This: Hard Hardness refers to various properties of matter in the solid phase that give it high resistance to various kinds of shape change when force is applied. Hard matter is contrasted with soft matter.

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 materials science, there are three principal operational definitions of hardness:

• Scratch hardness: Resistance to fracture or plastic (permanent) deformation due to friction from a sharp object
• Indentation hardness: Resistance to plastic (permanent) deformation due to a constant load from a sharp object
• Rebound hardness: Height of the bounce of an object dropped on the material, related to elasticity.

In physics, hardness encompasses:

• Elasticity, plasticity, viscosity, and viscoelasticity
• Strength and strain
• Brittleness/ductility and toughness

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.

Materials science

Hardness is a 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 on 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 only as hard as quartz). In other words, a claimed hard material should have similar hardness characteristics at any location on its surface.

Scratch hardness