Xiangyun has a point (see below). If one phase is coherently embedded
in the other, there will be inter-phase correlation terms in the PDF in
which case the two phases are not just the sum of the parts. Our
experience is that often (maybe even "in general") these correlation
terms are very hard to see though, even when they are there.
S
-------- Original Message --------
Subject: [Fwd: Re: Question]
Date: Thu, 28 Sep 2006 11:14:00 -0400
From: Xiangyun Qiu <[EMAIL PROTECTED]>
Organization: Cornell University
To: Simon Billinge <[EMAIL PROTECTED]>
Hi Simon,
It's odd that I found I am still in the Rietveld list by forwarding my
msu emails. I feel there is more to this question. In my understanding,
the two phases can be:
1) totally uncorrelated, e.g., if we mix Si and Ni powders and measure
them. Then, the total G(r) is the sum of the two parts.
2) partially correlated, e.g., the two phases coexist in well defined
relative orientations/positions. Then, the correlation term may exist,
and the significance will depend on the "interface"/volume ratio.
Thanks,
Xiangyun
Nicholas Armstrong wrote:
Mathematically, we know that the Fourier transform (FT) is a linear
operator, so FT{f1+f2}=FT{f1} +FT{f2}. No mangled convolution.
Nick
Brian H. Toby wrote:
I had to think for a bit: the Fourier transform of a sum is equal to
the sum of the terms transformed individually, so the G(r) for a
mixture is the weighted sum of G(r) for the components.
Brian
On Sep 27, 2006, at 9:05 AM, Andy Fitch wrote:
We have a question about pdf analysis. If my sample is two
phase, so the diffraction pattern is the sum of two individual
patterns, what does the G(r) show? Is it just the sum of two
individual G(r)s or some mangled convolution between the two?
--
Prof. Simon Billinge
Department of Physics and Astronomy
4268 Biomed. Phys. Sciences Building
Michigan State University
East Lansing, MI 48824
tel: +1-517-355-9200 x2202
fax: +1-517-353-4500
email: [EMAIL PROTECTED]
home: http://nirt.pa.msu.edu/
