In response to the question posted this morning by Frank Girgsdies:

Here is a little snatch of topas code for anisotropic broadening in 
orthorhombic system.  (The fitted parameters come from a particular 
refinement I took this from; the factor of 10^4 is empirically chosen to 
get parameter values that are generally between unity and several 
thousand.)  The "theory" behind this is given in PWS, Journal of Applied 
Crystallog. vol. 32, pp 281-289 (1999) and references therein. 
Generalization to other crystal systems is given in that paper as well.

                prm s400  0.00000`_LIMIT_MIN_0 min 0
                prm s004  1287.33878` min 0
                prm s040  1.56981`_LIMIT_MIN_0 min 0
                prm s220  32.53311`
                prm s202  5410.01715`
                prm s022  792.15586`
                prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + H^2 K^2 s220 + 
H^2 L^2 s202 + K^2 L^2 s022;
                lor_fwhm = D_spacing^2 * Tan(Th) * Sqrt(Max(0,mhkl)) / 

Application of this expansion to Lorentzian broadening is not 
mathematically rigorous, but seems to work OK within the framework of 
crystallographic refinements (i.e., if you don't try to interpret the 
fitted broadening parameters in some fundamental way).  My experience is 
based on refinements from synchrotron data, which have mostly Lorentzian 
shape - you might play with using a Gaussian width as well.

Note that the lor_fwhm command increases the width by that amount, so 
other terms in the lineshape, such as possibly a Lorentzian term in 
crystallite size (e.g., CS_L(@, 1000) ) are included as well.  This 
formalism handles all of the strain broadening - even an isotropic 

At the risk of triggering a lengthy discussion, I would point out that 
this 4-th order polynomial expansion in Miller indices actually has some 
basis in elasticity theory (e.g., discussion at the end of the JAC paper 
cited above and subsequent work, for example by T. Ungar et al.), whereas 
spherical harmonic expansions really do not.

Good luck with it,

Peter W. Stephens
Professor, Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800
fax 631-632-8176

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