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

# Step by step process of computing diffraction

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Step-by-step process of computing diffraction intensity :   Example = Au Si Structure factor for diamond structure a(Si)=5.4307Å, Cu-K =1.5405Å line h k l d hkl (Å) s i n f S i (1) F h k l 2 (2) p (3) p-L factor (1•2•3) Rel. int. (%) • Make a table like: • Information needed:      Lattice parameter(a) for Au Wave length of x-ray Atomic structure factor for Au    Structure factor determine which set of (hkl)planes diffract Calculate interspacing d hkl = a/ h 2 +k 2 +l 2    From                               compute    and  sin  (use n   1   n  = 2d hkl •sin Find the value corresponding to sin   from figure  j=1 N Compute   |F hkl |   from                                                  ,  where f is from  This is a multiplicity factor corresponding to (hkl)   P-L(Polarization-Lorentz) factor either calculate or read Atomic Scattering  Factor for Au 0 10 20 30 40 0.00 0.50 1.00 Sin  / Atomic Scattering Factor 50 60 70 80 Multiply (1), (2) and (3) Then normalize to obtain relative Intensity (%) Review

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(1) (2) (3) (4) (5) (6) FCC:   (h,k,l) are  unmixed (2) & (3) combined =  See table Not considered  s i n 2 • c o s ( 1 + c o s 2 2 ) Other information :   Cu-Ka line (1.5405 Å ) Lattice constant for Au=4.08 Å Review
Si Structure factor for diamond structure a(Si)=5.4307Å, Cu-K =1.5405Å line h k l d hkl (Å) s i n f S i (1) F h k l 2 (2) p (3) p-L factor (1•2•3) Rel. int. (%) Workshop :     Make a table like this Au Au=4.08 Å Au h,k,l are not mixed FCC: Review

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Si Structure factor for diamond structure a(Si)=5.4307Å, Cu-K =1.5405Å line h k l d hkl (Å) s i n f S i (1) F h k l 2 (2) p (3) p-L factor (1•2•3) Rel. int. (%) Workshop Au 111 200 220 311 222 400 331 1 2 3 4 5 6 7        (h k l) 1 100 2 110 3 111 4 200 5 210 6 211 7 --- 8 220 9 300    221 10 310 11 311 12 222 13 320 14 321 15 ---- 16 400 410    322 18 411    330   h 2 +k 2 +l 2             Possible (hkl) h,k,l are not mixed FCC: d hkl = a/  h 2 +k 2 +l 2.3556 2.0400 1.4425 1.2302 1.1778 1.0200 0.9360 2d hkl sin  sin       1 2d hkl 0.212 0.245 0.347 0.406 0.425 0.490 0.534 52 49 37 33 31 29 28 (4f) 2 2704 2401 1369 1089 961 841 784 8 6 12 24 8 6 24 19.1 22.2 32.3 38.7 40.9 49.0 55.3 15 11 4.7 3.5 3.1 2.9 3.0 324480 158466 77211 91476 23832 14633 56448 100 48.8 23.8 28.2 7.3 4.5 1.8 Au=4.08 Å Atomic Scattering Factor for Au 0 10 20 30 40 0.00 0.50 1.00 Sin  / Atomic Scattering Factor 50 60 70 80 0.212 0.245 0.347 0.406 0.425 0.490 0.534 52 49 37 33 31 29 28 19.1 22.2 32.3 38.7 40.9 49.0 55.3 15 11 4.7 3.5 3.1 2.9 3.0 Au Atomic Scattering Factor for Au                   Appendix 12 0 10 20 30 40 0.00 0.50 1.00 Sin  / Atomic Scattering Factor 50 60 70 80 0.212 0.245 0.347 0.406 0.425 0.490 0.534 52 49 37 33 31 29 28 19.1 22.2 32.3 38.7 40.9 49.0 55.3 15 11 4.7 3.5 3.1 2.9 3.0
19.1 22.2 32.3 38.7 40.9 49.0 55.3 100 48.8 23.8 28.2 7.3 4.5 1.8 % 2 38.6 44.4 64.6 77.4 81.8 98.0 110.6 1 11 1 9 8 7 6 5 4 3  Calculated XRD pattern  (111) (200) (220) (311) (400) (331) Diffraction angle  (222) 2 Review

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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.
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• Fall '12
• p
• Diffraction, Neutron diffraction, X-ray scattering techniques

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