Finding Miller indexes of a vector vertical to known layer

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SUMMARY

The discussion focuses on finding the Miller indices of a vector that is vertical to the layer defined by the indices (211). The initial approach suggested inverting the numbers to obtain coordinates (1/2, 1, 1) and then determining the vertical vector. However, this method is questioned as it conflates the concept of a layer with that of a vector. Clarification is sought regarding the definition and application of Miller indices in crystallography.

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  • Understanding of Miller indices in crystallography
  • Basic knowledge of vector mathematics
  • Familiarity with crystallographic planes and directions
  • Concept of orthogonality in vector analysis
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Sollicitans
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Homework Statement


Find Miller indexes of the vector that is vertical to the layer (211).

Homework Equations


Unknown.

The Attempt at a Solution


I'm not quite sure how to do this. The only thing I came up until now is to invert the numbers (so that I get 1/2, 1 and 1) and then find the vector that is vertical to a vector with these coordinates. But I don't think this is right at all, because this is a layer we are talking about. Not a vector.
 
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Sollicitans said:
I'm not quite sure how to do this. The only thing I came up until now is to invert the numbers (so that I get 1/2, 1 and 1) and then find the vector that is vertical to a vector with these coordinates. But I don't think this is right at all, because this is a layer we are talking about. Not a vector.

your above statement is not clear to me -why not ask a question :
What are Miller indexes in an array of atoms/crystalline arrangements ?
 

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