MAGEMin_C.jl: Examples

This page provides a set of quick examples showing how to use MAGEMin_C.jl to perform phase equilibrium calculations.

Info

Examples 1 to 8 are simple exercises to make you familiar with the various options available for the calculation

• E.1 Predefined compositions

• E.2 Minimization output

• E.3 Custom composition

• E.4 Export data to CSV

• E.5 Removing solution phase from consideration

• E.6 Oxygen buffer

• E.7 Activity buffer

• E.8 Many points

Note

• The examples are not optimized for performances, but are provided in hope they can be useful to present MAGEMin_C functionality.

Quickstart examples

E.1 Predefined compositions

This is an example of how to use it for a predefined bulk rock composition:

using MAGEMin_C
db   = "ig"  # database: ig, igneous (Holland et al., 2018); mp, metapelite (White et al 2014b)
data = Initialize_MAGEMin(db, verbose=true);
test = 0         #KLB1
data = use_predefined_bulk_rock(data, test);
P    = 8.0;
T    = 800.0;
out  = point_wise_minimization(P,T, data);

which gives

 Status             :            0 
 Mass residual      : +5.34576e-06
 Rank               :            0 
 Point              :            1 
 Temperature        :   +800.00000       [C] 
 Pressure           :     +8.00000       [kbar]

 SOL = [G: -797.749] (25 iterations, 39.62 ms)
 GAM = [-979.481432,-1774.104523,-795.261024,-673.747244,-375.070247,-917.557241,-829.990582,-1023.656703,-257.019268,-1308.294427]

 Phase :      spn      cpx      opx       ol 
 Mode  :  0.02799  0.14166  0.24228  0.58807

Note

Thermodynamic dataset acronym are the following:

• mtl -> mantle (Holland et al., 2013)

• mp -> metapelite (White et al., 2014)

• mb -> metabasite (Green et al., 2016)

• ig -> igneous (Green et al., 2025 updated from and replacing Holland et al., 2018)

• igad -> igneous alkaline dry (Weller et al., 2024)

• um -> ultramafic (Evans & Frost, 2021)

• sb11 -> Stixrude & Lithgow-Bertelloni (2011)

• sb21 -> Stixrude & Lithgow-Bertelloni (2021)

• sb24 -> Stixrude & Lithgow-Bertelloni (2024)

• ume -> ultramafic extended (Green et al., 2016 + Evans & Frost, 2021)

• mpe -> extended metapelite (White et al., 2014 + Green et al., 2016 + Franzolin et al., 2011 + Diener et al., 2007)

• mbe -> extended metabasite (Green et al., 2016 + Diener et al., 2007 + Rebay et al., 2022)

E.2 Minimization output

in the previous example the results of the minimization are saved in a structure called out. To access all the information stored in the structure simply do:

out.

Then press tab (tabulation key) to display all stored data:

out.
G_system Gamma MAGEMin_ver M_sys PP_vec P_kbar SS_vec T_C V Vp Vp_S Vs Vs_S X
aAl2O3 aFeO aH2O aMgO aSiO2 aTiO2 alpha bulk bulkMod bulkModulus_M bulkModulus_S bulk_F bulk_F_wt bulk_M
bulk_M_wt bulk_S bulk_S_wt bulk_res_norm bulk_wt cp dQFM dataset enthalpy entropy fO2 frac_F frac_F_wt frac_M
frac_M_wt frac_S frac_S_wt iter mSS_vec n_PP n_SS n_mSS oxides ph ph_frac ph_frac_vol ph_frac_wt ph_id
ph_type rho rho_F rho_M rho_S s_cp shearMod shearModulus_S status time_ms

In order to access any of these variables type for instance:

out.fO2

which will give you the oxygen fugacity:

out.fO2
-4.405735414252153

to access the list of stable phases and their fraction in mol:

out.ph
4-element Vector{String}:
"liq"
"g"
"sp"
"ru"

out.ph_frac
4-element Vector{Float64}:
0.970482189810529
0.003792750364729876
0.020229088594267013
0.0054959712304740085

Chemical potential of the pure components (oxides) of the system is retrieved as:

out.Gamma
11-element Vector{Float64}:
-1017.3138187719679
-1847.7215909497188
-881.3605772634041
-720.5475835413267
-428.1896629304572
-1051.6248892195592
-1008.7336303031074
-1070.7332593397723
-228.07833391903714
-561.1937065530427
-440.764181608507

out.oxides
11-element Vector{String}:
"SiO2"
"Al2O3"
"CaO"
"MgO"
"FeO"
"K2O"
"Na2O"
"TiO2"
"O"
"MnO"
"H2O"

The composition in wt of the first listed solution phase ("liq") can be accessed as

out.SS_vec[1].Comp_wt
11-element Vector{Float64}:
0.6174962747665693
0.1822124172602761
0.006265730986600257
0.0185105629478801
0.04555393290694774
0.038161590650707795
0.013329583423813463
0.0
0.0
0.0
0.07846990705720527

and the end-member fraction in wt and their names as

out.SS_vec[1].emFrac_wt
8-element Vector{Float64}:
0.4608062343057727
0.0972375952287159
0.17818888101139307
0.02313962538195582
0.12734359573100587
0.025819902698522926
0.047571646835750894
0.03989251880688298
out.SS_vec[1].emNames
8-element Vector{String}:
"q4L"
"abL"
"kspL"
"anL"
"slL"
"fo2L"
"fa2L"
"h2oL"

E.3 Custom composition

And here a case in which you specify your own bulk rock composition.

using MAGEMin_C
data    = Initialize_MAGEMin("ig", verbose=false);
P,T     = 10.0, 1100.0
Xoxides = ["SiO2"; "Al2O3"; "CaO"; "MgO"; "FeO"; "Fe2O3"; "K2O"; "Na2O"; "TiO2"; "Cr2O3"; "H2O"];
X       = [48.43; 15.19; 11.57; 10.13; 6.65; 1.64; 0.59; 1.87; 0.68; 0.0; 3.0];
sys_in  = "wt"
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, sys_in=sys_in)

which gives:

Pressure          : 10.0      [kbar]
Temperature       : 1100.0    [Celsius]
     Stable phase | Fraction (mol fraction) 
              liq   0.75133 
              cpx   0.20987 
              opx   0.03877 
     Stable phase | Fraction (wt fraction) 
              liq   0.73001 
              cpx   0.22895 
              opx   0.04096 
Gibbs free energy : -916.874646  (45 iterations; 86.53 ms)
Oxygen fugacity          : 2.0509883251350577e-8

After the calculation is finished, the structure out holds all the information about the stable assemblage, including seismic velocities, melt content, melt chemistry, densities etc. You can show a full overview of that with

print_info(out)

If you are interested in the density or seismic velocity at the point, access it with

out.rho
2755.2995530913095
out.Vp
3.945646731595539

Once you are done with all calculations, release the memory with

Finalize_MAGEMin(data)

E.4 Export data to CSV

Using previous example to compute a point:

using MAGEMin_C
dtb     = "ig"
data    = Initialize_MAGEMin(dtb, verbose=false);
P,T     = 10.0, 1100.0
Xoxides = ["SiO2"; "Al2O3"; "CaO"; "MgO"; "FeO"; "Fe2O3"; "K2O"; "Na2O"; "TiO2"; "Cr2O3"; "H2O"];
X       = [48.43; 15.19; 11.57; 10.13; 6.65; 1.64; 0.59; 1.87; 0.68; 0.0; 3.0];
sys_in  = "wt"
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, sys_in=sys_in)

Exporting the result of the minimization(s) to an CSV file is straightforward:

MAGEMin_data2dataframe(out,dtb,"filename")

where out is the output structure, dtb is the database acronym and "filename" is the filename 😃

The output structure can also be saved as inlined i.e., that every line of the .csv file will output one pressure-temperature phase equilibrium calculation:

MAGEMin_data2dataframe_inlined(out,dtb,"filename")

Note

• You don't have to add the file extension .csv

• The output path (MAGEMin_C directory) is displayed in the Julia terminal

• For multiple points, simply provide the Julia Vector{out}. See Example 8 for more details on how to create a vector of minimization output.

E.5 Removing solution phase from consideration

To suppress solution phases from the calculation, define a remove list rm_list using the remove_phases() function. In the latter, provide a vector of the solution phase(s) you want to remove and the database acronym as a second argument. Then pass the created rm_list to the single_point_minimization() function.

using MAGEMin_C
data    = Initialize_MAGEMin("mp", verbose=-1, solver=0);
rm_list = remove_phases(["liq","sp"],"mp");
P,T     = 10.713125, 1177.34375;
Xoxides = ["SiO2","Al2O3","CaO","MgO","FeO","K2O","Na2O","TiO2","O","MnO","H2O"];
X       = [70.999,12.805,0.771,3.978,6.342,2.7895,1.481,0.758,0.72933,0.075,30.0];
sys_in  = "mol";
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, sys_in=sys_in,rm_list=rm_list)

which gives:

Pressure          : 10.713125      [kbar]
Temperature       : 1177.3438    [Celsius]
     Stable phase | Fraction (mol fraction) 
              fsp   0.29236 
                g   0.13786 
             ilmm   0.01526 
                q   0.22534 
             sill   0.10705 
              H2O   0.22213 
     Stable phase | Fraction (wt fraction) 
              fsp   0.34544 
                g   0.17761 
             ilmm   0.0261 
                q   0.25385 
             sill   0.12197 
              H2O   0.07503 
     Stable phase | Fraction (vol fraction) 
              fsp   0.31975 
                g   0.10873 
             ilmm   0.01307 
                q   0.23367 
             sill   0.08991 
              H2O   0.23487 
Gibbs free energy : -920.021202  (25 iterations; 27.45 ms)
Oxygen fugacity          : -5.4221261006295105
Delta QFM                : 2.506745293747623

Note

Note that if you want to suppress a single phase, you still need to define a vector to be passed to the remove_phases() function, such as shown below.

using MAGEMin_C
data    = Initialize_MAGEMin("mp", verbose=-1, solver=0);
rm_list = remove_phases(["liq"],"mp");
P,T     = 10.713125, 1177.34375;
Xoxides = ["SiO2","Al2O3","CaO","MgO","FeO","K2O","Na2O","TiO2","O","MnO","H2O"];
X       = [70.999,12.805,0.771,3.978,6.342,2.7895,1.481,0.758,0.72933,0.075,30.0];
sys_in  = "mol";
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, sys_in=sys_in,rm_list=rm_list)

which gives:

Pressure          : 10.713125      [kbar]
Temperature       : 1177.3438    [Celsius]
     Stable phase | Fraction (mol fraction) 
              fsp   0.29337 
                g   0.12 
               sp   0.03036 
                q   0.23953 
             sill   0.08939 
               ru   0.00521 
              H2O   0.22213 
     Stable phase | Fraction (wt fraction) 
              fsp   0.34667 
                g   0.15368 
               sp   0.04514 
                q   0.26983 
             sill   0.10184 
               ru   0.00781 
              H2O   0.07503 
     Stable phase | Fraction (vol fraction) 
              fsp   0.31981 
                g   0.09422 
               sp   0.02492 
                q   0.24761 
             sill   0.07484 
               ru   0.00446 
              H2O   0.23413 
Gibbs free energy : -920.00146  (19 iterations; 27.79 ms)
Oxygen fugacity          : -5.760704474307317
Delta QFM                : 2.1681669200698166

E.6 Oxygen buffer

Here we need to initialize MAGEMin with the desired buffer (qfm in this case, see list at the beginning).

Note

Note that O/Fe2O3 value needs to be large enough to saturate the system. Excess oxygen-content will be removed from the output

using MAGEMin_C 
data    = Initialize_MAGEMin("ig", verbose=false, buffer="qfm");
P,T     = 10.0, 1100.0
Xoxides = ["SiO2","Al2O3","CaO","MgO","FeO","K2O","Na2O","TiO2","O","Cr2O3","H2O"];
X       = [48.43; 15.19; 11.57; 10.13; 6.65; 1.64; 0.59; 1.87; 4.0; 0.1; 3.0];
sys_in  = "wt"    
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, sys_in=sys_in)

Buffer offset in the log10 scale can be applied as

using MAGEMin_C 
data    = Initialize_MAGEMin("ig", verbose=false, buffer="qfm");
P,T     = 10.0, 1100.0
Xoxides = ["SiO2","Al2O3","CaO","MgO","FeO","K2O","Na2O","TiO2","O","Cr2O3","H2O"];
X       = [48.43; 15.19; 11.57; 10.13; 6.65; 1.64; 0.59; 1.87; 4.0; 0.1; 3.0];
offset  = -1.0
sys_in  = "wt"    
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, B=offset, sys_in=sys_in)

Note

Several buffers can be used to fix the oxygen fugacity

• qfm -> quartz-fayalite-magnetite

• qif -> quartz-iron-fayalite

• nno -> nickel-nickel oxide

• hm -> hematite-magnetite

• iw -> iron-wüstite

• cco -> carbon dioxide-carbon

E.7 Activity buffer

Like for oxygen buffer, activity buffer can be prescribe as follow

Note

Note that the corresponding oxide-content needs to be large enough to saturate the system. Excess oxide-content will be removed from the output

using MAGEMin_C 
data    = Initialize_MAGEMin("ig", verbose=false, buffer="aTiO2");
P,T     = 10.0, 700.0
Xoxides = ["SiO2","Al2O3","CaO","MgO","FeO","K2O","Na2O","TiO2","O","Cr2O3","H2O"];
X       = [48.43; 15.19; 11.57; 10.13; 6.65; 1.64; 0.59; 4.0; 0.1; 0.1; 3.0];
value  = 0.9
sys_in  = "wt"    
out     = single_point_minimization(P, T, data, X=X, Xoxides=Xoxides, B=value, sys_in=sys_in)

Note

Similarly activity can be fixed for the following oxides

• aH2O -> using water as reference phase

• aO2 -> using dioxygen as reference phase

• aMgO -> using periclase as reference phase

• aFeO -> using ferropericlase as reference phase

• aAl2O3 -> using corundum as reference phase

• aTiO2 -> using rutile as reference phase

• aSiO2 -> using quartz/coesite as reference phase

E.8 Many points

using MAGEMin_C
db   = "ig"  # database: ig, igneous (Holland et al., 2018); mp, metapelite (White et al 2014b)
data  = Initialize_MAGEMin(db, verbose=false);
test = 0         #KLB1
n    = 1000
P    = rand(8.0:40,n);
T    = rand(800.0:2000.0, n);
out  = multi_point_minimization(P,T, data, test=test);
Finalize_MAGEMin(data)

By default, this will show a progressbar (which you can deactivate with the progressbar=false option).

You can also specify a custom bulk rock for all points (see above), or a custom bulk rock for every point.

References

• Green, ECR, Holland, TJB, Powell, R, Weller, OM, & Riel, N (2025). Journal of Petrology, 66, doi: 10.1093/petrology/egae079

• Weller, OM, Holland, TJB, Soderman, CR, Green, ECR, Powell, R, Beard, CD & Riel, N (2024). New Thermodynamic Models for Anhydrous Alkaline-Silicate Magmatic Systems. Journal of Petrology, 65, doi: 10.1093/petrology/egae098

• Holland, TJB, Green, ECR & Powell, R (2022). A thermodynamic modelfor feldspars in KAlSi3O8-NaAlSi3O8-CaAl2Si2O8 for mineral equilibrium calculations. Journal of Metamorphic Geology, 40, 587-600, doi: 10.1111/jmg.12639

• Tomlinson, EL & Holland, TJB (2021). A Thermodynamic Model for the Subsolidus Evolution and Melting of Peridotite. Journal of Petrology,62, doi: 10.1093/petrology/egab012

• Holland, TJB, Green, ECR & Powell, R (2018). Melting of Peridotitesthrough to Granites: A Simple Thermodynamic Model in the System KNCFMASHTOCr. Journal of Petrology, 59, 881-900, doi: 10.1093/petrology/egy048

• Green, ECR, White, RW, Diener, JFA, Powell, R, Holland, TJB & Palin, RM (2016). Activity-composition relations for the calculationof partial melting equilibria in metabasic rocks. Journal of Metamorphic Geology, 34, 845-869, doi: 10.1111/jmg12211

• White, RW, Powell, R, Holland, TJB, Johnson, TE & Green, ECR (2014). New mineral activity-composition relations for thermodynamic calculations in metapelitic systems. Journal of Metamorphic Geology, 32, 261-286, doi: 10.1111/jmg.12071

• Holland, TJB & Powell, RW (2011). An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of Metamorphic Geology, 29, 333-383, doi: 10.1111/j.1525-1314.2010.00923.x