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As the title states, can a Miller index for a cubic structure have 4 digits? If I have a structure with intercepts (2,8,3) on the x-y-z axes respectively, the following Miller index would be (12,3,8), which is not 3 digits.

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what do you mean by 4 digit Miller Index? –  Jing Oct 7 '11 at 1:25

2 Answers 2

Four digit Miller index is sometimes used for hexagonal lattices. The idea is to have useful property: permutation of indexes gives an equivalent direction.

It is mentioned in wikipedia, by the way. So you could start from there.

Four-digit Miller indexes are never used for cubic structure. If you could provide the citation where you saw them the answer could be better.

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We need to be clear about the distinction between integers and digits. Miller indices may have an infinite number of digits, but they are always composed of three integers, each of which may be arbitralily large, and therefore take a large number of digits to write down (exception: hexagonal structures sometimes use four integers). A Miller index of (12,3,8) is perfectly fine in a cubic system!

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