Hardness Definitions:

Hardness: the resistance of a smooth surface to scratching or abrassion. A hard material may still be broken or cracked. For example, if you take a hammer to a diamond or sapphire watch crystal, it will break or shatter. Therefore, hardness is the measure of the material's ability to resist scratches or abrassions.

Mohs Hardness
Vickers Hardness
Knoop Hardness

Mohs Hardness:
Rough measure of the resistance of a smooth surface to scratching or abrasion, expressed in terms of a scale devised (1812) by the German mineralogist Friedrich Mohs. The Mohs hardness of a mineral is determined by observing whether its surface is scratched by a substance of known or defined hardness. To give numerical values to this physical property, minerals are ranked along the Mohs scale, which is composed of 10 minerals that have been given arbitrary hardness values. The minerals contained in the scale are shown in the Table below; also shown are other materials that approximate the hardness of some of the minerals. As is indicated by the ranking in the scale, if a mineral is scratched by orthoclase but not by apatite, its Mohs hardness is between 5 and 6. In the determination procedure it is necessary to be certain that a scratch is actually made and not just a "chalk" mark that will rub off. If the species being tested is fine-grained, friable, or pulverulent, the test may only loosen grains without testing individual mineral surfaces; thus certain textures or aggregate forms may hinder or prevent a true hardness determination. For this reason the Mohs test, while greatly facilitating the identification of minerals in the field, is not suitable for accurately gauging the hardness of industrial materials such as steel or ceramics. (For these materials a more precise measure is to be found in the Vickers hardness or Knoop hardness) Another disadvantage of the Mohs scale is that it is not linear; that is, each increment of one in the scale does not indicate a proportional increase in hardness. For instance, the progression from calcite to fluorite (from 3 to 4 on the Mohs scale) reflects an increase in hardness of approximately 25 percent; the progression from corundum to diamond, on the other hand (9 to 10 on the Mohs scale), reflects a hardness increase of more than 300 percent.

Vickers Hardness:
A measure of the hardness of a material, calculated from the size of an impression produced under load by a pyramid-shaped diamond indenter. Devised in the 1920s by engineers at Vickers, Ltd., in the United Kingdom, the diamond pyramid hardness test, as it also became known, permitted the establishment of a continuous scale of comparable numbers that accurately reflected the wide range of hardnesses found in steels.

The indenter employed in the Vickers test is a square-based pyramid whose opposite sides meet at the apex at an angle of 136°. The diamond is pressed into the surface of the material at loads ranging up to approximately 120 kilograms-force, and the size of the impression (usually no more than 0.5 mm) is measured with the aid of a calibrated microscope. The Vickers number (HV) is calculated using the following formula:

HV = 1.854(F/D²),

with F being the applied load (measured in kilograms-force) and D² the area of the indentation (measured in square millimetres). The applied load is usually specified when HV is cited.

The Vickers test is reliable for measuring the hardness of metals, and it is also used on ceramic materials.
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Knoop Hardness:
A measure of the hardness of a material, calculated by measuring the indentation produced by a diamond tip that is pressed onto the surface of a sample. The test was devised in 1939 by F. Knoop and colleagues at the National Bureau of Standards in the United States. By using lower indentation pressures than the Vickers hardness test, which had been designed for measuring metals, the Knoop test allowed the hardness testing of brittle materials such as glass and ceramics.

The diamond indenter employed in the Knoop test is in the shape of an elongated four-sided pyramid, with the angle between two of the opposite faces being approximately 170° and the angle between the other two being 130°. Pressed into the material under loads that are often less than one kilogram-force, the indenter leaves a four-sided impression about 0.01 to 0.1 mm in size. The length of the impression is approximately seven times the width, and the depth is 1/30 the length. Given such dimensions, the area of the impression under load can be calculated after measuring only the length of the longest side with the aid of a calibrated microscope. The final Knoop hardness (HK) is derived from the following formula:

HK = 14.229(F/D²),

with F being the applied load (measured in kilograms-force) and D² the area of the indentation (measured in square millimetres). Knoop hardness numbers are often cited in conjunction with specific load values.
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