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
