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
>