Apu,

The basics of instrument contributions to profile shapes for X-ray
laboratory data should really be well known by now. 

UVW (add Z if you like) is a calibration approach that can never fully
describe X-ray laboratory data as Gaussians and Lorentzians do not
describe the instrument aberrations nor can they describe the specimen
transparency aberration. From memory the UVW approach was developed for
neutron CW data.

Armel wrote:

>People prefer to convolute g (or a model of g) with a model of f in
>order to obtain h, this is much more stable than to deconvolute.
>Nobody works on the f full profile (you would be alone) because
>nobody can obtain a realistic representation of it, without strange
>effects (ripples, etc) due to error propagation (either by Fourier
>inversion method or else).

Convolution like Armel has mentioned needs to be performed in order to
get to the specimen contribution. I do however disagree in that programs
such as XFIT (take note Armel as its free from
http://www.ccp14.ac.uk/tutorial/xfit-95/xfit.htm) and later programs
such as TOPAS-Academic do remove the instrument contribution using
convolution. GSAS also uses some fundamental parameters ideas such as
the Finger and Cox model for axial divergence. Excuse me if I have not
mentioned other note worthy efforts.

Like Armel eluded to deconvolution is difficult for reasons I wont go
into here and it is not the preferred way of doing things in my view. 

Convolution techniques are well known, see: 

Wilson, A. J. C. (1963), "Mathematical Theory of X-ray Powder
Diffractometry", Gordon And Breach, Science Publishers, New York. 
Cheary, R. W. & Coelho, A. A.  (1992).   J Appl. Cryst. 25, 109-121.
Cheary, R. W. & Coelho, A. A.  (1998). "Axial Divergence in a
Conventional X-ray Powder Diffractometer I. Theoretical Foundations". J.
Appl. Cryst. 31, 851-861.

and they do work in practice on whole patterns and have been doing so
for the past 12 years. 

Typically diffractometers are misaligned to some degree (in some cases a
large degree) and refinement of one or two of the key instrumental
parameters are necessary. For a well aligned instrument these key
instrumental parameters should refine to +-10% of their true values.
Otherwise the diffractometer is misaligned.

It is worthwhile to use a standard such as LaB6 and to fit to LaB6 using
convolution in order to ensure proper instrument alignment. 

Having argued the point for the fundamental parameters approach I would
however add that an intelligent calibration can be fruitful for
non-standard diffractometer configurations. ie. it is almost always
possible to use a few generic convolutions with a hint of physical
meaning to fit to LaB6 whilst fixing the specimen contribution in order
to obtain the instrument contribution.

For standard Bragg-Brentano geometry, here are a few things that
fundamental parameters are good at describing:

1) A proper description of the emission profile.
2) Axial divergece. Strong preferred orientaion effects can also lead to
patchy diffraction cones which affect axial divergence.
3) Specimen transparancy especially for specimens that have low linear
absorption coefficients. Total penetration by the primary beam can also
be of signifiance and should be corrected when the sample is thin or
organics are collected with Mo radiation etc...
4) The receiving slit aberration for wide slits in the equitorial plane.
5) Equitorial divergence - important when variable divergence slits are
used.

When one looks at the shapes of these aberrations as a function 2Th, it
seems to not make sense to talk about Voigts in terms of describing the
convoluted effects unless of course the effects are small in comparison
to the sample related Voigt effects.

regards
alan

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