norm: 3.5716283239582e-06 Lin (026) step: 1.0005734051080e+00 func: -1.0739384284007e+05
Quad (006) norm: 2.0085466993128e-09 Lin (040) step: 4.7216433831497e-01 func: -1.0739384284007e+05
Minimal energy termination of quadratic loop.
T = 1317.80 °C, P = 0.1 MPa
Liquid moles: 0.669403 grams: 135.030
Fo form: Mg2SiO4 X: 0.0327 wt% SiO2 29.79
Fa form: Fe2SiO4 X: 0.9673 wt% FeO 68.91
wt% MgO 1.31
Olivine moles: 0.330597 grams: 59.285
Fo form: Mg2SiO4 X: 0.3876 wt% SiO2 33.51
Fa form: Fe2SiO4 X: 0.6124 wt% FeO 49.07
wt% MgO 17.42
Add: Olivine
Quad (000) norm: 2.0794856357104e-01 Lin (021) step: 5.2806377702831e-01 func: -1.0498115451600e+05
Quad (001) norm: 5.4960557582732e-02 Lin (037) step: 1.9999999486317e+00 func: -1.0537895573655e+05
Quad (002) norm: 1.0349900326869e-01 Lin (016) step: 1.0188187654698e+00 func: -1.0547784639120e+05
Quad (003) norm: 4.4619563918756e-02 Lin (013) step: 1.1247128399950e+00 func: -1.0549649928907e+05
Quad (004) norm: 3.4487847296435e-03 Lin (022) step: 9.8752670798971e-01 func: -1.0549657516277e+05
Quad (005) norm: 3.1391133892242e-05 Lin (016) step: 1.0000585534400e+00 func: -1.0549657516925e+05
Quad (006) norm: 1.3416486172291e-09 Lin (035) step: 4.7207970565543e-01 func: -1.0549657516925e+05
Minimal energy termination of quadratic loop.
T = 1284.15 °C, P = 0.1 MPa
Liquid moles: 0.692772 grams: 140.323
Fo form: Mg2SiO4 X: 0.0194 wt% SiO2 29.66
Fa form: Fe2SiO4 X: 0.9806 wt% FeO 69.56
wt% MgO 0.77
Olivine moles: 0.307228 grams: 57.145
Fo form: Mg2SiO4 X: 0.2817 wt% SiO2 32.30
Fa form: Fe2SiO4 X: 0.7183 wt% FeO 55.49
wt% MgO 12.21
Add: Olivine
Quad (000) norm: 1.1254439960757e-01 Lin (013) step: 5.6886545119054e-01 func: -1.0286064747519e+05
Quad (001) norm: 4.7212340551214e-02 Lin (037) step: 1.9999999470379e+00 func: -1.0309716844711e+05
Quad (002) norm: 1.1367867550790e-01 Lin (023) step: 9.5893721444821e-01 func: -1.0317623263192e+05
Quad (003) norm: 6.6929065305317e-02 Lin (014) step: 1.2552998124023e+00 func: -1.0320172077162e+05
Quad (004) norm: 1.0133058640396e-02 Lin (011) step: 9.5627186609852e-01 func: -1.0320208266356e+05
Quad (005) norm: 2.6970989681121e-04 Lin (022) step: 1.0004716759792e+00 func: -1.0320208286835e+05
Quad (006) norm: 1.0937803239169e-07 Lin (039) step: 1.5470767854492e+00 func: -1.0320208286835e+05
Minimal energy termination of quadratic loop.
T = 1250.50 °C, P = 0.1 MPa
Liquid moles: 0.716183 grams: 145.553
Fo form: Mg2SiO4 X: 0.0086 wt% SiO2 29.56
Fa form: Fe2SiO4 X: 0.9914 wt% FeO 70.09
wt% MgO 0.34
Olivine moles: 0.283817 grams: 55.070
Fo form: Mg2SiO4 X: 0.1544 wt% SiO2 30.97
Fa form: Fe2SiO4 X: 0.8456 wt% FeO 62.62
wt% MgO 6.42
plt.plot(xFoSol, tC, 'b-')
plt.plot(xFoLiq, tC, 'r-')
plt.ylabel('T °C')
plt.xlabel('Mole fraction')
plt.xlim(0.0, 1.0)
(0.0, 1.0)
