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From the Rietveld Mailing List
From: [email protected]
To: [email protected]
Subject: RE: As sent to the neutron mailing list
Date: Fri, 24 Sep 1999 15:56:19 +0100
Dear Frank,
I've just received an e-mail from the Rietveld mailing list courtesy of
Paolo Radaelli that has an HRPD diffraction pattern of MgO - it's big but
hopefully you will be able to plot the file. This should help you get a feel
for the data and the nature of the binning.
Now concerning the binning of time-of-flight data on HRPD ... As I said
yesterday the delta d /d resolution is constant - the d-spacing is
proportional to the time of flight and so the time width (delta t) is
proportional to t. We thus bin our data so that (delta t)/t is constant - on
HRPD this is usually 1 x 10-4. On a few occasions, when I have had extremely
sharp peaks then I have binned more finely at 5 x 10-5.
So how many points does that give - well we generally have a 100,000 or
200,000 microsecond starting somewhere between 15,000 (d = 0.25A in
backscattering) and 30,000 (d = 0.25A in backscattering) microseconds.
Since t(i+1) = (1+w)*t(i) where w = (delta t)/t then it's easy to show that
since w<<1 then the number of points N is very closely given by
Nw = ln(tmax/tmin)
For w=10-4, tmin=30000 and tmax=130000, this gives N=14663 - this is
typically the sort of number that we work with.
For the most heroic case, w=5x10-5, tmin=15000 and tmax=215000, we get 53252
but then that's the price you pay for high resolution. When I was last at
Andy Fitch's powder diffractometer at the ESRF in Grenoble, we collected
datasets that contained 20000 points.
Hope that clears things up.
Bill
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