Of course, for SI political correctness we should be using nm^2 anyway. This would add more confusion to a situation that most people don't worry about anyway.

Pete




On 20 Nov 2009, at 11:05, Ian Tickle wrote:

> 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: [log in to unmask] 
>> [mailto:[log in to unmask]] On Behalf Of James Holton
>> Sent: 20 November 2009 07:14
>> To: [log in to unmask]
>> 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
>> 
>> 
> 
> 
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