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972 B3102005 Xrd4

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1. Fig. 4.1 The geometry involved in calculating the integrated intensity from a small single crystal, which is rotated at constant angular velocity ω about an axis…
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  • 1. Fig. 4.1 The geometry involved in calculating the integrated intensity from a small single crystal, which is rotated at constant angular velocity ω about an axis normal to the paper.
  • 3. , ,
  • 4. …… Total energy collected from a small crystal of volume  V
  • 5. Fig. 4.2 The geometry involved in calculating the integrated intensity for an extended face mosaic crystal
  • 6. …… Total energy collected from a mosaic crystal with a linear absorption coefficient of  In a powder sample , only a fraction (  ) of the irradiated crystals is effective in intensity contribution. p = multiplicity factor
  • 8. Fig. Representation of the number of crystal in powder sample whose hkl planes make angles between θ+α and θ+α+dα with the primary beam.
  • 10. Total intensity collected from a powder sample by a pinhole camera : With effective volume V:
  • 11. Lorentz-polarization factor LP=(1+cos ² 2θ)/(sinθsin2θ) Integrated intensity collected from a powder sample by a pinhole camera : Integrated intensity collected from a powder sample by a diffractometer :
  • 12. 2  R Length of Debye ring = 2 π Rsin2 
  • 14. Lorentz-Polarization factor
  • 15. Absorption factor
  • 17. e 2  t /sin 
  • 19. Perfect crystal
  • 20. Extinction <ul><li>Primary extinction: after diffracted at A an B, K 2 has a phase shift of  and thus interfere destructively with K o (happens in perfect crystal). </li></ul><ul><li>Secondary extinction: In mosaic crystal, if mis-orientations among domains are not large enough, incident beam on an interior domain has been weakened by previous correctly oriented domains due to diffraction </li></ul>
  • 21. Integrated intensity from a thick perfect crystal with negligible absorption, N = number of unit cells per unit volume Reflectivity = 100% over a range of 2s in the rocking curve
  • 22. For CuK  ,  =1.542 Å , F 211 =26.2 per CaCO 3 , N=1.6x10 22 ,for an unpolarized beam
  • 23. Reflectivity = 1 over 2s in the rocking curve
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