Hi Richard,
I doubt if there is a formal reference for this estimate. If there
is, I appreciate if you let me know it.
However, we can do a math for estimates.
==============================================
1) According to Bragg's law, we have
2*d*sin(theta) = lambda (1)
2) d, the resolution, could be simplified as a/h (a is cell constant,
h is miller index)
so, we have
2*sin(theta)*a/h ~ lambda (2)
(this may not be mathematically rigorous)
3) We boldly suppose all contributions ( from divergence,
mosaicity, ....) as
a small angle Div, and we assume this Div cause the overlap between
two adjacent
reflections (only 1 difference in indices). Then, again, with
Braggs's law, we have
2*sin(theta + Div)*a/(h+1) ~ lambda
i.e., sin(theta+Div) = (h+1)*lambda/2a (3)
Extending (3) gives, if Div is small enough,
sin(theta)*cos(Div) + cos(theta)*sin(Div) ~ sin(theta) + Div*cos(theta)
= (h+1)*lambda/2a (4)
Compared (4) by (2), we have Div ~ lambda/(2*a*cos(theta)).
Now, assume a is 500, the Div is around 1 mr, when lambda is ~1.0,
theta is not too
close to Pi/2.
==============================================
Lijun
On Jul 19, 2008, at 7:24 AM, Richard Gillilan wrote:
There's a simple rule of thumb I have heard for predicting if spot
overlap is likely to be a problem for a given beam divergence: 500
A of unit cell corresponds to 1 mr of divergence. So, for example,
250 A would be a unit cell limit for a 2 mr beam. Has anyone heard
of this rule before? I heard it from someone who heard it from
someone, so I have no original reference and don't know how valid
it is.
There are a number of factors which influence spot overlap: beam
divergence, mosaic spread of crystal, point spread function of
detector, and resolution range of interest. I would love to find
some references to simple estimates based on these parameters. Best
I have seen so far is a paper by Sarvestani et. al. (J. Appl.
Cryst. (1998) 31 899-909, but it is a detailed simulation rather
than a single formula.
Richard Gillilan
MacCHESS
Lijun Liu, PhD
Institute of Molecular Biology
HHMI & Department of Physics
University of Oregon
Eugene, OR 97403
541-346-4080
