[pnacze199204]

Wikipedia says that diamond converts to graphite at ~700 °C. But then, in the same article we can find an information: "But diamonds (sp3C) are unstable against high temperature (above about 400 °C (752 °F)) under atmospheric pressure. The structure gradually changes into sp2C above this temperature". I'm a little bit confused. Does that mean that the surface of diamond is more susceptible to high temperatures or what? What would be the temperature in which this mineral starts to change its structure? Thank you for helping me!

[Corribus]

You can check out the phase diagram of carbon to see what phases are most stable as a function of temperature and pressure. Note, this only reflects thermodynamics, not kinetics. So, for example, the diamond phase can exist indefinitely at low temperature and pressure, because of the large activation energy for transformation of diamond to graphite.

http://www.bris.ac.uk/Depts/Chemistry/MOTM/diamond/diamond1.htm

[pnacze199204]

Thank you for replying me! We all know that diamond is one enormous molecule of Carbon and in one of the Physics handbooks I found the information, that the oxidation and graphitization of diamond is practically impossible at standard conditions. I read also that the transformation of diamond into graphite starts at temperature of  ≈700 ∘C. But today I've entered Wikipedia and I've found the two information, one of them in the section of "Surface Property" when it is said that diamond  are unstable above 400 ∘C. I thought that it would be related with Hydrogen and Oxygen termination of the diamond surface. I'm asking because I would like to know at what temperature diamond film starts to graphitize and at what temperature the reaction would be impossible to happen.

P.S. Sorry for my English, it's not my native language and I'm still learning it

[Corribus]

If you view the phase diagram in the link I provided above, you can see that as temperature increases, graphite is more thermodynamically favored even at moderately high pressures. E.g., if you start at a pressure of 5 GPa and ambient temperature, diamond is the thermodynamically favorable form. But as you increase temperature, you will eventually come to a point (maybe around 1500 C) where graphite becomes the more thermodynamically favorable form. It is important to note that this doesn't necessarily mean that a diamond held at 5 GPa will suddenly change to graphite at 1500 C! It just means that eventually (be it 5 seconds or timescales longer than the age of the universe) under these conditions, the equilibrium state will favor graphite.

You can link the wikipedia article you are referring to if you want - it is hard to comment on text I haven't read.

The question, "When does such and such a process begin?" or "when is the process impossible" doesn't make a lot of physical sense. If you have a diamond ring right now, and graphite is the thermodynamically favored state at ambient conditions, then the conversion process has begun. The process begins as soon as the system is created. A nonequilibrium state is always spontaneously moving toward equilibrium. But, the conversion rate may be imperceptibly small due to the large kinetic barrier of the process.

[pnacze199204]

Here's the article: https://en.wikipedia.org/wiki/Diamond

If it has no sense to ask when does the process begin, then why so many papers indicate that the transformation STARTS above 700 C? I don't get it. I know that the process is happening all the time and that it is extremely slow, but I thought maybe there's a temperature at which the surface of diamond starts to graphitize immediatelly or something like that.

[Corribus]

Here is a good example of being careful with Wikipedia. If you actually go to the link, you will see the cited paper is about oxidation of diamond surfaces, not transformation to graphite. This is a chemical oxidation process and seems to have little relevance to the direct phase transition of diamond to graphite. As to why it "begins" at 700 degrees: the figure in the paper shows that indeed oxidation of the diamond surfaces, as determined by weight loss of diamond in TGA as a function of temperature, becomes significant around this temperature. Note even the Wikipedia article says "approximately" (or "~"). Certainly from the figure shown in the cited paper (pasted below), you can't pick a single absolute, nonarbitrary temperature where the process "begins". The rate of oxidative decomposition just seems to become significant around this temperature (and it's a nice round number - we love those!). This temperature, as argued in the paper, is related to the activation energy for the oxidation process in air. Once the temperature gets high enough, a high probability of reaction events have enough energy to surmount the transition state energy and result in product conversion. Note that statistical mechanics are a probabilistic process - an inspection of the data show that some reaction events occur below 700 degrees C, because there are always a statistical distribution of molecular/atomic energies at every temperature. The point at where the reaction "begins" could be approximated as that were (XXX%) of them have enough to proceed to products. You can define XXX% however you want - there's no right answer. Even at room temperature there is a finite chance of one oxygen molecule somewhere oxidizing a diamond carbon atom. So the process never really "begins" at a discrete temperature - and, in a closed system, the process doesn't "end", either.

[pnacze199204]

Thank you!
So do I understand well that the activation energy accelerate the process of oxidation and graphitization of diamond and it still can happen spontanouesly without input of energy, but at the long period of time? Somewhere I've read that at standard temperature (25°) they can persist more than millions of years. What if I heated up diamond to 100 °C? I suppose the reaction would be faster, but would it be significant difference? Or a significant difference would start at approximately 450 °C as said in the paper? I know my questions may seem stupid, but I have nothing to do in my live with Chemistry or Physics and I would like to understand it well.

[Corribus]

No background in chemistry or physics? No problem!

But that does help to orient me a little bit. I’ve been throwing out some words that probably don’t mean a whole lot in that case. So let’s back up.

A process of going from diamond to graphite is something like this. Let’s say you have a herd of goats and there is a great grassy pasture a few miles to the east. Your goats naturally want to graze there because it’s good eating. If all your goats start off this morning going in the direction of the food, and let’s assume they all move independently (their motion to the food source is not dependent on following other goats), how long will it take for all the goats to arrive at the food?

You can imagine two scenarios – one in which there is a small hill between the herd and the grassy field, and one in which there is a big mountain in the way. In both cases the goats want to end up in the grassy field, because it is a state of lower energy (grass tastes good). But it is easy to understand that if there is a big mountain in the way, the chances of any goat making it to the field becomes small, such that the amount of time it takes for the whole herd to make it there is long. The rate at which the herd moves is inversely related to the height of the mountain. On the other hand, the rate may also depend on how hungry the goats are – if they are more motivated, they might be speedier about climbing over that mountain to get to the food.

In this analogy, the goats are carbon atoms. Initially, hungry goats are carbon atoms in diamond and full goats (gorged on yummy grass) are carbon atoms in graphite. All things being equal, the goats will end up at the grassy field because that’s the state of lower energy. Diamond will change to graphite. But there’s a mountain in the way. A big mountain. So big that the goats are very unlikely to cross over the mountain and get to the field. The question is: can we make them sufficiently hungry so that they cross the mountain on a realistic timescale?

The mountain is the “activation energy”, which is a characteristic of most chemical reactions – and indeed, most of life’s tasks. Even if the reaction is favorable, sometimes you have to put some energy in to get payoff later on, and the more energy you have to put in, the slower the reaction is, even if the payoff is large. (A good example of this is combustion – despite the fact that burning a carbon fuel releases a lot of energy and is very thermodynamically favorable, the reaction is very slow. A temperature of a few thousand degrees is necessary to make this reaction happen on any relevant timescale!)

Reaction mechanisms are complicated, even more so in the solid state, where surface characteristics become a factor of concern, but a simple model is the Arrhenius model, which fits to a surprisingly large number of chemical reactions, and also has been applied to many non-chemical processes. (I learned, while looking around for information on diamond to graphite, that is has even been used to model the blooming of Japanese cherry trees – who knew?! See: https://en.wikipedia.org/wiki/Cherry_blossom_front).

This will be the only equation I present, but it’s important:

[tex]rate = Ae^{-\frac{E_a}{RT}}[/tex]

The Arrhenius expression basically says this: the probability that a molecule (or whatever) will go from one state to another is related exponentially to the relationship between how much energy you need to make that transition happen and how much energy on average the molecules have by virtue of the temperature. In the expression, the rate is a function of: an activation energy, E_a; the temperature, T; the gas constant R; and a pre-exponential factor, A.

E_a is the height of the mountain – I.e., how much energy you have to put into a reaction to get payoff.

RT is a kind of measure of the amount of average thermal energy. In our analogy, this is how hungry the goats are. Higher temperature means more hungry and more motivated.

A is a measure of a lot of things, like, the probability that two reacting molecules are colliding from the right direction, stuff like that.

Generally, E_a and A are assumed to not be dependent of temperature, which is a good approximation for small changes in temperature. Anyway, what the Arrhenius equation basically says is that if the activation is large, the rate goes down, and if the temperature is high, the rate goes up. And those trends are highly exponential – a small change in activation energy makes a big change in rate. Now, there is a lot of chemistry and physics involved in determining what E_a and A are, but unless you want to go there, let’s ignore it and just play with numbers.

Not surprisingly, the transition from diamond to graphite is complicated. But I found some numbers we can play around with just to give you a sense of scale.

From the reference: G. Davies and T. Evans. Graphitization of diamond at zero pressure and at a high pressure. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 328, No. 1574 (Jun. 13, 1972), pp. 413-427

These guys basically took real diamonds, heated them in a vacuum at around 2000 degrees C), and measured the mass loss due to graphitization as a function of time. By measuring the reaction rate at different temperatures, they calculated an activation energy of around 730 kJ/mol for a particular crystalline plane of diamond.

You may not have a good sense for these things, but let’s be clear: that is a HUGE activation energy. It may at first seem strange that the energy mountain would be so large – after all, you are just taking carbon atoms and shifting their positions a little bit. In fact, the carbon atom arrangement in diamond is quite different from that of graphite, and so going from one to the other requires breaking a lot of strong carbon-carbon bonds, then rearranging them in space to form new ones. This is why the activation energy is so large. At 2000 degrees, of course, there is quite a bit of energy around to break bonds, and so the process happens over the course of a few hours at 1850 C, down to a matter of minutes at over 2000 degrees C.

Ok. What about at room temperature? Millions of years is actually probably a huge underestimate. Here’s where it takes a little bit of fudging the numbers and some big assumptions – namely that the activation energy and pre-exponential factors are the same at room temperature as they are at 2000 degrees. Plus I had to fudge a pre-exponential factor because the authors don’t directly report it in the paper. But if we bear in mind this aspect of crudeness, you can use the Arrhenius equation and project that at room temperature, the rate of graphitization is on the order of 1 x 10^-114 μg/s! Let’s put that in perspective. A 1 carat diamond weighs about 200 mg (200,000 μg). It would take on the order of 1 x 10¹¹⁸ s for the diamond to be completely graphitized. Or 1 x 10¹¹¹ years. That’s really a number beyond comprehension, so many times longer than the age of the universe that it doesn’t even bear thinking about.

Now, that number is based on such a crude calculation that it's probably very inaccurate, maybe off by dozens of orders of magnitude even, but I think it does at least show the sense of scale here. Truly, diamonds are (practically) forever. Unless you heat them to 2000 degrees, in which case you will get pencil lead in less time than it takes to watch  Sean Connery and Charles Gray duke it out over a diamond-powered death satellite.

[Enthalpy]

After checking Wiki's article... https://en.wikipedia.org/wiki/Diamond#Surface_property

There are two different ideas.
Diamond's oxidized surface can be reduced (=de-oxidized) but this needs a high temperature.
And the temperature is limited, anywhere in diamond, because of the transformation to graphite.
Wiki didn't detail this logic, that's confusing. A priori, no special risk that the surface is more sensitive to heat.

In case someone wants to de-oxidise a diamond surface, a logical action would use a reducing compound that acts at a temperature lower than molecular hydrogen needs. Something like a hydrogen plasma, or a liquid alloy that does not dissolve carbon (is there any?), or a molecule easily giving hydrogen atoms...

[pnacze199204]

Very interesting, thank you! So, what would happen  to diamond first if we left it at ambient temperature and pressure- it would turn into graphite or evaporate? Which of those two reactions occur more rapidly?

[pnacze199204]

Because if I understand well, there exists a possibility that the carbon atom on the surface of diamond would transform into CO2 even without input of energy, but it would require a lot of time, am I right? So at the ambient temperature and pressure, what would happen first? If we had eternity to check this, which of the two reaction would be faster? Diamond turning into graphite or diamond evaporating?

[pnacze199204]

On https://physics.stackexchange.com/questions/215950/diamonds-are-not-forever I found very interesting question;

"It is frequently stated that although graphite is the more stable allotrope of carbon at STP, the activation energy of the diamond-to-graphite transformation is so high that our diamonds will never spontaneously turn into black dust.

Some sources add (correctly) that nothing is ever never, and reactions merely slow down with lower temperature, they never stop entirely. (The Arrhenius equation comes here). But nobody ever quantifies the non-neverness of the death of a diamond. So my question is:

Under normal conditions at room temperature, which of the following will happen first; when, and how fast?

Diamond transforming to graphite.
Diamond evaporating. Marshall and Norton ,J. Am. Chem. Soc., 1950, 72 (5), pp 2166–2171, seem to say that latent heat of carbon is 170kcal/mole, but I haven't got access to the whole paper to see what they say about the rate of evaporation.
Diamond spontaneously combusting to CO2.
Carbon decaying to iron via tunnelling. Barrow and Tipler, in The Anthropic Cosmological Principle (Oxford, 1986), p.654, quote 10^1500 years for this."

[Corribus]

At room temperature, all those processes are so slow as to be effectively the same: no change observed. I mean, you're talking time frames longer than current lifetime of the universe, so it's splitting hairs. This makes it incredibly hard to compare experimental rate constants, which may variously depend on a lot of factors, including the different crystalline faces of diamond, oxygen concentration/atmospheric pressure, temperature changes, and so forth.

[Enthalpy]

In contrast, the oxidation of the surface happens immediately at the timescale of our sensing abilities.

This does not mean "carbon dioxide". The last atoms in a solid have "pending bonds" that are not satisfied by the rest of the crystal. These pending bonds are extremely reactive and catch about any other atom that passes by. In the air, it can typically be an oxygen atom. At a surface, you have badly defined and varying terminations, which can be -OH for instance.

These terminations are not CO₂. Only one bond from C is with the surface species, the rest is with other C atoms in the depth. The surface C atom is correctly called "oxidized" in this state despite it forms neither monoxide nor dioxide.

Even over the layer that saturates the pending bonds, you have a few layers of adsorbed molecules. These make no chemical bond with the crystal but hang by intermolecular forces. They can be desorbed more easily, their composition resembles the one of the surroundings and varies more easily over time.

[pnacze199204]

Ok, so does that mean that the surface of diamond can change slowly its structure over time and just dissapear? I mean, you have those pending bonds and C atom is oxidized, so as you said it can react more easily. I suppose that atom can be kicked out and step by step the mineral can just dissapear over time or change completely. Am I right?