Dear All,
Alan wrote:
>As local organiser of the workshop, I thought it went rather well
I sincerely and publicly apologise with Alan about the "infamous" adjective,
for which I asperge my head with ash. I can assure you it was *only*
referred to the software controversy, not the rest of the workshop that
indeed went *very* well and was highly stimulating, albeit amidst some
animated dibates. I admit the scientist who suggested the TOF machine at
the ILL and plotting data vs. Q are the same, that is, me. I will not talk
here about the TOF machine, that was nonetheless a serious suggestion. In
fact, Prof. Hans Boysen told me that a similar machine is planned (helas!
not yet funded) for the Munich reactor. I want to spend a few words about
plotting data vs. Q.
Constant-wavelength data are usually plotted vs. 2theta. This is perfectly
fine as long as you only use a single wavelength or you are not trying to
compare data from different sources (e.g., neutrons vs. synchrotron).
Another popular abscissa (mainly among TOF people, though) is d-spacing.
D-spacing can be used to plot everything on the same scale, and it is quite
handy to recognise some low-indices reflections if you have an idea of the
lattice constants. D-spacing is also sometimes used for plotting CW data in
limited ranges. However, d-spacing has never really cought on with CW
people for plotting full data sets, and for good reasons. Typical CW data
start around 0.7 A and end around 20 A near the beam stop. However, there
is a very uneven distribution of peaks in this range, with most peaks
crowded on the left side and huge background regions with few scattered
peaks on the right side. Another (slightly less good) reason not to use
d-spacing is that it emphasises the resolution variation. The
long-d-spacing peaks appear very broad and asymmetric (due to the well-known
axial divergence effect). TOF data typically have a cut-off at rather
moderate d-spacings (for HRPD in the typical setting, the highest d is 2.4
A) and have constant Dd/d resolution, so this is not a problem for them. In
my view, there is the need for a standard abscissa that serves all
communities. Indeed, we don't need to look very far. Our forefathers quite
often used sin(theta)/lambda as a standard unit. You find trace of this in
the absorption correction and form factors tables of the ITC. The beauty of
sin(theta)/lambda as a plotting abscissa is that the plot (almost) looks
like a 2theta plot, so your eye is not offended by an unusual view of the
data. I don't want to offend you by also pointing out that
sin(theta)/lambda=0.5/d. There are also some good arguments for a
1/d^2-type scaling, but this has no historical basis, and I don't think it
will catch on.
Now, let's assume for a moment that you all agree with me about the
advantages of the 1/d type of scaling. We still have to agree on the
multiplicative constant (which, of course, does not make any difference on
the appearance of the plot). In other words, we want a unit u such that
u=c/d, where c is a constant to be selected. I see only 3 possibilities:
1) c=0.5. This is sin(theta)/lambda, as said before.
2) c=1. This is d*.
3) c=2*pi This is Q.
Having been trained as a physicist, I personally like Q, because if you
multiply it by h-bar (Plank constant) you obtain the momentum transfer in
the elastic approximation. This unit is routinely used by most other
diffraction communities, like the small-angle scatterers and the
liquid-amorphous scatterers. I can, however, see good arguments for d* as
well. I stress that you don't need to do all your analysis in Q, if you are
more familiar with another unit. Here, I am only talking about the unit for
plotting your publication graphs. It would be nice if we could create some
kind of consensus on this.
Best
Paolo
Dr. Paolo G. Radaelli
ISIS Facility
Rutherford Appleton Laboratory, Bldg. R3
Chilton, Didcot
Oxon. OX11 0QX
United Kingdom
Phone : (+44) 1235-44 5685
FAX : (+44) 1235-44 5642
e-mail: [EMAIL PROTECTED]
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