Mohs scale of mineral hardness

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Mohs scale of mineral hardness was created by the German Frederich Mohs. He based it on ten readily available minerals. The scale is not linear, for example corundum is twice as hard as topaz.

HardnessMineralAbsolute Hardness
1
Talc
1
2
Gypsum
3
3
Calcite
9
4
Fluorite
21
5
Apatite
48
6
Orthoclase
72
7
Quartz
100
8
Topaz
200
9
Corundum
400
10
Diamond
1500

The table has been extended

HardnessMineral
1
Liquid
2
Gypsum
3
Calcite
4
Fluorite
5
Apatite
6
Orthoclase
7
Vitreous pure silica
8
Quartz
9
Topaz
10
Garnet
11
Fuzed zirconia
12
Fuzed alumina
13
Silicon carbide
14
Boron carbide
15
Diamond
Question: if the scale isn't linear is there a linear scale that geologists prefer to use? And what exactly is 'absolute hardness'? How is hardness defined (we know what it is intuitively, but what is its physical definition?) Are there SI units for hardness? -- SJK
There is no absolute hardness scale. No units for hardness either. As for what "hardness" really is, I think that is an open question. It would certainly be related to fracture toughness, but that defies analysis as well, relying on laboratory testing and depending on the geometry of the specimen.
A simple search on Google shows there is an 'absolute hardness' scale; in fact, there appear to be at least two: the Rosiwal absolute hardness scale; and the Knoop absolute hardness scale. Also, how can a non-existent scale yield real numbers like the ones in this article (although I've more commonly seen 140000 for Diamond, not the 1500 given above; I suppose this might be the Rosiwal vs. Knoop scales.) -- SJK
Isn't part of the definition of hardness the scratch test (if you can scratch something with something else, that something else is the harder of the two)?
Thats the point of the Mohs scale. Frankly, the most useful materials for hardness testing in the field are fingernails (hardness 2-3) and pocket knives (hardness 5-6). Used in conjunction with luster, crystal habit and color, fingernails and pocket knives do a pretty good job.