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So I was reading here that Mohs scale is not transitive and therefore could not overcome the comparative phase in order to be turned into a measurement procedure. As it is written in the webpage, "Mohs assumed that his relation of "scratches" was transitive and asymmetrical(...). This has been shown to be false. Some minerals (...) cannot scratch each other, and yet have different powers of scratching a third mineral"

Now I've looked at the references given in the article but couldn't find which minerals these were and a Google search yielded no information either.

So my question is what are these minerals. A reference would also be greatly appreciated. Thanks in advance.

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The idea discussed in the paper you reference is about transferability of Mohs ordinal scale to true hardness. A mineral's ability to scratch is related to it's hardness, but only an indentation test measures absolute hardness (e.g. the Vickers scale). Mineral orientation relative to planar structure can change the result in a scratch test, and two minerals that can't scratch each other may actually differ in hardness. This page discusses scratch test problems and has a thorough narrative of the development of testing hardness of minerals.

The table below (from here) compares hardness scales for several minerals, some of which have the same number on the Moh's scale, but a big difference in the Vickers number. This is an issue for Campbell in his theory of measurement, because Mohs is not an additive scale where mineral hardness goes up or down consistently.

Using the table below you could postulate some issues with Mohs scale. For example, rutile and pyrite would not scratch each other, but they would have different results when they were used to scratch chromite, since their rank is different across Mohs and Vickers. However, I am not a geologist, so I welcome corrections to this assertion.

mohs vs vickers

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It may be difficult to ascertain the hardness of a mineral relative to an other mineral in a Mohs streak test if one (or both) are not homogeneous. Already a small local grain of an impurity may put you off; you might remember the occasions of the sudden scratching sound of chalk on the green board. Which is why pen-shaped hardness picks are advantageous: to use a tip made a (synthetic) alloy with reproducible hardness (except for #2 and #3 made of plastic, or copper) to aim right on your region of interest:

enter image description here

(credit)

Equally, it is a question of technique (if adhering to this protocol), too, as mentioned by, e.g.,

«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).»

(credit to Mineralogical Society of America, emphasis added)

or

«Don't be wimpy! This is a very common problem. Some people casually rub one specimen back and forth against another and then look for a mark. That is not how the test is done! It is done with a single, slow, determined motion, with firm pressure, with the goal of cutting a scratch.»

(credit to geology.com, compiling some potential pitfalls)

while both a) the relative orientation of the mineral to be tested .vs. a reference, and b) the origin of a mineral may yield different degrees of hardness.

(Hardness by Mohs (and streak) isn't the only scale. In materials science, there equally are hardness tests by indentation e.g., Rockwell or Brinell.)

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