Frank von Delft wrote:
Hi Marc
Not at all, one uses units that are convenient. By your reasoning we
should get rid of Å, atmospheres, AU, light years... They exist not to
be obnoxious, but because they're handy for a large number of people in
their specific situations.
Hi Frank,
I think that you misunderstood me. Å and atmospheres are units which
really refer to physical quantities of different dimensions. So, of
course, there must be different units for them (by the way: atmosphere
is not an accepted unit in the SI system - not even a tolerated non SI
unit, so a conscientious editor of an IUCr journal would not let it go
through. On the other hand, the Å is a tolerated non SI unit).
But in the case of B and U, the situation is different. These two
quantities have the same dimension (square of a length). They are
related by the dimensionless factor 8*pi^2. Why would one want to
incorporate this factor into the unit ? What advantage would it have ?
The physics literature is full of quantities that are related by
multiples of pi. The frequency f of an oscillation (e.g. a sound wave)
can be expressed in s^-1 (or Hz). The same oscillation can also be
charcterized by its angular frequency \omega, which is related to the
former by a factor 2*pi. Yet, no one has ever come up to suggest that
this quantity should be given a new unit. Planck's constant h can be
expressed in J*s. The related (and often more useful) constant h-bar =
h/(2*pi) is also expressed in J*s. No one has ever suggested that this
should be given a different unit.
The SI system (and other systems as well) has been specially crafted to
avoid the proliferation of units. So I don't think that we can (should)
invent new units whenever it appears "convenient". It would bring us
back to times anterior to the French revolution.
Please note: I am not saying that the SI system is the definite choice
for every purpose. The nautical system of units (nautical mile, knot,
etc.) is used for navigation on sea and in the air and it works fine for
this purpose. However, within a system of units (whichever is adopted),
the number of different units should be kept reasonably small.
Cheers
Marc
Sounds familiar...
phx
Marc SCHILTZ wrote:
Hi James,
James Holton wrote:
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.
There is nothing wrong with this. In the case of derived units, there
is almost never a univocal relation between the unit and the physical
quantity that it refers to. As an example: from the unit kg/m^3, you
can not tell what the physical quantity is that it refers to: it could
be the density of a material, but it could also be the mass
concentration of a compound in a solution. Therefore, one always has
to specify exactly what physical quantity one is talking about, i.e.
B/dose or u^2/dose, but this is not something that should be packed
into the unit (otherwise, we will need hundreds of different units)
It simply has to be made clear by the author of a paper whether the
quantity he is referring to is B or u^2.
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.
This is like claiming that the radius and the circumference of a
circle would need different units because they are related by the
"scale factor" 2*pi.
What matters is the dimension. Both radius and circumference have the
dimension of a length, and therefore have the same unit. Both B and
u^2 have the dimension of the square of a length and therefoire have
the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and
does not change the unit.
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?
Good luck in submitting your proposal to the General Conference on
Weights and Measures.
--
Marc SCHILTZ http://lcr.epfl.ch
