Is there a theoretical upper limit for how hard something can be under "normal circumstances" (i.e., on the surface of Earth or similar or in the empty space)? Something like absolute zero/infinity on the Moh scale.
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$\begingroup$ "Ideal rigid body"? $\endgroup$– user196418Commented Dec 28, 2018 at 0:03
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1$\begingroup$ Special relativity imposes limits on the ratio of any material's Young's modulus per unit density. I don't think any real-world material comes anywhere near saturating this limit, and I guess Young's modulus isn't quite the same thing as hardness. $\endgroup$– user4552Commented Dec 28, 2018 at 1:13
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It is indeed possible to model the behavior of a "perfect crystal" of a solid element using the known values of the interatomic bonding strengths and the geometric layout of the crystal lattice itself, and from that derive the theoretical maximum strength and stiffness of the crystal.
When this is done, it is found that the computed strength of the crystal is far, far greater than the actual strength of the material when subjected to a lab test. The discrepancy is caused by defects in the crystal structure which are not present in the theoretical model.
This subject is treated in a third-year materials science class and the textbooks (for example, Van Vlack or Shackelford) will contain a full derivation of it, which would include the theoretical maximum strength number you seek for some common engineering materials.
answered Dec 28, 2018 at 1:02