James,
I could not help typing something!
Consider a circle of radius R, its circumstance L is then 2*Pi*R.
Both R and L have the same unit, the 2*Pi angle is unitless.
SI defines the unit of angle to be Ran just because this unitless
number is different because it is obtained by the length of an arc
over a fragment of straight line, not like sin/cos which are given by
straightline fragments. The unit of L is not Ran*unit(R) but unit(R).
OK, L = 2*Pi*R. (1)
Now B = 8*Pi*Pi*U*U. (2)
(Isotropic) B is defined as above. U is the average displacement
from the miller plane. B function is defined to be amplified
by U*U by 8*pi*pi. If you do not agree, apply your rule to (1).
Using the rule of (1) to (2), B has a unit of A*A, while the unit(U)
is A.
The 8*pi*pi is a convenient amplifier. From U to B, this is a one
single
factor to another single factor function. In this case, to describe
an amount
of physical meaning, both factors (U and B) are logically, equivalent,
depending
on which one is more convenient.
Lijun
On Nov 23, 2009, at 1:11 PM, James Holton wrote:
I would like to apologize to everyone for creating such a busy thread
(an what could perhaps be construed as an occasionally belligerent
tone), but I really do want to know the right answer to this! I am
trying to model radiation damage from first principles, and in such
models you cannot have arbitrary scale factors.
And I really do appreciate the effort Dale, Ian, Marc, and many
others,
put into their posts. Taking bits from many of them, I think I can
say
that:
The "unit of B factor" is: hemi-(cycle/Angstrom)^-2
and the dimensions of the B factor are length^2
Apparently, the B factor is derived from the square of a spatial
frequency, which has fundamental units "cycles per meter". However,
there is an extra factor of two that makes the B factor incompatible
with merely "spatial frequency squared" (with no scale prefix) as the
unit, so I think we have to include the prefix "hemi" before we can
make
the 2*pi radians/cycle go away. Marc and Ian I imagine will tell me
that cycle = 1 and hemi = 1 and therefore we have Angstrom^2 and they
are more than welcome to do that in their papers, but I think it
important here to clarify exactly what "one B factor unit" means.
-James Holton
MAD Scientist
Lijun Liu
Cardiovascular Research Institute
University of California, San Francisco
1700 4th Street, Box 2532
San Francisco, CA 94158
Phone: (415)514-2836
