On Mon, 26 Apr 1999, Peter Y. Zavalij wrote:
> The equation (2) is nothing else but specimen shift in the Bragg-Brentano
> geometry.
Yes, of course, and for this geometry I have no problems in comprehending
equation (2). But i.e. in the manual of FULLPROF the same equation is used
for the Debye-Scherrer-geometry and I can't understand how this could be
correct.
<cite from FULLPROF manual, last month's HTML-version>
Debye-Scherrer: the largest shifts of Debye-Scherrer rings result from
sample off-centering and absorption. Eccentricity perpendicular to the
incident beam direction is normally a second order effect if both sides
of the Debye-Scherrer ring are measured.
If only one side of the cone is measured, the line shift takes the form:
D2Theta = e/R cosTheta [in radians]
where e denotes the eccentricity, that is the refined parameter is
SYCOS = e/R.
</cite>
Standard books dealing with the basics of powder diffraction (at least
those I looked into) don't give an equation for the
Debye-Scherrer-geometry. It is mentioned that a displacment error
exists for Bragg-Brentano- and Debye-Scherrer-geometry, and then only the
formula (2) is given for Bragg-Brentano.
Therefore I'm searching for the article, in which the development of the
displacment error for Debye-Scherrer-geometry is described. I couldn't
find it up to now, since these equations seem to be so old that no proper
citations are given anymore.
Daniel T�bbens
>
> > I have a question concerning the systematic line shifts due to sample
> > off-centering in the Debye-Scherrer-geometry. The shift D2Theta due to an
> > eccentricity e in the incident beam direction is always given as
> > (1) D2Theta = (e/R)*sin(2*Theta)
> > with R being the radius of the goniometer circle. For the shift caused by
> > an eccentricity normal to the incident beam direction it is given in the
> > literature and used in refinement programms as
> >
> > (2) D2Theta = (e/R)*cos(Theta)
> >
> > When I tried to comprehend this equations I had no problems with (1), but
> > for the eccentricity normal to the incident beam direction I always got
> >
> > D2Theta = (e/R)*cos(2*Theta)
> >
> > instead of (2). So, does anybody here in the list know the article in
> > which the development of (2) is described?
> >
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Daniel M. T�bbens Tel.: +49 30 8062-2793
Hahn-Meitner-Institut Fax : +49 30 8062-2999
Glienicker Stra�e 100
D-14109 Berlin, Deutschland http://www.hmi.de/people/toebbens/
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