Dear Crystallographers,

While I find the ideas about multiple photons versus single photons interesting, and think I now understand the subject better, the original question was almost completely unrelated. 

The original question, as is manifest in the Subject line, was about twinning. To restate it:

Shouldn't all crystals with twinned domains have some components of both "static disorder" and twinning? I.e., the measured intensities should be some combination of

|F(hkl) + F(-k-hl)|^2

And

|F(hkl)|^2 + |F(-k-hl)|^2

Wouldn't the domains have to be much bigger than the coherence length to have only the latter case?

Is there a consensus on how big twin domains are? I had thought they were tiny, a couple of unit cells perhaps. But maybe they're bigger?

JPK





-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Colin Nave
Sent: Tuesday, August 18, 2015 12:29 PM
To: [log in to unmask]
Subject: Re: [ccp4bb] Twinning Question

I would prefer to say that you can calculate the longitudinal coherence length of a source of photons using the transition lifetime.
You can measure the energy of an individual photon to a certain precision (very high resolution monochromators exist) but only by compromising knowledge about its arrival time.

Similarly for the transverse coherence length of a source of photons and the position/momentum of the individual photons.

It is well known that Heisenberg realised all this when he was stopped for speeding and asked if he knew how fast he was going. He replied "No, but I know exactly where I am".
(the old ones are the good ones).
Colin
-----Original Message-----
From: [log in to unmask] [mailto:[log in to unmask]]
Sent: 18 August 2015 16:43
To: Nave, Colin (DLSLtd,RAL,LSCI)
Subject: RE: [ccp4bb] Twinning Question

>Why invoke photons (again) when interpreting interference effects. 

Thank you!

>They result in discussions about the quantum interpretation of the 
>double
slit experiment and these generally produce more questions (e.g." its own coherence length" applied to a photon) than answers.

That is actually not so problematic. The photon in fact does not interact with ALL of the crystal, but only with the piece that falls in this range.
It does not change anything regarding the F calculations, but it is at least a consistent QM interpretation. You can calculate the coherence length in fact via the transition life time in case of characteristic radiation, and for synchrotrons I think Holton posted a formula, as far as I recall. 

Cheers, BR

An example of interference effects in twinning - A twinned crystal has two domains of equal size with hkl and khl overlapping. An x-ray beam which is coherent across the whole crystal is used. If Fhkl = 0, and Fkhl = 1, the diffraction corresponds to a single domain and, in the direction between the domains, the spot will have features corresponding to that from a slit with a width of 1 domain. If Fhkl=Fkhl=0.5, sharper features will occur corresponding to a slit with width of two domains. In the general case, the features will correspond to the ratio of Fhkl and Fkhl and complex interference effects will occur depending on both the ratio of the components and any dislocations between the domains. In principle, the effects can be used for detwinning. In the normal case the beam is not coherent across the entire crystal and the interference effects will be blurred to give the sum of the integrated intensities.

The paper by Aranda et. al. J. Synchrotron Rad. (2010). 17, 751-760, http://journals.iucr.org/s/issues/2010/06/00/gf5030/index.html looked at the interference effects for a pseudo-merohedral example.  I am not aware of any observations for merohedral crystals.

Now I have probably generated more questions than answers!

Regards
Colin


-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Bernhard Rupp (Hofkristallrat a.D.)
Sent: 18 August 2015 05:48
To: ccp4bb
Subject: Re: [ccp4bb] Twinning Question

The question is perfectly legitimate, and the situation described in the cf paper originates from the presence of disorder where you just cannot assume that the amplitude addition  works because the small domains are not periodic hence the 'partial wave vectors'
(or whatever we wish to call/imagine the structure factors) are not aligned anymore. The resulting phase difference requires to add the vectors first and then square them up but this is still the probability of one photon coming out in a given direction.

 I just choke on the multi-photon picture that insinuates some interaction between the individual X-ray photons.
The description of the scattering process with the complex structure factors from each atom or cell works fine in any case. No contest here. 

> if I understand correctly, the single photon nevertheless diffracts 
> off
many molecules.

Correct. Upon scattering the photon excites (polarizes, oscillates, feel free to imagine the process) all electrons in its own coherence length.
Does not matter what the matter is, periodic or not. Just the structure factor - the probability for scattering (or the re-appearance of the photon) in a given direction - comes out differently depending on how the matter is arranged. The diffraction pattern is still just the
time- and illuminated material- averaged (!) probability distribution given by the individual photons' Fsquareds. Those themselves may not be trivial to compute, cf. above. 
  
Best, BR

-----Original Message-----
From: Keller, Jacob [mailto:[log in to unmask]]
Sent: Monday, August 17, 2015 8:16 PM
To: [log in to unmask]; [log in to unmask]
Subject: RE: [ccp4bb] Twinning Question


....And BR, I put in a special homage to you in my earlier post: 

"In what manner, then, do the diffracting photons interfere with each other?
(or with themselves, as some express it)?

But I think the question still remains. Whether it be an individual photon or many, there is still interference between diffracting protein molecules going on. How else will the lattice of diffraction spots arise? According to you, if I understand correctly, the single photon nevertheless diffracts off many molecules.

JPK

*******************************************
Jacob Pearson Keller, PhD
Looger Lab/HHMI Janelia Research Campus
19700 Helix Dr, Ashburn, VA 20147
email: [log in to unmask]
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