Teaching Phase Equilibria
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Thermodynamics

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


A short (13 page)summary (Acrobat (PDF) 212kB Nov11 07) (including several of the most significant satellite pages) of thermodynamics as it applies to geological phase equilibria, is available.

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.


Albite-jadeite-quartz phase diagram 02 Phase diagram showing the reaction:
albite = jadeite + quartz
Along the reaction line, ΔGrxn = 0. Above the line ΔGrxn < 0; below the line ΔGrxn > 0.

The Basis for Thermodynamic Calculations

All phases, whether mineralogical or not, have an associated Gibbs Free Energy of Formation value abbreviated ΔGf. The ΔGf 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 (ΔGrxn) 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 ΔGrxn < 0, the reaction proceeds to the right. If the ΔGrxn >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 ΔGf of a mineral varies with changes in pressure (P), temperature (T) and mineral composition (X). Consequently, the ΔGrxn 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, ΔGrxn = 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: 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).


A pseudosection calculated with THERMOCALC for comparison with Perplex "Pseudosection" output from Thermocalc

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:

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


Books on Fundamental Thermodynamics


Exercises to Promote Learning


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