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

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Presentation transcript:

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

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

SHKim 2007

Reciprocal Lattice

SHKim 2007

Scattering by atomic planes in crystal: Bragg geometry

SHKim 2007

Vector representation

SHKim 2007 Define “Reciprocal lattice vector S”

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 !!

SHKim 2007 In Crystal

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

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

SHKim 2007

Ewald Sphere of Reflection (Diffraction)

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

SHKim 2007  Magnitude of S

SHKim 2007 = 1/d

SHKim 2007

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

SHKim 2007

Bijvoet pair

SHKim 2007 Effect of wave length To Ewald sphere

SHKim 2007

Rotation “wedge”

SHKim 2007 Angular separation Mosaic spread

SHKim 2007 “Blind region”

SHKim 2007

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”

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

SHKim 2007