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Carbon exists in more than one allotropic forms, and the allotropes have different physical properties due to different arrangement of atoms. I am going to compare their hardness for now.

Below is the structure of graphene:

Source: Wikipedia article on Graphene

From what I read, graphene is hard but graphite is brittle.

  1. If graphite is made up of many layers of graphene, then why not graphite is stronger than graphene?
  2. I suppose when you say graphene (or diamond) is hard, it means that, for example, when you take a hammer to strike the layer of graphene, the layer is not easily broken, that is, the covalent bonds are hard to be broken by physical means.

By this reasoning, the layers in graphite are easily separated because they are held together by weak van der Waals forces, whereas it should be difficult for us to cut across the layers (in direction perpendicular to the plane of layers, cf: image below)

Does this mean that we can only cut the graphite in one dimension? I thought the graphite being brittle already implies that graphite can be cut in more than one dimension?

Original image source: Tirupati Graphite

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    $\begingroup$ By the way, you should not have problem crushing a large graphene sheet. .... $\endgroup$ – Alchimista Feb 9 at 8:32
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    $\begingroup$ A large graphene sheet, if not held in form by an underlying hard surface or otherwise fixed, crumbles up by itself. $\endgroup$ – Karl Feb 9 at 9:06
  • $\begingroup$ @Karl my point was to warn OP not to mix thinghs at molecular/nanoscale and material properties. Likely a pile of graphene sheets should be graphite. By the way, it would be nice to know the behaviour of graphene under is own weight. I think in principle it could extend quite far. $\endgroup$ – Alchimista Feb 9 at 9:47
  • $\begingroup$ @Alchimista Of course, the only thing "hard" about graphene is the E modulus. Btw. graphite has a 3D crystallographic structure. Randomly stacking sheets does not do it. And the first picture above is very misleading. A free graphene sheet is not flat. It forms undulations (a "bumpy" surface), and if not fixed at the edges, it crumbles up. $\endgroup$ – Karl Feb 9 at 9:58
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Hardness and brittleness are not contradictory properties. There are plenty of substances that are both hard and brittle (cast iron is a good example, glass is another).

And "strength" is different as well. It depends on context. Tensile strength is not necessarily related to ability to survive a blow: some compounds with high tensile strength (which basically means the compounds resist being stretched) are incredibly fragile (or brittle if you prefer that term). Some compounds with low tensile strength are very hard to break (nylon rope, for example).

Part of the problem is that many of the properties of materials are based on the structural properties of the bulk material not the idealised properties of the chemical bonds making up the material. Some metals, for example, are tough (not brittle) and are hard to break but this property arises because defects in the crystal structure can move around absorbing external stress. Brittleness is often caused because no such mechanism exists and, once a surface bond breaks, the stress on the next bond gets worse, releasing energy and propagating a crack, tearing the material apart. Glass often has many small surface cracks which, under tension, concentrate stress making them brittle and subject to falling apart. But very pure, carefully grown glass fibres can be nearly crack-free making them much stronger under the same stress. In short to explain brittleness, toughness or strength, you need to know the macroscopic makeup of the bulk material not just the chemical composition.

So it is with graphite. There is no easy mechanism in a single graphite crystal to dissipate stress if a bond breaks, so it will tend to be brittle. But most samples of graphite are not single crystals: in most cases they will consist of a bunch of small units with the layers oriented in different directions. So bulk graphite isn't just brittle but also soft as some orientations will slide easily around. And it is hard to even talk about bulk graphene because by definition it is a single layer or a very thin bundle of layers. When people say graphene is strong they usually mean that it has high tensile strength along the plane of the layers. This doesn't mean it isn't either brittle or hard and even if it were in some orientations, it probably would not be in others.

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(That graphene is "hard" is a somewhat dubious (or ambiguous) statement. It's true that it is has a high ($E$) modulus when you pull evenly in the direction of the plane. Under all other attempted deformations, it breaks almost instantly.)

The planes of graphite are easily shifted against each other. That means if you try to bend it, the individual planes cannot support each other and distribute the load. In a solid 3D structure like diamond or wood, the outer layers would just feel a linearly increasing extensional force, and the inner layers an increasing compression.

Not so in graphite, the few innermost layers at the bend get all the load, and snap. And then the next few, and so on. Graphite, despite being rather soft, is brittle.

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The layers in graphite are not perfectly aligned. They are aligned in many different directions, meaning that they can slide across each other if you apply a force in any direction. But for graphene, obviously the atoms are perfectly aligned on the hexagonal network, so it is much stronger.

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    $\begingroup$ Graphite layers are well aligned, in two different crystallographic stackings, and defect forms (alternating between the two different stackings). $\endgroup$ – Karl Feb 9 at 9:11

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