Hi James, Am 03.02.2009 um 17:38 schrieb James Holton:
Hey Dirk, You're wrong. ;)
okay, thanks a lot! ;-)
The remarkable part of this is that the integrated spot intensity (photons) is essentially invariant with how you divide up the unit cells into mosaic domains. Well, okay, if N=1, then you don't really have a crystal but an amorphous solid (seen a lot of those), so I should qualify that so long as N > ~1000, it doesn't matter if m is 1 or 10^12, the integrated spot intensity (photons) is still proportional to the total number of unit cells in the crystal. This was first shown by C. G. Darwin (1914) so I don't blame you if you can't find the original reference. However, "Darwin's Formula" can be found in most modern textbooks. It is Equation 9.1 in Blundell & Johnson (1976) and Equation 4.31 in Drenth (1999). You will note that the mosaic spread is not part of this equation.
thanks for the pointer - I found Darwin's formula both in my copy of Blundell & Johnson and in Giacovazzo's "Fundamentals of Crystallography", chapter 3.14. It is really interesting to see that the deposited total energy on a detector for a reflection is indeed proportional to V and thus to N.
I understand it was W. L. Bragg et al. (1921) who confirmed that the absolute scattered intensity from rock salt does indeed obey Darwin's Formula. I confirmed it recently for lysozyme on my beamline, but never published it as I figured I had been scooped 86 years earlier.
... such things happen to all of us sooner or later ...
The distribution of unit cells into mosaic domains does become important if the extent of a mosaic domain starts to become large compared with the attenuation length of the x-ray beam, then one must invoke the dynamical theory. Darwin derived equations for the dynamical case as well, but these almost never apply to protein crystals. They are just too small.
many thanks again for your explanations! Best regards, Dirk. ******************************************************* Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax: +49-89-2180-76999 E-mail: [email protected] *******************************************************
