I'm sure Gloria would be delighted if that were the case, but I don't
think this is an incommensurate lattice. These actually don't so much
give you diffuse scattering as little satellite spots near the main
spots at spacings that don't make any sense given the lattice repeat.
My understanding is that these arise from something that is slowly
varying from unit cell to unit cell (could be as simple as a side chain
waving back and forth) in a repetitive pattern that just doesn't line up
in any way with the repeat of the unit cells.
Still, I'll ask her.
However, I think that the difference is that modulated lattices are
gradual changes of structure across many unit cells and what I was
talking about is a more simplistic case of two different kinds of unit
cells with varying degrees of randomness in their arrangement. That is,
using the formalism I described below, a modulated lattice would have
unit cells that go: ABCDEFGHGFEDCBABCDEFG... etc. where A is not that
different from B, B similar to C, etc., but A and H are very different.
-James Holton
MAD Scientist
Jürgen Bosch wrote:
Hi James,
what your descriptions aims at is I think shown in this publication
Borgstahl, G. E. O. "Incommensurate Crystallography by Sander van
Smaalen" Crystallography reviews 14 , 259-260 (2008).
Or am I misunderstanding something here ?
Jürgen
On 28 Jan 2009, at 12:39, James Holton wrote:
I recommend you have a look at a book from OUP called "Diffuse X-Ray
Scattering and Models of Disorder" by T. R. Welberry. The first chapter
explains quite well (I think) where all these streaky things come from.
It will also make you feel better about having it when you see all the
small molecule structures that have horrible diffuse scattering! (such
as urea).
This looks to me like a fairly classic case of correlated static
disorder. Best way to think about it is this:
Imagine you have two different kinds of unit cells: A an B. Doesn't
really matter what the difference between A and B is, could be a
two-headed side chain in conformer A vs conformer B, or it could be as
complicated as a domain motion. But, for simplicity, lets assume it is
two rotamers of a side chain and also assume that each unit cell in your
crystal can only be one or the other (no "in betweens").
Now, if the arrangement of these unit cells is perfectly correlated and
an "A" always occurs right next door to a "B" along the c-axis (say),
then what you really have is a bigger unit cell than you think. That
is, you can draw a unit cell around each A-B pair and call it a
"supercell" with the contents of B as a simple NCS mate of A (with one
side chain in a different rotamer). Some people might call this a
"pseudotranslation". The effect on the diffraction pattern in this case
would be the appearance of a very weak spot in between each "old" spot
along your "c" axis. That is, your "supercell" is twice as big along
"c" so the reciprocal-space lattice has twice as many spots in it. The
new spots are weak because they only correspond to the differences
between A and B, which in this case is only a few atoms.
Now lets say A and B are not perfectly correlated, but only slightly.
That is, in some parts of the crystal A and B are side-by-side, but in
other parts you get AAB, ABBA, BABBA, etc. In each of these cases the
"supercell" you must draw is 3, 4 and 5x your original unit cell. Each
of these will produce new weak spots with progressively tighter
spacings. As the supercell becomes very long, these rows of tight spots
will become a streak. The streaks are particularly prominent if the A-B
disorder is along only one axis. In that case, you must have a whole
a-b layer of "A" and other whole a-b layers of "B", and the ordering of
these layers along "c" is fairly random. Colin just described this as a
"stacking disorder" which is probably a good name for it.
The final case is when A and B are completely uncorrelated and occur
absolutely at random locations in your crystal. In this case the
"supercell" can be anything and the "streaks" are in every direction
(including every diagonal) so they simply show up as increased
background. Every crystal does this. In fact, this is the origin of
the B-factor as no two unit cells are exactly alike. Ever wonder where
those photons go that scatter off protein atoms but don't go into
spots? They go into the background.
Now, since these streaks represent correlations of neighboring unit
cells this means that the diffuse scattering can tell you something
about how your molecule moves. There is something about your structure
that forces its neighbors to be the same in at least one direction.
There are a class of people who study this for a living. I am not one
of them.
BTW. This is definitely NOT a mosaic spread. Mosaicity occurs on
length scales thousands of times larger than this. By definition, a
mosaic spread is the width of the distribution of relative rotation
angles of "mosaic domains" and these domains all scatter independently
of each other. An infinite mosaic spread (or at least 180 degrees)
corresponds to a powder diffraction pattern, and the fact that powder
lines are sharp demonstrates how mosaicity cannot smear spots in
anything but the "tangential" direction. That is, no rotation can
change the d-spacing of a spot. Changes in unit cell size can do this,
but that is a very different phenomenon than mosaic spread as mosaic
domains are much much bigger than unit cells.
The good news is, it is highly unlikely that this will prevent you from
solving the structure. Indeed I think there are many structures in the
PDB that had streaks in their diffraction pattern like this. The reason
it won't hurt you is that the intensity of the Bragg peaks is the same
in the perfectly-correlated, partially-correlated and completely
uncorrelated cases. The electron density will simply have a two-headed
side chain in it.
So, I would suggest doing what most crystallographers do and completely
ignore any potentially informative weirdness along the way and sally
forth. But save these pictures (and the above book) for when your
reviewer tells you your R-merge is too high.
-James Holton
MAD Scientist
Margriet Ovaere wrote:
Dear all,
In the diffraction pattern of crystals of an RNA decamer, small lines
appeared (see pictures attached). We've tried different crystals but
they all showed the same small lines. Has anybody seen
this phenomena before and has got an explanation for it please..?
Many thanks
Margriet Ovaere
------------------------------------------------------------------------
------------------------------------------------------------------------
Margriet Ovaere
Chemistry Department K.U.Leuven
Biomolecular Architecture
Celestijnenlaan 200 F
B-3001 Heverlee (Leuven)
Tel: +32(0)16327477
-
Jürgen Bosch
Johns Hopkins Bloomberg School of Public Health
Biochemistry and Molecular Biology, W8708
615 North Wolfe Street
Baltimore, MD 21205
Phone: +1-410-614-4742
Fax: +1-410-955-3655
