science

Diamonds and Graphite: Thermodynamics vs Kinetics

Your engagement ring should slowly become pencil lead. Thermodynamics says so. Kinetics says not yet, and kinetics has the bigger number.

At room temperature and pressure, graphite is the more stable form of carbon. Diamond turning into graphite has ΔG ≈ −2.9 kJ/mol, so the change is thermodynamically favoured. It doesn't happen on any human or geological timescale, because the conversion has to break and rebuild a rigid network of covalent bonds, and the energy barrier for that is enormous. Diamonds are metastable. They're "forever" only because kinetics says not yet.

Graphite wins, diamonds stay

Here is the uncomfortable conclusion of the free-energy tables: your engagement ring should slowly become pencil lead.

It doesn't. Most natural diamonds are between 1 and 3.5 billion years old, formed 150 to 250 kilometres down in the mantle (Wikipedia). They have spent most of the age of the Earth in a state thermodynamics disapproves of, and they look fine.

This is the cleanest example in chemistry of the difference between what should happen and what does happen. The first question is answered by Gibbs free energy. The second is answered by kinetics.

The thermodynamics: a small, honest number

Standard data for carbon at 298 K and 1 bar (OpenStax Chemistry 2e, Appendix G):

Graphite: ΔH°f = 0, S° = 5.740 J/(mol·K)
Diamond: ΔH°f = +1.89 kJ/mol, ΔG°f = +2.90 kJ/mol, S° = 2.38 J/(mol·K)

So, for diamond relative to graphite:

ΔH = +1.89 kJ/mol

ΔS = 2.38 − 5.740 = −3.36 J/(mol·K)

ΔG = ΔH − TΔS = 1.89 − (298.15 × −0.00336) ≈ +2.89 kJ/mol

That matches the tabulated +2.90 kJ/mol. Diamond sits about 2.9 kJ/mol above graphite. Run the arrow the other way and diamond → graphite has ΔG ≈ −2.9 kJ/mol.

Both terms point the same way. Graphite has lower enthalpy, and it has higher entropy: its stacked sheets give its atoms more ways to hold and spread vibrational energy than diamond's stiff 3D lattice. If you want the deeper reason that extra entropy counts, it is in the essay on what entropy actually measures. Because ΔH and ΔS agree, there is no temperature at 1 bar where diamond becomes the stable phase. Heat only widens graphite's lead, because the −TΔS term grows with T.

The barrier: why "favoured" isn't "happening"

A negative ΔG is permission, not a schedule. In thermodynamics, a spontaneous process isn't necessarily a fast one, and diamond is the textbook proof.

To become graphite, diamond's carbon atoms have to leave a tetrahedral network, in which each atom is bonded to four neighbours, and reorganize into flat hexagonal sheets. Atoms have to break free of the lattice before anything new can form.

How big is that barrier? In 1972, Gordon Davies and Trevor Evans heated natural diamonds to between 1,850 and 2,000 °C at zero pressure and measured how fast they turned into graphite. They found activation energies of 728 ± 50 kJ/mol on {110} crystal faces and 1,159 ± 75 kJ/mol on {111} faces. They proposed that the rate-limiting step is the detachment of a single carbon atom from the diamond surface (Davies & Evans, 1972).

Those are huge numbers next to ΔG. The prize for converting is 2.9 kJ/mol; the price of admission is at least 728.

To see what that means at room temperature, look at the Boltzmann factor, exp(−Ea/RT), the fraction of attempts with enough energy to get over the barrier. With the lower measured value:

Ea / RT = 728,000 ÷ (8.314 × 298.15) ≈ 294

exp(−294) ≈ 10⁻¹²⁸

Roughly one attempt in 10¹²⁸ has the energy it needs. On the {111} faces it is about one in 10²⁰³. Two caveats keep this honest. The activation energies were measured near 2,000 °C, so applying them at 25 °C is an extrapolation. And a full rate needs a prefactor for how often atoms make attempts, which changes the answer by some orders of magnitude but not by a hundred. Either way, the rate at room temperature is effectively zero: far slower than anything on the timescale of the universe. As the standard summary puts it, at room conditions diamond "is metastable and converts to it at a negligible rate" (Wikipedia).

(An earlier version of this page gave an activation energy of about 540 kJ/mol and a rate constant of 10⁻⁷⁰ per second. Neither had a source, and the second didn't follow from the first. The measured values above replace both.)

Metastability is everywhere

Diamond is metastable: stuck in a local minimum of free energy, not the global one. Picture a ball resting in a dip halfway down a hillside. The bottom of the hill is lower, but to get there the ball first has to climb out of its dip.

The world is full of such balls. Liquid water can be cooled below 0 °C without freezing if nothing gives the ice a place to start. Wood and paper sit in air for centuries, though burning them would release a great deal of free energy. You are in the same position. Nearly every organic molecule in your body would be lower in free energy as carbon dioxide and water. What keeps you, your furniture and your jewellery intact is not thermodynamic approval. It is barriers.

Making diamonds: pressure flips the winner

So how does diamond form at all? Pressure. Diamond is denser than graphite, and at constant temperature the free energy of a phase rises with pressure in proportion to its molar volume. Squeeze hard enough and the compact phase wins.

The equilibrium line between graphite and diamond is well established: it runs from about 1.7 GPa at 0 K to about 12 GPa at 5,000 K, where graphite, diamond and liquid carbon meet (Wikipedia). Above the line, diamond is the stable phase. The same logic of a stable phase changing as conditions change governs every phase transition, from ice to steam.

Nature does this in the mantle. Diamonds then reach the surface in volcanic eruptions that deposit them in rocks called kimberlites and lamproites, much more recently than they formed: hundreds to tens of millions of years ago (Wikipedia). Once they are out of the mantle, the barrier keeps them as they are.

Laboratories have two main routes (Wikipedia):

High pressure, high temperature (HPHT). Large presses reach about 5 GPa at 1,500 °C. Molten metals such as nickel, cobalt or iron act as solvent-catalysts, dissolving carbon and speeding its conversion to diamond. That catalyst is kinetics at work: it lowers the barrier rather than changing the destination.
Chemical vapour deposition (CVD). Carbon atoms from a plasma are deposited onto a substrate and build diamond layer by layer, at pressures where graphite is still the stable form. This one is pure kinetic steering.

Thermodynamics also explains why diamond conversion is hard even in the right conditions. Rapid conversion of graphite to diamond needs pressures well above the equilibrium line; at 2,000 K, around 35 GPa (Wikipedia). Being on the right side of the line makes diamond favoured. It doesn't make it fast.

Heat it, and it finally converts

Kinetics is exquisitely sensitive to temperature, because temperature sits in the exponent. Using the same 728 kJ/mol barrier, raise the temperature to 1,900 °C (2,173 K) and the Boltzmann factor goes from about 10⁻¹²⁸ to about 10⁻¹⁸. That is roughly 10¹¹⁰ times more attempts succeeding. Which is why Davies and Evans could watch diamonds graphitize in their furnace in the 1,850 to 2,000 °C range, in an experiment instead of an eternity (Davies & Evans, 1972).

Oxygen offers a faster exit. In pure oxygen, diamond ignites somewhere between about 690 and 840 °C, with smaller crystals burning more easily, and a clear, flawless stone converts completely to carbon dioxide. In ordinary air the flame goes out once the heat source is removed, because the oxygen is diluted by nitrogen. A house fire or a blowtorch is hot enough to do the damage; a cigarette lighter is not (Wikipedia). Jewellers resizing a ring keep that in mind.

A world held together by "not yet"

Stability and permanence are different things. Thermodynamics tells you which state is lowest. Kinetics tells you whether you will ever get there. Most of the solid, familiar world, from rings to bones to the paper in old books, lives in the gap between those two answers.

The pebble: every diamond is a thermodynamic debt that has been accruing for a billion years, and kinetics is the most patient creditor there is.

FAQ

Do diamonds eventually turn into graphite?

At room temperature and pressure, thermodynamically yes; practically no. The conversion is favoured by about 2.9 kJ/mol, but the activation barrier (measured at 728 kJ/mol or more) makes the rate effectively zero.

Why is diamond stable if graphite has lower free energy?

Diamond isn't stable; it's metastable. It sits in a local free-energy minimum, separated from graphite by a barrier so high that almost no atoms get over it at ordinary temperatures.

Can you burn a diamond?

Yes. Diamond is carbon, and it burns to carbon dioxide. In pure oxygen it ignites at roughly 690 to 840 °C. In air, combustion stops once the heat is removed, but house fires and blowtorches are hot enough to damage one.

How are synthetic diamonds made?

Mostly by HPHT, using presses at about 5 GPa and 1,500 °C with a molten-metal solvent-catalyst, or by chemical vapour deposition, which grows diamond from a carbon plasma onto a substrate.

What does "metastable" mean?

A metastable state is one that is not the lowest-energy option but persists anyway, because getting to the lower state requires crossing an energy barrier. Diamond, supercooled water and most organic matter in air are all examples.