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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