These quantities are components of the total structure factor, and
therefore must have the same units as the overall structure factor.
The definition of a structure factor is the ratio between the scattered
amplitude from some "structure" of interest and the amplitude scattered
by a single electron. The "structure" can be an atom, a protein, or
even an entire crystal. In this way, we separate the contribution of
the molecular structure from all the other "factors" of scattering (like
polarization and Lorentz factors). This definition heralds back to
Hartree (1925) Philos. Mag. 50, 289-306, which was the first time the
term "structure factor" appeared in the English literature. Although
Debye & Scherrer (1918) Physik. Zeit. 19, 474-483 probably deserve
credit for coining the term (in German), something very similar to a
structure factor (without the modern name) appeared as a variable "f" in
Darwin's original paper on scattering theory: Darwin, C. G. (1914)
Philos. Mag. 27, 315-333. It was immediately after measuring the
resolution dependence of "f" that Debye amazingly and immediately
realized that we were going to have to accept quantum theory (Debye
(1915). Ann. Phys. 351, 809-823).
Anyway, the structure factor is a ratio, and therefore is technically a
dimensionless quantity, but even a dimensionless quantity has a "unit"
in that there is some situation where the structure factor is equal to
unity (1.0). This "unit" is when the object of interest scatters "just
as much" as one of Thomson's classical electrons would (Thomson, (1906);
Woolfson, (1997) Ch. 2). So, it is convenient to describe structure
factors in terms of how many electrons it would take to produce the same
signal. Hence, the "unit" of structure factor is the "electron", but
probably better denoted as the "electron equivalent" to avoid the
present confusion. For example, the "F" values calculated by SFALL or
REFMAC have units of "electron equivalents per unit cell". Again, a
dimensionless quantity, but far more informative when the unit is
spelled out. Abbreviations are great, but not when taken to the point
where they introduce ambiguity.
I see nothing wrong with using a particle or other physical object as a
"unit" as long as the meaning is made clear. After all, until recently
the unit of "meter" was a metal stick they had in France. And the
"unit" of mass is still a lump of metal which weighs exactly 1.0 kg.
This object is slowly oxidizing, and that means that the mass of
everything else in the universe is actually decreasing (by definition).
Which could perhaps account for recent observations that the expansion
rate of the universe is accelerating (Riess et al. (1998) Astro. J. 116,
1009).
I'm sure Ian and Mark will have more to say about this...
-James Holton
MAD Scientist
Tim Gruene wrote:
Dear all,
I just stumbled across the question about what is the unit of f' and f''. The
first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit
but symbolises an elemtary particle (of which fractions are considered
non-existent), I was wondering whether the unit of f, f', and f'' is actually e
(a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e
or -26e - see e.g. Table 1 in
http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html
Cheers, Tim
--
Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen
GPG Key ID = A46BEE1A
