>>Its best to use the terms axial plane and horizontal plane to avoid
>>confusion.
>
>Alan, I'm confused! What do you mean by those terms?
>I thought "axial divergence" was "beam hits
>different points along the two theta axis" -
>is that a misconception?
John, if you had a point source, a point sample and a point receiving
slit then the plane formed by the three points is called the equitorial
plane. Drawing a circle that passes through the three points is called
the focusing circle. Thus the 2Th arm moves in the equitorial plane.
Perpendicular to the equitorial plane are any number of axial planes.
Aberrations can therefore be grouped into two categories, axial and
equitorial aberrations.
Equitorial aberrations include:
The width of the source in the equitorial plane
The divergence of the primary beam in the equitorial plane
The width of the receiving slit in the equitorial plane
The length of the LPSD in the equitorial plane
The length of the sample in the equitorial plane
Tube tails which shows up in old tubes
Sample penetration (Absorption)
Sample displacement (Goniometer axis not being at the sample
surface)
Sample tilt in the axial plane
Sample surface roughness
Axial aberrations include:
The divergence of the primary beam allowed in the axial plane
at each point along the source.
The divergence of the secondary beam allowed in the axial plane
The length of the source, sample and receiving slit in the axial
plane
where allowed is limited by Soller slits and the lengths
There are cross terms which can be reasonably neglected or approximated;
ie. the sine of a small angle is the angle itself in radians etc.
Soller slits are typically inserted to limit axial divergence. In a
parallel beam setup employing a LPSD, an additional secondary Soller
slits (analyser slits) are often inserted to limit eqitorial divergence.
Thus as you pointed out John, Soller slits limit what ever you want but
they do come with their own aberration.
Of importance when thinking about the effects of these aberrations are
the integral breadths of the aberrations as a function of 2Th and the
centroid shifts of the peak as a function 2Th.
These relationships are all defined in TA as simple equations and are
simple enough to keep in one's mind. For a more thorough explanation see
for example:
Wilson, A. J. C. (1963), "Mathematical Theory of X-ray Powder
Diffractometry", Gordon And Breach, Science Publishers, New York.
For a more uptodate review and I think the most pertinent is:
R. W. Cheary, A. A. Coelho and J. P. Cline. J. Res. Natl. Inst. Stand.
Technol. 109, 1-25 (2004). "Fundamental Parameters Line Profile Fitting
in Laboratory Diffractometers"
Available on line at:
http://nvl.nist.gov/pub/nistpubs/jres/109/1/j91che.pdf
This excellent work occupied three out of the last six months of Bob
Cheary's life.
Alan
