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2spp_MEMS1054_wks7-9 - MEMS1054 Week 6-8 Diffraction 2/3...

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1 MEMS1054 Week 6-8 - Diffraction 2/3 Professor Jörg 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 α = β = γ =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, Θ hkl . Compute for a cubic crystal (note same for P-, I- & F-lattices) with lattice parameter a 0 = x nm=a. 1) Diffracted Directions - The Bragg Law
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2 2) Diffracted Beam Intensities Elements! Motif of one or two identical atoms! Cubic Crystals, a=3.5Å; Copper-k-alpha X-radiation; HCP, a=2.5Å and c/a=1.6333
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3 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!
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4 Compounds, …more complex motif than single atom Lattice (FCC) … and the Motif, …. Two interpenetrating FCC lattices shifted relative to each other, see phase factor.
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5 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…
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6 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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