Hi James If we're going to sort out the units we need to get the terminology right too. The mean square atomic displacement already has a symbol U = <u^2> (or to be precise Ueq as we're talking about isotropic displacements here), and u is conventionally not defined as the RMS displacement as you seem to be implying, but the *instantaneous* displacement (otherwise you then need another symbol for the instantaneous displacement!).
See: http://www.iucr.org/resources/commissions/crystallographic-nomenclature/ adp (or Acta Cryst. (1996). A52, 770-781). My theory is that B became popular over U because it needs 1 fewer digit to express it to a given precision, and this was important given the limited space available in the 80-column PDB format. So a B of 20.00 to 4 sig figs requires 5 columns, whereas the equivalent U of 0.2500 to 4 sig figs requires 6 columns (personally I've got nothing against '.2500' but many compiler writers don't see it my way!). Interestingly the IUCr commission in their 1996 report did not address the question of units for B and U. Cheers -- Ian > -----Original Message----- > From: owner-ccp...@jiscmail.ac.uk > [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton > Sent: 20 November 2009 07:14 > To: CCP4BB@jiscmail.ac.uk > Subject: units of the B factor > > Many textbooks describe the B factor as having units of > square Angstrom > (A^2), but then again, so does the mean square atomic > displacement u^2, > and B = 8*pi^2*u^2. This can become confusing if one starts > to look at > derived units that have started to come out of the radiation damage > field like A^2/MGy, which relates how much the B factor of a crystal > changes after absorbing a given dose. Or is it the atomic > displacement > after a given dose? Depends on which paper you are looking at. > > It seems to me that the units of "B" and "u^2" cannot both be A^2 any > more than 1 radian can be equated to 1 degree. You need a scale > factor. Kind of like trying to express something in terms of "1/100 > cm^2" without the benefit of mm^2. Yes, mm^2 have the > "dimensions" of > cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That > would be silly. However, we often say B = 80 A^2", when we > really mean > is 1 A^2 of square atomic displacements. > > The "B units", which are ~1/80th of a A^2, do not have a name. So, I > think we have a "new" unit? It is "A^2/(8pi^2)" and it is > the units of > the "B factor" that we all know and love. What should we call it? I > nominate the "Born" after Max Born who did so much fundamental and > far-reaching work on the nature of disorder in crystal lattices. The > unit then has the symbol "B", which will make it easy to say > that the B > factor was "80 B". This might be very handy indeed if, say, > you had an > editor who insists that all reported values have units? > > Anyone disagree or have a better name? > > -James Holton > MAD Scientist > > Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
