1. SHKim 2007 Lecture 4 Reciprocal lattice “Ewald sphere” Sphere of reflection (diffraction) Sphere of resolution

2. SHKim 2007 Reciprocal lattice: Diffraction pattern of the crystal lattice Diffraction data: Reciprocal lattice X diffraction pattern of the unit cell content

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4. Reciprocal Lattice

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6. Scattering by atomic planes in crystal: Bragg geometry

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9. Vector representation

10. SHKim 2007 Define “Reciprocal lattice vector S”

11. SHKim 2007 Equivalence = 1/d for crystal If we set the magnitude of s and s o vectors equal to 1/  then Bragg’s law and Laue conditions are the same !!

12. SHKim 2007 In Crystal

13. SHKim 2007 (hkl) plane intersects at: a/h, b/k, and c/l

14. SHKim 2007 a* is perpendicular to bc plane etc. (from a set of parallel atomic planes)

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17. Ewald Sphere of Reflection (Diffraction)

18. SHKim 2007 Construction of Ewald sphere set the magnitude of s and s o vectors equal to 1/ -

19. SHKim 2007  Magnitude of S

20. SHKim 2007 = 1/d

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22. a* is perpendicular to bc plane etc. when the point touches the Ewald sphere !!

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27. Bijvoet pair

28. SHKim 2007 Effect of wave length To Ewald sphere

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30. Rotation “wedge”

31. SHKim 2007 Angular separation Mosaic spread

32. SHKim 2007 “Blind region”

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34. 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”

35. SHKim 2007 a*, b*, c* are the axis of a reciprocal unit cell Where a, b, c are the axis of a real unit cell Mathematical description of crystal lattice and reciprocal lattice

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