There are no Miller planes but I guess you can think of a "Miller volume"F000 is normally not use in map calculations and that is why the average value of any such map is zero (all other Fourier terms are cosines that have just as much signal above as below zero). If you want to create a density map that actually represent electrons per cubic Angstrom, you need to add F000 which you can approximate as the number of electrons in the unit cell (assuming all other reflections are on absolute scale already) There is never really interference with scattered photons. Like James last message, a single photon can be scattered by two slits simultaneously. Likewise a photon is scattered by all scatterers in a certain volume of the crystal which includes many unit cell. This is the same for F000 reflections with the difference being that all atoms scatter in phase
What took me a bit by surprise is that F000 would have a non-zero phase but I guess it is correct. If there were no imaginary component to F000 in the presence of anomalously diffracting atoms than the imaginary part of the density map would have an average of zero whereas it needs to be positive.
Bart On 10-10-14 10:59 AM, Jacob Keller wrote:
This F000 reflection is hard for me to understand:-Is there a F-0-0-0 reflection as well, whose anomalous signal would have a phase shift of opposite sign?-Is F000 always in the diffraction condition? -Is there interference between the scattered photons in F000?-Does F000 change in amplitude as the crystal is rotated, assuming equal crystal volume in xrays?-Are there Miller planes for this reflection?-Is it used in the Fourier synthesis of the electron density map, and if so, do we just guess its amplitude?JPK----- Original Message ----- From: "Dale Tronrud" <det...@uoxray.uoregon.edu>To: <CCP4BB@JISCMAIL.AC.UK> Sent: Thursday, October 14, 2010 11:28 AMSubject: Re: [ccp4bb] embarrassingly simple MAD phasing question (another)Just to throw a monkey wrench in here (and not really relevant to the original question)... I've understood that, just as the real part of F(000) is the sum of all the "normal" scattering in the unit cell, the imaginary part is the sum of all the anomalous scattering. This means that in the presence of anomalous scattering the phase of F(000) is not zero. It is also the only reflection who's phase is not affected by the choice of origin. Dale Tronrud On 10/13/10 22:38, James Holton wrote:An interesting guide to doing phasing "by hand" is to look at direct methods (I recommend Stout & Jensen's chapter on this). In general there are several choices for the origin in any given space group, so for the "first" reflection you set about trying to phase you get to resolve the phase ambiguity arbitrarily. In some cases, like P1, you can assign the origin to be anywhere in the unit cell. So, in general, you do get to phase one or two reflections essentially "for free", but after that, things get a lot more complicated. Although for x-ray diffraction F000 may appear to be mythical (like thesound a tree makes when it falls in the woods), it actually plays a very important role in other kinds of "optics": the kind where the wavelengthgets very much longer than the size of the atoms, and the scattering cross section gets to be very very high. A familiar example of this is water or glass, which do not absorb visible light very much, but do scatter it very strongly. So strongly, in fact, that the incident beam is rapidly replaced by the F000 reflection, which "looks" the same as the incident beam, except it lags by 180 degrees in phase, giving theimpression that the incident beam has "slowed down". This is the originof the index of refraction.It is also easy to see why the phase of F000 is zero if you just look at a diagram for Bragg's law. For theta=0, there is no change in direction from the incident to the scattered beam, so the path from source to atomto direct-beam-spot is the same for every atom in the unit cell, including our "reference electron" at the origin. Since the structure factor is defined as the ratio of the total wave scattered by a structure to that of a single electron at the origin, the phase of the structure factor in the case of F000 is always "no change" or zero.Now, of course, in reality the distance from source to pixel via an atomthat is not on the origin will be _slightly_ longer than if you just went straight through the origin, but Bragg assumed that the source and detector were VERY far away from the crystal (relative to the wavelength). This is called the "far field", and it is very convenient to assume this for diffraction. However, looking at the near field can give you a feeling for exactly what a Fourier transform "looks like". That is, not just the before- and after- photos, but the "during". It is also a very pretty movie, which I have placed here: http://bl831.als.lbl.gov/~jamesh/nearBragg/near2far.html -James Holton MAD Scientist On 10/13/2010 7:42 PM, Jacob Keller wrote:So let's say I am back in the good old days before computers, hand-calculating the MIR phase of my first reflection--would I just set that phase to zero, and go from there, i.e. that wave will define/emanate from the origin? And why should I choose f000 over f010 or whatever else? Since I have no access to f000 experimentally, isn't it strange to define its phase as 0 rather than some other reflection? JPK On Wed, Oct 13, 2010 at 7:27 PM, Lijun Liu<lijun....@ucsf.edu> wrote:When talking about the reflection phase: While we are on embarrassingly simple questions, I have wondered for a long time what is the reference phase for reflections? I.e. a given phase of say 45deg is 45deg relative to what? ========= Relative to a defined 0. Is it the centrosymmetric phases? ===== Yes. It is that of F(000). Or a theoretical wave from the origin? ===== No, it is a real one, detectable but not measurable. Lijun Jacob Keller ----- Original Message ----- From: "William Scott"<wgsc...@chemistry.ucsc.edu> To:<CCP4BB@JISCMAIL.AC.UK> Sent: Wednesday, October 13, 2010 3:58 PMSubject: [ccp4bb] Summary : [ccp4bb] embarrassingly simple MAD phasingquestion Thanks for the overwhelming response. I think I probably didn't phrase thequestion quite right, but I pieced together an answer to the question Iwanted to ask, which hopefully is right. On Oct 13, 2010, at 1:14 PM, SHEPARD William wrote:It is very simple, the structure factor for the anomalous scatterer isFA = FN + F'A + iF"A (vector addition) The vector F"A is by definition always +i (90 degrees anti-clockwise) with respect to the vector FN (normal scattering), and it represents the phase lag in the scattered wave.So I guess I should have started by saying I knew f'' was imaginary, theabsorption term, and always needs to be 90 degrees in phase ahead of the f' (dispersive component). So here is what I think the answer to my question is, if I understood everyone correctly: Starting with what everyone I guess thought I was asking, FA = FN + F'A + iF"A (vector addition)for an absorbing atom at the origin, FN (the standard atomic scatteringfactor component) is purely real, and the f' dispersive term is purely real,and the f" absorption term is purely imaginary (and 90 degrees ahead).Displacement from the origin rotates the resultant vector FA in the complex plane. That implies each component in the vector summation is rotated by that same phase angle, since their magnitudes aren't changed fromdisplacement from the origin, and F" must still be perpendicular to F'. Hence the absorption term F" is no longer pointed in the imaginary axisdirection. Put slightly differently, the fundamental requirement is that the positive90 degree angle between f' and f" must always be maintained, but theirabsolute orientations are only enforced for atoms at the origin. Please correct me if this is wrong. Also, since F" then has a projection upon the real axis, it now has a realcomponent (and I guess this is also an explanation for why you don't getthis with centrosymmetric structures). Thanks again for everyone's help. -- Bill William G. Scott Professor Department of Chemistry and Biochemistry and The Center for the Molecular Biology of RNA 228 Sinsheimer Laboratories University of California at Santa Cruz Santa Cruz, California 95064 USA phone: +1-831-459-5367 (office) +1-831-459-5292 (lab) fax: +1-831-4593139 (fax) = ******************************************* Jacob Pearson Keller Northwestern University Medical Scientist Training Program Dallos Laboratory F. Searle 1-240 2240 Campus Drive Evanston IL 60208 lab: 847.491.2438 cel: 773.608.9185 email: j-kell...@northwestern.edu ******************************************* Lijun Liu Cardiovascular Research Institute University of California, San Francisco 1700 4th Street, Box 2532 San Francisco, CA 94158 Phone: (415)514-2836******************************************* Jacob Pearson Keller Northwestern University Medical Scientist Training Program Dallos Laboratory F. Searle 1-240 2240 Campus Drive Evanston IL 60208 lab: 847.491.2438 cel: 773.608.9185 email: j-kell...@northwestern.edu *******************************************
-- ============================================================================ Bart Hazes (Associate Professor) Dept. of Medical Microbiology& Immunology University of Alberta 1-15 Medical Sciences Building Edmonton, Alberta Canada, T6G 2H7 phone: 1-780-492-0042 fax: 1-780-492-7521 ============================================================================