Macroscopic hardness is generally characterized by strong intermolecular bonds. However, the behavior of solid materials under force is complex, resulting in several different scientific definitions of what might be called "hardness" in everyday usage.
In physics, hardness encompasses:
The equation based definition of hardness is the pressure applied over the projected contact area between the indenter and the material being tested. As a result hardness values are typically reported in units of pressure, although this is only a "true" pressure if the indenter and surface interface is perfectly flat.
Hardness is the characteristic of a solid material expressing its resistance to permanent deformation. Hardness can be measured on the Mohs scale or various other scales. Some of the other scales used for indentation hardness in engineering—Rockwell, Vickers, and Brinell—can be compared using practical conversion tables.
Hardness increases with decreasing particle size. This is known as the Hall-Petch relationship. However, below a critical grain-size, hardness decreases with decreasing grain size. This is known as the inverse Hall-Petch effect.
It is important to note that hardness of a material to deformation is dependent to its microdurability or small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus. Scientists and journalists often confuse stiffness for hardness, and spuriously report materials that are not actually harder than diamond because the anisotropy of their solid cells compromise hardness in other dimensions, resulting in a material prone to spalling and flaking in squamose or acicular habits in that dimension. E.g., osmium is stiffer than diamond but is as hard as quartz. In other words, a claimed hard material should have similar hardness characteristics at any location on its surface.
Pure diamond is the hardest known natural mineral substance and will scratch any other natural material. Diamond is therefore used to cut other diamonds; in particular, higher-grade diamonds are used to cut lower-grade diamonds.
The hardest substance known today is aggregated diamond nanorods, with a hardness over 12 of and a stiffness 1.11 of diamond. Estimates from proposed molecular structure indicate the hardness of beta carbon nitride should also be greater than diamond (but less than ultrahard fullerite). This material has not yet been successfully synthesized.
Indentation hardness tests are primarily used in engineering and metallurgy fields. The tests work on the basic premise of measuring the critical dimensions of an indentation left by a specifically dimensioned and loaded indenter.
One scale that measures rebound hardness is the Bennett hardness scale.
Strength is a measure of the extent of a material's elastic range, or elastic and plastic ranges together. This is quantified as compressive strength, shear strength, tensile strength depending on the direction of the forces involved. Ultimate strength is measure of the maximum strain a material can withstand.
Brittleness, in technical usage, is the tendency of a material to fracture with very little or no detectable deformation beforehand. Thus in technical terms, a material can be both brittle and strong. In everyday usage "brittleness" usually refers to the tendency to fracture under a small amount of force, which exhibits both brittleness and a lack of strength (in the technical sense). For brittle materials, yield strength and ultimate strength are the same, because they do not experience detectable plastic deformation. The opposite of brittleness is ductility.
The toughness of a material is the maximum amount of energy it can absorb before fracturing, which is different than the amount of force that can be applied. Toughness tends to be small for brittle materials, because it is elastic and plastic deformations that allow materials to absorb large amounts of energy.
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