Gibbs free energy potential minimization (T, P)¶
With rhyolite-MELTS and \(\mu\)O2 constrained using the empirical method of Kress and Carmichael (1991)¶
This notebook demonstates the use of the Equilibrate class in the equilibrate module to perform equilibrium crystallization clculations for the special case of oxygen fugacity constrained using the model of Kress and Carmichael (1991). This model is applicable to natural composition silicate liquids and is usually applied in conjunction with thermodynamic models published by Ghiorso and Sack (1995) [MELTS], Ghiorso et al., (2003) [pMELTS], Gualda et al. (2012) [rhyolite-MELTS] or Ghiorso and Gualda (2015) [rhyoliteMELTS + CO2].
References:
Ghiorso, Mark S., and Sack, Richard O. (1995) Chemical Mass Transfer in Magmatic Processes. IV. A Revised and Internally Consistent Thermodynamic Model for the Interpolation and Extrapolation of Liquid-Solid Equilibria in Magmatic Systems at Elevated Temperatures and Pressures. Contributions to Mineralogy and Petrology, 119, 197-212
Ghiorso, Mark S., Hirschmann, Marc M., Reiners, Peter W., and Kress, Victor C. III (2002) The pMELTS: An revision of MELTS aimed at improving calculation of phase relations and major element partitioning involved in partial melting of the mantle at pressures up to 3 GPa. Geochemistry, Geophysics, Geosystems 3(5), 10.1029/2001GC000217
Gualda G.A.R., Ghiorso M.S., Lemons R.V., Carley T.L. (2012) Rhyolite-MELTS: A modified calibration of MELTS optimized for silica-rich, fluid-bearing magmatic systems. Journal of Petrology, 53, 875-890
Ghiorso M.S., Gualda, G.A.R., (2015) An H2O-CO2 mixed fluid saturation model compatible with rhyolite-MELTS. Contributions to Mineralogy and Petrology 2015, doi:10.1007/s00410-015-1141-8
Kress and Carmichael (1991, The compressibility of silicate liquids containing Fe2O3 and the effect of composition, temperature, oxygen fugacity and pressure on their redox states, Contributions to Mineralogy and Petrology 108:82-92
Note that the method demonstrated in this notebook should ideally be cast into a proper Khorzhinskii potential minimization, as is done for the \(\mu\)H2O constraint method illustrated in the next notebook. However, the method of Kress and Carmichael (1991) is inconsistent with the thermodynamic models of Ghiorso and others, even though the latter were dependently calibrated on the basis of the former. This inconsistency prevents a minima in the Khorzhinskii potential of a system containing a Ghiorso-like liquid model from reproducing the calibration of Kress and Carmichael. Hence, the empirical method of this notebook is made avaialble for practical application; the method used here mimics the method used in MELTS, etc.
import numpy as np
import scipy.optimize as opt
import scipy.linalg as lin
import sys
from thermoengine import core, phases, model, equilibrate
Create phases for equilibrium assemblages¶
Minimal rhyolitic phase assemblage
modelDB = model.Database(liq_mod='v1.0')
Liquid = modelDB.get_phase('Liq')
Feldspar = modelDB.get_phase('Fsp')
Quartz = modelDB.get_phase('Qz')
Spinel = modelDB.get_phase('SplS')
Opx = modelDB.get_phase('Opx')
RhomOx = modelDB.get_phase('Rhom')
The Berman model database provides the SWIM water model by default. Instead, override that choice by instantiating the MELTS 1.0.2 water model directly.
Water = phases.PurePhase('WaterMelts', 'H2O', calib=False)
Define elements in system and phases in system¶
These 15 elements are required for the silicate liquid model of MELTS (rhyolite-MELTS)
elm_sys = ['H','O','Na','Mg','Al','Si','P','K','Ca','Ti','Cr','Mn','Fe','Co','Ni']
phs_sys = [Liquid, Feldspar, Water, Quartz, Spinel, Opx, RhomOx]
Composition of the system¶
This is a high-silica rhyolite
grm_oxides = {
'SiO2': 77.5,
'TiO2': 0.08,
'Al2O3': 12.5,
'Fe2O3': 0.207,
'Cr2O3': 0.0,
'FeO': 0.473,
'MnO': 0.0,
'MgO': 0.03,
'NiO': 0.0,
'CoO': 0.0,
'CaO': 0.43,
'Na2O': 3.98,
'K2O': 4.88,
'P2O5': 0.0,
'H2O': 5.5
}
tot_grm_oxides = 0.0
for key in grm_oxides.keys():
tot_grm_oxides += grm_oxides[key]
Cast this composition as moles of elements for input to the Equilibrate class
mol_oxides = core.chem.format_mol_oxide_comp(grm_oxides, convert_grams_to_moles=True)
moles_end,oxide_res = Liquid.calc_endmember_comp(
mol_oxide_comp=mol_oxides, method='intrinsic', output_residual=True)
if not Liquid.test_endmember_comp(moles_end):
print ("Calculated composition is infeasible!")
mol_elm = Liquid.covert_endmember_comp(moles_end,output='moles_elements')
blk_cmp = []
for elm in elm_sys:
index = core.chem.PERIODIC_ORDER.tolist().index(elm)
blk_cmp.append(mol_elm[index])
blk_cmp = np.array(blk_cmp)
Run the calculation¶
equil = equilibrate.Equilibrate(elm_sys, phs_sys)
Uncomment here and in the next cell to generate a call graph that traces execution times by method and module
#%load_ext snakeviz
For reference, equilibrate at an initial temperature and pressure¶
#%%snakeviz --new-tab
t = 1034.0
p = 1750.0
state = equil.execute(t, p, bulk_comp=blk_cmp, debug=0, stats=False)
state.print_state()
Minimal energy termination of quadratic loop.
Minimal energy termination of quadratic loop.
Minimal energy termination of quadratic loop.
Minimal energy termination of quadratic loop.
Minimal energy termination of quadratic loop.
T = 760.85 °C, P = 175.0 MPa
Liquid moles: 0.631594 grams: 40.489
SiO2 form: SiO2 X: 0.6742 wt% SiO2 73.59
TiO2 form: TiO2 X: 0.0010 wt% TiO2 0.13
Al2O3 form: Al2O3 X: 0.0401 wt% Al2O3 11.50
Fe2O3 form: Fe2O3 X: 0.0007 wt% Fe2O3 0.19
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.90
Fe2SiO4 form: Fe2SiO4 X: 0.0040 wt% MgO 0.07
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.24
Mg2SiO4 form: Mg2SiO4 X: 0.0006 wt% Na2O 3.79
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.74
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 4.86
CaSiO3 form: CaSiO3 X: 0.0027
Na2SiO3 form: Na2SiO3 X: 0.0392
KAlSiO4 form: KAlSiO4 X: 0.0644
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1730
Feldspar moles: 0.040758 grams: 10.843
albite form: NaAlSi3O8 X: 0.7619 wt% SiO2 65.42
anorthite form: CaAl2Si2O8 X: 0.1035 wt% Al2O3 21.15
sanidine form: KAlSi3O8 X: 0.1346 wt% CaO 2.18
wt% Na2O 8.87
wt% K2O 2.38
Water moles: 0.196050 grams: 3.532
Quartz moles: 0.356430 grams: 21.416
Spinel moles: 0.001206 grams: 0.273
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.92
hercynite form: FeAl2O4 X: 0.0046 wt% Al2O3 1.65
magnetite form: Fe3O4 X: 0.6825 wt% Fe2O3 48.19
spinel form: MgAl2O4 X: 0.0321 wt% FeO 39.67
ulvospinel form: Fe2TiO4 X: 0.2808 wt% MgO 0.57
Orthopyroxene affn: 1601.07
diopside form: CaMgSi2O6 X: -1.3631
clinoenstatite form: Mg2Si2O6 X: 0.9900
hedenbergite form: CaFeSi2O6 X: 1.3223
alumino-buffoni form: CaTi0.5Mg0 X: 0.0384
buffonite form: CaTi0.5Mg0 X: -0.0379
essenite form: CaFeAlSiO6 X: 0.0479
jadeite form: NaAlSi2O6 X: 0.0024
Ilmenite ss affn: 1532.58
geikielite form: MgTiO3 X: 0.0541
hematite form: Fe2O3 X: 0.0926
ilmenite form: FeTiO3 X: 0.8213
pyrophanite form: MnTiO3 X: 0.0000
corundum form: Al2O3 X: 0.0320
Feldspar moles: 0.107063 grams: 29.027
albite form: NaAlSi3O8 X: 0.4476 wt% SiO2 66.13
anorthite form: CaAl2Si2O8 X: 0.0161 wt% Al2O3 19.11
sanidine form: KAlSi3O8 X: 0.5363 wt% CaO 0.33
wt% Na2O 5.12
wt% K2O 9.32
Compute the system oxygen fugacity using Kress and Carmichael (1991) along with the total moles of oxygen in the system
results = []
results.append((t-273.15,p/10.0) + equil.kc_print_state(state))
System log 10 fO2 -1.7164406456824466 realtive to NNO.
System log 10 NNO -14.689033256787773
Moles of O in system 3.3896811476490214
Assign an oxygen buffer, and recalculate …¶
NNO_offset = 0.0
state = equil.execute(t, p, bulk_comp=blk_cmp, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
Add: Feldspar
Quad (000) norm: 1.1088965209070e-02 Lin (023) step: 9.5997569002109e-01 func: -1.7237374118436e+06
Quad (001) norm: 8.1604987400092e-04 Lin (021) step: 1.0857467425863e+00 func: -1.7237370619054e+06
Quad (002) norm: 3.2991904519225e-04 Lin (029) step: 1.0213975589435e+00 func: -1.7237370197636e+06
Quad (003) norm: 3.4086301589486e-06 Lin (032) step: 1.0064460754365e+00 func: -1.7237370056517e+06
Quad (004) norm: 2.4588439250310e-08 Lin (037) step: 6.2519199060268e-01 func: -1.7237370057651e+06
Quad (005) norm: 9.2165369704004e-09 Lin (039) step: -1.0747080246838e+00 func: -1.7237370057646e+06
Minimal energy termination of quadratic loop.
Add: Water
Quad (000) norm: 6.3618321033766e-02 Lin (019) step: 8.8747190098187e-01 func: -1.7237483102659e+06
Quad (001) norm: 5.3303612550691e-03 Lin (020) step: 1.1199292927701e+00 func: -1.7237487872091e+06
Quad (002) norm: 1.0788905113964e-03 Lin (018) step: 1.0438220098859e+00 func: -1.7237485802443e+06
Quad (003) norm: 1.0300483180752e-05 Lin (030) step: 1.0008740453093e+00 func: -1.7237485454949e+06
Quad (004) norm: 3.0800336161768e-08 Lin (038) step: 1.0442103805261e+00 func: -1.7237485454033e+06
Quad (005) norm: 1.3605931626475e-09 Lin (037) step: 1.0851449005413e+00 func: -1.7237485454024e+06
Minimal energy termination of quadratic loop.
Add: Quartz
Quad (000) norm: 1.2056195438626e-01 Lin (022) step: 9.4583825548841e-01 func: -1.7237524777846e+06
Quad (001) norm: 1.1920199389206e-02 Lin (020) step: 1.5463617100034e+00 func: -1.7237543536443e+06
Quad (002) norm: 4.1847268598403e-03 Lin (022) step: 1.0549958681705e+00 func: -1.7237541976735e+06
Quad (003) norm: 3.4836373545317e-04 Lin (030) step: 1.0071263854185e+00 func: -1.7237542303590e+06
Quad (004) norm: 2.0577440062515e-06 Lin (029) step: 1.0560946587188e+00 func: -1.7237542268188e+06
Quad (005) norm: 1.1536333342486e-07 Lin (041) step: 5.4657225374552e-01 func: -1.7237542268307e+06
Minimal energy termination of quadratic loop.
Unmixing: Feldspar
Quad (000) norm: 5.9291455859757e-01 Lin (024) step: 6.4434966514216e-01 func: -1.7237606829510e+06
Quad (001) norm: 2.0996136091821e-02 Lin (016) step: 1.3282093865142e+00 func: -1.7237600223682e+06
Quad (002) norm: 1.4117419236090e-02 Lin (029) step: 1.0292363957991e+00 func: -1.7237598503303e+06
Quad (003) norm: 3.4956779781134e-04 Lin (030) step: 1.0006067972068e+00 func: -1.7237597503985e+06
Quad (004) norm: 5.7233272908965e-07 Lin (046) step: -1.1222183310892e-01 func: -1.7237597529522e+06
Quad (005) norm: 6.3657620206228e-07 Lin (019) step: 1.9475175468053e+00 func: -1.7237597529526e+06
Minimal energy termination of quadratic loop.
Add: Spinel
Quad (000) norm: 3.0680775090454e-01 Lin (018) step: 5.5129438039842e-01 func: -1.7237620066069e+06
Quad (001) norm: 2.3109675795017e-01 Lin (017) step: 6.3444708819673e-01 func: -1.7238666764237e+06
Quad (002) norm: 1.6105407008731e-01 Lin (023) step: 6.7860487840586e-01 func: -1.7239335162576e+06
Quad (003) norm: 7.4077371350414e-02 Lin (026) step: 7.5444995263151e-01 func: -1.7239710792901e+06
Quad (004) norm: 2.8142236109093e-02 Lin (023) step: 8.4988115683744e-01 func: -1.7239911179668e+06
Quad (005) norm: 1.3108274306646e-02 Lin (024) step: 9.0094876936307e-01 func: -1.7240032421603e+06
Quad (006) norm: 7.2450175149946e-03 Lin (021) step: 9.3324715261238e-01 func: -1.7240108272472e+06
Quad (007) norm: 4.2808137849794e-03 Lin (029) step: 9.5641841594201e-01 func: -1.7240155995396e+06
Quad (008) norm: 2.6014167104895e-03 Lin (024) step: 9.7198145996323e-01 func: -1.7240186040995e+06
Quad (009) norm: 1.6014354975508e-03 Lin (025) step: 9.8194976913110e-01 func: -1.7240204932053e+06
Quad (010) norm: 9.9285230654093e-04 Lin (027) step: 9.8898930422666e-01 func: -1.7240216796059e+06
Quad (011) norm: 6.1796198823174e-04 Lin (034) step: 9.9239010500033e-01 func: -1.7240224248362e+06
Quad (012) norm: 3.8583314598256e-04 Lin (027) step: 9.9564057907902e-01 func: -1.7240228920112e+06
Quad (013) norm: 2.4121530007305e-04 Lin (030) step: 9.9755635324963e-01 func: -1.7240231853401e+06
Quad (014) norm: 1.5094056139566e-04 Lin (029) step: 9.9820592784760e-01 func: -1.7240233693481e+06
Quad (015) norm: 9.4536730531719e-05 Lin (032) step: 9.9944672151471e-01 func: -1.7240234846730e+06
Quad (016) norm: 5.9214219429387e-05 Lin (029) step: 9.9894056190156e-01 func: -1.7240235570349e+06
Quad (017) norm: 3.7119663300749e-05 Lin (021) step: 1.0006600891535e+00 func: -1.7240236023533e+06
Quad (018) norm: 2.3252825997875e-05 Lin (035) step: 9.9337695656695e-01 func: -1.7240236308174e+06
Quad (019) norm: 1.4632379648442e-05 Lin (018) step: 1.0063685909704e+00 func: -1.7240236485210e+06
Quad (020) norm: 9.1379550640479e-06 Lin (032) step: 1.0117165723119e+00 func: -1.7240236598080e+06
Minimal energy termination of quadratic loop.
T = 760.85 °C, P = 175.0 MPa
Liquid moles: 0.245286 grams: 15.672
SiO2 form: SiO2 X: 0.6750 wt% SiO2 73.88
TiO2 form: TiO2 X: 0.0013 wt% TiO2 0.17
Al2O3 form: Al2O3 X: 0.0387 wt% Al2O3 11.23
Fe2O3 form: Fe2O3 X: 0.0010 wt% Fe2O3 0.25
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.56
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.15
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.23
Mg2SiO4 form: Mg2SiO4 X: 0.0012 wt% Na2O 3.97
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.67
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 4.89
CaSiO3 form: CaSiO3 X: 0.0026
Na2SiO3 form: Na2SiO3 X: 0.0409
KAlSiO4 form: KAlSiO4 X: 0.0634
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1734
Feldspar moles: 0.048162 grams: 12.813
albite form: NaAlSi3O8 X: 0.7631 wt% SiO2 65.64
anorthite form: CaAl2Si2O8 X: 0.0939 wt% Al2O3 20.96
sanidine form: KAlSi3O8 X: 0.1430 wt% CaO 1.98
wt% Na2O 8.89
wt% K2O 2.53
Water moles: 0.262776 grams: 4.734
Quartz moles: 0.493846 grams: 29.672
Spinel moles: 0.002832 grams: 0.639
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 8.41
hercynite form: FeAl2O4 X: -0.0252 wt% Al2O3 1.55
magnetite form: Fe3O4 X: 0.7281 wt% Fe2O3 51.50
spinel form: MgAl2O4 X: 0.0594 wt% FeO 37.49
ulvospinel form: Fe2TiO4 X: 0.2376 wt% MgO 1.06
Orthopyroxene affn: 1464.93
diopside form: CaMgSi2O6 X: -1.0075
clinoenstatite form: Mg2Si2O6 X: 0.9909
hedenbergite form: CaFeSi2O6 X: 0.9783
alumino-buffoni form: CaTi0.5Mg0 X: 0.0272
buffonite form: CaTi0.5Mg0 X: -0.0264
essenite form: CaFeAlSiO6 X: 0.0354
jadeite form: NaAlSi2O6 X: 0.0021
Ilmenite ss affn: 734.99
geikielite form: MgTiO3 X: 0.1007
hematite form: Fe2O3 X: 0.1183
ilmenite form: FeTiO3 X: 0.7534
pyrophanite form: MnTiO3 X: 0.0000
corundum form: Al2O3 X: 0.0276
Feldspar moles: 0.155280 grams: 42.066
albite form: NaAlSi3O8 X: 0.4611 wt% SiO2 66.18
anorthite form: CaAl2Si2O8 X: 0.0161 wt% Al2O3 19.12
sanidine form: KAlSi3O8 X: 0.5228 wt% CaO 0.33
wt% Na2O 5.27
wt% K2O 9.09
results.append((t-273.15,p/10.0) + equil.kc_print_state(state))
System log 10 fO2 4.760636329592671e-13 realtive to NNO.
System log 10 NNO -14.689033256787773
Moles of O in system 3.390696315476103
Next, loop through a series of temperatures¶
deltaT = 1
state = equil.execute(t-float(deltaT), p, state=state, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
results.append((t-float(deltaT)-273.15,p/10.0) + equil.kc_print_state(state))
Quad (000) norm: 1.1716193655914e-01 Lin (019) step: 6.2651985718892e-01 func: -1.7237675803246e+06
Quad (001) norm: 6.1088672599057e-03 Lin (022) step: 9.2495728264936e-01 func: -1.7237755526931e+06
Quad (002) norm: 2.1761558468316e-03 Lin (017) step: 9.5291598297549e-01 func: -1.7237796195321e+06
Quad (003) norm: 1.2408504075135e-03 Lin (022) step: 9.6911811107389e-01 func: -1.7237821730298e+06
Quad (004) norm: 7.6495031674791e-04 Lin (025) step: 9.7974589461997e-01 func: -1.7237838070235e+06
Quad (005) norm: 4.8112752525092e-04 Lin (031) step: 9.8692391082430e-01 func: -1.7237848534456e+06
Quad (006) norm: 3.0483606284705e-04 Lin (019) step: 9.9173674493789e-01 func: -1.7237855241471e+06
Quad (007) norm: 1.9394853817389e-04 Lin (025) step: 9.9587335525550e-01 func: -1.7237859541642e+06
Quad (008) norm: 1.2365722175777e-04 Lin (031) step: 9.9790433266723e-01 func: -1.7237862301398e+06
Quad (009) norm: 7.8977763857675e-05 Lin (017) step: 9.9817426305689e-01 func: -1.7237864069693e+06
Quad (010) norm: 5.0527487481494e-05 Lin (021) step: 9.9889898642025e-01 func: -1.7237865201498e+06
Quad (011) norm: 3.2350995821889e-05 Lin (021) step: 9.9927742290195e-01 func: -1.7237865926988e+06
Quad (012) norm: 2.0724579235076e-05 Lin (021) step: 9.9972805409784e-01 func: -1.7237866392030e+06
Quad (013) norm: 1.3279634567496e-05 Lin (026) step: 1.0001228329674e+00 func: -1.7237866690226e+06
Quad (014) norm: 8.5099352162928e-06 Lin (033) step: 1.0151040899645e+00 func: -1.7237866881437e+06
Quad (015) norm: 5.4087172271374e-06 Lin (032) step: 1.0073030248227e+00 func: -1.7237867005830e+06
Minimal energy termination of quadratic loop.
Add: Orthopyroxene
Quad (000) norm: 8.5628032584059e-03 Lin (025) step: 9.0988059528844e-01 func: -1.7237867192707e+06
Quad (001) norm: 9.5310057568647e-05 Lin (016) step: 1.0456400979295e+00 func: -1.7237855440615e+06
Quad (002) norm: 2.1939070270258e-04 Lin (012) step: 1.0074831376080e+00 func: -1.7237845954139e+06
Quad (003) norm: 1.1291804441265e-04 Lin (022) step: 1.0053030547400e+00 func: -1.7237839010628e+06
Quad (004) norm: 8.3354590771905e-05 Lin (027) step: 1.0030414293043e+00 func: -1.7237833790243e+06
Quad (005) norm: 6.2146388371921e-05 Lin (026) step: 1.0022807675146e+00 func: -1.7237829864048e+06
Quad (006) norm: 4.6481147017440e-05 Lin (030) step: 1.0026606985133e+00 func: -1.7237826905575e+06
Quad (007) norm: 3.4825832683591e-05 Lin (025) step: 1.0013140773975e+00 func: -1.7237824673700e+06
Quad (008) norm: 2.6141742392939e-05 Lin (023) step: 1.0010250651609e+00 func: -1.7237822993348e+06
Quad (009) norm: 1.9645591106098e-05 Lin (035) step: 9.9990066876400e-01 func: -1.7237821726494e+06
Quad (010) norm: 1.4780945563084e-05 Lin (021) step: 1.0006375732695e+00 func: -1.7237820772177e+06
Quad (011) norm: 1.1124809299801e-05 Lin (033) step: 1.0022235173255e+00 func: -1.7237820051740e+06
Quad (012) norm: 8.3724734217140e-06 Lin (025) step: 9.9991774637626e-01 func: -1.7237819507561e+06
Quad (013) norm: 6.3080177207430e-06 Lin (033) step: 1.0030302960268e+00 func: -1.7237819098341e+06
Quad (014) norm: 4.7489718380006e-06 Lin (038) step: 9.9220329968826e-01 func: -1.7237818788715e+06
Quad (015) norm: 3.5886311264534e-06 Lin (020) step: 9.9893451472596e-01 func: -1.7237818557932e+06
Quad (016) norm: 2.7062221760145e-06 Lin (034) step: 1.0025774796223e+00 func: -1.7237818382242e+06
Quad (017) norm: 2.0385961575181e-06 Lin (032) step: 9.8838420643944e-01 func: -1.7237818249205e+06
Minimal energy termination of quadratic loop.
Add: Ilmenite ss
Quad (000) norm: 3.9887860130423e-04 Lin (029) step: 1.0121371611223e+00 func: -1.7237818150997e+06
Quad (001) norm: 1.1138178097085e-04 Lin (024) step: 9.8598815068760e-01 func: -1.7237818503456e+06
Quad (002) norm: 9.9027993676813e-07 Lin (033) step: 1.0015701871848e+00 func: -1.7237818777930e+06
Quad (003) norm: 2.8454360284714e-07 Lin (033) step: 9.9780049815636e-01 func: -1.7237818996928e+06
Quad (004) norm: 2.2275877862611e-07 Lin (031) step: 1.0022485331229e+00 func: -1.7237819166105e+06
Quad (005) norm: 1.7281597966302e-07 Lin (035) step: 9.7982150596083e-01 func: -1.7237819298017e+06
Minimal energy termination of quadratic loop.
T = 759.85 °C, P = 175.0 MPa
Liquid moles: 0.130198 grams: 8.305
SiO2 form: SiO2 X: 0.6743 wt% SiO2 74.05
TiO2 form: TiO2 X: 0.0014 wt% TiO2 0.18
Al2O3 form: Al2O3 X: 0.0367 wt% Al2O3 10.81
Fe2O3 form: Fe2O3 X: 0.0010 wt% Fe2O3 0.26
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.55
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.21
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.24
Mg2SiO4 form: Mg2SiO4 X: 0.0016 wt% Na2O 4.19
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.57
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 4.93
CaSiO3 form: CaSiO3 X: 0.0027
Na2SiO3 form: Na2SiO3 X: 0.0431
KAlSiO4 form: KAlSiO4 X: 0.0619
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1747
Feldspar moles: 0.050478 grams: 13.428
albite form: NaAlSi3O8 X: 0.7639 wt% SiO2 65.70
anorthite form: CaAl2Si2O8 X: 0.0914 wt% Al2O3 20.92
sanidine form: KAlSi3O8 X: 0.1447 wt% CaO 1.93
wt% Na2O 8.90
wt% K2O 2.56
Water moles: 0.282553 grams: 5.090
Quartz moles: 0.534470 grams: 32.113
Spinel moles: 0.003147 grams: 0.709
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.16
hercynite form: FeAl2O4 X: -0.0407 wt% Al2O3 1.45
magnetite form: Fe3O4 X: 0.7097 wt% Fe2O3 50.29
spinel form: MgAl2O4 X: 0.0728 wt% FeO 37.80
ulvospinel form: Fe2TiO4 X: 0.2582 wt% MgO 1.30
Orthopyroxene moles: 0.000079 grams: 0.018
diopside form: CaMgSi2O6 X: -0.9051 wt% SiO2 51.67
clinoenstatite form: Mg2Si2O6 X: 0.9935 wt% TiO2 0.02
hedenbergite form: CaFeSi2O6 X: 0.8794 wt% Al2O3 1.13
alumino-buffoni form: CaTi0.5Mg0 X: 0.0195 wt% Fe2O3 0.40
buffonite form: CaTi0.5Mg0 X: -0.0186 wt% FeO 27.59
essenite form: CaFeAlSiO6 X: 0.0299 wt% MgO 19.05
jadeite form: NaAlSi2O6 X: 0.0014 wt% CaO 0.13
wt% Na2O 0.02
Ilmenite ss moles: 0.000005 grams: 0.001
geikielite form: MgTiO3 X: 0.1207 wt% TiO2 46.98
hematite form: Fe2O3 X: 0.1069 wt% Al2O3 1.78
ilmenite form: FeTiO3 X: 0.7466 wt% Fe2O3 11.57
pyrophanite form: MnTiO3 X: 0.0000 wt% FeO 36.37
corundum form: Al2O3 X: 0.0257 wt% MgO 3.30
Feldspar moles: 0.169578 grams: 45.932
albite form: NaAlSi3O8 X: 0.4637 wt% SiO2 66.20
anorthite form: CaAl2Si2O8 X: 0.0159 wt% Al2O3 19.12
sanidine form: KAlSi3O8 X: 0.5204 wt% CaO 0.33
wt% Na2O 5.31
wt% K2O 9.05
System log 10 fO2 1.1404210908949608e-12 realtive to NNO.
System log 10 NNO -14.711885893595664
Moles of O in system 3.3907519057677327
deltaT = 2
state = equil.execute(t-float(deltaT), p, state=state, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
results.append((t-float(deltaT)-273.15,p/10.0) + equil.kc_print_state(state))
Quad (000) norm: 7.5695898580778e-02 Lin (028) step: 5.0493519563345e-01 func: -1.7235268312828e+06
Quad (001) norm: 2.8004998242375e-04 Lin (020) step: 9.9045376386634e-01 func: -1.7235266246677e+06
Quad (002) norm: 3.4992097467373e-06 Lin (030) step: 1.0031173160087e+00 func: -1.7235264687474e+06
Quad (003) norm: 1.4049735387857e-06 Lin (031) step: 1.0018309929430e+00 func: -1.7235263358813e+06
Quad (004) norm: 1.1785979817255e-06 Lin (033) step: 1.0031286511991e+00 func: -1.7235262245294e+06
Quad (005) norm: 9.8981862263130e-07 Lin (033) step: 1.0014851158518e+00 func: -1.7235261309484e+06
Quad (006) norm: 8.3136252566102e-07 Lin (017) step: 1.0007169534797e+00 func: -1.7235260525576e+06
Quad (007) norm: 6.9825704246073e-07 Lin (018) step: 1.0008217289770e+00 func: -1.7235259868173e+06
Quad (008) norm: 5.8636652875720e-07 Lin (031) step: 1.0014290103664e+00 func: -1.7235259316325e+06
Quad (009) norm: 4.9228888834348e-07 Lin (031) step: 1.0019285518599e+00 func: -1.7235258852880e+06
Quad (010) norm: 4.1322347070990e-07 Lin (008) step: 1.0010065313479e+00 func: -1.7235258463777e+06
Quad (011) norm: 3.4688724685297e-07 Lin (034) step: 1.0039585461546e+00 func: -1.7235258137595e+06
Quad (012) norm: 2.9101529361279e-07 Lin (034) step: 1.0053367404128e+00 func: -1.7235257863059e+06
Quad (013) norm: 2.4406243344218e-07 Lin (032) step: 9.9976247272188e-01 func: -1.7235257632489e+06
Quad (014) norm: 2.0489298780127e-07 Lin (030) step: 9.9947960199157e-01 func: -1.7235257440237e+06
Quad (015) norm: 1.7201187361741e-07 Lin (034) step: 1.0048143845123e+00 func: -1.7235257278916e+06
Minimal energy termination of quadratic loop.
T = 758.85 °C, P = 175.0 MPa
Liquid moles: 0.082776 grams: 5.268
SiO2 form: SiO2 X: 0.6735 wt% SiO2 74.28
TiO2 form: TiO2 X: 0.0014 wt% TiO2 0.17
Al2O3 form: Al2O3 X: 0.0344 wt% Al2O3 10.33
Fe2O3 form: Fe2O3 X: 0.0011 wt% Fe2O3 0.26
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.56
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.21
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.26
Mg2SiO4 form: Mg2SiO4 X: 0.0016 wt% Na2O 4.47
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.46
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 5.00
CaSiO3 form: CaSiO3 X: 0.0029
Na2SiO3 form: Na2SiO3 X: 0.0459
KAlSiO4 form: KAlSiO4 X: 0.0603
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1765
Feldspar moles: 0.051675 grams: 13.746
albite form: NaAlSi3O8 X: 0.7646 wt% SiO2 65.72
anorthite form: CaAl2Si2O8 X: 0.0904 wt% Al2O3 20.90
sanidine form: KAlSi3O8 X: 0.1450 wt% CaO 1.91
wt% Na2O 8.91
wt% K2O 2.57
Water moles: 0.290684 grams: 5.237
Quartz moles: 0.551080 grams: 33.111
Spinel moles: 0.003194 grams: 0.720
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.21
hercynite form: FeAl2O4 X: -0.0416 wt% Al2O3 1.37
magnetite form: Fe3O4 X: 0.7098 wt% Fe2O3 50.28
spinel form: MgAl2O4 X: 0.0720 wt% FeO 37.85
ulvospinel form: Fe2TiO4 X: 0.2598 wt% MgO 1.29
Orthopyroxene moles: 0.000220 grams: 0.050
diopside form: CaMgSi2O6 X: -0.9050 wt% SiO2 51.71
clinoenstatite form: Mg2Si2O6 X: 0.9930 wt% TiO2 0.01
hedenbergite form: CaFeSi2O6 X: 0.8820 wt% Al2O3 1.04
alumino-buffoni form: CaTi0.5Mg0 X: 0.0177 wt% Fe2O3 0.38
buffonite form: CaTi0.5Mg0 X: -0.0169 wt% FeO 27.66
essenite form: CaFeAlSiO6 X: 0.0278 wt% MgO 19.03
jadeite form: NaAlSi2O6 X: 0.0014 wt% CaO 0.14
wt% Na2O 0.02
Ilmenite ss moles: 0.000068 grams: 0.010
geikielite form: MgTiO3 X: 0.1200 wt% TiO2 47.05
hematite form: Fe2O3 X: 0.1066 wt% Al2O3 1.68
ilmenite form: FeTiO3 X: 0.7491 wt% Fe2O3 11.53
pyrophanite form: MnTiO3 X: 0.0000 wt% FeO 36.46
corundum form: Al2O3 X: 0.0243 wt% MgO 3.28
Feldspar moles: 0.175204 grams: 47.455
albite form: NaAlSi3O8 X: 0.4641 wt% SiO2 66.20
anorthite form: CaAl2Si2O8 X: 0.0157 wt% Al2O3 19.12
sanidine form: KAlSi3O8 X: 0.5201 wt% CaO 0.33
wt% Na2O 5.31
wt% K2O 9.04
System log 10 fO2 -6.288303211476887e-13 realtive to NNO.
System log 10 NNO -14.734783298453006
Moles of O in system 3.3907478066363748
deltaT = 3
state = equil.execute(t-float(deltaT), p, state=state, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
results.append((t-float(deltaT)-273.15,p/10.0) + equil.kc_print_state(state))
Quad (000) norm: 2.0243026303418e-02 Lin (021) step: 7.0082983487209e-01 func: -1.7232710032814e+06
Quad (001) norm: 1.6656396148692e-04 Lin (024) step: 9.9784472612397e-01 func: -1.7232708971859e+06
Quad (002) norm: 1.1870343795491e-06 Lin (022) step: 1.0013430841889e+00 func: -1.7232708025140e+06
Quad (003) norm: 9.5988553108768e-07 Lin (033) step: 1.0024086002173e+00 func: -1.7232707201750e+06
Quad (004) norm: 8.3180023976553e-07 Lin (021) step: 1.0009072984148e+00 func: -1.7232706487809e+06
Quad (005) norm: 7.2082830410361e-07 Lin (031) step: 1.0007872021771e+00 func: -1.7232705870482e+06
Quad (006) norm: 6.2461005108588e-07 Lin (034) step: 1.0056017573443e+00 func: -1.7232705335855e+06
Quad (007) norm: 5.4078675303037e-07 Lin (029) step: 1.0008625064891e+00 func: -1.7232704870572e+06
Quad (008) norm: 4.6851729237499e-07 Lin (008) step: 1.0012345832159e+00 func: -1.7232704469787e+06
Quad (009) norm: 4.0585616482288e-07 Lin (023) step: 1.0003979429953e+00 func: -1.7232704122549e+06
Quad (010) norm: 3.5160088576436e-07 Lin (030) step: 1.0006084923947e+00 func: -1.7232703822092e+06
Quad (011) norm: 3.0457326875907e-07 Lin (033) step: 1.0023026342140e+00 func: -1.7232703561812e+06
Quad (012) norm: 2.6375539872188e-07 Lin (034) step: 1.0046557285035e+00 func: -1.7232703336012e+06
Quad (013) norm: 2.2831627214069e-07 Lin (025) step: 9.9965515779842e-01 func: -1.7232703140052e+06
Quad (014) norm: 1.9778485140346e-07 Lin (035) step: 9.9252806668756e-01 func: -1.7232702971294e+06
Quad (015) norm: 1.7152049456173e-07 Lin (033) step: 1.0005198987296e+00 func: -1.7232702826166e+06
Minimal energy termination of quadratic loop.
T = 757.85 °C, P = 175.0 MPa
Liquid moles: 0.065228 grams: 4.144
SiO2 form: SiO2 X: 0.6727 wt% SiO2 74.43
TiO2 form: TiO2 X: 0.0013 wt% TiO2 0.16
Al2O3 form: Al2O3 X: 0.0327 wt% Al2O3 9.99
Fe2O3 form: Fe2O3 X: 0.0011 wt% Fe2O3 0.27
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.57
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.20
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.27
Mg2SiO4 form: Mg2SiO4 X: 0.0016 wt% Na2O 4.68
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.38
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 5.05
CaSiO3 form: CaSiO3 X: 0.0030
Na2SiO3 form: Na2SiO3 X: 0.0480
KAlSiO4 form: KAlSiO4 X: 0.0590
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1780
Feldspar moles: 0.052405 grams: 13.939
albite form: NaAlSi3O8 X: 0.7652 wt% SiO2 65.73
anorthite form: CaAl2Si2O8 X: 0.0900 wt% Al2O3 20.89
sanidine form: KAlSi3O8 X: 0.1448 wt% CaO 1.90
wt% Na2O 8.92
wt% K2O 2.56
Water moles: 0.293688 grams: 5.291
Quartz moles: 0.557237 grams: 33.481
Spinel moles: 0.003209 grams: 0.724
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.24
hercynite form: FeAl2O4 X: -0.0421 wt% Al2O3 1.32
magnetite form: Fe3O4 X: 0.7100 wt% Fe2O3 50.27
spinel form: MgAl2O4 X: 0.0712 wt% FeO 37.90
ulvospinel form: Fe2TiO4 X: 0.2609 wt% MgO 1.27
Orthopyroxene moles: 0.000274 grams: 0.063
diopside form: CaMgSi2O6 X: -0.9057 wt% SiO2 51.73
clinoenstatite form: Mg2Si2O6 X: 0.9927 wt% TiO2 0.01
hedenbergite form: CaFeSi2O6 X: 0.8845 wt% Al2O3 0.98
alumino-buffoni form: CaTi0.5Mg0 X: 0.0165 wt% Fe2O3 0.37
buffonite form: CaTi0.5Mg0 X: -0.0157 wt% FeO 27.73
essenite form: CaFeAlSiO6 X: 0.0263 wt% MgO 19.00
jadeite form: NaAlSi2O6 X: 0.0014 wt% CaO 0.15
wt% Na2O 0.02
Ilmenite ss moles: 0.000090 grams: 0.013
geikielite form: MgTiO3 X: 0.1193 wt% TiO2 47.10
hematite form: Fe2O3 X: 0.1063 wt% Al2O3 1.61
ilmenite form: FeTiO3 X: 0.7511 wt% Fe2O3 11.49
pyrophanite form: MnTiO3 X: 0.0000 wt% FeO 36.54
corundum form: Al2O3 X: 0.0233 wt% MgO 3.26
Feldspar moles: 0.176997 grams: 47.942
albite form: NaAlSi3O8 X: 0.4637 wt% SiO2 66.20
anorthite form: CaAl2Si2O8 X: 0.0156 wt% Al2O3 19.11
sanidine form: KAlSi3O8 X: 0.5208 wt% CaO 0.32
wt% Na2O 5.30
wt% K2O 9.06
System log 10 fO2 2.788880237858393e-13 realtive to NNO.
System log 10 NNO -14.757725602091266
Moles of O in system 3.390745117287217
deltaT = 4
state = equil.execute(t-float(deltaT), p, state=state, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
results.append((t-float(deltaT)-273.15,p/10.0) + equil.kc_print_state(state))
Quad (000) norm: 1.0077722247735e-02 Lin (022) step: 7.8729338922378e-01 func: -1.7230158185347e+06
Quad (001) norm: 1.1919229445379e-04 Lin (026) step: 9.9897620783456e-01 func: -1.7230157421731e+06
Quad (002) norm: 9.2287473033048e-07 Lin (027) step: 1.0011107494646e+00 func: -1.7230156722621e+06
Quad (003) norm: 7.5330495551305e-07 Lin (035) step: 9.9698701679482e-01 func: -1.7230156104356e+06
Quad (004) norm: 6.6505755183412e-07 Lin (025) step: 1.0007254676522e+00 func: -1.7230155561285e+06
Quad (005) norm: 5.8677326028703e-07 Lin (028) step: 1.0007179107803e+00 func: -1.7230155080243e+06
Quad (006) norm: 5.1767304168180e-07 Lin (035) step: 9.9863149853616e-01 func: -1.7230154655962e+06
Quad (007) norm: 4.5681317383747e-07 Lin (034) step: 1.0028396283571e+00 func: -1.7230154282532e+06
Quad (008) norm: 4.0286364888853e-07 Lin (025) step: 9.9991754179568e-01 func: -1.7230153951696e+06
Quad (009) norm: 3.5540916915708e-07 Lin (028) step: 1.0088059250695e+00 func: -1.7230153660846e+06
Quad (010) norm: 3.1316117287442e-07 Lin (030) step: 1.0000073180698e+00 func: -1.7230153402025e+06
Quad (011) norm: 2.7625064477759e-07 Lin (036) step: 9.9406788719497e-01 func: -1.7230153175998e+06
Quad (012) norm: 2.4387728127361e-07 Lin (025) step: 1.0001053298964e+00 func: -1.7230152977826e+06
Quad (013) norm: 2.1511902350563e-07 Lin (024) step: 1.0010126590966e+00 func: -1.7230152801837e+06
Quad (014) norm: 1.8972475965658e-07 Lin (031) step: 9.9190487783632e-01 func: -1.7230152646478e+06
Minimal energy termination of quadratic loop.
T = 756.85 °C, P = 175.0 MPa
Liquid moles: 0.055440 grams: 3.516
SiO2 form: SiO2 X: 0.6720 wt% SiO2 74.55
TiO2 form: TiO2 X: 0.0013 wt% TiO2 0.16
Al2O3 form: Al2O3 X: 0.0314 wt% Al2O3 9.70
Fe2O3 form: Fe2O3 X: 0.0011 wt% Fe2O3 0.28
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.57
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.20
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.28
Mg2SiO4 form: Mg2SiO4 X: 0.0016 wt% Na2O 4.86
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.31
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 5.09
CaSiO3 form: CaSiO3 X: 0.0031
Na2SiO3 form: Na2SiO3 X: 0.0497
KAlSiO4 form: KAlSiO4 X: 0.0580
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1793
Feldspar moles: 0.053016 grams: 14.101
albite form: NaAlSi3O8 X: 0.7659 wt% SiO2 65.74
anorthite form: CaAl2Si2O8 X: 0.0897 wt% Al2O3 20.89
sanidine form: KAlSi3O8 X: 0.1444 wt% CaO 1.89
wt% Na2O 8.92
wt% K2O 2.56
Water moles: 0.295360 grams: 5.321
Quartz moles: 0.560678 grams: 33.688
Spinel moles: 0.003217 grams: 0.726
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.27
hercynite form: FeAl2O4 X: -0.0425 wt% Al2O3 1.27
magnetite form: Fe3O4 X: 0.7102 wt% Fe2O3 50.27
spinel form: MgAl2O4 X: 0.0706 wt% FeO 37.93
ulvospinel form: Fe2TiO4 X: 0.2617 wt% MgO 1.26
Orthopyroxene moles: 0.000306 grams: 0.070
diopside form: CaMgSi2O6 X: -0.9065 wt% SiO2 51.75
clinoenstatite form: Mg2Si2O6 X: 0.9923 wt% TiO2 0.01
hedenbergite form: CaFeSi2O6 X: 0.8868 wt% Al2O3 0.94
alumino-buffoni form: CaTi0.5Mg0 X: 0.0156 wt% Fe2O3 0.36
buffonite form: CaTi0.5Mg0 X: -0.0148 wt% FeO 27.80
essenite form: CaFeAlSiO6 X: 0.0252 wt% MgO 18.97
jadeite form: NaAlSi2O6 X: 0.0014 wt% CaO 0.15
wt% Na2O 0.02
Ilmenite ss moles: 0.000102 grams: 0.015
geikielite form: MgTiO3 X: 0.1187 wt% TiO2 47.14
hematite form: Fe2O3 X: 0.1059 wt% Al2O3 1.55
ilmenite form: FeTiO3 X: 0.7529 wt% Fe2O3 11.45
pyrophanite form: MnTiO3 X: 0.0000 wt% FeO 36.62
corundum form: Al2O3 X: 0.0225 wt% MgO 3.24
Feldspar moles: 0.177792 grams: 48.159
albite form: NaAlSi3O8 X: 0.4630 wt% SiO2 66.20
anorthite form: CaAl2Si2O8 X: 0.0154 wt% Al2O3 19.11
sanidine form: KAlSi3O8 X: 0.5217 wt% CaO 0.32
wt% Na2O 5.30
wt% K2O 9.07
System log 10 fO2 2.7569058147491887e-12 realtive to NNO.
System log 10 NNO -14.780712935750506
Moles of O in system 3.3907430417032036
deltaT = 5
state = equil.execute(t-float(deltaT), p, state=state, con_deltaNNO=NNO_offset, debug=0, stats=True)
state.print_state()
results.append((t-float(deltaT)-273.15,p/10.0) + equil.kc_print_state(state))
Quad (000) norm: 6.2705293515395e-03 Lin (020) step: 8.3595839378991e-01 func: -1.7227610125102e+06
Quad (001) norm: 9.1631825018789e-05 Lin (031) step: 9.9861877590068e-01 func: -1.7227609493691e+06
Quad (002) norm: 7.7347751364953e-07 Lin (031) step: 1.0010691219059e+00 func: -1.7227608910511e+06
Quad (003) norm: 6.5211568767003e-07 Lin (033) step: 1.0025759611940e+00 func: -1.7227608388227e+06
Quad (004) norm: 5.8230995844100e-07 Lin (026) step: 1.0005546266468e+00 func: -1.7227607921203e+06
Quad (005) norm: 5.2004526399082e-07 Lin (030) step: 1.0012523366404e+00 func: -1.7227607505144e+06
Quad (006) norm: 4.6438035331624e-07 Lin (012) step: 1.0009033138034e+00 func: -1.7227607133399e+06
Quad (007) norm: 4.1467558611098e-07 Lin (031) step: 1.0031861319825e+00 func: -1.7227606801628e+06
Quad (008) norm: 3.7017733191050e-07 Lin (025) step: 9.9950741392646e-01 func: -1.7227606504747e+06
Quad (009) norm: 3.3058976239564e-07 Lin (032) step: 1.0007823983598e+00 func: -1.7227606240738e+06
Quad (010) norm: 2.9518307847799e-07 Lin (029) step: 1.0007982467351e+00 func: -1.7227606004697e+06
Quad (011) norm: 2.6356158980475e-07 Lin (033) step: 1.0032511165411e+00 func: -1.7227605793959e+06
Quad (012) norm: 2.3525336802940e-07 Lin (034) step: 1.0056258430467e+00 func: -1.7227605605358e+06
Quad (013) norm: 2.0992195831765e-07 Lin (037) step: 9.9344457321834e-01 func: -1.7227605436633e+06
Minimal energy termination of quadratic loop.
T = 755.85 °C, P = 175.0 MPa
Liquid moles: 0.048992 grams: 3.103
SiO2 form: SiO2 X: 0.6713 wt% SiO2 74.65
TiO2 form: TiO2 X: 0.0012 wt% TiO2 0.16
Al2O3 form: Al2O3 X: 0.0302 wt% Al2O3 9.46
Fe2O3 form: Fe2O3 X: 0.0011 wt% Fe2O3 0.28
MgCr2O4 form: MgCr2O4 X: 0.0000 wt% FeO 0.58
Fe2SiO4 form: Fe2SiO4 X: 0.0025 wt% MgO 0.20
MnSi0.5O2 form: MnSi0.5O2 X: 0.0000 wt% CaO 0.29
Mg2SiO4 form: Mg2SiO4 X: 0.0016 wt% Na2O 5.02
NiSi0.5O2 form: NiSi0.5O2 X: 0.0000 wt% K2O 4.24
CoSi0.5O2 form: CoSi0.5O2 X: 0.0000 wt% H2O 5.13
CaSiO3 form: CaSiO3 X: 0.0032
Na2SiO3 form: Na2SiO3 X: 0.0513
KAlSiO4 form: KAlSiO4 X: 0.0570
Ca3(PO4)2 form: Ca3(PO4)2 X: 0.0000
H2O form: H2O X: 0.1804
Feldspar moles: 0.053574 grams: 14.249
albite form: NaAlSi3O8 X: 0.7666 wt% SiO2 65.75
anorthite form: CaAl2Si2O8 X: 0.0895 wt% Al2O3 20.88
sanidine form: KAlSi3O8 X: 0.1439 wt% CaO 1.89
wt% Na2O 8.93
wt% K2O 2.55
Water moles: 0.296459 grams: 5.341
Quartz moles: 0.562949 grams: 33.824
Spinel moles: 0.003221 grams: 0.727
chromite form: FeCr2O4 X: 0.0000 wt% TiO2 9.29
hercynite form: FeAl2O4 X: -0.0427 wt% Al2O3 1.23
magnetite form: Fe3O4 X: 0.7105 wt% Fe2O3 50.27
spinel form: MgAl2O4 X: 0.0700 wt% FeO 37.96
ulvospinel form: Fe2TiO4 X: 0.2623 wt% MgO 1.25
Orthopyroxene moles: 0.000328 grams: 0.075
diopside form: CaMgSi2O6 X: -0.9075 wt% SiO2 51.76
clinoenstatite form: Mg2Si2O6 X: 0.9921 wt% TiO2 0.01
hedenbergite form: CaFeSi2O6 X: 0.8891 wt% Al2O3 0.90
alumino-buffoni form: CaTi0.5Mg0 X: 0.0148 wt% Fe2O3 0.35
buffonite form: CaTi0.5Mg0 X: -0.0141 wt% FeO 27.86
essenite form: CaFeAlSiO6 X: 0.0243 wt% MgO 18.93
jadeite form: NaAlSi2O6 X: 0.0014 wt% CaO 0.16
wt% Na2O 0.02
Ilmenite ss moles: 0.000110 grams: 0.016
geikielite form: MgTiO3 X: 0.1181 wt% TiO2 47.18
hematite form: Fe2O3 X: 0.1055 wt% Al2O3 1.51
ilmenite form: FeTiO3 X: 0.7545 wt% Fe2O3 11.41
pyrophanite form: MnTiO3 X: 0.0000 wt% FeO 36.69
corundum form: Al2O3 X: 0.0218 wt% MgO 3.22
Feldspar moles: 0.178159 grams: 48.261
albite form: NaAlSi3O8 X: 0.4621 wt% SiO2 66.20
anorthite form: CaAl2Si2O8 X: 0.0152 wt% Al2O3 19.11
sanidine form: KAlSi3O8 X: 0.5226 wt% CaO 0.32
wt% Na2O 5.29
wt% K2O 9.09
System log 10 fO2 -3.1956659540810506e-12 realtive to NNO.
System log 10 NNO -14.803745431181873
Moles of O in system 3.390741274412504
Plot results of the sequence¶
Plot total oxygen content of the system against temperature
import matplotlib.pyplot as plt
%matplotlib inline
x = []
y = []
for t,p,log10fO2,log10NNO,moles_O in results:
x.append(t)
y.append(moles_O)
plt.plot(np.array(x), np.array(y), 'r-')
plt.xlabel('T °C')
plt.ylabel('moles of O')
plt.show()
