Yes, but Å is really only just tolerated.
It has evaded the Guillotine - for the time being ;-)
Frank von Delft wrote:
> Eh? m and Å are related by the dimensionless quantity 10,000,000,000.
>
> Vive la révolution!
>
>
>
>
> Marc SCHILTZ wrote:
>> 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
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