 |
 |
>The implications of this, at least for some experiments, are not without interest. I wonder if you are alluding to the possibility of two-photon resonance effects, like two-photon microscopy? I would strongly suspect that with sufficient flux there should be two-photon x-ray fluorescence (why not?), but perhaps two-photon resonance/anomalous scattering would be possible as well? JPK Regards Colin ________________________________________ From: James Holton [[log in to unmask]] Sent: 21 August 2015 16:21 To: Nave, Colin (DLSLtd,RAL,LSCI); ccp4bb Subject: Re: [ccp4bb] Twinning Question Well, OK. "irrelevant" is a strong word. Spectral dispersion definitely blurs spots in the radial direction, and some call that a degradation of "coherence". What I was referring to is the size of the region in the crystal that is being "averaged over" (with phases) by a single photon diffraction event. Spectral dispersion does not change this. The diffraction pattern you see is the "intensity sum" over all the wavelengths in the beam. You can try adding the phased waves with different frequencies together, but after averaging over pixels of any conceivable size, it falls back to the "intensity sum" again. At least, that's how I think of it. -James Holton MAD Scientist On 8/21/2015 2:11 AM, [log in to unmask] wrote: > I disagree that the longitudinal coherence length is irrelevant for diffraction. The degradation with limited longitudinal coherence length increases with diffraction order. Veen, F. van der & Pfeiffer, F. (2004). J. Phys. Condens. Matter, 16, 5003-5030. gives a good explanation. > Colin > > ________________________________________ > From: CCP4 bulletin board [[log in to unmask]] on behalf of James > Holton [[log in to unmask]] > Sent: 21 August 2015 05:29 > To: ccp4bb > Subject: Re: [ccp4bb] Twinning Question > > An excellent diagram of the "coherence length" was drawn by Bragg. It > is Fig 15 in the introduction of his book "Optical Principles of the > Diffraction of X-rays". This book was later taken over by R. W. James. > A copy of that page is here: > http://bl831.als.lbl.gov/~jamesh/pickup/James_p35.pdf > > Note that this is what one might call the "transverse coherence > length". The longitudinal coherence length is irrelevant for > diffraction. You can see that the edges of the coherence region are > in no way sharp. Rather, the "weight" over the plane is a "sinc" > function, and there are even rings where atoms contribute negatively > relative to the central atoms. The size of the central patch (half > the scattering > power) is easy to calculate from trigonometry if you know the > wavelength (lambda), the distance to the source (rs) and the distance > to the detector (rd). It is just the deviation from the central path > (rp) that makes the distance from source to plane to detector 0.5 wavelengths longer: > lambda/2 +rs +rd = sqrt(rs^2+rp^2)+sqrt(rd^2+rp^2) > > For 1 A X-rays, infinite source distance and 100 mm detector distance > this central, coherent patch is 4.47 microns in diameter (2*rp). You > can call this the "coherence length" or not, but it is the distance in > the crystal over which the electron density is averaged (F1+F2)^2. > Outside this region you are adding scattered intensities F1^2 + F2^2. > > -James Holton > MAD Scientist > > > On 8/18/2015 10:16 AM, Keller, Jacob wrote: >> 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] >> ******************************************* >> >> -- >> This e-mail and any attachments may contain confidential, copyright and or privileged material, and are for the use of the intended addressee only. If you are not the intended addressee or an authorised recipient of the addressee please notify us of receipt by returning the e-mail and do not use, copy, retain, distribute or disclose the information in or attached to the e-mail. >> Any opinions expressed within this e-mail are those of the individual and not necessarily of Diamond Light Source Ltd. >> Diamond Light Source Ltd. cannot guarantee that this e-mail or any attachments are free from viruses and we cannot accept liability for any damage which you may sustain as a result of software viruses which may be transmitted in or with the message. >> Diamond Light Source Limited (company no. 4375679). Registered in >> England and Wales with its registered office at Diamond House, >> Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, >> United Kingdom