Lecture16-XRD-AtomicScattringFactors

Lecture16-XRD-AtomicScattringFactors - EMSE 312 –...

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Unformatted text preview: EMSE 312 – Diffraction Principles Lecture 16 Powder X-ray Diffraction (XRD) Techniques Atomic Scattering Factor Unit Cell Structure Factor EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 – Diffraction Principles Diffraction • B r a g g s L a w – Diffraction Occurs for Positive Interference ( ) B hkl 2d sin n θ λ = ⋅ hkl d λ 1 1’ 2 2’ B θ B θ ( ) B hkl d s i n θ ( ) B hkl d s i n θ Path Difference ( ) B 1'2' hkl 2d sin n δ θ λ = = ⋅ EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD – Powder X-ray Diffraction – Constant Wavelength ( λ =const) – Each plane (d hkl ) will diffract when the angle between the incident beam and the plane normal satisfy Bragg’s Law – Peak Locations are related to Reciprocal Space • i.e., the Unit Cell Lattice Parameters – What about the Intensity? ( ) B hkl 2d sin n θ λ = ⋅ Plane Normal Plane d hkl B θ B θ n Diffracted Beam Detector B 2 θ Incident Beam EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Scattering by an Atom – X-rays interact with electrons • probability of interaction – The probability of interaction between an X-ray an Atom is proportional to the number of electrons around the atom (Z) – The atomic scattering factor – θ = 0, Additive X Atom f = Amplitude of the wave scattered by an atom Amplitude of the wave scattered by an electron X Atom f Z = EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Scattering by an Atom – θ ≠ 0, depends on Atom Size and Scattering Angle • Small phase shifts 2 θ X Atom f Z = 2 θ hkl sin 1 2d θ λ = Plot as a function of EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Scattering by an Atom [Cullity Appendix 12] EMSE 312 – Diffraction Principles x Diffraction Techniques - XRD • Scattering by a Unit Cell ( ) B hkl 2d sin n θ λ = ⋅ hkl d B θ B θ Path Difference ( ) B 1'2' hkl 2d sin n δ θ λ = = ⋅ ( ) B hkl d s i n θ ( ) B hkl d s i n θ 2 2’ 1 1’ 3 3’ ( ) B 1'3' 2xsin n δ θ λ = < ⋅ ( ) B xsin θ ( ) B xsin θ EMSE 312 – Diffraction Principles...
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This note was uploaded on 12/01/2011 for the course EMSE 312 taught by Professor Lagerlof,p during the Spring '08 term at Case Western.

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Lecture16-XRD-AtomicScattringFactors - EMSE 312 –...

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