Re: What is the sharpest substance on earth?

Sharpness is one of the ways we describe how materials behave. But unlike ideas 
like hardness, sharpness relates to particular objects rather than to materials 
as such. A steel blade is sharp, but a steel hammer head is not. So to make the 
question a question about materials, we would have to re-word the question:

--What material should we use to make the sharpest possible object?

There is still a problem. Sharpness is not a term that has been taken over from 
everyday language by scientists and given a scientific definition. Other terms 
like strength, hardness, toughness of materials have all been taken over and 
given strict definitions, so that we can make precise measurements and say that 
one material is harder than another, or that it is stronger in compression, or 
less strong in tension.

What do we mean when we say that one blade is sharper than another? We could 
think of defining it as the ability to produce a cut in a softer material with 
minimal force. Even then, the answer we get might depend on the context. A 
scalpel is good at cutting matches, but a chain saw works better on pine trees! 
the size scale we are operating on is an important factor. The type of material 
we are cutting also makes a difference. Toolmakers shape lathe tools differently 
depending on what material they will be working on. And even the speed of the 
cutter can be important. The tooth shape, and even the optimum material might be 
quite different for handsaw and chainsaw blades.

Yet another problem is that mostly we think of "sharp" in terms of cutting, but 
occasionally in terms of puncturing (a "sharp" needle).

To give you some sort of satisfying answer to your question, I will suppose that 
you are wanting to know the best material for cutting

-- on a small scale, possibly even microscopic.
-- a wide variety of materials, but not including any particularly hard ones
-- with a relatively low cutting speed, for hand operation for example.

Translating that into molecular-scale properties, we are wanting a material that 
is very hard, not too brittle, and that can be worked to a very fine edge. The 
optimum is probably one of the refractory metals, e.g. tungsten or iridium. These 
metals can be worked to an edge or a point just a few atoms thick. For practical 
purposes it would be supported as an edging or a composite in or on a very strong 
material, such as tungsten steel. Another very sharp type of blade on this or a 
slightly larger scale uses an extremely hard material like diamond dust or 
carborundum on a steel support.