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

• Notes
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(How does the geometry influence?) Those who wish to learn more about this should read    p.145-150

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Lorentz factor   1 s i n 2 • c o s Polarization factor ( 1 + c o s 2 2 ) Lorentz-Polarization factor =  s i n 2 • c o s ( 1 + c o s 2 2 ) (2, 3)
Appendix 13 How to read this table? Example: Cubic h k l 4 8 h h l 2 4 0 k l 2 4 0 k k 1 2 0 0 l 6 (4) See    p.145

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(5) Measurements at constant temperature,  no effect For  in-situ  temperature variable XRD, you need to take into account Those who wish to learn more about this should read    p.154-157
(6) For first approximation, you may ignore this factor  Those who wish to learn more about this should read    p.150-152

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1.0 0.8 0.6 0.4 0.2 0.0 Intensity (Arb. Units) 110 100 90 80 70 60 50 40 30 20 Angle (2 ) Rutile (110) Single Crystal Diffracted Beam Intensity= (1) • (2) • (3) • (4) • (5) • (6) Peak intensity Structure           Polarization    -   Lorentz            Multiplicity          Temp          Absorption factor  i n c o m i n g x - r a y d i f f r a c t i n g x - r a y r e l a t i v e i n t e n s i t y = 1 / s i n ( 2 B )          n  = 2d hkl •sin Diffraction Angle L-P =   sin 2 cos  (1 +  cos 2 2 )       Not considering
d • Nucleus is much larger than electrons,   so cannot be made to oscillate to any    appreciable extent. • Whereas electrons can oscillate fast     enough  to scatter the x-ray.   Questions: (1) Is the wave scattered by an atom simply the sum of the waves scattered  by         its component of electrons? Or more scattering for higher Z?  (2) Does an atom of atomic number Z, i.e. an atom containing Z electrons,       scatter a wave whose amplitude is Z times of the amplitude of  the wave        scattered by a single electron?    YES   for   ~ 0 or  forward scattering.   No     for   large angle scattering. Atomic scattering factor YES, in general How much larger? Scattering by atoms

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Class Business: Nov 16 (F) • No class business • Today’s lecture  Chapter-5(2): Diffraction theory     Do a lot of math  for today!
1.0 0.8 0.6 0.4 0.2 0.0 Intensity (Arb. Units) 110 100 90 80 70 60 50 40 30 20 Angle (2 ) Rutile (110) Single Crystal Diffracted Beam Intensity= (1) • (2) • (3) • (4) • (5) • (6) Peak intensity Structure           Polarization    -   Lorentz            Multiplicity          Temp          Absorption factor  i n c o m i n g x - r a y d i f f r a c t i n g x - r a y r e l a t i v e i n t e n s i t y = 1 / s i n ( 2 B )          n  = 2d hkl •sin Diffraction Angle L-P =   sin 2 cos  (1 +  cos 2 2 )       Not considering Review

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amplitude scattered by all atoms in a unit cell
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• Fall '12
• p
• Diffraction, Neutron diffraction, X-ray scattering techniques

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