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6. Using structure factor rules, show that the selection rules for BCC crystal is h+k+l=even. Also show what are the reflection planes that are Bragg active?

6. Using structure factor rules, show that the selection rules for BCC crystal is h+k+l=even. Also show what are the reflection planes that are Bragg active?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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6. Using structure factor rules, show that the selection rules for BCC crystal is h+k+l=even. Also show what are the reflection planes that are Bragg active?
Transcribed Image Text:6. Using structure factor rules, show that the selection rules for BCC crystal is h+k+l=even. Also show what are the reflection planes that are Bragg active?
Expert Solution
Step 1

For BCC lattice, If atom at (0,0,0) and (1/2,1/2,1/2) and equivalent position

 F = fj eiφj 

    = fj ei [2π(hx'j + ky'j + lz'j)]

    = f ei [2π (h.0 + k.0 + l.0)] + f ei [2π (h/2 + k/2 + l/2)]

     = f e0 + f eiπ(h+k+l)

    = f [1 + eiπ (h+k+l)]

    So, for (h+k+l) = odd, F = 0.

  For (h+k+l) = even, F = 2f, F2 = 4f2

 

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