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Lecture19-XRD-Line(Peak)PositionsIntensities

Lecture19-XRD-Line(Peak)PositionsIntensities - EMSE 312 –...

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Unformatted text preview: EMSE 312 – Diffraction Principles Lecture 19 Powder X-ray Diffraction (XRD) Techniques Analysis of XRD Spectra: Peak/Line Locations Peak/Line Intensities 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 π θ θ ⎡ ⎤ ∝ = + + + × ⎢ ⎥ ⎣ ⎦ ( ) ( ) Basis X X g S Zn F f f θ θ ⎡ ⎤ = + ⎣ ⎦ ( ) ( ) ( ) 2 X X S Zn I 1 6 f f θ θ ∝ ⋅ + ( ) ( ) Basis X X g S Zn F f i f θ θ ⎡ ⎤ = + ⋅ ⎣ ⎦ ( ) ( ) ( ) 2 2 X X S Zn I 1 6 f f θ θ ⎡ ⎤ ⎡ ⎤ ∝ ⋅ + ⎣ ⎦ ⎣ ⎦ ( ) ( ) Basis X X g S Zn F f i f θ θ ⎡ ⎤ = − ⋅ ⎣ ⎦ ( ) ( ) ( ) 2 2 X X S Zn I 1 6 f f θ θ ⎡ ⎤ ⎡ ⎤ ∝ ⋅ + ⎣ ⎦ ⎣ ⎦ ( ) ( ) Basis X X g S Zn F f f θ θ ⎡ ⎤ = − ⎣ ⎦ ( ) ( ) ( ) 2 X X S Zn I 1 6 f f θ θ ∝ ⋅ − High Med Med Low EMSE 312 – Diffraction Principles Diffraction Techniques - XRD ZnS Basis Lattice g g g F F F = × • 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 EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Select y and z so that P is in the x-z plane – The total scattered intensity: gives or O P ____ r O P = x z 2 θ y z α 2 P P P y z 2 K 1 c o s 2 I I I I r 2 θ ⎛ ⎞ + = + = ⎜ ⎟ ⎝ ⎠ P 2 2 I K 1 c o s 2 I r 2 θ ⎛ ⎞ + = ⎜ ⎟ ⎝ ⎠ Polarization Factor P y 2 I K I 2 r = ⋅ P 2 z 2 I K I c o s 2 2 r θ = ⋅ EMSE 312 – Diffraction Principles 0.000 0.250 0.500 0.750 1.000 1 2 3 4 5 6 7 8 9 ( ) 2 1 c o s 2 P 2 θ θ ⎛ ⎞ + = ⎜ ⎟ ⎝ ⎠ Polarization Factor θ EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Geometric Aspects – Forward Scattering:...
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Lecture19-XRD-Line(Peak)PositionsIntensities - EMSE 312 –...

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