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.
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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, ΔGa, 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.
