Lecture24-XRD-PreciseLatticeParameterMeasurements

Lecture24-XRD-PreciseLatticeParameterMeasurements - EMSE...

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Unformatted text preview: EMSE 312 Diffraction Principles Lecture 24 Powder X-ray Diffraction (XRD) Techniques Precise Lattice Parameter Measurements (Review) Residual Stress Measurements EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 Diffraction Principles Remaining Classes Today Nov. 22: Precise Lattice Parameter Review and examples Residual Stress Measurements Monday Nov. 29: Chemical Analysis Using X-ray Techniques (Cont) Qualitative and Quantitative Analysis Thursday Dec. 2: Last Class 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 Precise Lattice Parameter Determinations Indirect Method Measure 2 Determine d hkl (reciprocal space) Calculate lattice parameters (real space) from d-spacings Sample Detector 1 2 hkl 2d sin = 2 2 2 hkl hkl 2 2 2 a d a d h k l h k l = = + + + + EMSE 312 Diffraction Principles Diffraction Techniques - XRD Precise Lattice Parameter Determinations sin vs. Small Error for 90 o Extrapolation of data points to 90 o What function should be used? ( ) o 90 a l i m a = EMSE 312 Diffraction Principles Diffraction Techniques - XRD Precise Lattice Parameter Determinations Example 2 sin or 2 cos EMSE 312 Diffraction Principles Diffraction Techniques - XRD Precise Lattice Parameter Determinations Cohens Method Cubic Crystals a true is the quantity that we try to determine or and [ ] ( ) 2 2 2 2 2 2 true sin true h k l 4a = + + [ ] ( ) 2 2 2 2 2 2 2 true sin observed h k l D'sin 2 4a + + = [ ] [ ] 2 2 2 sin observed sin true sin = 2 sin C A = + 2 2 true C 4 a = ( ) 2 2 2 h k l = + + A D ' 1 = 2 10sin 2 = Solve Using LSF Methods EMSE 312 Diffraction Principles Diffraction Techniques - XRD Precise Lattice Parameter Determinations The Taylor Sinclair or Nelson-Riley Method They proposed the same technique at the same time independently Start with the expected error determined from differentiation of Braggs Law The largest error is the displacement of the sample from the Diffractometer axis 2 2 d D c o s c o s d R s i n s i n = Sample Detector 1 2 D R 1 2 B 2 + = EMSE 312 Diffraction Principles Diffraction Techniques - XRD Precise Lattice Parameter Determinations Example 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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Lecture24-XRD-PreciseLatticeParameterMeasurements - EMSE...

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