Understanding Vector Direction in a Cubic System | Explanation & Examples

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SUMMARY

In a cubic system, the vectors [100], [010], [001], [bar{1} 00], [0 bar{1} 0], and [00 bar{1}] are equivalent due to the symmetry of the crystal structure. This means that, despite pointing in different directions, they are indistinguishable when examining the crystal. The discussion clarifies that the planes (1 1 2) and (-1 -1 -2) are not identical but are parallel, highlighting the importance of understanding vector equivalence in crystallography.

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  • Basic concepts of Miller indices
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superwolf
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What is meant by this sentence:

"In a cubic system, all directions of the vectors [100], [010], [001], [tex][bar{1} 00][/tex], [tex][0 bar{1} 0][/tex], and [tex][00 bar{1}][/tex], areequivalent and indistinguishable."

They point in different directions!
 
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I assume they are talking about a crystal here. Then the statement just says that you cannot tell along which of the given vectors you are looking by examining the crystal.
 
Is plane (1 1 2) identical to (-1 -1 -2), or are they just parallel?
 

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