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

Click For Summary
SUMMARY

The discussion centers on the diffraction condition for a body-centered cubic (BCC) lattice, specifically addressing the requirement that the sum of Miller indices (h+k+l) must be even for observable reflections. The equation presented, involving the exponential and cosine functions, highlights the relationship between the structure factor and the diffraction pattern. The user questions the absence of the imaginary part in the equation and seeks clarification on the purpose of converting the exponential to trigonometric functions, indicating a deeper exploration of the mathematical foundations of diffraction in crystallography.

PREREQUISITES
  • Understanding of Miller indices in crystallography
  • Familiarity with complex numbers and their properties
  • Knowledge of diffraction patterns in solid-state physics
  • Basic grasp of trigonometric functions and their relationships to exponential functions
NEXT STEPS
  • Study the structure factor for body-centered cubic lattices
  • Learn about the mathematical derivation of diffraction conditions
  • Explore the relationship between exponential and trigonometric functions in complex analysis
  • Investigate the implications of the imaginary component in diffraction equations
USEFUL FOR

Physicists, materials scientists, and students studying crystallography or solid-state physics who are interested in understanding the mathematical principles behind diffraction in BCC lattices.

Tom83B
Messages
45
Reaction score
0
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?
 
Physics news on Phys.org
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 :-)
 

Similar threads

Undergrad Use the Ewald sphere to calculate h,k,l?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding Ewald's sphere in the context of X-Ray diffraction
  • · Replies 3 ·
Replies
3
Views
6K
Undergrad The missing factor of 2π in reciprocal lattice calculations
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Monte Carlo Wang-Landau_antiferromagnetic perovskite
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Basic questions on crystal lattice: k-vectors and Brillouin
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How Does Bragg's Diffraction Apply to FCC Lattices?
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Why is there reflection in 222 plane of Silicon?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Determine the intensities of GaAs crystal planes
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Multiplication and Addition to get an integer
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Formula for Interplanar Distance in Cubic Lattice
  • · Replies 4 ·
Replies
4
Views
6K