Lecture26-XRD-QuantitativeAnalysis

Lecture26-XRD-QuantitativeAnalysis - EMSE 312 Diffraction...

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Unformatted text preview: EMSE 312 Diffraction Principles Lecture 26 Powder X-ray Diffraction (XRD) Techniques Chemical Analysis using XRD Quantitative Analysis Review Texturing Analytical Electron Microscopy X-ray Spectroscopy (WDXS and EDXS) EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 Diffraction Principles Remaining Classes Today Dec. 3: Last Day of Classes: Analytical Electron Microscopy X-ray Spectroscopy (WDXS and EDXS) Wrap-up (including texturing) Independent Study: 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 Set of Known Mixtures External Standards Internal Standards Least Square Fit of Many peaks EMSE 312 Diffraction Principles Diffraction Techniques - XRD Quantitative Compositional Analysis Internal Standards Standard part of the Sample Use All Peaks to minimize the Error due to Texturing Note: This will allow for Peak Overlap ( ) 2 hkl hkl UC S F 1 I m LP V = Start with the General Expression for Intensities: 1) Each peak will be proportional to the volume fraction of the specific compound contributing to the peak 2) More than one compound can contribute to a particular peak EMSE 312 Diffraction Principles Diffraction Techniques - XRD Quantitative Compositional Analysis Consider a total of m XRD Peaks from n different phases The contribution to each peak is proportional to the volume fraction (x j ) of each phase contributing to the peak Define Matrix Elements for peak i and element j Note: the linear absorption coefficient is the same for each peak and can be ignored ( ) ( ) ( ) 2 hkl hkl i j j j UC S j F 1 I I m L P x V = = ( ) 2 j j i ij i i j UC F a m LP V = ( ) i ij j j I a x = EMSE 312 Diffraction Principles Diffraction Techniques - XRD Quantitative Compositional Analysis The Theoretical Peak intensities (T i ) of the X-ray Diffractogram for the Sample is then given by: where and a ij = 0 for a compound that does not contribute to a particular peak Note: The Theoretical Intensities could be the Normalized Intensities m n mn j mj m m i n in j ij i i n n j j n n j j T x a x a x a x a T x a x a x a x a T x a x a x a x a T x a x a x a x a = + + + + + = + + + + + = + + + + + = + + + + + " " # # # # # " " # # # # # " " " " 2 2 1 1 2 2 1 1 2 2 2 2 22 1 21 1 1 1 2 12 1 11 j j x 1 = EMSE 312 Diffraction Principles Diffraction Techniques - XRD...
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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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Lecture26-XRD-QuantitativeAnalysis - EMSE 312 Diffraction...

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