Lecture25-XRD-ChemicalAnalysisUsingXRD

Lecture25-XRD-ChemicalAnalysisUsingXRD - EMSE 312 –...

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Unformatted text preview: EMSE 312 – Diffraction Principles Lecture 25 Powder X-ray Diffraction (XRD) Techniques Chemical Analysis using XRD Qualitative Analysis Quantitative Analysis EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 – Diffraction Principles Remaining Classes • Today: Wednesday – Nov. 28: – Chemical Analysis Using X-ray Techniques (Cont) • Qualitative and Quantitative Analysis • Monday – Dec. 3: – Analytical Electron Microscopy • X-ray Spectroscopy (WDXS and EDXS) – Wrap-up (including texturing) • Wednesday – Dec. 5: – Review of the 2 nd half of the course – Review of Old Exams EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Qualitative and Quantitative Analysis – Qualitative Methods • Detect the Presence of Different Compounds in a Sample – Quantitative Methods • Determine the Volume Fraction of Different Compounds in a Sample • First – what volume is examined – Depth of X-ray Penetration EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Depth of X-ray Penetration – Diffractometer • Consider the geometry for the diffractometer: β γ 1 I x dx A A B C ( ) D dI a b I exp AB BC dx μ ⎡ ⎤ = ⋅ ⋅ ⋅ − + ⎣ ⎦ A a: Volume fraction of the sample having grains in good orientation b: The fraction of the incident beam diffracted by a unit volume B β γ θ ≈ ≈ Sample EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Depth of X-ray Penetration – Diffractometer D a b I 2 x dI exp dx sin sin μ θ θ ⋅ ⋅ ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ 1 sin γ = A x AB sin γ = x BC sin β = D D I ab 2 x I dI exp dx sin sin I ab I ab sin 2 x exp const. sin 2 sin 2 μ θ θ θ μ θ μ θ μ ∞ ∞ ∞ ⎛ ⎞ = = − ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ ⎡ ⎤ ⎛ ⎞ = − − = = ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ ⎝ ⎠ ∫ ∫ 1 A const. μ ∝ = Sample EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Depth of X-ray Penetration • The Fraction of the total integrated intensity at a depth x from a sample of infinite thickness is: – Diffractometer: – Back reflection: • (e.g., Laue) γ β θ ≈ ≈ o 90 γ = o 2 9 β θ = − x D x D dI 1 1 G 1 exp x sin sin dI μ γ β ∞ ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ = = − − + ⎢ ⎜ ⎟⎥ ⎢ ⎥ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦ ∫ ∫ D x 2 x G 1 e x p sin μ θ ⎡ ⎤ ⎛ ⎞ = − − ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ BR x 1 G 1 e x p x 1 sin μ β ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ = − − + ⎢ ⎜ ⎟⎥ ⎢ ⎥ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦ EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Depth of X-ray Penetration – Example Diffractometer: Cu (331) peak x K s i n x 2 θ μ = o 2 136.7 θ = 1 52.9 8.936 473cm μ μ ρ ρ − ⎛ ⎞ = ⋅ = ⋅ ≈ ⎜ ⎟ ⎝ ⎠ x D x 2 x 1 K l n sin 1 G μ θ ⎛ ⎞ = = ⎜ ⎟ − ⎝ ⎠ where D x 2 x G 1 e x p sin μ θ ⎡ ⎤ ⎛ ⎞ = − − ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ x K x G 0.69 0.50 1.39 0.75 2.30 0.90 3.00 0.95 4.61 0.99 6.91 0.999 ( ) x m μ 6.8 13.6 22.6 29.4 45.2 67.9 EMSE 312 – Diffraction Principles...
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  • Spring '08
  • Lagerlof,P
  • Qualitative Research, diffraction techniques, diffraction principles, Quantitative Compositional Analysis

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Lecture25-XRD-ChemicalAnalysisUsingXRD - EMSE 312 –...

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