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There are three principal operational definitions of hardness:
In mineralogy, hardness commonly refers to a material's ability to penetrate softer materials. An object made of a hard material will scratch an object made of a softer material. Scratch hardness is usually measured on the Mohs scale of mineral hardness. Pure diamond is the hardest known substance so it will scratch any other material. Diamond, being the hardest material, is the substance used to cut diamond. Higher-grade diamonds are used to cut lower-grade diamonds.
Primarily used in engineering and metallurgy, indentation hardness seeks to characterise a material's resistance to permanent, and in particular plastic, deformation. It is usually measured by loading an indenter of specified geometry onto the material and measuring the dimensions of the resulting indentation.
There are several alternative definitions of indentation hardness, the most common of which are:
There is, in general, no simple relationship between the results of different hardness tests. Though there are practical conversion tables for hard steels, for example, some materials show qualitatively different behaviours under the various measurement methods.
Also known as dynamic or absolute hardness, rebound hardness measures the height of rebound of an indenter dropped onto a material using an instrument known as a scleroscope .
In mathematics, hardness refers to the difficulty of proving a conjecture, solving an equation, etc. See also computational complexity theory.