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

# In particular describe how you obtain necessary

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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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Relative to a lattice point the centre of atom  j  of the basis is  R  = x j a  + y j b  + z j c   NaCl structure ZnS structure CsCl structure Primitive cubic lattice Face  centred cubic lattice Lecture 4 Basis: 1/2,1/2,1/2 0,0,0 Basis: 1/2,1/2,1/2 0,0,0 Basis: 1/4,1/4,1/4 0,0,0
u, v, w = 0,   0,    0               1/2,1/2,1/2 CsCl structure   versus  BCC structure   1st             2nd

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Basis: 1/4,1/4,1/4 0,0,0
Structure factors for  diamond  and  zincblende  structures Diamond: Two FCC interpenetrated with the second FCC originated at (1/4, 1/4, 1/4) position (same kind of atoms) Zincblende: Two FCC interpenetrated with the second FCC originated at (1/4, 1/4, 1/4) position, but different kind of atoms 4-atoms 4-atoms 4-atoms 4-atoms

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Diamond Structure and  Zincblende 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 ( 1/4 1/4 1/4) 1st FCC atom positions 2nd FCC atom positions 0        0        0  1/4     1/4    1/4 1/2   1/2       0  3/4     3/4    1/4 0      1/2      1/2                                  1/4      3/4    3/4 1/2     0      1/2 3/4      1/4    3/4 • Looking at the structure  very carefully • Find the atom positions that fill in 4-tetrahedral sites 1st FCC atom positions 4-tetrahedral sites 0        0        0   1/4     1/4    1/4 1/2   1/2       0  3/4     3/4    1/4 0      1/2      1/2                                  1/4      3/4    3/4 1/2     0      1/2 3/4      1/4    3/4 Which one do you prefer?    It is up to you!
How do you compute structure factor for Diamond?

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

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