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CCP4BB  November 2009

CCP4BB November 2009

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Subject:

Re: {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor

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Fri, 20 Nov 2009 13:23:25 +0100

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But in this case you are no longer defining distances but some other arbitrary quantity, like vendors do when they convert a small computer speaker into a rockband PA by using PMPO instead of music power.  
Herman

-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Frank von Delft
Sent: Friday, November 20, 2009 1:11 PM
To: [log in to unmask]
Subject: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor

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.
>>>
>>>
>>
>

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