Reciprocal lattice

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Lecture 4

• Reciprocal lattice
• Ewald sphere
• Sphere of reflection (diffraction)
• Sphere of resolution

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Reciprocal lattice Diffraction pattern of the
crystal latticeDiffraction data Reciprocal
lattice X diffraction pattern of the unit cell
content
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Reciprocal Lattice

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Scattering by atomic planes in crystal Bragg
geometry
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Vector representation
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Define Reciprocal lattice vector S
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Equivalence
for crystal
1/d
If we set the magnitude of s and so vectors equal
to 1/l, then Braggs law and Laue conditions are
the same !!
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In Crystal
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(hkl) plane intersects at a/h, b/k, and c/l
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(from a set of parallel atomic planes)
a is perpendicular to bc plane etc.
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Ewald Sphere of Reflection (Diffraction)
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Construction of Ewald sphere
set the magnitude of s and so vectors equal to
1/l
-
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Magnitude of S
q
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1/d
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when the point touches the Ewald sphere !!
a is perpendicular to bc plane etc.
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Bijvoet pair
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Effect of wave length To Ewald sphere
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Rotation wedge
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Angular separation Mosaic spread
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Blind region
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Summary

• Reciprocal lattice is the diffraction pattern of
  the crystal (real) lattice
• Diffraction pattern of a crystal is the product
  of the reciprocal lattice and the diffraction
  pattern of the unit cell content
• Equivalence of Bragg diffraction condition and
  Laue diffraction condition
• Ewald construction of Diffraction sphere

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Mathematical description of crystal lattice and
reciprocal lattice
a, b, c are the axis of a real unit cell
Where
a, b, c are the axis of a reciprocal unit
cell
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