Thank you, Nicolae, A Williamson-Hall plot shows different positive slopes for lines along 200,400 and 111,222. They intersect close to d*=0 so as I understand it this means that there is an effect of anisotropic strain, but the size effect is isotropic, right?
I was not aware of your paper on the subject on anisotropic broadening, but found it very illuminating. regards, Jens > -----Original Message----- > From: Nicolae Popa [mailto:[EMAIL PROTECTED] > Sent: 24. august 2004 11:06 > To: [EMAIL PROTECTED] > Subject: Re: Anisotropic line broadening in cubic material > > > Dear Jens, > > Peter Sthephens is right, try first to see if you have an > anisotropic strain effect. But if not, it doesn't mean that > you have not a simple size effect, not necessarily staking > faults. The size anisotropy model in GSAS is in fact the rod > (or plate) model (I wonder why the needles model was not > introduced - sin(phi) in place of cos(phi)) and you have to > give apriori the "broadening axis". For non cubic is easy to > guess because frequently is the n-fold axis (n=2,3,4,6) and > the average over equivalents has no effect. But as Peter said > the guess is ambiguous for cubic (and not only). Nevertheless > you have an approach for size anisotropy that needs no > apriori information (except the Laue group), the spherical > harmonics approach. For details see the same (J. Appl. Cryst. > 31, 176 (1998)). In spite of some skeptical opinions (not > clearly argued) the approach is enough robust and you can > expect to obtain accurate volume averaged column length as > function of direction. > > Best wishes, > > Nicolae Popa > > > > > > > Jens, > > > > Your effect might be more related to strain than size > broadening. You > > would have to check widths at various diffraction orders in a given > > direction (i.e., 111, 222, 333, etc., vs 200, 400, 600, etc. for an > > fcc material). If the widths increase roughly in proportion to > > diffraction order, but with a different slope for the two > directions, > > you have anisotropic strain broadening. > > > > This was noted by Stokes and Wilson (Proc. Phys. Soc. London 56, > > 174-181 > > (1944)) in cold-worked fcc metals, who had a model as a random > distribution > > of stresses. N. Popa and I have independently considered > the effect > > more recently from a phenomenological viewpoint (J. Appl. > Cryst. 31, > > 176 (1998) and ibid 32, 281 (1999), respectively). And there is a > > growing > literature, > > especially from the group of Tamas Ungar, on the effect of specific > lattice > > defects on strain-broadening in diffraction patterns. > > > > Regarding your use of the anisotropic size broadening model > in GSAS, > > as > you > > point out, "broadening axis" for a cubic material is a rather iffy > concept. > > If my understanding is correct, GSAS does not do the full symmetry > > equivalents in that calculation, and so it's a matter of > luck how the > > calculation will be done. That is, if you list a (111) broadening > > axis, and the reflection list contains (111), you'll get > one answer, > > but if you list (-1 1 1) broadening axis, the (111) > reflection will be > > calculated differently. > > > > -Peter > > > > ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ > > Peter W. Stephens, Professor > > Department of Physics & Astronomy > > State University of New York > > Stony Brook, NY 11794-3800 > > > > >
