MEMS1054_wks7-9

MEMS1054_wks7-9 - MEMS1054 Week 6-8- Diffraction 2/3...

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Unformatted text preview: MEMS1054 Week 6-8- Diffraction 2/3 Professor Jrg Wiezorek, PhD, Materials Science and Metallurgy, University of Cambridge, UK, 1994. Meets in room G37 BEH, Mon/Wed/Fri, 1-1:50PM Planes in Crystals described by Miller indices, (hkl); the interplanar spacing for a set of planes in a crystal represents the shortest distance between adjacent members in the infinite set of parallel planes and can be expressed in terms of the lattice parameters: e.g. for the orthorhombic system (a, b, c and = = =90), d hkl = (h 2 /a 2 + k 2 /b 2 + c 2 /l 2 )-0.5 Can compute a table of possible spacings d hkl in descending order and then use Bragg Law to find the corresponding Bragg angles, hkl . Compute for a cubic crystal (note same for P-, I- & F-lattices) with lattice parameter a = x nm=a. 1) Diffracted Directions - The Bragg Law 2) Diffracted Beam Intensities Elements! Motif of one or two identical atoms! Cubic Crystals, a=3.5; Copper-k-alpha X-radiation; HCP, a=2.5 and c/a=1.6333 So, here for element with motif comprised of two identical atoms, additional structural extinctions (destructively interfering X-ray waves for certain hkl) occur as compared to the single atom motif F-lattice crystals. Changes in Crystal System! Compounds, more complex motif than single atom Lattice (FCC) and the Motif, . Two interpenetrating FCC lattices shifted relative to each other, see phase factor. From Structure Factor calculation idealized Intensity and fingerprint patterns From Bragg Law calculation obtain all the relevant Bragg angles then can produce idealized / theoretical Powder Diffraction Patterns NaCl idealized diffraction pattern for a powder diffractometer X-ray diffraction experiment, exhibits WEAK and STRONG diffracted intensities note that the diffraction peaks do not have a specific shape under idealized conditions. Scattering Physics Basics; THE STRUCTURE FACTOR revisited Diffraction; Elastic!...
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This note was uploaded on 01/07/2011 for the course MEMS Mems1054 taught by Professor Wiezorek during the Fall '10 term at Pittsburgh.

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MEMS1054_wks7-9 - MEMS1054 Week 6-8- Diffraction 2/3...

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