yes there is a F000, it is always in diffraction condition independent
of crystal orientation (hx+ky+lz) is always zero for any xyz when hkl = 000
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"
> <[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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Bart Hazes (Associate Professor)
Dept. of Medical Microbiology& Immunology
University of Alberta
1-15 Medical Sciences Building
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Canada, T6G 2H7
phone: 1-780-492-0042
fax: 1-780-492-7521
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