P-T-X paths tutorials

Here we provide a set of tutorials to generate various kind of pressure-temperature-composition paths: including batch melting, fractional melting, fractional crystallization, assimilation, variable oxygen buffer and isentropic paths. All of them are set up from the same PTX path tab and can be combined (e.g., isentropic fractional crystallization with assimilation, see E.8)

The default solver of the PTX path tab is the Legacy solver and the default local minimizer is Nullspace (see the Solver sub-tab of the General setup tab).

E.1. Quick start - first P-T-X path

For the first P-T-X path, simply launch MAGEMinApp and navigate to the PTX path tab. Keep the default thermodynamic database (Igneous, Green et al., 2025 after Holland et al., 2018) and the default bulk-rock composition (KLB1 Peridotite anhydrous). In the Path definition panel click on Find solidus and Find liquidus and define the P-T points accordingly:

Note

• New points for the P-T-X path can be added by clicking on Add new point.

• To delete a point simply click on the cross icon on the left of point.

Load a P-T-X path from file

As an alternative to adding points one by one, drag and drop a CSV file onto the Drag and drop path box below the path table to define (and replace) the whole path at once. The file needs a header line P;T (or P,T; pressure always in kbar regardless of the app's current pressure-unit setting), and comment lines start with #:

P;T
10.0;1200
7.0;1000
4.0;800
2.0;600

Two optional columns, Assim and Buffer, can be added for use with the Assimilation and Variable buffer modes described in E.4. Assimilation and E.5. Variable buffer below - if omitted, both default to 0.0:

P;T;Assim;Buffer
10.0;1200;0.0;0.0
7.0;1000;5.0;-1.0
4.0;800;10.0;-2.0
2.0;600;15.0;-3.0

Ready-to-use examples are shipped in MAGEMinApp as examples/ptx-path.csv (P,T only) and examples/ptx-path_assim-buffer.csv (with Assim/Buffer).

Note

• Loading a file replaces all rows currently in the path table.

• Assim/Buffer values are kept in the table even if the corresponding mode is off; they are simply ignored until Assimilation/Variable buffer is switched on.

In the Path options panel, change the resolution to 32. This option defines the number of point-wise calculation between two defined points. Hit Compute path and after a few seconds you should get the following result:

Stable phase fraction

Stable phase composition

Then in the Phase composition tab, click liq which will display the evolution of the melt composition along the path:

Note

• Double-clicking on one ooxide will isolate it.

• Double-clicking again on the same oxide, will bring back all the oxides.

TAS diagram

When liq is selected you can access the TAS diagram which displays the evolution of the melt composition (Total Alkali Silica):

Warning

• When computing a new PTX diagram, to refresh the TAS diagram, you need to unselect and reselect liq in the Composition panel.

E.2. Fractional melting

In this example, we are going to perform fractional melting using the SM89 oxidised average MORB composition bulk using the Metabasite thermodynamic database (Green et al., 2016). First make sure you select Aug in the clinopyroxene selection, then define the P-T points of the path as follow:

In the Path options panel, choose a resolution of 32, and select P-T-X mode = fractional melting, keep Assimilation = false, Cumulate/Connectivity unit = mol, Connectivity threshold [mol%] = 7 and Residual Threshold [mol%] = 7:

Note

• The connectivity threshold is the melt fraction above which melt is extracted.

• The residual threshold is the melt fraction left in the rock after an extraction event. It cannot exceed the connectivity threshold (it is clamped to it). With both set to 7, only the melt above 7 mol% is extracted, so the melt fraction is brought back to the connectivity threshold. Lowering the residual threshold (e.g., to 2) drains the melt further each time the connectivity threshold is exceeded, mimicking extraction events that leave less melt in the source.

• Cumulate/Connectivity unit (mol, wt or vol) is the basis on which both thresholds, the extraction and the assimilation blend are expressed.

• When computing a fractional melting path using a connectivity threshold, the displayed fraction of melt can be slightly above the threshold as the removed fraction of melt is only applied to the subsequent calculation step. This effect can however be minimized by increasing the resolution.

Process with the P-T-X path calculation, which should yield:

Note

• The black continuous line remaining % represents the remaining % with respect to the starting material.

• The black dashed line removed % is the mass % of material removed with respect to the starting material.

• remaining % + removed % = 100.0

E.3. Fractional crystallization

Let us use the same database and bulk rock composition as for the fractional melting example. Simply change the path definition as follow:

In the Path options panel, choose a resolution of 32, and select P-T-X mode = fractional crystallization, keep Assimilation = false, Cumulate/Connectivity unit = mol and Residual rock fraction [mol%] = 1:

Note

• Residual rock fraction [mol%] can be thought as a small fraction of the solid rock carried by the fractionating melt.

Process with the P-T-X path calculation, which should yield:

and TAS diagram (Total Alkali Silica):

Note

• The size of the circle symbol in the TAS diagram scales with the remaining %. This gives an idea of the volume of generated magma along the fractional crystallization path.

E.4. Assimilation

In this example we are going to compute an equilibrium batch crystallization path of a wet basalt, and, progressive assimilation of tonalitic composition. Keep the Igneous database (Green et al., 2025, after Holland et al., 2018) and define the P-T path as follow:

Note

• Notice the new column in the P-T path definition Add [mol%]. Here you can define how much of the assimilated composition will be added for each P-T step.

In Path options, set Resolution = 32, P-T-X Mode = Equilibrium and Assimilation = true. When Assimilation = true a second bulk-rock composition is available for selection in the Bulk-rock compositionleft panel. Choose Wet Basalt for the left (starting) composition and Tonalite 101 for the right (assimilated) composition:

Performing the calculation of the P-T path gives:

and the following TAS diagram:

E.5. Variable buffer

To simulate a change in oxydation/reduction state of the system you can also provide variable buffer offsets. Let's start from previous assimilation example 4, and select Buffer = QFM and Variable buffer = true in the Configuration panel.

A new column named Buffer is now available in the Path definition panel and you can modify the buffer offset to your liking. For instance:

Tip

Don't forget to oversaturate the O content of the bulk-rock compositions.

Performing the calculation of the P-T path gives:

and the following TAS diagram:

E.6. Isentropic path

An isentropic path represents a process where a rock undergoes changes in pressure and temperature without any exchange of heat with its surroundings (adiabatic) and without entropy production (reversible), e.g., mantle convection or adiabatic decompression melting. Isentropic paths are part of the PTX path tab: the Isentropic option can be combined with the other options of the Path options panel (fractional crystallization, fractional melting, assimilation, trace elements).

Launch MAGEMinApp, navigate to the PTX path tab and keep the default database (Igneous) and bulk-rock composition. In the Path options panel, select Isentropic = true and keep all other parameters by default:

With Isentropic = true, the Path definition panel changes: temperature is no longer a column of the table, only the starting temperature (Starting Temp. [°C]) is defined, together with the pressures of the path. Set Starting Temp. = 800 and define a path from 10 to 2 kbar, then click Compute path:

Note

• The entropy of the system is computed at the starting P-T point. For every following pressure, the temperature is found by bisection so that the entropy of the system matches the starting entropy within the temperature Tolerance [K] of the Path definition panel.

• In the Path preview panel (top right) you can retrieve the Starting entropy [kJ/K] and the isentropic pressure-temperature path:

E.7. Isentropic fractional crystallization

Building upon the previous example, select P-T-X Mode = Fractional crystallization together with the isentropic option:

Computing the path generates two diagrams: the stable phase fractions and the fractionated phases.

E.8. Isentropic fractional crystallization with assimilation

One can also compute isentropic crystallization paths with assimilation of a secondary bulk-rock composition (host-rock, second magma etc.)

First set Assimilation = true. Then, in the Path definition panel, a new column Add [mol%] appears next to pressure, which defines the fraction of the second bulk-rock composition added in mol%. Modify the entry of the second point to 50%:

Note

• If you put a non zero value for the first row of the Add [mol%] column this will change the starting bulk-rock composition accordingly

• When changing any other rows, the Add [mol%] will be added progressively from the previous point

You can now select the second bulk-rock composition in the left Bulk-rock composition panel. For instance:

Compute the path:

Modify colormap

It is possible to adjust the colormap of the area plots. In the Display options panel on the right, click on Modify phase colors:

This unfold a window a the left of your screen where the colors of all stable phases are displayed:

To modify a color, click the corresponding cell in the Change column, then change the thin colored bar on the right. This option the color picker:

Note

• Only the phases stable in your calculation can be modified

• Once your happy with the updated colors, to apply the changes, you need to redo the PTX path calculation

• You can save your changes by clicking on the green button Save colors/styles. The changes are saved even when restarting the App.

Trace-element partitioning

Trace-element (TE) partitioning can be computed simultaneously with any P-T-X path (batch melting, fractional melting, fractional crystallization, isentropic). The module uses lattice-strain parameterized Kd databases and optionally applies mineral or volatile saturation models (Zr, S, P₂O₅, CO₂).

E.9. Trace-element partitioning setup

Step 1 - Activate the TE predictive model

In the Path options panel, set TE predictive model = true. This reveals the Trace Elements panel in the left sidebar.

Step 2 - Configure KD model and saturation options

In the Trace Elements panel, the following options are available:

Option	Description	Available values
KD model	Lattice-strain Kd database	OL - O. Laurent (2012) ; CO - J. Cornet (2019)
Zr saturation	Zircon saturation model	none ; Watson 1979 (WH) ; Blundy 2022 (CB)
S saturation	Sulfide saturation model	none ; Liu 2021 (Liu07)
P₂O₅ saturation	Fluorapatite saturation model	none ; Tollari 2006
CO₂ saturation	CO₂ fluid saturation model	none ; SY26 - Sun & Yao (2026)

Note

• Saturation models only activate when the corresponding element is present in the TE bulk composition.

• The CO₂ saturation model (SY26) requires dissolved H₂O in the melt: it inverts the H₂O solubility equation to derive P_H₂O, then evaluates CO₂ solubility at P_CO₂ = P − P_H₂O.

Step 3 - Load the trace-element bulk composition

Two options are available:

• Built-in database: use the dropdown below the saturation options to select a predefined TE composition; the Initial TE bulk composition [μg/g] table updates automatically.

• Custom file: drag and drop a CSV file onto the upload area. The file must contain element and μg/g columns.

Values in the table are editable directly in the interface.

When Assimilation = true, a second table (Assimilant TE bulk composition [μg/g]) is also displayed and follows the same loading logic.

Step 4 - Compute the path

Click Compute path. Thermodynamic minimization and TE partitioning are performed simultaneously at each step along the path.

E.10. Visualizing trace-element results

After computation, the Trace Elements tab becomes enabled. It contains:

• REE spectrum (top panel): rare-earth element pattern at the selected path point, normalized to bulk or chondrite. Use the Show dropdown to switch between ree (REE only) and all (extended trace-element set).

• Diagram (bottom panel): P-T diagram colored by a user-selected TE or saturation field.

In the Display options panel (right side) use the Field type dropdown to choose what to display:

Field type	Available fields
Zircon	Sat_Zr_liq [ug/g] - Zr saturation in melt ; zrc_wt - zircon weight fraction
Sulfide	Sat_S_liq [ug/g] - S saturation in melt ; sulf_wt - sulfide weight fraction
Fluorapatite	Sat_P2O5_liq [ug/g] - P₂O₅ saturation in melt ; fapt_wt - apatite weight fraction
CO2 saturation	Sat_CO2_liq [ug/g] - CO₂ saturation in melt ; fl_CO2_wt - CO₂ fluid weight fraction
Trace element	Any TE concentration or user-defined expression (see below)

For the Trace element field type, the Field builder allows you to enter arbitrary expressions, for example:

• [M_Dy] / [M_Yb] - Dy/Yb ratio in the melt

• [M_La] / [M_Sm] - La/Sm ratio

where [M_X] refers to element X in the melt. Set a normalization (none, bulk, chondrite) and click Compute and display.

Isopleths (contour lines) for any field can be added from the Isopleths tab: select the field type and field, set the range and step, and click Add.

E.11. Exporting trace-element results to CSV

When TE predictive model = true, additional export buttons appear in the Path options panel:

Button	Filename field	Content
Save path → csv	Save path input	Full PTX path: P, T, phase fractions and oxide compositions at each step (one row per step)
Save path → csv line	Save path input	Same content but all steps written on a single row (useful for batch processing)
Save cumulate → csv file	Save cumulate input	Cumulate (extracted solid) composition along the path
Save trace elements → csv file	Save trace elements input	TE concentrations in the melt, bulk solid and individual mineral phases at each step
Save cumulate TE → csv file	Save cumulate TE input	Integrated cumulate TE composition at each step

Note

• Save trace elements and Save cumulate TE are only active after trace elements have been computed. A warning badge is shown if you try to export beforehand.

• All CSV files are saved to the output/ subdirectory of the working directory displayed in the Julia terminal.

Tip

Use the Export references → bibtex file button to export a BibTeX file listing all references for the active KD model, saturation models and thermodynamic database.