Measuring hardness

The hardness of minerals is usually measured on Moh's hardness scale. Unlike the scales of hardness used in some other sciences (e.g. mechanical engineering) this is a simple, qualitative scale, defined by reference to a series of ten reference minerals . As such, the steps in the scale are not linear, and with each step up the scale (from 1 to 9) the absolute hardness increases disproportionately. For example, corundum (9) is twice as hard as topaz (8), but diamond (10) is four times as hard as corundum.. The scale is defined in the table below.

Moh's Hardness	Reference Mineral	Absolute ​hardness
1	Talc	1
2	Gypsum	2
3	Calcite	14
4	Fluorite	21
5	Apatite	48
6	Orthoclase feldspar	72
7	Quartz	100
8	Topaz	200
9	Corundum	400
10	Diamond	1500

To measure hardness, all we therefore have to do is scratch a specimen with one of the reference minerals in this table and see if it scores the surface, in which case we know that the specimen is softer than the test mineral. (Alternatively, we can reverse the process and scratch the test mineral with the sample - which would tell us that the specimen is harder than the test mineral). If we repeat this until we bracket the specimen between two test minerals - one that scratches and one that doesn't - we can give the its approximate hardness. For example if it is scratched by apatite but not by fluorite, we know that it has a hardness of 4 to 5 or approximately  4.5.

To  measure hardness in this way, we therefore need a set of reference minerals. These (or most of them) can easily be bought, or many we might manage to find if we search hard enough - though using the diamond from your partner's or mother's diamond ring might not be advisable! However, if you want to save your money there are commonly found materials which provide a proxy for some points on the scale. Some suggestions are listed in the below.

Material                                      Moh's Hardness
BB pencil                                             1.0
Fingernail                                            2.5
​Copper (pure)                                     3.0
Wire nail                                              4.5
Window glass                                     5.5
Steel knife                                          6.5
Tungsten drill bit                               8.5
Diamond-bit saw                               9.5               

These are clearly not as regularly spaced,. nor as accurate as the reference minerals (some vary  depending on their composition) but they provide an approximate guide - and might help keep your relationship intact.

There is another, and better, alternative, which is to buy a set of hardness test-pens. A set of six pens is likely to cost in the order of $250.
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The science of hardness

The hardness of a mineral is not to be confused with its strength. Hardness is essentially a measure of a material's ability to withstand penetration by a sharp object; strength is a measure of its ability to withstand an applied load without deformation or breakage. Hardness thus relates fundamentally to the surface characteristics of a mineral, while strength is more a property of its internal character. Reflecting this, hardness is usually measured with a scratch test, using materials of known hardness, while strength is measured using some form of loading test.

In mineral identification, hardness is a particularly important property, because most minerals give very specific values of hardness, which don't vary greatly between different forms (e.g. colours). This makes it diagnostic. Hardness may, however, vary within a single crystal, depending on which axis is tested. In kyanite, for example, hardness is usually in the order of 5,5 when measured parallel to the long axis, but may reach 6 to 7 on the Moh's scale, when tested at right angles to the long axis. (This variability is a useful diagnostic test for kyanite.)

As this example indicates, hardness is dependent on more than the chemistry of the mineral. It is also affected by the crystal structure, and thus by the physical arrangement of the atoms within the crystal, and the type of bonding involved. The hardness of a mineral relates to its weakest bond strength.

Three main types of bonding occur in a mineral:

• covalent bonding,  where two atoms share an electron;
• ionic bonding, where a negatively charge ion in one atom is bonded to a positively charged ion in another; 
• and metallic bonding, where a cloud of electrons bonds with positively charged ions in the metal; and 

These vary in their strength (covalent are strongest, metallic weakest), so minerals that are composed of more covalent bonds (e.g. diamond, sphalerite) tend to be harder (and denser) because their atoms are bound together more tightly. Minerals that have more metallic bonds (e.g. most metallic minerals) tend to be less hard and less dense.  

This is by no means the whole story. The overall structure of the atoms is also important. Minerals with a three-dimensional structure have more bonds and fewer lines of weakness. Minerals with a two dimensional structure, such a the phyllosilicates like  mica and kyanite, lack bonds in the third dimension, so tend to be softer in that direction.

The diagram below shows the relationship between hardness and type of bonding for a range of different minerals.