Thermodynamics

Dexter Perkins (University of North Dakota), Andrea Koziol (University of Dayton), John Brady (Smith College)

Basic Definition of Thermodynamics

The Oxford English Dictionary says: "Thermodynamics: the theory of the relations between heat and mechanical energy, and of the conversion of either into the other." In simpler terms, we can think of thermodynamics as the science that tells us which minerals or mineral assemblages will be stable under different conditions.

In practical terms, thermodynamics not only allows us to predict what minerals will form at different conditions (forward modeling), but also allows us to use mineral assemblages and mineral compositions to determine the conditions at which a rock formed (thermobarometry). The calculations are often complex and are best carried out using thermodynamic modeling programs or programs specifically designed for thermobarometry.

The Basis for Thermodynamic Calculations

All phases, whether mineralogical or not, have an associated Gibbs Free Energy of Formation value abbreviated ΔG_f. The ΔG_f value describes the amount of energy that is released or consumed when a phase is created from other phases.

We can calculate the Gibbs Free energy of any reaction (ΔG_rxn) by summing the energies of the right-hand side (products) of the reaction and subtracting the energies of the left hand side (reactants). If the calculation reveals that ΔG_rxn < 0, the reaction proceeds to the right. If the ΔG_rxn >0, the reaction proceeds to the left.

Consider the reaction: albite = jadeite + quartz.
Under normal earth surface conditions, the Gibbs Energy of this reaction is greater than zero. Consequently, albite is stable and the assemblage jadeite + quartz is unstable.

The ΔG_f of a mineral varies with changes in pressure (P), temperature (T) and mineral composition (X). Consequently, the ΔG_rxn for any reaction will vary with P, T and X, being positive in some portions of P-T-X space and negative in others. The result is that we can plot reactions on phase diagrams. Along any reaction line, such as the one separating the albite and jadeite + quartz fields shown in the diagram here, ΔG_rxn = 0.

Doing thermodynamic calculations requires reliable thermodynamic data. Additionally, although the calculations can be done by hand or with a calculator, they are complicated and time consuming.

More information about Gibbs Free Energy and other thermodynamic functions . . .

More information about fundamental thermodynamic calculations . . .

Internally Consistent Thermodynamic Data Bases

Thermodynamic data are obtained by calorimetry or derived on the basis of petrologic experiments, each with associated uncertainties. Combining thermodynamic values from different sources (especially Gibbs Free energy values) can lead to erroneous or misleading results because:

• some calorimetry or experiments may be unreliable
• systematic errors may skew some results one way and others a different way
• different studies have different amounts of uncertainty

Thus, there is need for a database that does not include erroneous data, that reconciles calorimetric and phase equilibrium data, and that is internally consistent. Different workers have approached this problem in different ways, leading to the well-known datasets of Holland and Powell (Holland and Powell reference list) or of Berman (Berman reference list).

Computer Programs for Thermodynamic Calculations and Modeling

Thermodynamic calculations can be very complex. Fortunately, a number of different authors have created programs designed for calculating thermodynamic equilibria and making phase diagrams. Some of the most popular and complete programs are:

• TWQ is an easy to use Windows based program that allows you to calculate the position of phase equilibria in P-T, T-XCO2, and P-XCO2 space. You can also use it to calculate various activity diagrams.
• Thermocalc performs the same calculations as TWQ for a much larger number of phases and includes more complicated types of calculations that involve the effects of bulk composition on mineral stability.
• Melts is the only widely available program that allows thermodynamic calculations to be made for equilibria involving magmas.
• Perplex is a thermodynamic calculation package suitable for rapidly creating phase diagrams of all types, creating equilibrium phase diagrams (pseudosections: phase diagrams that include only those reactions experienced by a particular bulk composition).
• Theriak-Domino is a suite of programs that can be used for calculating equilibrium phase diagrams (pseudosections: phase diagrams that include only those reactions experienced by a particular bulk composition) and for a number of other kinds of calculations.

Phase Diagrams: The Results of Thermodynamic Calculations

Phase diagrams are graphical representations of the equilibrium relationships between minerals (or others phases). These relationships are governed by the laws of thermodynamics. Standard phase diagrams show how phases or phase assemblages change as a function of temperature, pressure, phase composition, or combinations of these variables.

Some phase diagrams (those for 1-component diagrams) depict relationships involving multiple phases having the same composition (for example, the relationships between the vapor, liquid and solid forms of H₂O). Other diagrams (such as the one shown on the right), depict the relationships between a number of compounds having different compositions. Still others show how compositions of phases change under different conditions. More information about phase diagrams and examples . . .

Thermobarometry

Thermobarometry refers to the quantitative determination of the temperature and pressure at which a metamorphic or igneous rock reached chemical equilibrium. Many programs exist to facilitate such calculations, but most are only applicable to specific kinds of rocks and mineral assemblages.
More information about thermobarometry . . .

Electronic References and Resources: Fundamental Thermodynamics

• W. R. Salzman (Dept. of Chemistry, Univ. Arizona): On-line Thermodynamics Primer
• Thermodynamics (more info) - PowerPoint based on Chapter 5, An Introduction to Igneous and Metamorphic Petrology (Winter 2001)
• Thermodynamics (more info) - PowerPoint based on Chapter 27, An Introduction to Igneous and Metamorphic Petrology (Winter 2001)
• Thermodynamics and Metamorphism ( This site may be offline. ) - lecture notes by Stephen Nelson, Department of Geology, Tulane University

Books on Fundamental Thermodynamics

• Cemic, L. (2005) Thermodynamics in Mineral Sciences: An Introduction. Springer. 386 p.
• Fraser, D. (1977) Thermodynamics in Geology. NATO Science Series: C. Kluwer Academic Publishers. 424 p.
• Nordstrom, D.K. (2006) Geochemical Thermodynamics. Blackburn Press. 504 p.
• Greenwood, H. J. (ed) (1977) Short Course In Application of Thermodynamics to Petrology and Ore Deposits. Mineralogical Association of Canada, 230 p.
• Kern, R. and Weisbrod, A. (1967) Thermodynamics for Geologists. Freeman, Cooper and Co. 3-4 p.
• Spear, F.S. (1994) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Monograph of the Mineralogical Society of America. 799 p.
• Wood, B.J. (1977) Elementary Thermodynamics for Geologists. Oxford University Press. 318 p.
• Wood, B.J., and Fraser, D. G. (1976), Elementary Thermodynamics for Geologists. Oxford University Press, 303 p.

Exercises to Promote Learning

• Lab Activity: Introduction to Gibbs Energy Dexter Perkins, University of North Dakota
• Learning Thermodynamics Using Spreadsheets - Sumit Chakraborty, Institut fuer Geologie, Mineralogie und Geophysik Somnath Dasgupta, Jadavpur University, Kolkata, India