Refinement parameters

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Presentation transcript:

Refinement parameters What are the parameters to be determined? atom positional parameters atom thermal motion parameters atom site occupancy parameters background function parameters peak shape parameters sample displacement, sample transparency, zero-shift errors unit cell dimensions preferred orientation, absorption, porosity, extinction parameters scale factor(s)

Peak shape parameters What determines peak shape? Instrumental source image flat specimen axial divergence specimen transparency receiving slit monochromator(s)

Peak shape parameters What determines peak shape? Spectral inherent spectral width most prominent effect - Ka1 Ka2 Ka3 Ka4 overlap

Peak shape parameters What determines peak shape? Specimen mosaicity crystallite size microstrain

Peak shape parameters Historical Began with neutron diffraction - peak shapes nearly Gaussian

Peak shape parameters 1st basic peak parameter - FWHM Caglioti formula: H = (U tan2 q + V tan q + W)1/2 i.e., FWHM varies with q or 2q

Peak shape parameters 1st basic peak parameter - FWHM Caglioti formula: H = (U tan2 q + V tan q + W)1/2 i.e., FWHM varies with q or 2q

Peak shape parameters X-ray case more complicated not usually Gaussian not usually Lorentzian usually need to mix the two somehow

Peak shape parameters

Peak shape parameters 4 most common profile fitting fcns

Peak shape parameters 4 most common profile fitting fcns

Peak shape parameters 4 most common profile fitting fcns G(z) = ∫ tz-1 et dt

Peak shape parameters 4 most common profile fitting fcns

Peak shape parameters But peaks are usually asymmetric - even after a2 stripping!

Peak shape parameters Finally - use NIST std 660 (LaB6) to determine broadening from instrumental and spectral contributions & kept constant (U, V, W)