Download Diffraction maxima include diffraction from All atoms in the crystal

Diffraction maxima include diffraction from
All atoms in the crystal
Diffraction in Uniform Direction
h=1
k=0
• “Planes” divide unit cell
in hkl divisions
• Each maxima is from
planes with spacing dhkl
h=1
k=1
• Smaller spacing yields
higher angle maxima:
2 dhkl sin θ = λ
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h=2
k=1
• “Planes” divide unit cell
in hkl divisions
h=2
• Each maxima is from
planes with spacing dhkl
k=3
• Smaller spacing yields
higher angle maxima:
2 dhkl sin θ = λ
h=2
k = -1
Fhkl is the Fourier Transform of ρxyz
Fhkl = V∑∑∑ρxyz cos [2π(hx+ky+lz)] + ρxyz sin [2π(hx+ky+lz)] xyz
Structure
Factor
Electron
Density
Diffraction in direction hkl is from constructive
interference of diffraction by all electrons xyz
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Waves and Diffraction
Fhkl α √Ihkl
Fhkl = Fhklcos αhkl + iFhklsin αhkl
Phase lost
Diffraction by Atoms
Fhkl = V∑∑∑ρxyz cos [2π(hx+ky+lz)] + ρxyz sin [2π(hx+ky+lz)] xyz
Fhkl = ∑ fi cos [2π(hx+ky+lz)] + fi sin [2π(hx+ky+lz)]
N
Atomic Scattering Factor
Note: the volume (V) is used in the top equation to account for ρ being
expressed in electrons per unit volume, whereas F is in electrons per unit
cell. 3
Argand Diagram
Vector Addition of Atomic Scattering
Factors
Fhkl
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Calculating Electron Density
ρxyz = 1/V∑∑∑ Fhkl cos [2π(hx+ky+lz) + αhkl] hkl
- Fhkl sin [2π(hx+ky+lz) + αhkl]
A question:
Crystal A is identical to crystal B, except
crystal B contains one less atom in each
molecule. How will the diffraction
patterns of the two crystals differ? (Hint: consider the Fourier summation for Fhkl)
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