Concrete may have found it's killer app in graphene (and carbon nanotubes), but don't underestimate the power of carbon – it's still the one element that's capable of surviving the highest temperature of any other chemical element, and can react with all three others.
However, most carbon allotropes are so thermodynamically stable that they're used almost exclusively in extreme environments, in which case only the three listed in the following table will come into play. The other carbon compounds usually only contain carbon, hydrogen, oxygen and nitrogen.
(There's no point having a carbon allotropes list if no one ever bothers to look at it. I wrote about this a while back, so let's continue with the same table)
The diamond or graphite (c-C, diamondoid) allotrope of carbon is, for one, very stable, which is why its one of the hardest substances known. The graphite allotrope of carbon is a layered, stacked arrangement of multiple planes of graphene. Both diamonds and graphite have very high melting and boiling points.
The other allotrope of carbon – the cubic (c-C) allotrope of carbon – is a thermodynamically stable solid. The carbon cubic allotrope of carbon is often referred to as "wurtzite", which is also a layered solid.
The other allotrope of carbon is tetragonal (t-C) allotrope of carbon. This allotrope of carbon has the same crystal structure as diamond and hexagonal boron nitride (hBN). It has a layer-by-layer structure made of octahedral boron atoms in the middle and tetrahedral nitrogen atoms on either side. The cubic carbon allotrope of carbon is thermodynamically unstable.
Then there's amorphous carbon (a-C). This allotrope of carbon is not crystalline. It has none of the characteristics of the other carbon allotropes. It's a solid-like amorphous carbon. It is not as thermodynamically stable as the other allotropes of carbon. However, it is much harder than graphite. It is the hardest known allotrope of carbon.
(As a brief aside, the allotrope of carbon with a spongy, sponge-like, 3D structure is actually diamond an cubic boron nitride (c-BN) with a small inclusion of amorphous carbon. It's just a bit denser, stronger, and stiffer than diamond. BN's high hardness makes it very hard, so it isn't surprising that it is even harder than diamond.)
Amorphous carbon, having no structure, is difficult to classify as a type of allotrope of carbon because of its non-crystalline structure, but it still makes up the bulk of organic material (see, a small chunk of it has this shape).
What about diamond, graphite and amorphous carbon? Diamond is the hardest known allotrope of carbon. Amorphous carbon is not as hard as diamond, but it is still much harder than graphite. It is the hardest known allotrope of carbon. And while the graphite allotrope of carbon is also stable and even finds many uses in daily life, it is not as hard as diamond. It's hard enough to protect diamonds from thermal shock in a fire, but it's not a serious hard material by any means.
Here's a short video to give an idea of how graphite is formed from crystalline carbon – a long slow process that requires intense heat, pressure and a strong presence of a catalyst.
While graphite will grow at any temperature, it's not as thermodynamically stable as diamond, so the formation of graphene (which is itself a very thermodynamically unstable form of carbon) only occurs at extremely high temperatures.
Once again, the diamond allotrope of carbon is the most stable allotrope of carbon, which makes it extremely hard. And there's a nice explanation to that: a cubic diamond is the most thermodynamically stable form of carbon because of its tetrahedral structure.
The hexagonal diamond is close behind, and this is due to the fact that the graphene structure, which is like layers of graphene, forms very close to the diamond structure.
One consequence of this is that some diamonds have grown in and around volcanoes. Not all the carbon gets incorporated into the diamond as a result of a volcano eruption. There will be a layer of graphite on top of the diamond at the side where the eruption took place.
It's just that the diamond grows extremely fast compared to the other carbon allotropes.
Amorphous carbon (a-C) is in many ways like graphite. However, diamond is more cubic and hexagonal, whereas graphite is layered and layered. (In the case of graphite, the graphene structure resembles, to a great extent, the diamond structure.) So, diamond is more cubic and hexagonal than graphite, which is again like a lattice of graphite.
Diamond and graphite are both hard materials – the most hard materials known to man, in fact.
What about a-C and cubic BN? Diamond and cubic boron nitride are very hard, but again, not as hard as graphite and diamond. One way you can tell whether a material is hard is by measuring its yield strength, that is, the amount of force you have to put on the material to deform it. Diamond has the highest yield strength of all known solids.
These materials are the hardest known materials we know.
So, the high-temperature formation of carbon compounds is an important aspect of their properties. It forms graphite, which is thermodynamically unstable and is what we call a hard, thermodynamically stable allotrope of carbon (see: the table above).
(If you want to take the concept a bit further, allotropes of carbon are thermodynamically stable only in the environment they're found in, otherwise they will revert to each other, forming the other stable allotropes of carbon. This makes things really complicated, but, for the simple carbon compounds, one stable allotrope exists and makes for easy explanations)
The tetragonal carbon allotrope is hard, but it's more thermodynamically unstable than graphite and diamond, so it doesn't last very long. BN is the hardest known material because it's cubic, but it's much more unstable. It reverts to diamond and graphite more easily.
What about a-C and cubic BN? They're tough as nails, but not as hard as diamonds and graphite. Their high strength is due to the fact that they're really hard, and can be a lot more tough than, say, cubic boron nitride.
This graph is kind of a pain, so bear with me and try to stick with it.
Diamond and graphite are the hardest known materials, and they're harder than diamonds and graphite. Amorphous carbon, in contrast, is the hardest known material.
Now you might be wondering why the others aren't mentioned. Well, the cubic boron nitride allotrope of carbon and diamond aren't listed because they're not found on Earth, while the other three are.
The "wurtzite" carbon allotrope of carbon was discovered by Wurtz in 1886, and the "anthracite" carbon allotrope of carbon was discovered by Fischer in 1891. This is because Fischer's "wurtzite" carbon allotrope of carbon was actually cubic, making it in effect a diamond allotrope of carbon.
Even though Fischer's allotrope of carbon was discovered first, it's the allotrope of carbon called "anthracite" that's the one of the hardest known allotropes of carbon.
Came here to look for allotrope of C-B 2N and found the answer by accident while surfing.
What is interesting about this graph is that while the cubic BN allotrope of carbon is the hardest, the "wurtzite" carbon allotrope of carbon is actually harder.
What's interesting is that the diamond allotrope of carbon is thermodynamically stable and is the hardest known substance. However, the graphite allotrope of carbon is thermodynamically stable, and it is actually more thermodynamically stable than diamond.
So, while the most stable allotrope of carbon is diamond, it's the most thermodynamically stable carbon allotrope is graphite.
So why isn't it diamond? Why does it only make up carbon, hydrogen, and oxygen?
Well, because the cubic diamond allotrope of carbon is also the most thermodynamically stable allotrope of carbon.
In other words, they're both the hardest known allotropes of carbon. The only reason the graphite allotrope is more stable than the diamond allotrope of carbon is that the graphite allotrope of carbon has a higher density, so it doesn't expand and contract as much.
Both diamonds and graphite are very hard. Their hardness can be measured using a "Nanoindentation Hardness Tester" (in which the hardness is calculated from indentations made with a tiny pin) or a "Durometer". Either way, a harder material will show indentations that have smaller tops and deeper bottoms than a softer material.
In reality, graph
