Diffraction on a body centered lattice, h+k+l even?

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Discussion Overview

The discussion revolves around the mathematical treatment of diffraction in a body-centered cubic (BCC) lattice, specifically focusing on the conditions under which reflections occur based on the parity of the indices h, k, and l. Participants explore the implications of these conditions on the resulting equations and their components.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents an equation involving exponential and trigonometric functions, suggesting that for reflections to be visible, the sum h+k+l must be even.
  • Another participant questions the purpose of converting the exponential form to trigonometric functions and expresses confusion over the multiplication of the structure factor with an additional exponential term.
  • A participant asks about the sine of an integer multiple of pi, indicating a potential exploration of the implications of this mathematical property in the context of the discussion.
  • A later reply reiterates the question about the sine of an integer multiple of pi, suggesting a need for clarification or further exploration of this concept.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the equations and the necessity of certain terms, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are unresolved assumptions regarding the derivation of the equations and the specific context in which the sine function is being evaluated, which may affect the overall understanding of the diffraction conditions.

Tom83B
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This is in my book:

exp[2\pi i(hx+ky+lz)][1+exp(\pi i(h+k+l))]=2exp[2\pi i(hx+ky+lz)]\cos^2[\frac{\pi}{2}(h+k+l)]

And in order for the cosine not to be zero, h+k+l must be even when we want to see the reflection.

But I think that the result should be exp[2\pi i(hx+ky+lz)](2\cos^2[\frac{\pi}{2}(h+k+l)]+i\sin[\pi(h+k+l)])
Why isn't the imaginary part there? My idea was that we only need the real part, but because we multiply two complex numbers, I can't do this because i^2=-1, can I?
 
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That does seem strange. What is this equation supposed to be anyway? For what purpose is the author converting the exponential to trig functions? Also, I recognize the (1+exp) factor as the structure factor for BCC, but I can't remember ever seeing it multiplied by a second exponential that way.
 
What is the sine of an integer multiple of pi?
 
Modulated said:
What is the sine of an integer multiple of pi?

Thank you very much :-)
 

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