On Thursday, October 14, 2010 12:12:18 pm Lijun Liu wrote:
> I think I need make it clear. Not their changes (f' and f") but their
> contribution to reflection intensities changes.
f' and f" are not "changes".
They are the real and imaginary components of anomalous scattering.
They are wavelength dependent but not angle dependent.
> It is right at higher resolution, it turned to be increased.
> Changes against resolution is itself an evidence to that the
> contribution is angle dependent.
> The lower the resolution, the lower the contribution from those guys.
The contribution from normal scattering, f0, is strong at low resolution
but becomes weaker as the scattering angle increases.
The contribution from anomalous scattering, f' + f", is constant at
all scattering angles.
Let us define the contribution from FAS = (f' + f").
At low resolution: FAS / f0(angle) is a small number
At high resolution: FAS / f0(angle) is a bigger number.
> To the lowest one (000), the contribution is 0.
The contribution to all reflections including F[0,0,0]
is the non-zero constant FAS.
To see the effect this has on phasing power, etc, you might have a look
at
http://skuld.bmsc.washington.edu/scatter/AS_signal.html
>
> Lijun
>
> On Oct 14, 2010, at 11:13 AM, Ethan Merritt wrote:
>
> > On Thursday, October 14, 2010 10:41:17 am Lijun Liu wrote:
> >> Power on scattering by atoms is angle dependent, which is true for
> >> both the real and imaginary parts.
> >
> > Actually, no. The f' and f" terms are independent of scattering
> > angle,
> > at least to first approximation. This is why the signal from
> > anomalous
> > scattering increases with resolution.
> >
> > cheers,
> >
> > Ethan
> >
> >
> >> (Think about the plot of f vs sin(theta)/lamda).
> >> The f" contribution to anomalous scattering of F(000) is 0, just in
> >> contrast to that the real part in this (000)
> >> direction is the full number of electrons; i.e., electron does not
> >> anomalously scatter in this (000) direction.
> >> So, the phase of (000) stays safely at 0, or the symmetry-broken
> >> Friedel's law is broken (F000.ne.F-0-0-0).
> >>
> >> (000) is not only centrosymmetric, but to itself, which is the only
> >> one in the diffraction space.
> >>
> >> Lijun
> >>
> >> On Oct 14, 2010, at 9:28 AM, Dale Tronrud wrote:
> >>
> >>> 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
> >>>>>>
> >>>>>>
> >>>>>>
> >>
> >> Lijun Liu
> >> Cardiovascular Research Institute
> >> University of California, San Francisco
> >> 1700 4th Street, Box 2532
> >> San Francisco, CA 94158
> >> Phone: (415)514-2836
> >>
> >>
> >>
> >>
> >
> > --
> > Ethan A Merritt
> > Biomolecular Structure Center, K-428 Health Sciences Bldg
> > University of Washington, Seattle 98195-7742
>
> Lijun Liu
> Cardiovascular Research Institute
> University of California, San Francisco
> 1700 4th Street, Box 2532
> San Francisco, CA 94158
> Phone: (415)514-2836
>
>
>
>
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
University of Washington, Seattle 98195-7742
|
