hardness, property of matter commonly described as the resistance of a substance to being scratched by another substance. The degree of hardness is relative, different substances being compared with one another. Mohs's scale of hardness (named for Friedrich Mohs), used commonly in mineralogy, lists certain minerals in order of hardness: talc, 1; gypsum, 2; calcite, 3; fluorite, 4; apatite, 5; orthoclase, 6; quartz, 7; topaz, 8; corundum, 9; diamond, 10. The listing indicates merely that gypsum (hardness=2) is harder than—i.e., capable of scratching—talc (hardness=1). The listing does not indicate that gypsum (2) is twice as hard as talc (1). The hardness of many minerals falls between those included in the list. For example, the hardness of barite is 3.3. Hardness may differ with the direction of the scratch made on the substance. Thus the mineral kyanite has a hardness of 5 parallel to the length of its crystals and of 7 at right angles to this direction. There are several other methods based on the resistance to indentation for testing engineering materials. The solid elements have been thus classified: diamond (an allotropic form of carbon) is hardest and listed as 10, with cesium the softest, rated as 0.2, the same degree of hardness as wax (hardness=0.2 at 0°C;). The hardness numeral of the Brinell scale is based upon the indentation produced when pressure is exerted by a sphere on the substance. The value thus obtained has a direct relation to the tensile strength of the substance. The hardness of a material may be modified by the presence of small quantities of another substance, as in metallic alloys, or by impurities in minerals.

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 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.

Scratch 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. One tool to make this measurement is the sclerometer.

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.

Other materials which can scratch diamond include boron suboxide and rhenium diboride.

Indentation hardness

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.

Rebound hardness

Also known as dynamic hardness, rebound hardness measures the height of the "bounce" of a diamond-tipped hammer dropped from a fixed height onto a material. The device used to take this measurement is known as a scleroscope.

One scale that measures rebound hardness is the Bennett hardness scale.

Physics

In solid mechanics, solids generally have three responses to force, depending on the amount of force and the type of material:

• They exhibit elasticity—the ability to temporarily change shape, but return to the original shape when the pressure is removed. "Hardness" in the elastic range—a small temporary change in shape for a given force—is known as stiffness in the case of a given object, or a high elastic modulus in the case of a material.
• They exhibit plasticity—the ability to permanently change shape in response to the force, but remain in one piece. The yield strength is the point at which elastic deformation gives way to plastic deformation. Deformation in the plastic range is non-linear, and is described by the stress-strain curve. This response produces the observed properties of scratch and indentation hardness, as described and measured in materials science. Some materials exhibit both elasticity and viscosity when undergoing plastic deformation; this is called viscoelasticity.
• They fracture—split into two or more pieces. The "ultimate strength" or toughness of an object is the point at which fracture occurs.

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.

Materials whose properties are different in different directions (because of an asymmetrical crystal structure) are referred to as anisotropic.

See also

• Hardness of ceramicsOther strengthening mechanisms
• Grain boundary strengthening
• Precipitation hardening
• Solid solution strengthening
• Work HardeningHard materials
• Ceramics
• Composites
• Metals
• Semiconductors

References

Notes

Bibliography

• Dieter, George E. (1989). Mechanical Metallurgy. SI Metric Adaptation, Maidenhead, UK: McGraw-Hill Education.
• Malzbender, J (2003). "Comment on hardness definitions". Journal of the European Ceramics Society 23 1355.

External links

• An introduction to materials hardness