Part-5+XRD(2)+theory(2018)+CP.ppt

# Mse 331 hw4 due friday 1 precisely describe a step by

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MSE-331 HW#4 (Due Friday Nov 30, 2018) [1]. Precisely describe a step-by-step process involved in calculating the diffraction intensity for Al. In particular describe how you obtain necessary information. [2]. Applying [1], theoretically calculate the diffraction intensities for Ge using a Cu-K a line, and make a plot of relative intensities of XRD pattern. Find necessary information to solve this question. [3]. Theoretically calculate the diffraction pattern for CaO using a Cu-K a line. (a) What is the crystal structure for CaO? (b) Derive simplified expressions for the structure factor F for CaO in terms of h, k and l . (c) Find the lattice constant of CaO from the ionic radius. (d) List the first five diffraction lines based on the structure factor of CaO derived in (b). (e) Plot atomic scattering factors for calcium and oxygen ions as a function of sin / . Note: use appropriate form of the valence state for calcium and oxygen in CaO form. (e) Calculate the theoretical intensity of the diffraction peaks for (c). (f) Make a plot of the calculated X-ray diffraction intensity with diffraction angle. (g) The diffraction pattern from CaO powder is shown bellow. Compare your calculated pattern with the experimentally determined pattern shown bellow.

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How do you compute structure factor for Zincblend? A B F f j e 2 i ( hu j kv j lw j ) j 1 8 f A [1 e i ( k l ) e i ( h l ) e i ( h k ) ] f B e i 2 ( h k l ) [1 e i ( k l ) e i ( h l ) e i ( h k ) ] To be none-zero, h, k and l are unmixed. = +1, when (h+k+l)/2=even # =  -1, when (h+k+l)/2=odd # = + i,   when (h+k+1)=odd#
Do by yourself

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Which one do you prefer?    It is up to you!   NaCl (or Rock-Salt) Structure   (Two ways of setting atom positions in order to compute structure factor) Procedure-1 Procedure-2 • Using lattice translation  basis • 1st FCC lattice originating from ( 0 0 0) • 2nd FCC lattice originating from ( 1/2 1/2 1/2) 1st FCC atom positions 2nd FCC atom positions 0        0        0  1/2     1/2    1/2 1/2   1/2       0  1        1      1/2 0      1/2      1/2                                  1/2      1       1 1/2     0      1/2 1        1/2     1 • Looking at the structure  very carefully . • Find the atom position corresponding to Cl-. 1st FCC atoms  0        0        0  1/2   1/2       0 0      1/2      1/2          1/2     0      1/2 2nd FCC atoms 1/2    0     0 0      1/2   0 0      0     1/2 1/2  1/2   1/2 •  Try to do both cases to verify that the results become identical (good exercise for you!)

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NaCl structure NaCl structure • Mixed indices : 0 F 0 2 F • Unmixed indices :

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Appendix 10 (page 634) 1.5 1.4 1.3 1. 1.1 1. .9 .8 .7 .6 .5
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• Fall '12
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• Diffraction, Neutron diffraction, X-ray scattering techniques

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