I thank for the references and the comprehensive discussion from Dr.
Holton. Also, for the reference indicated by Dr. Berry. I think I will get
what I am looking for, now I need to "process" all this information.
Partially answering Dr. Holton, my aim is to have a side guide for
improving parameters to process images with ice diffraction rings. In
general, the idea is to exclude the minimum area from the detector, but
large enough to avoid bad regions. In this, ice ring widths have a role,
so, besides the amount of ice, exposure time and beam intensity, relative
diffraction intensities contribute, and this way one could decide better
what the "best" width might be for each individual ring. Sure, looking at
the images are the base here, but it is interesting to be seconded by the
ring expected positions and "relative intensities".
Yours,
Jorge
On Tuesday 26 June 2012 09:16 PM, James Holton wrote:
I think an appropriate reference is Bragg (1921)
http://dx.doi.org/10.1088/1478-7814/34/1/322 who compared various
possible crystal structures to the relative "strength" of the
reflections from "ice powder" measured by Dennison (1921)
http://dx.doi.org/10.1103/PhysRev.17.20.
However, as Bragg noted Dennison's intensities don't agree all that
well with those you would expect from what we now know is the
structure of hexagonal ice (Ih). It is possible that Dennison's
preparation (plunge-cooling pure water in a capillary) actually
created some cubic ice (ice Ic) along with his hexagonal ice (ice Ih).
The high intensity he saw for the "middle" line of the triplet we
normally see for true hexagonal ice is consistent with this. Cubic
ice is actually more commonly seen in MX diffraction patterns than
hexagonal ice (in my experience).
However, you do have to be very careful about what you mean by
"intensity". Are you talking about photons/pixel? Photons/spot?
Photons integrated over a powder_ring? All these will be different
relative numbers. I'm not sure if they knew about Lorentz factors yet
in 1921 There is no mention of correcting for them in either paper.
Anyway, if you are after the "true" hexagonal ice ring intensities, I
would advise taking the following PDB file:
CRYST1 4.511 4.511 7.346 90.00 90.00 120.00 P 63/m m c
SCALE1 0.221680 0.127987 -0.000000 -0.00000
SCALE2 -0.000000 0.255974 -0.000000 0.00000
SCALE3 0.000000 -0.000000 0.136129 -0.00000
ATOM 1 O WAT A 1 0.000 2.604 0.457 1.00
0.00 O
ANISOU 1 O WAT A 1 603 630 172 302 0
0 O
ATOM 2 H WAT A 1 0.000 2.604 1.308 0.50
0.00 H
ANISOU 2 H WAT A 1 510 510 56 255 0
0 H
ATOM 3 H WAT A 1 0.000 3.432 0.148 0.50
0.00 H
ANISOU 3 H WAT A 1 487 361 163 185 199
95 H
Calculate structure factors from it, add up F2 of same-resolution
indicies and plot them out that way. remember, the square of a
structure factor is proportional to the integrated intensity of a
single-crystal spot, which is not the same thing as a powder ring
intensity. The relationship was described most recently by Norby
(1997) http://dx.doi.org/10.1107/S0021889896009995
Which I paraphrase as:
for a flat detector, the average intensity of a pixel in a powder ring
is given by:
Ipix = k*p*sum(F2)*omega/sin(theta)/sin(2*theta)
where Ipix is the recorded value of one pixel, 'k" is a
resolution-independent scale factor, "p" is the polarization factor
(see Holton& Frankel 2010), "F" is the structure factor of an hkl
index that falls on the ring (there can be more than one, hence the
"sum"), "omega" is the solid angle subtended by the pixel and "theta"
is the Bragg angle.
For the above PDB, I get:
d sum(F2)
3.907 121
3.673 156
3.449 111
2.676 88.5
2.255 111
2.075 153
1.953 62.9
1.922 84.2
1.888 62.5
1.836 4.33
1.725 47.8
1.662 1.84
1.527 96.7
1.477 42.8
1.448 39.5
1.375 78.9
1.370 34.6
HTH,
-James Holton
MAD Scientist
On Tue, Jun 26, 2012 at 2:34 PM, Edward A.
Berry<[log in to unmask]><[log in to unmask]>
wrote:
Maybe figure 4 in
Viatcheslav Berejnov et al. Vitrification of aqueous solutions
J. Appl. Cryst. (2006). 39, 244–251 ?
JORGE IULEK wrote:
Hi, all,
I thought I could easily find a reference to comment upon the relative
intensity of
rings in an image due to diffraction by polycrystal ice, but no luck
googling for that. A
reference that would contain a picture (with visual relative intensities)
would be even
better. Of course absolute intensity depends on the amount of ice, but a
relative "scale"
is what I am looking for now.
Yours,
Jorge
