Subject: The whole truth about hard material scratching softer material

In elementary school, we are taught the one-through-ten scale of hardness with
the explaination that harder things scratch softer things.

However, that can't be the whole story, or saw blades would never wear out.  My
gut feeling is that any two materials scratch each other, at some function of
the relative hardnesses.  So, iron will "scratch" wood to the point of producing
many pounds of sawdust, while the wood scratches the metal by a microscopic
amount that will eventually be noticed.

So, what is the function?  And what mechanisms account for it?  If a non-ductile
material such as a diamond crystal is abrading a target, does one atom of carbon
get knocked out every so often, by chance?  Is there a point where the diamond
would never wear at all, if cutting something soft enough slowly enough?

Likewise, in a ductile material like steel the atoms of metal move around and
the edge deforms.  Does it move at a microscopic rate constantly, or do the
atoms only fit in certain positions and it can only change by a "jump" or not at
all?

Either way, how does a hard material wear when the rate of wear seems to be
smaller than the discrete structure of the material would allow?

Re: The whole truth about hard material scratching softer material