26 overheads Ewald sphere Kinematic

26 overheads Ewald sphere Kinematic - B.E Warren x ‐ ray...

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Reciprocal lattice representation of the satisfying of the Bragg law for a set of planes hkl. The diffraction vector (S So)/ must terminate on the point hkl of the RL lattice B.E. Warren, x ray diffraction http://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/03_KinDiff,%20Laue,%20Powder.pdf
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Ewald Construction P. P. Ewald was responsible for interpreting Laue's results in terms of reciprocal lattices. He devised a simple geometric constr ction that demonstrates the relationship in q ite elegant b t simple terms simple geometric construction that demonstrates the relationship in quite elegant but simple terms. He separated the origins of direct and reciprocal space placing the crystal at the center of a sphere of radius 1/ . The origin of reciprocal space is placed on the surface of the sphere where S 0 (the incident beam) exits the sphere. http://capsicum.me.utexas.edu/ChE386K/html/ewald_construction.htm
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2D representation of the Ewald sphere in the Reciprocal Lattice. Bragg law is satisfied for any set of planes whose point hkl falls on the surface of the sphere
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Unformatted text preview: B.E. Warren, x ‐ ray diffraction http://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/03_KinDiff,%20Laue,%20Powder.pdf http://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/03_KinDiff,%20Laue,%20Powder.pdf The basics of crystallography and diffraction By Christopher Hammond, pg198 new book Bragg's Law is Equivalent to Laue Condition So Or In the Bragg construction both the incident beam an the scattered beam are inclined to the ( hkl) plane at an angle q making the angles of incidence and "reflection" equal. This can be achieved in the Laue ti ki l hi h d t k i l tti t l equations by making the angles which the S and S vectors make to the reciprocal lattice vector equal. Call this angle n. Remember that the reciprocal lattice direction is perpendicular to the ( hkl) plane. These conditions can be shown on an Ewald sphere diagram. http://capsicum.me.utexas.edu/ChE386K/html/braggislaue.htm...
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