Quoting Dale Tronrud <[log in to unmask]>:

>
>    I've held off on getting involved in this as long as I could,
> but you are so definitive in your comment.  I could make the
> same argument that the unit of electron density is "1" because,
> after all, the volume is just the count of the number of Å^3 and
> a count is not a unit.  In fact, as Dr. Holton pointed out,
> every unit is just a count of something, length is the count of
> wavelengths of a particular beam of light, mass is the number
> of blocks of metal from Paris that total to the same mass, etc.


But this is precisely the point: when we count apples, we don't need a  
unit. Everyone in the world will count the same number of red stripes  
on the American flag without the need to agree on a unit beforehand.  
But when asked to give the length of a stripe, people will first have  
to agree on a unit.

For length and volume you need a unit, whereas for number of stripes  
or number of electrons you don't. So I don't see by what chain of  
arguments you could arrive at the conclusion that the unit of electron  
density is "1".


>    We put units in our discussion of numbers because it aids in
> our ability to communicate meaning to one another.  Yes, electrons


This is precisely not the role of units. The meaning of a physical  
quantity is given by its definition, not by its unit. Looking at a  
value like "23.46 kg/m^3", you can not infer from the unit whether  
this is a density or a concentration - both have the same unit. So the  
idea that units should convey the meaning of a physical quantity is  
simply not correct. Units have never been intended for that purpose.


> are like apples and are simply counts, but we have the old saying
> that you can't add apples and oranges, which means you have to
> keep track of which numbers are counts of apples and which are
> counts of oranges.  Where this different is important it is
> convenient to label the counts with a note as to the appleness
> or orangeness of each number.


When asked "how many fruits are in the basket ?", you would still add  
apples and oranges....

It would probably not make much sense to add up the height of the  
Eiffel tower and the Thomson scattering length. Yet, both of these  
quantities are measured in the same unit (meter, in the SI system). We  
don't invent an Eiffel-meter and a Thomson-meter just to remind us  
that we should not add these two quantities together.



>
>    For maps it is important for people to know if their map is
> in e/Å^3 or sigma/Å^3.  Both maps are commonly encountered in
> this field and both are called electron density maps.  I could


I think both are the same map. It is just the way they are contoured  
which differs.



> put a note on my home page stating that whenever I talk about
> a map I give numbers in e/Å^3 but it is more convenient for the
> reader if I just put the convention next to the number.
>
>    You have a subset of quantities that you use as labels (I'm
> guessing cm, sec, Kg and others.).  I find it convenient to
> use additional labels when certain quantities arise in my work.


I think that no one can object if you find it convenient to use  
additional labels to specify your quantities. But the initial question  
here was about the units of f0, f', f".


Marc





It
> isn't a matter of you being right and me being wrong or the other
> way around.  The only logically consistent solution is to have
> no units at all, and that would be terribly confusing to everyone.
>
> Dale Tronrud
>
> [log in to unmask] wrote:
>> I fully agree with Ian and would again point to the authoritative
>> documentation :
>>
>> http://www.bipm.org/en/si/derived_units/2-2-3.html
>>
>> The quantities f^0, f' and f" are unitless, i.e. simply numbers (or
>> rather: their unit is the number one, which is usually omitted).
>>
>> The unit of the electron density is really just 1/Å^3. To see this,
>> consider that the electron density is defined to be
>>
>> \rho = (Number of electrons)/volume
>>
>> The numerator is simply a count, and thus unitless (or rather: its unit
>> is the number one).
>>
>> In practice, we like to a remind ourselves that these values refer to
>> electrons and therefore like to think of e/Å^3 as the unit of electron
>> density, but this is somewhat incoherent, if not incorrect. The fact
>> that we are dealing with electrons (as opposed to apples) is contained
>> in the definition of the quantity "electron density". It does not need
>> to be explicitly specified in the unit.
>>
>>
>> Marc
>>
>>
>>
>>
>> Quoting Bernhard Rupp <[log in to unmask]>:
>>
>>> <NOTATION>
>>> Notation
>>> ========
>>>
>>> f0: atomic scattering factor for normal scattering, defined as the ratio
>>> of scattered amplitude to that for a free electron.
>>> </NOTATION>
>>>
>>> ----------------------------------------------------------------------
>>> Hmmm...where does the 'electron' in electron density then come from after
>>> integration/summation over the structure factors?
>>> ----------------------------------------------------------------------
>>>
>>> BR
>>>
>