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cascaillou
Joined: 27 Nov 2011
Posts: 257
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 Posted: Jan 26, 2012 10:18 Post subject: Question about crystallography (Miller indices) |
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Hi
I'm curious to know how one can link Miller indices to the facets of a crystal.
I know how miller indices work in a theoretical point of view, but in practice a given mineral can show many different crystal shapes (which are usually quite different from the simple lattice shape) so I don't know where to place the abc axes in a given crystal.
Thus my problem is that when I can see a cleavage plane in a given unidentified crystal, I'm unable to tell what are the miller indices for this cleavage plane (which is a shame as this would be quite helpful for identification)
Can this be done when I still havn't any idea of what the crystal is? Or do I have to start from an hypothesis of what the crystal might be and see if the referenced cleavage plane does fit my observations?
thanks |
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Pete Richards
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| Posted: Jan 26, 2012 10:37 Post subject: Re: question about crystallography (miller indices) |
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| cascaillou wrote: | Hi
I'm curious to know how one can link Miller indices to the facets of a crystal....
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I'm sorry to tell you that from a practical standpoint this is not easily done, particularly if you don't know what mineral you have. If you know the mineral, you either have to measure face orientations using a goniometer, which most people cannot do for lack of knowledge and equipment, or compare your crystal with drawings in textbooks or reference works such as Goldschmidt's Atlas of Crystal Forms, and/or draw crystals with hypothesized Miller indices using a crystal drawing program to see if the hypothesized indices give a shape that matches the crystal at hand.
With some luck and careful observation, you may be able to identify the forms on your crystal, but to be certain you are correct you would still need to measure the crystal with a goniometer.
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cascaillou
Joined: 27 Nov 2011
Posts: 257
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| Posted: Jan 26, 2012 11:26 Post subject: Re: question about crystallography (miller indices) |
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even for placing very simple planes (like 100 010 001 110) the problem is still the same?
my main goal being determination of cleavage planes indices when I have a sample showing neat cleavege planes |
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Pete Richards
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| Posted: Jan 26, 2012 12:56 Post subject: Re: question about crystallography (miller indices) |
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| cascaillou wrote: | even for placing very simple planes (like 100 010 001 110) the problem is still the same?
my main goal being determination of cleavage planes indices when I have a sample showing neat cleavege planes |
Especially with simple planes like 100 010 and 001. For a simple orthorhombic example, a crystal bounded by these forms will be like a box. The distance from the center of the crystal does not need to conform to the length of the axis in question. There is a general tendency for crystals to be shortest along the longest axis, but that does not have to be true.
A form like 110 (if it's really 110 and not 210 or 120 or hk0, h±k) at least gives information about the ratio between the length of the a and b axes, via the angle between the adjacent faces of the form.
In the old days of morphological crystallography, the unit cell parameters were determined by identifying faces that intersected all three axes and defining that form to be {111}. The ratios of a : b : c were then determined from the interfacial angles, as well as angles between the axes for lower symmetry minerals.
If you know what mineral it is, the cleavages can be of great help in getting the crystal oriented to the axes. A good example is calcite. If you don't know what the mineral is, cleavage may not be much help, or it might be helpful, depending on details. An isometric example: halite has 100 cleavage, sphalerite has 110 cleavage, and fluorite has 111 cleavage. If you only see one cleavage plane, it's not much help (though it's easy enough to tell these minerals apart anyway). But if the cleavage is fully developed, 100 cleavage is shown by the six-faced fragments with right angles, 110 cleavage by fragments that are dodecahedra, and 111 cleavage by fragments that are octahedra.
It's also worth saying that cleavage planes are generally low-index planes - 1's and/or 0's usually.
Perhaps you can tell us a little more about your specific mineral?
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cascaillou
Joined: 27 Nov 2011
Posts: 257
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| Posted: Jan 26, 2012 14:01 Post subject: Re: question about crystallography (miller indices) |
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I do not have a specific mineral in mind, but on several occasions I have been confronted to unknowns with neat cleavage planes and each time I was wondering if I could eliminate unlikely candidates through observation of cleavage orientation.
Thanks for your explanations.
By the way, as we are talking cleavage, do you know were I could find definitions and pictures showing the difference between the different types of cleavage referenced on mindat:
poor(indistinct)
imperfect(fair)
distinct(good)
very good
perfect
Of course it's easy to visually make the difference between indistinct and good, but I still have difficulties in qualifying precisely a cleavage when I see it. |
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Antonio Alcaide
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| Posted: Jan 26, 2012 14:31 Post subject: Re: question about crystallography (miller indices) |
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| Pete Richards wrote: | | It's also worth saying that cleavage planes are generally low-index planes - 1's and/or 0's usually. |
Useful statement. I was not aware of that. Thanks, Pete. "The old days of the morphological crystallography" as you say, well, those who have not the adequate equipment still "live" in those days.
Regards
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Pete Richards
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| Posted: Jan 26, 2012 16:07 Post subject: Re: question about crystallography (miller indices) |
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| cascaillou wrote: |
...by the way, as we are talking cleavage, do you know were I could find definitions and pictures showing the difference between the different types of cleavage referenced on mindat:
poor(indistinct)
imperfect(fair)
distinct(good)
very good
perfect
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Here's a pretty good verbal description:
https://dave.ucsc.edu/myrtreia/physical_character.html#Cleavage
and another:
https://www.minsocam.org/msa/collectors_corner/id/mineral_id_keyi6.htm
(links normalized by FMF)
but I did not find any full set of illustrations.
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Collecting and studying crystals with interesting habits, twinning, and epitaxy |
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