Dear James,
I have a slightly different way to think about transverse coherence. I
heard Mark Sutton give a talk about this at the APS a few years ago, and
here are graphics from a similar talk given by Alec Sandy at BNL:
http://www.bnl.gov/nsls2/workshops/docs/XPCS/XPCS_Sandy.ppt
The eqn. he gives on figure 8 is this:
L(coherence) =
Lambda*(source-to-observation-point-distance) / 2*pi*sigma(source)
This is the wavelength divided by the angle subtended by the source viewed
by the observer, with a 2.pi in there for some reason. The way I explain
it (though I cannot derive it this way) is that as you view the source,
consider that your eye sees a ray coming from the top of the source, and
one coming from the bottom. As you move your eye up and down, the two
rays will slide back and forth against one another. The coherence length
is how far you move your eye to have them slip about 1/4 of a wave. In
Mark's APS example you see the horizontal is 7 microns, the vertical is
200. This reflects the fact that the typical synchrotron source is much
wider than it is high.
Bob
________________________________________
From: CCP4 bulletin board [[email protected]] on behalf of James Holton
[[email protected]]
Sent: Thursday, April 24, 2014 6:59 PM
To: [email protected]
Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
There are two kinds of "coherence length": transverse and longitudinal.
Longitudinal coherence is often quoted as delta-lambda/lambda, which is easy to calculate
but unfortunately completely irrelevant for diffraction from crystals. If it weren't
then Laue diffraction wouldn't produce spots.
Transverse coherence tends to be around 3-10 microns with 1 A x-rays, depending on the
detector distance. Yes, that's right, the detector distance. Longer detector distances
give you a bigger coherence length, especially when the source is "very far
away", like it is at a synchrotron.
How this happens is easiest to picture if you consider the simplest possible diffraction situation: a
"point" source of x-rays, two atoms, and a detector. As long as the atoms are very close together
relative to the distances from the sample to the source and the detector, then you have the "far
field" diffraction situation. This is where both atoms are within the "coherence length",
Bragg's diagram for Bragg's Law holds: parallel incoming rays and parallel outgoing rays.
But what if the atoms are very far apart? Obviously, the scattering from two atoms on different
sides of the room will just add as intensities. And if they are very close together, then Bragg's
Law holds and they scatter "coherently". What most people think of as the
"coherence length" is the point of transition between these two kinds of scattering.
This point is rather conveniently defined as the distance between two atoms when the path from the source to one atom
to a given detector pixel becomes 0.5 wavelengths longer than the same path through the other atom. As long as both
atoms lie in the "Bragg plane" (that's the plane perpendicular to the "s" vector, which is the
vector difference between the incoming and outgoing beam directions), the far-field approximation tells us they should
also be "in phase", but if they are far enough apart the 0.5 A change in total path length is enough to
change the scattering completely from constructive to destructive interference. In ordinary optics, this is called the
edge of the first "Fresnel zone".
So, if your source is "very far away", emitting 1 A x-rays, and your detector is 1 meter away, then
moving one atom 10 microns away from the centerline of the beam makes the path from that atom to the detector
1-sqrt(1^2+10e-6^2) = 0.5 A longer. So that implies the "coherence length" is 10 microns. But if
the detector is only 100 mm away, that gives you 0.1-sqrt(0.1^2+3e-6^2) = 0.5 A, so 3 um is the
"coherence length".
Of course, this is for the ideal case of a point source very far away. In reality finite beam divergence will mess up
the "coherence" inasmuch as a divergent source looks like an array of sources all viewing the sample through
a pinhole. What you then get on the detector is the sum of the patterns from all those sources, so the
"coherence" is not as clean. That is, you don't see the Fourier transform of the crystal shape in every
spot. Mosaic spread also messes up "coherence" in this way. Some might even define the mosaic "domain
size" as the inverse of the effective coherence length.
But, the long and short of all this is that as long as your detector pixels are bigger
than the "coherence length" the coherence doesn't really matter.
Hope that makes sense,
-James Holton
MAD Scientist
On Thu, Apr 24, 2014 at 2:32 PM,
<[email protected]<mailto:[email protected]>> wrote:
Dear Chen,
Twinning can be thought of as of two or more macro-crystals glued or grown
together. The reason that the reflections often overlap is that they share one
common plane from which they grow in different directions. Many twinning tests
are based on the fact that the two (or more) macro crystals do not interfere,
which changes the intensity distributions. Since there is no interference,
twinning cannot make spots disappear. Moreover, translational operations
between twin domains would be equivalent to move the crystal a little in the
beam, as with centering, which will not have any influence on the diffraction
pattern (except for weak diffraction because of missing the beam).
Disorder can have many causes, but is caused by different orientations of
residues/molecules/whatever in different asymmetric units. It is close range,
so there will be interference. However, since it is usually randomly
distributed over the crystal, it will not cause disappearance of spots.
The X-ray coherent length is depending on the crystal, not the synchrotron and
my gut feeling is that it is at least several hundred unit cells, but here
other experts may correct me.
Disappearance of spots can occur due to a wrong space group assignment (e.g.
screw axis have been overlooked) or translational non-crystallographic
symmetry. In this case, I would first run a modern MR program to see if you get
a solution and otherwise you will have to analyze very careful your space
group, unit cell etc. to find out what is going on.
My 2 cents,
Herman
Von: CCP4 bulletin board
[mailto:[email protected]<mailto:[email protected]>] Im Auftrag von
Chen Zhao
Gesendet: Donnerstag, 24. April 2014 22:13
An: [email protected]<mailto:[email protected]>
Betreff: [ccp4bb] Twinning VS. Disorder
Dear all,
Hello! I am kinda confused and am thinking about the definition of twinning and
disorder. I am just a starting student and might make some fundamental
mistakes.
1) Twinning is a macroscopic phenomenon and the result is the addition of the intensity
from different lattices; disorder is a microscopic phenomenon and the result is the
addition of structure factors from different crystal "domains". Is this
statement valid?
2) I am now very confused about how to define the macroscopic versus the
microscopic level when I think of the systematic absences introduced by
translational operation. Or in other words, can the translational operation
between the twin domains create systematic absences? My answer is probably no
because the distance between the two domains are too far away compared to the
coherent length of the X-ray, i.e. the addition of the intensity alone cannot
make some spots disappear. Is it true? If yes, what is the x-ray coherence
length at the synchrotron in general?
3) If the statement in 2) is valid, then if a "twinning operation" can
introduce systematic absences, this should be a disorder instead of a twin based on the
definitions in 1). Is this right?
Your answers will be greatly appreciated!
Sincerely,
Chen
On Thu, 24 Apr 2014, James Holton wrote:
There are two kinds of "coherence length": transverse and longitudinal.
Longitudinal coherence is often quoted as delta-lambda/lambda, which is
easy to calculate but unfortunately completely irrelevant for diffraction
from crystals. If it weren't then Laue diffraction wouldn't produce spots.
Transverse coherence tends to be around 3-10 microns with 1 A x-rays,
depending on the detector distance. Yes, that's right, the detector
distance. Longer detector distances give you a bigger coherence length,
especially when the source is "very far away", like it is at a synchrotron.
How this happens is easiest to picture if you consider the simplest
possible diffraction situation: a "point" source of x-rays, two atoms, and
a detector. As long as the atoms are very close together relative to the
distances from the sample to the source and the detector, then you have the
"far field" diffraction situation. This is where both atoms are within the
"coherence length", Bragg's diagram for Bragg's Law holds: parallel
incoming rays and parallel outgoing rays.
But what if the atoms are very far apart? Obviously, the scattering from
two atoms on different sides of the room will just add as intensities. And
if they are very close together, then Bragg's Law holds and they scatter
"coherently". What most people think of as the "coherence length" is the
point of transition between these two kinds of scattering.
This point is rather conveniently defined as the distance between two atoms
when the path from the source to one atom to a given detector pixel becomes
0.5 wavelengths longer than the same path through the other atom. As long
as both atoms lie in the "Bragg plane" (that's the plane perpendicular to
the "s" vector, which is the vector difference between the incoming and
outgoing beam directions), the far-field approximation tells us they should
also be "in phase", but if they are far enough apart the 0.5 A change in
total path length is enough to change the scattering completely from
constructive to destructive interference. In ordinary optics, this is
called the edge of the first "Fresnel zone".
So, if your source is "very far away", emitting 1 A x-rays, and your
detector is 1 meter away, then moving one atom 10 microns away from the
centerline of the beam makes the path from that atom to the detector
1-sqrt(1^2+10e-6^2) = 0.5 A longer. So that implies the "coherence length"
is 10 microns. But if the detector is only 100 mm away, that gives you
0.1-sqrt(0.1^2+3e-6^2) = 0.5 A, so 3 um is the "coherence length".
Of course, this is for the ideal case of a point source very far away. In
reality finite beam divergence will mess up the "coherence" inasmuch as a
divergent source looks like an array of sources all viewing the sample
through a pinhole. What you then get on the detector is the sum of the
patterns from all those sources, so the "coherence" is not as clean. That
is, you don't see the Fourier transform of the crystal shape in every
spot. Mosaic spread also messes up "coherence" in this way. Some might
even define the mosaic "domain size" as the inverse of the effective
coherence length.
But, the long and short of all this is that as long as your detector pixels
are bigger than the "coherence length" the coherence doesn't really
matter.
Hope that makes sense,
-James Holton
MAD Scientist
On Thu, Apr 24, 2014 at 2:32 PM, <[email protected]> wrote:
Dear Chen,
Twinning can be thought of as of two or more macro-crystals glued or grown
together. The reason that the reflections often overlap is that they share
one common plane from which they grow in different directions. Many
twinning tests are based on the fact that the two (or more) macro crystals
do not interfere, which changes the intensity distributions. Since there is
no interference, twinning cannot make spots disappear. Moreover,
translational operations between twin domains would be equivalent to move
the crystal a little in the beam, as with centering, which will not have
any influence on the diffraction pattern (except for weak diffraction
because of missing the beam).
Disorder can have many causes, but is caused by different orientations
of residues/molecules/whatever in different asymmetric units. It is close
range, so there will be interference. However, since it is usually randomly
distributed over the crystal, it will not cause disappearance of spots.
The X-ray coherent length is depending on the crystal, not the synchrotron
and my gut feeling is that it is at least several hundred unit cells, but
here other experts may correct me.
Disappearance of spots can occur due to a wrong space group assignment
(e.g. screw axis have been overlooked) or translational
non-crystallographic symmetry. In this case, I would first run a modern MR
program to see if you get a solution and otherwise you will have to analyze
very careful your space group, unit cell etc. to find out what is going on.
My 2 cents,
Herman
*Von:* CCP4 bulletin board [mailto:[email protected]] *Im Auftrag von
*Chen Zhao
*Gesendet:* Donnerstag, 24. April 2014 22:13
*An:* [email protected]
*Betreff:* [ccp4bb] Twinning VS. Disorder
Dear all,
Hello! I am kinda confused and am thinking about the definition of
twinning and disorder. I am just a starting student and might make some
fundamental mistakes.
1) Twinning is a macroscopic phenomenon and the result is the addition of
the intensity from different lattices; disorder is a microscopic phenomenon
and the result is the addition of structure factors from different crystal
"domains". Is this statement valid?
2) I am now very confused about how to define the macroscopic versus the
microscopic level when I think of the systematic absences introduced by
translational operation. Or in other words, can the translational operation
between the twin domains create systematic absences? My answer is probably
no because the distance between the two domains are too far away compared
to the coherent length of the X-ray, i.e. the addition of the intensity
alone cannot make some spots disappear. Is it true? If yes, what is the
x-ray coherence length at the synchrotron in general?
3) If the statement in 2) is valid, then if a "twinning operation" can
introduce systematic absences, this should be a disorder instead of a twin
based on the definitions in 1). Is this right?
Your answers will be greatly appreciated!
Sincerely,
Chen
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Group Leader, PXRR: Macromolecular ^ (that's L
Crystallography Research Resource at NSLS not 1)
http://px.nsls.bnl.gov/
Photon Sciences and Biosciences Dept
Office and mail, Bldg 745, a.k.a. LOB-5
Brookhaven Nat'l Lab. Phones:
Upton, NY 11973 631 344 3401 (Office)
U.S.A. 631 344 2741 (Facsimile)
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