Lecture18-XRD-LorentzPolarizationFactor

Lecture18-XRD-LorentzPolarizationFactor - EMSE 312...

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Unformatted text preview: EMSE 312 Diffraction Principles Lecture 18 Powder X-ray Diffraction (XRD) Techniques Intensity of Diffracted Beams: Polarization Factor [P( )] Lorentz Factor [L( )] Lorentz Polarization Factor [LP( )] EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 Diffraction Principles Diffraction Techniques - XRD Consider ZnS Intensity Even: (h+k+l) = 4n = 2(2n) Odd: (h+k+l) = 4n + 1 Even: (h+k+l) = 4n + 2 =2(2n+1) Odd: (h+k+l) = 4n + 3 ZnS Basis Lattice g g g F F F = ( ) ( ) ( ) { } 2 2 ZnS X X Lattice g S Zn g i I F f f e x p h k l F 2 = + + + ( ) ( ) Basis X X g S Zn F f f = + ( ) ( ) ( ) 2 X X S Zn I 1 6 f f = + ( ) ( ) Basis X X g S Zn F f i f = + ( ) ( ) ( ) 2 2 X X S Zn I 1 6 f f = + ( ) ( ) Basis X X g S Zn F f i f = ( ) ( ) ( ) 2 2 X X S Zn I 1 6 f f = + ( ) ( ) Basis X X g S Zn F f f = ( ) ( ) ( ) 2 X X S Zn I 1 6 f f = High Med Med Low EMSE 312 Diffraction Principles Diffraction Techniques - XRD ZnS Basis Lattice g g g F F F = Prediction: (100) mixed - zero intensity (110) mixed - zero intensity (111) 4n+3 - med intensity (200) 4n+2 - low intensity (210) mixed - zero intensity (211) mixed - zero intensity (220) 4n - high intensity (221) mixed - zero intensity (300) mixed - zero intensity (310) mixed - zero intensity (311) 4n+1 - med intensity (222) 4n+2 - low intensity (321) mixed - zero intensity etc. Consider ZnS Prediction: (111) 4n+3 - med intensity (200) 4n+2 - low intensity (220) 4n - high intensity (311) 4n+1 - med intensity (222) 4n+2 - low intensity (400) 4n - high intensity Something else must also be important EMSE 312 Diffraction Principles Consider the scattering by an electron The intensity of the scattered beam depends on the scattering angle J.J. Thompson (1897) Scattering of an x-ray intensity of the incident beam charge of an electron mass of an electron [rest mass] permeability of vacuum Diffraction Techniques - XRD acceleration 2 2 4 2 2 2 2 2 e K I I sin I sin 4 m r r = = O P ____ r O P = ( ) 7 4.7 10 Vs Am = ( ) 19 e 1 . 6 1 C = ( ) 31 m 9 . 1 1 k g = ( ) I 2 2 e K 4 m = Intensity at point P e EMSE 312 Diffraction Principles Diffraction Techniques - XRD X-rays are un-polarized EM waves Consider an X-ray traveling along the x-axis The electric polarization vector is in a random direction in the y-z plane The electric polarization vector can be resolved into two plane polarized components and ; i.e., and On average The intensity is proportional to and E y E 2 2 2 2 y z E E...
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Lecture18-XRD-LorentzPolarizationFactor - EMSE 312...

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