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" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Thursday, October 14, 2010 11:28 AM
Subject: 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 the
>> sound 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 wavelength
>> gets 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 the
>> impression that the incident beam has "slowed down". This is the origin
>> of 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 atom
>> to 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 atom
>> that 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<[log in to unmask]> 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"<[log in to unmask]>
>>>> To:<[log in to unmask]>
>>>> Sent: Wednesday, October 13, 2010 3:58 PM
>>>> Subject: [ccp4bb] Summary : [ccp4bb] embarrassingly simple MAD phasing
>>>> question
>>>>
>>>>
>>>> Thanks for the overwhelming response. I think I probably didn't
>>>> phrase the
>>>> question quite right, but I pieced together an answer to the question I
>>>> wanted 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 is
>>>>
>>>> FA = 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,
>>>> the
>>>> absorption 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 scattering
>>>> factor 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 from
>>>> displacement from the origin, and F" must still be perpendicular to F'.
>>>> Hence the absorption term F" is no longer pointed in the imaginary axis
>>>> direction.
>>>>
>>>> Put slightly differently, the fundamental requirement is that the
>>>> positive
>>>> 90 degree angle between f' and f" must always be maintained, but their
>>>> absolute 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
>>>> real
>>>> component (and I guess this is also an explanation for why you don't
>>>> get
>>>> this 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: [log in to unmask]
>>>> *******************************************
>>>>
>>>> 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: [log in to unmask]
*******************************************
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