Thermodynamics vs. Kinetics: the ongoing battle

By Alexandra Seclaman

Change … a simple world capable of explaining so many things. Change is deeply rooted in the fabric of the Universe, of our solar system and our planet.

Change for a geologist should not be surprising because it is natural; it defines and shapes our planet.

The conservation of energy is described in the first law of thermodynamics. The energy can be changed from one form to another but it cannot be destroyed or created.

This introduces concepts like internal energy ( U ), and its relationship with heat and work:

dU= dQ – PdV

For a mineral, because we are interested in minerals, the internal energy is the sum of the potential energies stored in the interatomic bonding and the kinetic energy of the atomic vibrations.

            Minerals or rocks can be viewed as systems, open, closed or isolated. Other important concepts in thermodynamics that help us understand geological systems are enthalpy, entropy and the most important concept is that of free energy, especially Gibb’s free energy.

Enthalpy (H) is defined as H=U + PV, and thus is the total energy of the system, i.e. the energy required to create the system and the energy needed in order to modify it (for example the energy needed to expand its boundaries). 

Entropy (S) is the measure of change in the disorder of the system. It is vital because in a mineral transformation the new structure can be more ordered or more disordered than the previous one, in either way it is quite improbable that the entropy of a system, after it has experienced a change in its environment, will remain the same.

Gibbs free energy (G) is central in applying thermodynamics to minerals and rocks, because it is not important only to know that the systems change, but when they will change. Gibbs free energy is defined as:

G = H – TS, and dG = VdP – SdT

The system can change spontaneously if dG < 0, i.e. if the free energy of the new state is smaller than that of the initial state. If dG > 0 then the change is impossible, and if dG = 0 the system is at equilibrium. As it can be seen, the factors that influence change are pressure, temperature and the order of the system.

Basically, what thermodynamics tells us is that when we take a mineral out of its equilibrium range it must re-equilibrate to the new pressure-temperature conditions and change in a new stable phase for those given conditions. If we take a crystal of kyanite, aragonite, diamond or whatever mineral phase that it is formed at high pressures, and thus stable in those conditions, and bring it to normal conditions (1 atm and 20 ˚C) it should become unstable and transform into its low pressure polymorph. But this does not always happen. Why? Is thermodynamics wrong? We have entire mountains made of rocks that formed in other pressure-temperature conditions than the surface and yet they are partially equilibrate or not at all.

In order to explain this we have to take into account some variables that were ignored in the above crash course in thermodynamics, speed or time, activation energy and the mechanism of change. The branch of physics that takes into account these variables is called Kinetics. If thermodynamics tells us that systems can exchange energy and by doing so they change, and how they will change, kinetics tells us if they will change and how fast.

The problem is very complex and it is essential in understanding the changes that take place or not in rocks. Let us try and explain this in a simple way using a very simplified example. Aragonite is the high pressure polymorph of CaCO₃ and the stable form of crystalline CaCO₃ for normal values of pressure is calcite. Thermodynamics tells us that it is impossible to hold in your hand a crystal of aragonite (if your hand is found at a lower pressure than 5 Kb), but we know that this is not true. We have crystals of aragonite, and we call them metastable. This means that they are outside their stability field and yet they did not change into a phase stable for the current pressure-temperature conditions.

Why? Kinetics gives the answer to this one. The crystal structures of calcite and aragonite are very different; one crystallizes in the trigonal system and the other in orthorhombic system. Calcite has a higher symmetry than aragonite. The atoms need to change their spatial arrangement, change their bonding, and this can be done only by giving the system enough energy (heat) so that the kinetic energy of the atoms is sufficiently large for them to break their bonds and rearrange themselves in the new structure. It is intuitive that there is an amount of heat above which the system changes easily, this critical value of energy is called activation energy, and it is usually given as a Boltzmann type exponential. For a system to change from one state to another it needs to pass through an activated state; in order to reach this activated state the system must gain energy, i.e. must gain the energy equal to the activation energy (Fig. 1). 

Fig. 1 For the system to change from the initial state to the final state it must surpass the activated state. In order to do so the system must gain energy, ΔG_a, the activation Gibbs free energy, for this example. From Introduction to Mineral Sciences

A negative free energy of a system is mandatory for the system to change but it is not a sole requirement. The mechanisms of change are also important and these depend on the energy input, the structure of the crystal (does it have defects or not), the path that the phase takes in its pressure-temperature window etc.

For example if we bring very slowly an aragonite crystal to the surface, and we bring it in a relatively high geothermal gradient then the chances are that it will transform into calcite. But if we bring it fast, even though the geotherm is high and the crystal lacks or has very few lattice defects than it can reach the surface as a metastable phase. Defects are important because they influence the entropy of the crystal, and they also provide good spots for nucleation.

            If we want to understand mineral processes then we have to take into consideration both thermodynamics and kinetics. In Introduction to Mineral Sciences, a book which I recommend for any student interested in mineralogy is a paragraph that explains very well the relationship between thermodynamics and kinetics:

“[…] thermodynamics predicts what ought to happen, but the kinetics of the processes involved will decide what will happen.”

            In a way, we, as geologists, should be thankful that the kinetics of mineral reactions is “getting in the way” of thermodynamics because without it we would have a very boring upper crust made up only of minerals and rocks stable in surface conditions, and we would have none or very few clues about the inner workings of our planet.

            The nature of mineral transformation is fascinating and complex, and it is also vital in the understanding of the processes that govern our planet, or any other planet for that matter; thermodynamics and kinetics are the perfect tools for understanding these processes.  

References: 

Introduction to Mineral Sciences, A. Putnis, Cambridge University Press, 2002

Hopefully this article will be published in the Bucharest Student Chapter magazine, and until further noticed it will be treated as such.