[ccp4bb] correlation length - reloaded

[James Holton]

Thanks Colin,

Yours is one of several lessons I have received on coherence and optics 
in the past few days.  I do appreciate all effort and the input.  
However, as I mentioned before I am a biologist and I don't so much care 
about the fundamental nature of the universe as I do about how it 
relates to helping people solve protein structures.  So, I think I would 
like to perhaps re-phrase Bernhard's question, but primarily ask a 
question of my own:

______________________________________________________________________________________________________
Is there a way to use a fancy x-ray beam to overcome lattice pathologies 
... such as, shall we say: turn a nightmare like a lattice translocation 
defect into a "simple" merohedral twin?
______________________________________________________________________________________________________

That is, I think this whole discussion started with those streaky spots 
Margriet Ovaere posted last week.  We have all seen streaky spots and 
wondered what they mean, but far more important than that we wanted to 
get rid of them.  So, let me pose the following 4 situations:

1)  The easiest kind of merohedral twin to think about is when you have 
two "good" crystals stuck together.  They are both in the beam and 
oriented so that their lattices line up and there is no practical 
detector distance that will resolve the spots produced from crystal A vs 
crystal B.  This is not a problem so long as the overlapping spots 
correspond to symmetry-equivalent HKL indicies, but if you have one of 
those annoying space groups (like P4, P3, and others) where the "a" and 
"b" axes are the same length, but non-equivalent, then the "a" axis of 
"A" can be aligned with the "b" axis of "B", and then you have a 
merohedral twin.  You then feel like you are a bad crystallographer for 
wanting to go and grow new crystals. 
   However, you can be saved from 1) if you have a fancy x-ray beam.  
That is, shoot just one of the two crystals that are stuck together 
(either with a small beam, or simply by translating crystal B out of the 
beam) and voila!  De-twinning!  I love this beamline and the beamline 
scientist should get a really really big raise for showing me how to do 
that!  This leads us to:

2)   The "crystal" you have in the beam contains a large number of very 
small "twin domains".  Half of them are oriented as "A" above and the 
other half as "B".  This is annoying because you really don't want to 
learn about twinning and the x-ray beam is not small enough to just 
shoot one of the "A" crystals at a time.  So, you write a big grant to 
build a beamline with a smaller x-ray beam.  Hooray!  Problem solved by 
physics again.  However, there must be a limit to how far you can push 
this "strategy":

3)  The twin domains are so small that you cannot go more than a few 
unit cells in the crystal without stumbling across an "A" to "B" 
boundary.  With so few unit cells in each "twin domain" the scattering 
from "A" actually starts to scatter "coherently" with "B" inasmuch as 
the amplitudes and phases are adding instead of simply adding the 
intensities contributed by each type of twin domain together into each 
spot.  To add to the headache, every other spot in the diffraction 
pattern is smeary and your beamline scientist tells you that you have 
something called a "lattice translocation defect" (then he goes off to 
"lunch" and never comes back).  This is very annoying because noone 
seems to distribute a program for removing this problem from your data, 
and you wonder how much money it will take to build a beamline that will 
"solve" this problem for you.  Perhaps if you could somehow reduce the 
"coherence length" you could graduate from having a "lattice 
translocation defect" into merely having a merohedral twin?  On the 
other hand, what if you unit cell gets really big and starts to get 
comparable to the "coherence length"?  Will that somehow mess up your 
data?  What the heck is a "coherence length" anyway?

4)  The "twin domains" are only one unit cell each and for every "A" 
unit cell there is a "B" unit cell right next to it and always in the 
same direction.  This is actually a "regular" crystal (with NCS and 
twice the unit cell size of 1).  It is deviations from the "A always 
next to B" rule that I think leads to the streakiness in Margriet's 
spots (the description I posted last week).  That is, I think she is in 
the twilight zone between 3) and 4).   This will perhaps have a 
"pseudotranslation" which is another scary word to hear at the beamline, 
but I don't think there will ever be a fancy x-ray beam that can solve 
this problem.


So, it appears that somewhere between 2) and 3) there is a dark place in 
x-ray physics?  Is there a fancy type of x-ray beam that will let us do 
some new science here?

Perhaps the most relevant definition of "correlation length" for protein 
crystallography is:
______________________________________________________________________________________________________
How far apart can two unit cells be before the integrated spot 
intensities are given by |F_A|^2+|F_B|^2 instead of 0.5*|F_A+F_B|^2?
______________________________________________________________________________________________________

I am going to insist that the answer to this question has everything to 
do with the structure of the crystal and nothing to do with the 
"coherence" of the x-ray beam until someone can describe to me and 
experiment to MEASURE the real answer.

-James Holton
MAD Scientist

Nave, C (Colin) wrote:
Bernard, James
Well, we are struggling to find a simple description of coherence length

One thing I would advise is not to mix up wave and photon descriptions at the 
same time. You end up trying to solve the same problem as how a single photon 
goes through 2 slits and interfers. Richard Feynman (no less) said he could not 
understand this. Things have advanced since then but there is still no rational 
description of it which is accepted. The spooky descriptions do not count. 
There may be some more fundamental underlying theory (hopefully not Strings) 
which rationalises all this but it remains a fundamental problem of physics 
(along with 4 others I think).

If wanting a photon description, one concept is how many photons there are in 
the coherence volume. This photon redundancy is 10^6 or more for visible 
lasers, less than 1 for most synchrotron beamlines and more than 1 for short 
pulse width FELs. However, one does not need to have a high photon redundancy 
to get coherence effects.

A distant star twinkles due to the fact the light is coherent and one gets 
interference effects through the atmosphere. The atmospheric turbulence 
produces the variation of intensity seen by eye. Venus (a fine sight at the 
moment) does not produce this effect because it is too near. Similar affects 
are used in dynamic light scattering to measure particle size. Also in x-ray 
photon correlation spectroscopy (but I mentioned the word photon when I wanted 
a wave description!).

I will dig out a reference (from a group at Cornell) giving a photon based 
description of coherence.

Cheers
 Colin




-----Original Message-----
From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
Sent: Mon 02/02/2009 19:38
To: Nave, C (Colin)
Subject: RE: [ccp4bb] X-ray photon correlation length
 
Thanks - but I think I made a fundamental thinking flaw: also the coherence
length
seems only relevant/defined according to you reference for a 
two photon process - is that in fact true?

what I am looking for in diffraction is the
length of coherence for the single photon scattering -
or how many electrons it rings in a 'single photon coherence volume' 
or whatever that term would be.....

I thought the dimension of the wave packet might be a limiting factor
for single photon coherent scattering. But the photon particle is
nondispersive
and apparently of no dimension.... 

James Holton and I are now trying to find a particle/scattering physicist...


Cheers, BR

-----Original Message-----
From: Nave, C (Colin) [mailto:colin.n...@diamond.ac.uk] 
Sent: Monday, February 02, 2009 2:15 AM
To: Bernhard Rupp
Subject: RE: [ccp4bb] X-ray photon correlation length

Bernard
Yes it depends on a combination of both the intrinsic bandwidth of the mono
(approx 1.2 x 10^-4 for Si 111) and the range of angles on it (which the
beamline designer will try and minimise).
Bending magnet beamlines might approach the intrinsic bandwidth of the mono.
It is easier to get there with low divergence undulator radiation. 1.5 x
10^-4 to 10^-3 are ballpark figures but will change depending on how the
beamline is set up.

However, you should consider both the transverse and longitudinal coherence
when working out the volume of the specimen which is coherently illuminated.
This volume also changes with scattering angle as the path differences
increase at higher angle. This can be understood simply by considering that
a variation in wavelength of 1% say will smear the 100th diffraction order
in to the 101st order.

If considering just the forward direction, for the longitudinal coherence
alone (i.e. assuming beam is as parallel as it can be within the diffraction
limit), one has to consider the variation in the optical path length
(allowing for refractive index changes) through the specimen when working
out the path length over which the specimen is coherently illuminated. The
forward beam is retarded due to this variation in refractive index. This
effect is used for phase contrast imaging.

Cheers
  Colin






-----Original Message-----
From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
Sent: Sat 31/01/2009 21:24
To: Nave, C (Colin)
Subject: RE: [ccp4bb] X-ray photon correlation length
 
OK thx - very useful update indeed. then I need to find the source bandwidth
for each beam line -I take it that the
monochromator bandwidth etc is secondary and NOT the delLambda to be used
for longitudinal 
coherence, but enters a prefactor or so.

Do you perhaps have a ball park for what a source bandwidth is for certain
SR devices? 

Thx, BR
-----Original Message-----
From: Nave, C (Colin) [mailto:colin.n...@diamond.ac.uk] 
Sent: Saturday, January 31, 2009 3:15 AM
To: Bernhard Rupp
Subject: RE: [ccp4bb] X-ray photon correlation length


Bernard
If talking strictly about longitudinal coherence, there is probably not much
difference between the two. A copper Kalpha line width is approximately 2.4
eV  (http://wwwastro.msfc.nasa.gov/xraycal/linewidths.html ) or about
3X10^-4. This is not too different from many beamlines at synchrotrons.

Colin

-----Original Message-----
From: Bernhard Rupp [mailto:bernhardr...@sbcglobal.net]
Sent: Fri 30/01/2009 18:49
To: Nave, C (Colin)
Subject: RE: [ccp4bb] X-ray photon correlation length
 
I think the major contribution is in fact from the 
fundamental lambda**/delLambda longitudinal coherence.

As a qualitative statement, the range of A few 1000 A
for anodes to several microns for synchrotrons seems 
reasonable and in agreement with prior knowledge.

What would you say?

BR 

-----Original Message-----
From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Nave,
C (Colin)
Sent: Friday, January 30, 2009 1:20 AM
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] X-ray photon correlation length

Hi
Both transverse and longitudinal coherence length need to be considered in
this. These parameters are detemined by monochromators, focusing optics and
the position of the specimen along the path not just the undulator (or x-ray
generator).

Matching to the specimen is not necessarily as simple as the dimensions of
the mosaic blocks in the specimen. It is the optical path length which is
important. One would have to consider the variation in refractive index
between mosaic blocks and the surroundings.
Cheers
 Colin

-----Original Message-----
From: CCP4 bulletin board on behalf of Ethan Merritt
Sent: Thu 29/01/2009 19:24
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] X-ray photon correlation length
 
On Thursday 29 January 2009 10:59:23 Bernhard Rupp wrote:
  
Ok, following seems to be correct:

 

a)      interaction length = mean free path : relevant for absorption

b)      correlation length = time correlation between photons : relevant
    
for
  
multi-photon scattering

c)      coherence length = longitudinal coherence length : relevant for
single photon scattering.

 

It follows from Heisenberg for a Lorentzian source (anode) with natural
emisson line width per

formula on p 5007 of Colin's ref

 

Lc=(2/pi)lambda**2/delLambda

 

Using  8084 eV and 2.1 eV respectively for Cu, I obtain ~3800 A coherence
length for a Cu (anode) X-ray photon

 

The pre-factor is different for other source types like synchrotron.
    

The coherence length for an undulator source is the relativistically
contracted length of the undulator.
Ref:
        http://xdb.lbl.gov/Section2/Sec_2-1.html


  
In any case I would accept the vague term of 'a few 1000 A'  or  'several
1000 A' as a general statement for

coherence length in materials where the interaction length is larger
(practically always).

 

Does this sound reasonable?
    

My impression is that the coherence length from synchrotron sources
is generally larger than the x-ray path through a protein crystal.
But I have not gone through the exercise of plugging in specific
storage ring energies and undulator parameters to confirm this
impression.  Perhaps James Holton will chime in again?


        Ethan

  
 

From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of
    
Nave,
  
C (Colin)
Sent: Thursday, January 29, 2009 10:14 AM
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] X-ray photon correlation length

 

Bernard

I guess this came from

"Aren't detwinning methods appropriate only in the case of true twin
    
domains
  
which are larger than the X-ray photon correlation length in order for the
assumption to be valid that |F|^2 from each domain can be summed? This
wouldn't give rise to the apparent 'diffuse scatter' phenomenon."

 

I think this is normally called coherence length. Probably best not to
    
think
  
of photons at all but waves (though there is an equivalent quantum
mechanical treatment based, as V Nagarajan says, on the uncertainty
principle). I don't think the domains have to be larger then the
    
correlation
  
(sorry coherence) length of the incident x-rays in any case. They have to
    
be
  
large enough to give an intensity which can be integrated. If smaller
domains are present, the intensity just spread out a bit more.When the
domains are very large, the size of the spots would be determined by the
incident beam properties.

 

The article cited some years ago on CCP4BB gives a primer on all this

J. Phys.: Condens. Matter 16 (2004) 5003-5030 PII: S0953-8984(04)75896-8.
Coherent x-ray scattering Friso van der Veen1,2 and Franz Pfeiffer1


    
http://www.iop.org/EJ/article/0953-8984/16/28/020/cm4_28_020.pdf?request-id=
  
8848d3f0-5a4b-4ffe-8ea4-c1eabfaf1657

 

Cheers

 Colin

 

  _____  

From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of
Bernhard Rupp
Sent: 29 January 2009 17:51
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] X-ray photon correlation length

I always wondered  - how is the X-ray photon correlation length defined

and where do I find it?  This is not the interaction length, I assume. 

 

So, to the physicists: How large is the 'X-ray photon correlation length' 

for a given wavelength in a given material?

 

I had the impression that the term photon correlation refers

to the time correlation of the scattering such as in photon correlation
spectroscopy.

 

 Best regards, BR

 

 

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