Re: [ccp4bb] X-ray photon correlation length

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CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

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From: Paul Langan langan_paul {- at -} LANL {- dot -} GOV
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From: James Holton JMHolton {- at -} LBL {- dot -} GOV
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Subject: Re: X-ray photon correlation length
From: Dirk Kostrewa kostrewa {- at -} LMB {- dot -} UNI-MUENCHEN {- dot -} DE
Date: 2009-02-03

Dear James,

what an interesting discussion!

Am 30.01.2009 um 19:42 schrieb James Holton:

...

> I think the coherence length is related to how TWO different photons
> can interfere with each other, and this is a rare event indeed. It
> has nothing to do with x-ray diffraction as we know it. No matter
> how low your flux is, even one photon per second, you will
> eventually build up the same diffraction pattern you get at 10^13
> photons/s. Colin is right that photons should be considered as
> waves and on the length scale of unit cells, it is a very good
> approximation to consider the electromagnetic wave front coming from
> the x-ray source to be a flat plane, as Bragg did in his famous
> construction.

This is also my current understanding, since no matter what the
longitudinal coherence (spectral purity) or transversal coherence
(size of the source and detector distance) of the X-ray beam is, there
is no time coherence in the beam, neither for rotating anode
generators, nor for undulator beamlines (see Lengeler,
Naturwissenschaften, Vol. 88, p 249-260; it is in English).
Apparently, even a single photon "sees" the whole crystal as a wave
and deposits its energy as a particle with a probability according to
Bragg's law.

...

> Now, if a perfect crystal is really really small (much smaller than
> the interaction length of scattering), then there is no opportunity
> for the re-scattering and extinction and all that "weird stuff" to
> happen. In this limiting case, the scattered intensity is simply
> proportional to the number of unit cells in the beam and also to
F

> ^2. This is the basic intensity formula that Ewald showed how to
> integrate over all the depleting beams and re-scattering stuff to
> explain a large perfect crystal.
...
>
> I'm not sure where this rumor got started that the intensity
> reflected from a mosaic block or otherwise perfect lattice is
> proportional to the square of the number of unit cells. This is
> never the case. The reason is explained in Chapter 6 of M. M.
> Woolfson's excellent textbook, but the long and short of it is: yes
> the instantaneous intensity (photons/steradian/s) at the near-
> infinitesimal moment when a mosaic domain diffracts is proportional
> to the number of unit cells squared, but this is not useful because
> x-ray beams are never perfectly monochromatic nor perfectly parallel.

Hmm, I don't have Woolfson's book at hand, so I can't read this
chapter. My current understanding is: if N unit cells scatter in
phase, the scattered total amplitude is N times the scattered
amplitude of the unit cell in that direction. Since the recorded
intensity is proportional to the square of the amplitude, the
scattered total intensity is proportional to N^2 (for simplicity, I
assume perfect sources, crystals and detectors, so I don't discuss
spot shapes). Now, if the coherence lengths is limited by the size of
the mosaic blocks, each block scatters like a tiny crystal independent
of the other mosaic blocks. Thus, if we have m < N mosaic blocks (of
equal size), each block results in a scattered intensity ~(N/m)^2, and
the m blocks add their intensities, yielding a total intensity ~N^2/m.
Dependent of the perfection of the crystal, the total scattering
intensity for the two extremes between m=N (which wouldn't make any
sense) and m=1 is proportional to between N and N^2, respectively.
Please, correct me, if I'm wrong.

Best regards,

Dirk.

*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: kostrewa@lmb.uni-muenchen.de
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CCP4bb navigation

CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Neutron Protein Crystallography Call for Proposals
From: Paul Langan langan_paul {- at -} LANL {- dot -} GOV
Date: 2009-02-02

Next message:
Subject: correlation length - reloaded
From: James Holton JMHolton {- at -} LBL {- dot -} GOV
Date: 2009-02-03