Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2023-05-18 22:48:56

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 47,159

Mohs scale

Mohs scale

Summary

The Mohs scale of mineral hardness is a qualitative ordinal scale, from 1 to 10, characterizing scratch resistance of minerals through the ability of harder material to scratch softer material.

The scale was introduced in 1812 by the German geologist and mineralogist Friedrich Mohs, in his book "Versuch einer Elementar-Methode zur naturhistorischen Bestimmung und Erkennung der Fossilien"; it is one of several definitions of hardness in materials science, some of which are more quantitative.

The method of comparing hardness by observing which minerals can scratch others is of great antiquity, having been mentioned by Theophrastus in his treatise On Stones, c. 300 BC, followed by Pliny the Elder in his Naturalis Historia, c. AD 77. The Mohs scale is useful for identification of minerals in the field, but is not an accurate predictor of how well materials endure in an industrial setting – toughness.

Reference Minerals

The Mohs scale of mineral hardness is based on the ability of one natural sample of mineral to scratch another mineral visibly. The samples of matter used by Mohs are all different minerals. Minerals are chemically pure solids found in nature. Rocks are made up of one or more minerals. As the hardest known naturally occurring substance when the scale was designed, diamonds are at the top of the scale. The hardness of a material is measured against the scale by finding the hardest material that the given material can scratch, or the softest material that can scratch the given material. For example, if some material is scratched by apatite but not by fluorite, its hardness on the Mohs scale would be between 4 and 5.

"Scratching" a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the unaided eye. Frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural integrity, they are not considered "scratches" for the determination of a Mohs scale number.

Each of the ten hardness values in the Mohs scale is represented by a reference mineral, most of which are widespread in rocks.

The Mohs scale is an ordinal scale. For example, corundum (9) is twice as hard as topaz (8), but diamond (10) is four times as hard as corundum.

Details

Mohs hardness is a 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; 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.

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.

Additional Information

The Mohs' hardness scale was developed in 1822 by Frederich Mohs. This scale is a chart of relative hardness of the various minerals (1 - softest to 10 - hardest). Since hardness depends upon the crystallographic direction (ultimately on the strength of the bonds between atoms in a crystal), there can be variations in hardness depending upon the direction in which one measures this property. One of the most striking examples of this is kyanite, which has a hardness of 5.5 parallel to the 1 direction ( c-axis), while it has a hardness of 7.0 parallel to the 100 direction ( a-axis). Talc (1), the softest mineral on the Mohs scale has a hardness greater than gypsum (2) in the direction that is perpendicular to the cleavage. Diamonds (10) also show a variation in hardness (the octahedral faces are harder than the cube faces).

Mohs' hardness is a measure of the relative hardness and resistance to scratching between minerals. Other hardness scales rely on the ability to create an indentation into the tested mineral (such as the Rockwell, Vickers, and Brinell hardness - these are used mainly to determine  hardness in metals and metal alloys). The scratch hardness is related to the breaking of the chemical bonds in the material, creation of microfractures on the surface, or displacing atoms (in metals) of the mineral. Generally, minerals with covalent bonds are the hardest while minerals with ionic, metallic, or van der Waals bonding are much softer.

When doing the tests of the minerals it is necessary to determine which mineral was scratched. The powder can be rubbed or blown off and surface scratches can usually be felt by running the fingernail over the surface. One can also get a relative feel for the hardness difference between two minerals. For instance quartz will be able to scratch calcite with much greater ease than you can scratch calcite with fluorite. One must also use enough force to create the scratch (if you don't use enough force even diamond will not be able to scratch quartz - this is an area where practice is important). You also have to be careful to test the material that you think you are testing and not some small inclusion in the sample. This is where using a small hand lens can be very useful to determine if the test area is homogenous.

Why is hardness important?

The effects of high hardness are important in many fields. Abrasives are used to form and polish many substances. Diamonds are an important mineral component in cutting tools for the manufacturing of metals and other substances, forming dies for the drawing of wires, and for cutting cores in oil wells and mineral exploration. Emery - a variety of corundum, is used in many abrasive products that do not require the hardness (or expense) of diamond tools. Garnets were used as an abrasive in sandpaper. Talc is an extremely soft mineral that has been used in bath powders (talcum powder).

Mineral harness is also important in sedimentary rocks. Harder minerals tend to be able to travel longer distances down river systems. Quartz can often undergo several cycles of erosion, transportation and lithification ( change of sediments to rock). Zircons are persistent minerals in the environment and can often tell geologists the types of rock that were the original source rock for metamorphic or sedimentary rocks.

Mineral hardness can also be seen in the topography of many landscapes. Quartz bearing rocks are often more resistant to weathering and will produce the capstones that protect the tops of buttes and mesas from erosion.

Mohs_Scale2_1.jpg?maxwidth=1300&autorotate=false&quality=78&format=webp


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

Board footer

Powered by FluxBB