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I'm wondering if a given solid material can, in general, score or cut the same material, when applied by (at most) human muscular strength.

I've tried searching for this online, but it seems like a difficult-to-express search target. For example, the site Answers.com has a brief entry:

Q: What mineral can scratch diamonds?

A: The mineral diamond can scratch diamonds.

There's no further elaboration or justification at that site.

My question differs from prior somewhat-related questions on SE Physics, because those answers all end up addressing cases where the cutting material is accelerated to very high (possibly relativistic) speed. The present question is only about whether a limited amount of solid material, hand-held by a person, and applying only normal muscular strength, can generally visibly score or cut the same kind of material, within a few seconds to a minute of time (but assume the cutting material might be sharpened to a high degree).

Is there any general rule for what kind of solid materials can cut themselves in this way?

Daniel R. Collins
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The material quality you're looking for is hardness. The Mohs Hardness Scale is an empirical table of minerals sorted by hardness. Two materials are said to be the same harness if each can scratch the other. A homogeneous or mostly homogeneous solid, like diamond, has an identifiable hardness. A nonhomogeneous solid, like concrete, does not.

A solid-liquid mixture, like a tomato, or a solid-gas mixture, like aerogel, does not. Nonhomogeneous Solid mixtures like concrete will scratch like their hardest component and be scratched like their least hard component. Solid-liquid and solid-gas mixtures may also crush, tear, or burst, unrelated to scratching.

So: if an object has a well-defined hardness, it can scratch itself because it has the same hardness as itself. And an object has a well-defined hardness if it is a homogenous solid.

g s
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  • Minor remark: Granite is not homogeneous and its constituents have different hardnesses. It has large grains of different minerals (typically feldspar, quartz and plagioclase) visible by the naked eye. See wikipedia. – Sebastian Riese Oct 19 '21 at 18:16
  • Two samples of the same material will have the same hardness. Does that imply that they can scratch each other? Your answer addresses a different question: if two materials can scratch each other, do they have the same hardness. (Yes) The converse is not necessarily true. – garyp Oct 19 '21 at 18:17
  • SebastianRiese - thanks, I replaced with a better example. garyp - I edited my answer to include explicitly what I thought was already implied. – g s Oct 19 '21 at 22:44
  • This is interesting, but I'm not sure it directly addresses the issue of material-on-same-material. E.g., the Wikipedia article on the Mohs scale never addresses same-hardness materials; it addresses only unequal types. Do you have a citation that equal-hardness types scratch each other? Or better, like-materials? – Daniel R. Collins Oct 20 '21 at 03:18
  • @DanielR.Collins I don't have a reference, just recalling school. Personal experiments are easy, though. This sort of experiment isn't especially precise but anybody can do it. Just now I used a plastic table knife on a plastic spoon (yes); a steel table knife on a steel fork (yes); a chipped ceramic mug on a glass mug handle (yes), and the sharp edge of an aluminum soda can tab on the base of the can (yes). This exhausts my immediate supply of sharp-edged homogenous solids. – g s Oct 20 '21 at 06:52
  • To be clear, I probably won't select this as the answer without citations or more generally supported principles. – Daniel R. Collins Oct 20 '21 at 18:24