# Advanced Modeling Programs: Perplex

## What is Perplex?

Perplex is a thermodynamic calculation package suitable for rapidly creating phase diagrams of all types, creating pseudosections (phase diagrams that include only those reactions experienced by a particular bulk composition). It allows easy estimation of rock and mineral properties as a function of conditions (pressure, temperature, composition).

## Principles

In order to create a phase diagram, the identity, abundance, and composition of the stable phases must be determined for each condition over a range of pressure, temperature, composition, or some combination of these. Thermodynamics requires that the stable phases be those with the minimum Gibbs energy. This low-energy set of phases can be determined in two ways: either by the solution of a set of non-linear equations, or by a "brute force" method, in which the energy of each set of possible phases is calculated, and that set with the minimum energy is selected, for each condition. The conditions are organized on a Cartesian grid, with grid refinement typically iterating to better constrain the position of reactions.

This process is complicated greatly by the fact that many minerals have solid solution, and their energy changes with changes in their compositions. The strategy Perplex uses to address this is to subdivide each mineral into a large number (~50) *pseudocompounds*. The energy of each pseudocompound is determined in advance (it's actually a function of pressure and temperature), and while this creates a myriad of 'minerals' (the pure ones together with the pseudocompounds), it makes the calculation quite straightforward.

There are a number of optimizations that Perplex can use to speed up the calculation, especially with the advent of the 2007 version of Perplex.

Perplex relies on two primary datasets:

**thermodynamic databases**that give properties of a wide range of end-members (both mineral, liquid, and melt)**activity models**that describe how the energies of the end-members contribute to the energies of intermediate compositions.

Perplex has the ability to choose among a wide range of databases and activity models at run-time, offering great flexibility.

## Applications

### Phase Diagram Calculations

**Projections**(or 'Shreinemakers diagrams') show stable invariant points and univariant reaction lines for all of the bulk compositions in a model system (e.g. petrogenetic grids).**Composition diagrams**show the mineral assemblages and ranges of mineral solid solutions at a specified P and T, for all the bulk compositions in the model system (e.g. AFM diagrams).**Mixed-variable diagrams**show all phase relationships as a function of P or T and one compositional variable.**Pseudosections**show just those phase relationships for a specified bulk composition.

### Rock Property Calculations

Once a pseudosection has been determined, the properties of the rock can be calculated, including variables such as seismic velocity.

## Strengths & Limitations

Univariant reactions in a petrogenetic grid are extremely useful in providing bounding constraints on the stability of mineral assemblages. However, petrogenetic grids, especially complex ones with lots of reactions, can be difficult to interpret, and most mineral assemblages in real rocks are higher variance. Moreover, for specific rock compositions, many of these reactions are not 'seen' by a particular bulk composition.

Most people are interested in specific mineral assemblages in the rocks they are studying, for which they have collected and analyzed. The advantage of the pseudosection approach is that this type of diagram portrays only the reactions we are interested in by examining a compositional slice through the full multi-component chemical system.

One caveat of the pseudosection approach is the choice of bulk composition. This can be done via a whole rock geochemical (XRF) analysis if equilibrium is achieved on the 'rock' scale. However, many metamorphic rocks preserve chemical zoning of porphyroblasts and the choice of an 'effective' bulk composition is more appropriate, by combining mineral chemistry data with modal proportions (e.g. by only including garnet cores and excluding the rims).

There are other thermodynamic modeling programs available, including THERMOCALC, MELTS, and TWQ. Each has its merits, and a comparison of these may be useful. In addition, because Perplex is so similar to THERMOCALC in its goals, a direct comparison of the two may be informative.

## Worked Examples

### Phase Diagrams

The basic approach to creating a diagram in Perplex involves the following sequence of steps:

- Choose a model system in which to do the calculations (choose components).
- Formulate the thermodynamics (a-X relationships) of the phases in the system.
- Decide which phase diagrams are to be constructed and, for pseudosections, choose an appropriate bulk composition. Here are links to worked examples from the Perplex website. Most of these are also included in the Learning Pseudosections with Perplex teaching activity.
- P-T Projections
- Compatibility Diagrams
- Mixed-variable diagrams
- P-T Pseudosections
- P-X or T-X Pseudosections
- Run program BUILD to make a file that describes the calculation you desire.
- Run program VERTEX to perform the calculation.
- Optionally, run program PSVDRAW and/or WERAMI to make a postscript file of your graphical output.
- Optionally, use a separate package (e.g., Adobe Illustrator) to read the postscript and print or manipulate the output.

## References

- Connolly JAD (2005) Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. EPSL 236:524-541.
- Connolly JAD, Kerrick DM (2002) Metamorphic controls on seismic velocity of subducted oceanic crust at 100-250 km depth. EPSL 204:61-74
- Connolly JAD, Petrini K (2002) An automated strategy for calculation of phase diagram sections and retrieval of rock properties as a function of physical conditions. J Met Geol, 20:697-708.
- Connolly JAD (1995) Phase diagram methods for graphitic rocks and application to the system C-O-H-FeO-TiO2-SiO2. Contrib Mineral Petrol 119:94-116.
- Connolly JAD, Cesare B (1993) C-O-H-S fluid composition and oxygen fugacity in graphitic metapelites. J Metamorphic Geol 11:368-378.
- Abart R, Connolly JAD, Trommsdorff V (1992) Singular point analysis: construction of Schreinemakers projections for systems with a binary solution. Am J Sci 292:778-805.
- Connolly JAD, Trommsdorff V (1991) Petrogenetic grids for metacarbonate rocks: pressure-temperature phase diagrams for mixed volatile systems. Contrib Mineral Petrol 108: 93-105.
- Connolly JAD (1990) Multivariable phase diagrams: an algorithm based on generalized thermodynamics. Am J Sci 290:666-718.
- Connolly JAD, Kerrick DM (1987) An algorithm and computer program for calculating composition phase diagrams. CALPHAD 11:1-55.

## Related Links

## Teaching Activities

- Learning Pseudosections with Perplex - Dave Hirsch, Western Washington University
- Phase Diagram Projections and Phase Diagram Sections Lab (Microsoft Word 40kB Mar29 07) - This two week exercise, provided by Dave Pattison at the University of Calgary, includes problems sets involving phase diagram sections using Gibbs (for demonstration of principles) and Perplex.