Sorry, of course I meant to say: "Problems with units often stem from an
*ambiguous* definition."!

I.

> -----Original Message-----
> From: [log in to unmask] [mailto:[log in to unmask]]
On
> Behalf Of Ian Tickle
> Sent: 26 February 2010 17:18
> To: James Holton; Tim Gruene
> Cc: [log in to unmask]
> Subject: RE: [ccp4bb] units of f0, f', f''
> 
> I would only re-iterate my observation (see our previous discussion
> about the 'units' of angles) concerning the importance in any document
> (including e-mails!) to have a "Notation" section where all quantities
> in use are rigorously defined.  The definitions can be as wordy as you
> like, since they only appear once per quantity per document, or I
> suppose you could reference the Notation section in another document
if
> you really wanted to save space.  However you do it, all quantities
> absolutely must be defined somewhere once and once only.  Then you can
> refer to the quantity as many times as you like in the body of the
paper
> with the appropriate units (if any) and there's no possibility of
> ambiguity.  If anyone is unclear about your meaning they just have to
> refer back to your definition.  Problems with units often stem from an
> unambiguous definition.  So following my own advice:
> 
> <NOTATION>
> Notation
> ========
> 
> f0: atomic scattering factor for normal scattering, defined as the
ratio
> of scattered amplitude to that for a free electron.
> </NOTATION>
> 
> The word 'ratio' gives the game away: f0 is dimensionless and
therefore
> unitless, it's just a pure number.  It doesn't have dimensions of
> electric charge or length or anything else, and it doesn't have units
of
> electrons, it's just a pure number.  If anyone is uncertain about what
> this number refers to, they have only to refer to the above
definition,
> there's no possibility of ambiguity through abbreviation.  Note that
> every quantity that has dimensions has units and vice-versa, you can't
> have one without the other.  What may appear in some cases to be units
> are actually just shorthand for scale factors that are pure numbers:
> here's the definition of some scale factors in common use:
> 
> radian = 1
> pi = ratio of circumference/diameter of any circle
> degree = pi/180
> 
> If you really must you can say that the scale factor for f0 is 'e', so
> then you can say 'f0 = 10e', but then you have to define 'e': 'e=1',
in
> which case 'f0 = 10' so you're really no better off.
> 
> Cheers
> 
> -- Ian
> 
> 
> > -----Original Message-----
> > From: [log in to unmask]
[mailto:[log in to unmask]]
> On
> > Behalf Of James Holton
> > Sent: 26 February 2010 15:04
> > To: Tim Gruene
> > Cc: [log in to unmask]
> > Subject: Re: [ccp4bb] units of f0, f', f''
> >
> > 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
> > >
> > >
> 
> 
> 
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