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Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor |
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CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999Subject: Re: {Spam?} Re: {Spam?} Re: {Spam?} Re: {Spam?} Re: units of the B factor From: Marc SCHILTZ marc {- dot -} schiltz {- at -} EPFL {- dot -} CH Date: 2009-11-20 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 CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999 |
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