6.7 Whole Rock Equilibrium Models

Modeling equilibrium for an arbitrary rock bulk composition requires thermodynamic data and solution models for all the possible minerals, and software to compare the data and solve (minimize Gibbs energy) for the equilibrium mineral assemblage, including mineral compositions, as a function of temperature and pressure. Many geoscientists have contributed to the efforts to make this possible by collecting data, building solution models, and writing software. You can find citations to some of this work on the web pages, listed here, describing available software.

An example of what is possible with whole rock equilibrium calculations is shown in Figure 6.14, a T-P diagram of chemical reactions that can occur in metamor-phosed shales. As you can see from the complex web of reaction lines, there are many reactions to consider, even though Figure 6.14 is simplified to include only the major chemical components KFMASH
(K₂O-FeO-MgO-Al₂O₃-SiO₂-H₂O). And continuous reactions are not shown. To see the continuous reactions that occur at equilibrium between the discontinuous reactions shown click here, to open Figure 15, mouse over the T-P diagram, and watch equilibrium assemblages and mineral compositions change on a Thompson AFM diagram.

Although equilibrium information for all bulk compositions is shown in Figure 6.14 with the associated AFM diagrams in Figure 6.15, many petrologists choose to focus on one bulk composition at a time, reducing the complexity of information presented. With one bulk composition selected, the thermodynamic models and software can identify the equilibrium mineral assemblage, mineral compositions, and mode for any temperature and pressure within the range of the models. Results of those calculations are typically shown by dividing the T-P diagram into regions defined by the equilibrium mineral assemblages. Figure 6.16 shows a Mineral Assemblage Diagram (MAD, also called a pseudosection) for a single metamorphosed shale (KFMASH) bulk composition. Colors on the T-P diagram show temperatures and pressures where a specific mineral assemblage is at equilibrium for the rock composition. Click on Figure 6.16 to see a larger, interactive version where you can explore the effects of bulk composition on the MAD. Follow the instructions on the Figure 6.16 page.

Using model calculations like those shown in Figures 6.15 and 6.16, equilibrium conditions for a metamorphic rock can be determined. But what do those temperatures and pressures mean in terms of the total history of the rock?

P-T Paths