Re: [ccp4bb] units of f0, f', f''
On 01/03/2010, at 08.02, Dale Tronrud wrote: Dear X-ray Community, I'm sorry to have dragged you all along on this journey. There is something to Ian and Marc's arguments but I have been unable to understand their point. That is my failure and I don't wish to subject the rest of you to continued argument. Ian, Marc, and I should get together in a bar somewhere and hash this out. That sounds like fun! Can we come? :-) PS: Enjoyed the journey! Cheers, Morten -- Morten Kjeldgaard, asc. professor, MSc, PhD BiRC - Bioinformatics Research Center, Aarhus University C. F. Møllers Alle, Building 1110, DK-8000 Århus C, Denmark. Lab +45 8942 3130 * Fax +45 8942 3077 * Home +45 8618 8180
Re: [ccp4bb] units of f0, f', f''
Let me give my input to the confusion :-) Things that can be counted are integers, and have no unit. They may, however, have a _nominal_ unit, which can be stripes, apples, pieces of fruit. Those units are solely used for clarity. For example, I can have 13 pieces of fruit, but that may be 5 oranges and 8 bananas, or 12 apples and 1 kiwi, so to avoid confusion, I'd better name those units; they become nominal (nomen == name). Some things cannot be counted. Like the height of the tree outside my window. I would say its height is 12, and Dale would say its height is 37. The height of the tree is a continuous variable, and so it needs to be measured in some unit. Therefore, the height of the tree can't be specified as just 12; it is indeed 12 m or 37 feet. It so happens that we think of electrons as particles, so on one hand, you might imagine that you can count electrons. We can argue whether or not that is true; someone might claim that electrons are delocalized, and can only be positioned via some kind of probability function. Perhaps it would make more sense to count the number of protons in the atomic nucleii of the unit cell, since those are used to compute the number of electrons anyway. I always enjoy asking students what the unit of an equilibrium constant is, and they always answer molar or micromolar squared or milimolar to the minus first ... etc. That is of course wrong; equilibrium constants are dimensionless, but are almost always given nominal units for clarity, especially by biologists. Cheers, Morten
Re: [ccp4bb] units of f0, f', f''
Dear Ian, Perhaps I should have made a more explicit connection to your message in what I wrote yesterday. I do not think there is any paradox, or apples vs. oranges problem, in this situation. The structure factor is a count of electrons as X-ray scatterers, so that the Fourier synthesis computed from them is a number density for these unit scatterers. The density can get clothed with a charge a-posteriori, because we know what the charge of an electron is, but it is not that charge as such that is sensed by the diffraction experiment: it is the complicated combination of charge and mass and various physical constants that ends up determining an electron's ability to scatter X-rays. I think that if one bears this in mind at all times, paradoxes never appear. With best wishes, Gerard. -- On Sun, Feb 28, 2010 at 02:40:15PM -, Ian Tickle wrote: Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for an atom to that for a free electron (dimensionless). g: atomic scattering free point equivalent charge, defined as the free point charge which scatters with the same amplitude as the atom (dimensions of electric charge). Now we can validly write 'g = 10e' since we have dimensions of charge on both sides. This again highlights the importance of 1) rigorously defining all quantities in use, and 2) that the definition and the dimensions are linked: you cannot arbitrarily change the dimensions of some quantity without also changing its definition, or vice versa; and in particular you can't mix the definition of 'f' with the units of 'g', which is what seems to be happening here! This logical inconsistency can only be resolved by recognising that 'f' is a pure number so removing the 'e' unit. The same argument obviously applies to anything derived from 'f' such as the structure factor and the electron density. Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674 -- === * * * Gerard Bricogne g...@globalphasing.com * * * * Global Phasing Ltd. * * Sheraton House, Castle Park Tel: +44-(0)1223-353033 * * Cambridge CB3 0AX, UK Fax: +44-(0)1223-366889 * * *
Re: [ccp4bb] units of f0, f', f''
On 01/03/2010, at 13.55, Boaz Shaanan wrote: As for equilibrium constants, I'm somewhat puzzled by your remark on their lack of units (I'm a chemist by the way). Is the equilibrium constant (or dissociation constant) of the reaction A+B-AB identical to that of the reaction: A+2B -- AB2 ? I didn't think so. I could of course misunderstand your statement, so please correct me. The equilibrium constant is defined as a ratio of the products of the chemical activities on the right and left sides of the equilibrium, and chemical activities themselves are dimensionless. In practical work, we use concentrations, which do have dimensions, but are multiplied by an activity factor which is usually ignored because it is very close to 1. For this reason, it appears that K has a unit, but it's only nominal. Cheers, Morten
Re: [ccp4bb] units of f0, f', f''
Dear Gerard I would certainly agree that in general, provided one takes sufficient care over dimensions and units, paradoxes can never appear. However, in this particular case I was pointing out the dimensionality error of writing equations such as f = 10e, and equivalent ones for the structure factor and electron density, given that 'f' is defined as a dimensionless ratio (as I believe it usually is). Even if you replaced the 'e' with whatever unit represents an electron's ability to scatter X-rays (which would be the amplitude of the scattered wave), you still have the same problem. I only focused on electric charge because 'e', the elementary unit of charge, was being posited as the unit of 'f'. The alternative solution that you suggested of using the word 'electron' as an abbreviation for an electron's worth of scattering, is likely to cause just as much confusion and probably would be further abbreviated to 'e' anyway, thus leading people to believe it represented the electronic charge! The correct solution, as you, Marc and myself have pointed out, is to treat f as a pure number, with corresponding treatment of any other quantity that depends on f. Cheers -- Ian On Mon, Mar 1, 2010 at 1:13 PM, Gerard Bricogne g...@globalphasing.com wrote: Dear Ian, Perhaps I should have made a more explicit connection to your message in what I wrote yesterday. I do not think there is any paradox, or apples vs. oranges problem, in this situation. The structure factor is a count of electrons as X-ray scatterers, so that the Fourier synthesis computed from them is a number density for these unit scatterers. The density can get clothed with a charge a-posteriori, because we know what the charge of an electron is, but it is not that charge as such that is sensed by the diffraction experiment: it is the complicated combination of charge and mass and various physical constants that ends up determining an electron's ability to scatter X-rays. I think that if one bears this in mind at all times, paradoxes never appear.
Re: [ccp4bb] units of f0, f', f''
On Monday 01 March 2010, Ian Tickle wrote: Dear Gerard I would certainly agree that in general, provided one takes sufficient care over dimensions and units, paradoxes can never appear. However, in this particular case I was pointing out the dimensionality error of writing equations such as f = 10e, and equivalent ones for the structure factor and electron density, given that 'f' is defined as a dimensionless ratio (as I believe it usually is). In my experience, f' and f are given in units of e, just as f itself is, and e is read out loud as electrons. Ethan Even if you replaced the 'e' with whatever unit represents an electron's ability to scatter X-rays (which would be the amplitude of the scattered wave), you still have the same problem. I only focused on electric charge because 'e', the elementary unit of charge, was being posited as the unit of 'f'. The alternative solution that you suggested of using the word 'electron' as an abbreviation for an electron's worth of scattering, is likely to cause just as much confusion and probably would be further abbreviated to 'e' anyway, thus leading people to believe it represented the electronic charge! The correct solution, as you, Marc and myself have pointed out, is to treat f as a pure number, with corresponding treatment of any other quantity that depends on f. Cheers -- Ian On Mon, Mar 1, 2010 at 1:13 PM, Gerard Bricogne g...@globalphasing.com wrote: Dear Ian, Perhaps I should have made a more explicit connection to your message in what I wrote yesterday. I do not think there is any paradox, or apples vs. oranges problem, in this situation. The structure factor is a count of electrons as X-ray scatterers, so that the Fourier synthesis computed from them is a number density for these unit scatterers. The density can get clothed with a charge a-posteriori, because we know what the charge of an electron is, but it is not that charge as such that is sensed by the diffraction experiment: it is the complicated combination of charge and mass and various physical constants that ends up determining an electron's ability to scatter X-rays. I think that if one bears this in mind at all times, paradoxes never appear.
Re: [ccp4bb] units of f0, f', f''
Dear Ian, The iteration seems to be converging :-)) . Regarding your last paragraph, however, I do not think that we have to forbid ourselves to call a spade a spade because of possible confusions that might be caused by misleading abbreviations. If the unit is an electron's worth of scattering, its abbreviation to electron has to be accompanied by a suitable annotation so that it does not get confused with some physical attribute of an electron such as its charge. I don't think that anticipated inadequacies of notation should stand in the way of correct terminology. If necessary, we should draft a one-liner that could be added as a footnote to every Table 1 (like the formula for the R-factor!) and would explain that the word electron, as used in the context of that Table, actually means an electron's worth of scattering; and to show how important we are, we could even have the exact wording reviewed and approved by the Computing Commission of the IUCr! But this would start sounding like Russian history in the 1920's ... . With best wishes, Gerard. -- On Mon, Mar 01, 2010 at 04:14:57PM +, Ian Tickle wrote: Dear Gerard I would certainly agree that in general, provided one takes sufficient care over dimensions and units, paradoxes can never appear. However, in this particular case I was pointing out the dimensionality error of writing equations such as f = 10e, and equivalent ones for the structure factor and electron density, given that 'f' is defined as a dimensionless ratio (as I believe it usually is). Even if you replaced the 'e' with whatever unit represents an electron's ability to scatter X-rays (which would be the amplitude of the scattered wave), you still have the same problem. I only focused on electric charge because 'e', the elementary unit of charge, was being posited as the unit of 'f'. The alternative solution that you suggested of using the word 'electron' as an abbreviation for an electron's worth of scattering, is likely to cause just as much confusion and probably would be further abbreviated to 'e' anyway, thus leading people to believe it represented the electronic charge! The correct solution, as you, Marc and myself have pointed out, is to treat f as a pure number, with corresponding treatment of any other quantity that depends on f. Cheers -- Ian On Mon, Mar 1, 2010 at 1:13 PM, Gerard Bricogne g...@globalphasing.com wrote: Dear Ian, Perhaps I should have made a more explicit connection to your message in what I wrote yesterday. I do not think there is any paradox, or apples vs. oranges problem, in this situation. The structure factor is a count of electrons as X-ray scatterers, so that the Fourier synthesis computed from them is a number density for these unit scatterers. The density can get clothed with a charge a-posteriori, because we know what the charge of an electron is, but it is not that charge as such that is sensed by the diffraction experiment: it is the complicated combination of charge and mass and various physical constants that ends up determining an electron's ability to scatter X-rays. I think that if one bears this in mind at all times, paradoxes never appear. -- === * * * Gerard Bricogne g...@globalphasing.com * * * * Global Phasing Ltd. * * Sheraton House, Castle Park Tel: +44-(0)1223-353033 * * Cambridge CB3 0AX, UK Fax: +44-(0)1223-366889 * * * ===
Re: [ccp4bb] units of f0, f', f''
Hi. I'm a little reluctant to get into this discussion, but I'm greatly confused by it all, and I think much of my confusion comes from trying to understand one of Ian's assumptions. Why are the scattering factors viewed as dimensionless quantities? In the International Tables (for example, Table 6.1.1.1 in the blue books), the scattering factors are given in electrons. In the text for that section, the scattering factors are obtained from an integral (over space) of the electron density. So there's some consistency there between scattering factors in units of electrons and electron density in electrons/(Angstrom**3). What's gained at this point by dropping the word electron from all of these dimensions? Ron On Sat, 27 Feb 2010, Ian Tickle wrote: I'm not aware that anyone has suggested the notation rho e/Å^3. I think you misunderstood my point, I certainly didn't mean to imply that anyone had suggested or used that notation, quite the opposite in fact. My point was that you said that you use the term 'electron density' to define two different things either at the same time or on different occasions, but that to resolve the ambiguity you use labels such as 'e/Å^3' or 'sigma/Å^3' attached to the values. My point was that if I needed to use these quantities in equations then the rules of algebra require that distinguishable symbols (e.g. rho and rho') be assigned, otherwise I would be forced into the highly undesirable situation of labelling the symbols with their units in the equations in the way you describe in order to distinguish them. Then in my 'Notation' section my definitions of rho rho' would need to be different in some way, again in order to distinguish them: I could not simply call both of them 'electron density' as you appear to be doing. The question of whether your units of electron density are '1/Å^3' or 'e/Å^3' clearly comes down to definition, nothing more. If we can't agree on the definition then we are surely not going to agree on the units! Actually we don't need to agree on the definition: as long as I know what precisely your set of definitions is, I can make the appropriate adjustments to my units you can do the same if you know my definitions; it just makes life so much easier if we can agree to use the same definitions! Again it comes down to the importance of having a 'Notation' section so everyone knows exactly what the definitions in use are. My definition of electron density is number of electrons per unit volume which I happen to find convenient and for which the appropriate units are '1/Å^3'. In order for your choice of units 'e/Å^3' to be appropriate then your definition would have to be electric charge per unit volume, then you need to include the conversion factor 'e' (charge on the electron) in order to convert from my number of electrons to your electric charge, otherwise your values will all be very small (around 10^-19 in SI units). I would prefer to call this quantity electric charge density since electron density to me implies density of electrons not density of charge. I just happen to think that it's easier to avoid conversion factors unless they're essential. Exactly the same thing of course happens with the scattering factor: I'm using what I believe is the standard definition (i.e. the one given in International Tables), namely the ratio of scattered amplitude to that for a free electron which clearly must be unitless. So I would say 'f = 10' or whatever. I take it that you would say 'f = 10e'. Assuming that to be the case, then it means you must be using a different definition consistent with the inclusion of the conversion factor 'e', namely that the scattering factor is the equivalent point electric charge, i.e. the point charge that would scatter the same X-ray amplitude as the atom. I've not seen the scattering factor defined in that way before: it's somewhat more convoluted than the standard definition but still usable. The question remains of course - why would you not want to stick to the standard definitions? BTW I assume your 'sigma/Å^3' was a slip and you intended to write just 'sigma' since sigma(rho) must have the same units as rho (being its RMS value), i.e. 1/Å^3, so in your second kind of e.d. map rho/sigma(rho) is dimensionless (and therefore unitless). However since rho and sigma(rho) have identical units I don't see how their ratio rho/sigma(rho) can have units of 'sigma', as you seem to imply if I've understood correctly? What I'm more concerned about is when you assign a numerical value to a quantity. Take the equation E=MC^2. The equation is true regardless of how you measure your energy, mass, and speed. It is when you say that M = 42 that it becomes important to unambiguously label 42 with its units. It is when you are given a mass equal to 42 newtons, the speed of light in furlongs/fortnight, and asked to calculate the energy in
Re: [ccp4bb] units of f0, f', f''
Hi Silvia, I don't know about sophisticated, but it's certainly interminable! Whether you need to modify your slides (actually only your 3rd slide seems to be relevant to the discussion) obviously depends on which definition you choose to along with. If you use what I can call the 'dimensionless' definition you need do nothing, since you are already using that definition, i.e. f is a ratio of amplitudes (or sqrt of ratio of intensities), therefore any units must cancel out and the result must be dimensionless and unitless, just as in the definition of refractive index (as Marc pointed out). If you accept the alternative where f is not dimensionless (it has dimensions of an amplitude, i.e. length), you need to re-define f as the amplitude (or sqrt of the intensity) of scattering by the atom, i.e. the sqrt of the numerator in your equation for 'f^2'. Then you need to define a new unit of f (call it [f]) as the amplitude of scattering by a free electron, i.e. the sqrt of the denominator of your equation: this is what pretty well everyone is calling an 'electron' - though definitely not to be confused with a real electron! Finally f is expressed as a multiple of its unit in the usual way: f = n[f] where 'n' is the numerical value of f (for example: f = 10 electrons if n=10). So to summarise, using this definition f has dimensions of 'length' and units of 'electrons'. Further for the 2nd definition, if you're tempted to abbreviate 'electrons' to 'e' as is often seen, you also have to remember that 'e' here has nothing to do with the conventional physicists' definition, namely the charge on the electron (though it seems I'm the only one here who thinks this is very confusing notation). If you do decide to go down this path I would recommend following the notation in Bernhard Rupp's book: he uses the correct abbreviation for the electron, namely 'e-' avoiding the confusion with 'e', but again don't confuse this with the real electron! As Gerard pointed out you could equally well use the terms 'positron' and 'e+' since the sign is irrelevant for scattering. Note that both definitions are perfectly internally self-consistent - no dimensionality issues - so the choice is purely a matter of definition, certainly neither can be said to be right or wrong, and therefore the definitions are essentially totally arbitrary. It really comes down to whether you wish to change the definition you're accustomed to, and whether you can live with the ambiguities in the definition of 'electron' (and 'e' if you use it). It seems to me that it's this ambiguity that actually instigated this whole thread! One point highlighted by your slides: you say that at zero scattering angle f0 = Z (atomic number). This is perfectly correct, however note that Z being a pure number is never expressed as say 'Z = 10 electrons', always as just 'Z = 10' so if you express f in 'e-' units you need to say 'f0 = Ze-', otherwise the equation is dimensionally inconsistent. Anyway I beginning to sound like Microsoft explaining how to install their competitors' browsers in as fair a way as possible in order to placate the European Commission, so I'll stop there! Cheers -- Ian On Mon, Mar 1, 2010 at 7:06 PM, Silvia Onesti silvia.one...@elettra.trieste.it wrote: I feel uneasy at entering this sophisticated discussion, but since it looks like the very interesting, learned but subtle and complex statements by Ian, Marc, Gerard co seem unable to shake people assumptions that the atomic scattering factor is expressed in electrons, can I provide a couple of very basic slides that I have been using for teaching an undergraduate course? As far as I know that is the DEFINITION of the atomic scattering factor. The scattering-equivalent of one electron is just a convenient unit. Analogous to saying that the charge of a proton is +1, rather than 1.6x10-19 Coulomb. Now I hope that the experts are not going to find other mistakes in my slides! Silvia Silvia Onesti Sincrotrone Trieste S.C.p.A. SS 14 - km 163,5 - AREA Science Park, 34149 Basovizza, Trieste ITALY Email: silvia.one...@elettra.trieste.it Tel. +39 040 3758451 Mob +39 366 6878001 http://www.elettra.trieste.it/PEOPLE/index.php?n=SilviaOnesti.HomePage http://www.sissa.it/sbp/web_2008/research_structuralbio.html On Mon, 1 Mar 2010 09:10:44 -0800 Ronald E Stenkamp stenk...@u.washington.edu wrote: Hi. I'm a little reluctant to get into this discussion, but I'm greatly confused by it all, and I think much of my confusion comes from trying to understand one of Ian's assumptions. Why are the scattering factors viewed as dimensionless quantities? In the International Tables (for example, Table 6.1.1.1 in the blue books), the scattering factors are given in
Re: [ccp4bb] units of f0, f', f''
On 01/03/2010, at 20.44, Dale Tronrud wrote: Morten Kjeldgaard wrote: On 01/03/2010, at 19.01, James Holton wrote: personal discourse. If I review a paper that lists electron density in 1/A^3, I will tell the authors to fix it. If a reviewer tells me to change my electron/A^3 to A^-3, then I will simply tell the editor that the reviewer is mistaken. Nothing I read on the BB is going to convince me otherwise, and Both are correct. Electrons is a nominal unit, you can omit it if you wish. Mathematically, electrons never enter the electron density equation, because the atomic scattering factor is dimensionless, so the dimension of rho is given by the 1/V term. This is seriously close to a circular argument. You can leave off electrons because they weren't there in the scattering factor? We unit lovers are not proposing to put it in one place and not the other. The ambiguity probably arises because some authors choose to tabulate the atomic form factor in units of electrons. If you use that unit in the electron density equation, rho gets a unit of electrons per cubic Ångstrøm. Mathematically, the atomic form factor is an function that -- for a specific atom type -- specifies the scattering efficiency, and it has no unit. Whether you specify the unit electrons or not doesn't matter, since there is no other unit that makes sense for the problem at hand. What *is* important is to specify what basic unit of length you are using to compute the unit cell volume. Thus, electron density could in principle be given in meter **-3 which would be correct according the the SI standard (but admittedely weird to a crystallographer.) The same is true when talking about population density... you can specify it as 10 per square mile or 10 humans per square mile or 10 persons per square mile. It's all the same, persons and humans are nominal units for the number and you can optionally omit it. Specifically, concerning dimensionless quantities, read section 1.3 of The International System of Units [1]. I'm puzzled by how you define nominal units. Certainly it cannot be related to whether the variable is declared int or float? I don't see a logical connection and I don't see an operational difference between the units you consider nominal and those you do not. This distinction is at the heart of the discussion here: which units can be dropped at will and which must be kept? It doesn't necessarily need to be a counting variable (integer). The atom form factor is an example of a variable that has the nominal unit of electrons. An angle can be measured in degrees, but if specified in radians, that unit is nominal and can be omitted (I have personally heard you say the phase angle is pi but never the phase angle is pi radians.) If countability is the principal difference between the two classes of units what do you think of the unit mole (and I don't mean the animal that burrows underground ;-) ). This is just a count of molecules and yet it is used pretty consistently. I don't see people talking of the energy of a reaction in Kcal with out the per mole always being there. Are you in favor of reporting reaction energies in Kcal? This whole thing has to do with what units have been defined and standardized. One mole is a defined unit consisting of NA molecules, it's a basic unit in the SI system, and so when we work with properties of molecules, we need to use it. If we didn't have a definition for a mole, I suppose we would specify reaction energies per molecule in which case the unit would be implicitly understood and could be omitted. When we work with lengths, there are several standardized measures we can use, and we need to choose one, and we need to specify which one we are using. When working with volumes or areas, we need to derive the unit from the basic unit of length. This is specified and defined by whatever unit standard we choose to work with (SI, CGS, ...). So to answer your question: being an SI man, I'm in favour of reporting Gibbs free energy in kJ/mol ;-) Cheers, Morten [1] http://physics.nist.gov/Pubs/SP330/sp330.pdf
Re: [ccp4bb] units of f0, f', f''
Maia, Usually we live in a macroscopic world and usually gravity is the most important force. In x-ray diffraction the charge/mass ratio is the most important paramater (and the density of that). Hans Maia Cherney schreef: Hi all, Usually density means mass divided by volume. The mass of an electron is known. Then it will be no arguments. Maia
Re: [ccp4bb] units of f0, f', f''
Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for an atom to that for a free electron (dimensionless). g: atomic scattering free point equivalent charge, defined as the free point charge which scatters with the same amplitude as the atom (dimensions of electric charge). Now we can validly write 'g = 10e' since we have dimensions of charge on both sides. This again highlights the importance of 1) rigorously defining all quantities in use, and 2) that the definition and the dimensions are linked: you cannot arbitrarily change the dimensions of some quantity without also changing its definition, or vice versa; and in particular you can't mix the definition of 'f' with the units of 'g', which is what seems to be happening here! This logical inconsistency can only be resolved by recognising that 'f' is a pure number so removing the 'e' unit. The same argument obviously applies to anything derived from 'f' such as the structure factor and the electron density. Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] units of f0, f', f''
Thanks, I was actually joking because I was a little annoyed about the discussion, but then I realized that this discussion is great, (now I will not forget the units of electron density) and it's still not resolved. You said the charge/mass ratio and the density of that, but other people said the electron density is number of electrons (not charge) divided by volume (1/A^3). Maia H. Raaijmakers wrote: Maia, Usually we live in a macroscopic world and usually gravity is the most important force. In x-ray diffraction the charge/mass ratio is the most important paramater (and the density of that). Hans Maia Cherney schreef: Hi all, Usually density means mass divided by volume. The mass of an electron is known. Then it will be no arguments. Maia
Re: [ccp4bb] units of f0, f', f''
I suppose I could point out that the letter e has many more universal meanings that just denoting electric charge, such the base of the natural logarithm, the identity element in set theory, or even a musical note. But, today I found that e can also stand for eristic, a new word I learned while reading the following web page: http://en.wikipedia.org/wiki/Flame_war -James Holton MAD Scientist Ian Tickle wrote: Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for an atom to that for a free electron (dimensionless). g: atomic scattering free point equivalent charge, defined as the free point charge which scatters with the same amplitude as the atom (dimensions of electric charge). Now we can validly write 'g = 10e' since we have dimensions of charge on both sides. This again highlights the importance of 1) rigorously defining all quantities in use, and 2) that the definition and the dimensions are linked: you cannot arbitrarily change the dimensions of some quantity without also changing its definition, or vice versa; and in particular you can't mix the definition of 'f' with the units of 'g', which is what seems to be happening here! This logical inconsistency can only be resolved by recognising that 'f' is a pure number so removing the 'e' unit. The same argument obviously applies to anything derived from 'f' such as the structure factor and the electron density. Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] units of f0, f', f''
What I meant of course was that the electronic charge (note: not the same thing at all as electric charge) is universally given the symbol 'e', but with e-mail being what it is one usually doesn't take the time to consider such logical niceties as whether 'A implies B' is equivalent to 'B implies A'. Of course, all the letters of the Roman and Greek alphabets are already heavily overloaded, maybe we should consider using symbols from Chinese, Japanese, Cyrillic, Arabic, Sanskrit ... in our equations. Cheers -- Ian -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton Sent: 28 February 2010 15:20 To: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] units of f0, f', f'' I suppose I could point out that the letter e has many more universal meanings that just denoting electric charge, such the base of the natural logarithm, the identity element in set theory, or even a musical note. But, today I found that e can also stand for eristic, a new word I learned while reading the following web page: http://en.wikipedia.org/wiki/Flame_war -James Holton MAD Scientist Ian Tickle wrote: Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for an atom to that for a free electron (dimensionless). g: atomic scattering free point equivalent charge, defined as the free point charge which scatters with the same amplitude as the atom (dimensions of electric charge). Now we can validly write 'g = 10e' since we have dimensions of charge on both sides. This again highlights the importance of 1) rigorously defining all quantities in use, and 2) that the definition and the dimensions are linked: you cannot arbitrarily change the dimensions of some quantity without also changing its definition, or vice versa; and in particular you can't mix the definition of 'f' with the units of 'g', which is what seems to be happening here! This logical inconsistency can only be resolved by recognising that 'f' is a pure number so removing the 'e' unit. The same argument obviously applies to anything derived from 'f' such as the structure factor and the electron density. Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent
Re: [ccp4bb] units of f0, f', f''
Dear all, Two slight confusions seem to have popped up intermittently in this thread, in messages other than those included here. The first one was related to the charge of the electron - even the colour code according to which its electron density should be displayed - and the other one to its mass, i.e. the assumption that the word density was to be taken literally as being in some way connected to a mass by unit volume. Regarding the first, the sign of the charge plays no role, as shown by the fact that the Thomson scattering formula involves the square of the electron charge. This could be seen as an instance of TCP invariance: a free positron would scatter X-rays to exactly the same degree as a free electron. If there is something that would deserve to be called a unit in the original context of this question, i.e. a unit for structure factors, it would be (as was pointed out by many contributors) the X-ray scattering power of a free electron (or positron). A pedantic name for such a unit could be electron qua X-ray scatterer, which the general aversion to Latin would immediately shorten to electron, thereby explaining the current practice. At least the pedantic name would have the merit of making it clear that we are not referring to the electron in relation to its charge, but in relation to its scattering behaviour towards X-rays. Regarding the second, the word density has long been freed from its original connection with mass. For instance one speaks about a probability density, which is stripped of any physical association and is related to the notion of a measure in the theory of integration. One even encounters the expression number density independently of any notion of probability, to designate a concentration of things that can be counted (as opposed to measured). The meaning of density, as has again been explained by several contributors, is that the density of 'whatever' is the amount of 'whatever' per unit volume; so that integrating it over a specified region delivers a result in the unit in which 'whatever' is measured. Replacing 'whatever' by X-ray scattering power measured in units of electron qua X-ray scatterer - or just electron - would seem to make everything that has been said consistent. To get back to the original question: if the reference X-ray scatterer was taken to be the proton (or antiproton), then the numerical values of f0, f' and f giving the strength of the anomalous scattering of *electrons* would obviously change, so there is indeed an underlying dimensionality to these numbers via Thomson's formula; but since crystallographers live off X-ray scattering from electrons, such a change of units would seem a rather daft idea, the possibility of which I would not expect to have occurred to any journal editor or reviewer while staring at Table I ... - so if we have such a natural unit for what we are looking at, f0, f', f are, for all intents and purposes, pure numbers. I hope this long message is only minimally eristic, and rather more dialectical :-)) ... . With best wishes, Gerard. -- On Sun, Feb 28, 2010 at 07:19:48AM -0800, James Holton wrote: I suppose I could point out that the letter e has many more universal meanings that just denoting electric charge, such the base of the natural logarithm, the identity element in set theory, or even a musical note. But, today I found that e can also stand for eristic, a new word I learned while reading the following web page: http://en.wikipedia.org/wiki/Flame_war -James Holton MAD Scientist Ian Tickle wrote: Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for an atom to that for a free electron (dimensionless). g: atomic scattering free point equivalent charge, defined as the free point charge which scatters with the same amplitude as the atom (dimensions of electric charge). Now we can validly write 'g = 10e' since we have dimensions of charge on both sides. This again highlights the importance of 1)
Re: [ccp4bb] units of f0, f', f''
Dear X-ray Community, I'm sorry to have dragged you all along on this journey. There is something to Ian and Marc's arguments but I have been unable to understand their point. That is my failure and I don't wish to subject the rest of you to continued argument. Ian, Marc, and I should get together in a bar somewhere and hash this out. Dale Tronrud Gerard Bricogne wrote: Dear all, Two slight confusions seem to have popped up intermittently in this thread, in messages other than those included here. The first one was related to the charge of the electron - even the colour code according to which its electron density should be displayed - and the other one to its mass, i.e. the assumption that the word density was to be taken literally as being in some way connected to a mass by unit volume. Regarding the first, the sign of the charge plays no role, as shown by the fact that the Thomson scattering formula involves the square of the electron charge. This could be seen as an instance of TCP invariance: a free positron would scatter X-rays to exactly the same degree as a free electron. If there is something that would deserve to be called a unit in the original context of this question, i.e. a unit for structure factors, it would be (as was pointed out by many contributors) the X-ray scattering power of a free electron (or positron). A pedantic name for such a unit could be electron qua X-ray scatterer, which the general aversion to Latin would immediately shorten to electron, thereby explaining the current practice. At least the pedantic name would have the merit of making it clear that we are not referring to the electron in relation to its charge, but in relation to its scattering behaviour towards X-rays. Regarding the second, the word density has long been freed from its original connection with mass. For instance one speaks about a probability density, which is stripped of any physical association and is related to the notion of a measure in the theory of integration. One even encounters the expression number density independently of any notion of probability, to designate a concentration of things that can be counted (as opposed to measured). The meaning of density, as has again been explained by several contributors, is that the density of 'whatever' is the amount of 'whatever' per unit volume; so that integrating it over a specified region delivers a result in the unit in which 'whatever' is measured. Replacing 'whatever' by X-ray scattering power measured in units of electron qua X-ray scatterer - or just electron - would seem to make everything that has been said consistent. To get back to the original question: if the reference X-ray scatterer was taken to be the proton (or antiproton), then the numerical values of f0, f' and f giving the strength of the anomalous scattering of *electrons* would obviously change, so there is indeed an underlying dimensionality to these numbers via Thomson's formula; but since crystallographers live off X-ray scattering from electrons, such a change of units would seem a rather daft idea, the possibility of which I would not expect to have occurred to any journal editor or reviewer while staring at Table I ... - so if we have such a natural unit for what we are looking at, f0, f', f are, for all intents and purposes, pure numbers. I hope this long message is only minimally eristic, and rather more dialectical :-)) ... . With best wishes, Gerard. -- On Sun, Feb 28, 2010 at 07:19:48AM -0800, James Holton wrote: I suppose I could point out that the letter e has many more universal meanings that just denoting electric charge, such the base of the natural logarithm, the identity element in set theory, or even a musical note. But, today I found that e can also stand for eristic, a new word I learned while reading the following web page: http://en.wikipedia.org/wiki/Flame_war -James Holton MAD Scientist Ian Tickle wrote: Yes, I think this is exactly the point. 'Electrons' gives the whole thing a consistent meaning. The big problem with statements like 'f = 10e' or 'rho = 1.5e/Å^3' is of course that they are dimensionally invalid, and I'm surprised that people are not doing such simple checks! For example I think we've all agreed that 'f' is defined as the ratio of two amplitudes and is therefore dimensionless, whereas 'e' is universally defined as the electronic charge, which in SI units has the value 1.602176487×10^−19 coulombs, but obviously has the dimensions of electric charge (time*electric current in terms of the base SI dimensions). So we have a real apples oranges situation! You could of course get around this by redefining 'f' as I suggested previously, as the free point equivalent charge, but to avoid confusion we should call it something else, so let's say: Notation f: atomic scattering factor, defined as the ratio of scattered amplitude for
Re: [ccp4bb] units of f0, f', f''
Quoting Dale Tronrud det...@uoxray.uoregon.edu: P.S. to respond out-of-band to Dr. Schiltz: On the US flag I see 7 red stripes, 6 white stripes, and 50 stars. If I state I see 7 I have conveyed no useful information. Yes, but cast in a mathematical equations one would write : Number of red stripes = 7 Number of white stripes = 6 Number of stars = 50 i.e. without units one would not write : Number = 7 red stripes Number = 6 white stripes Number = 50 stars Marc
Re: [ccp4bb] units of f0, f', f''
Dear all,
I think Marc has hit the nail on the head: somehow the dictatorship of
journal editors and of rules (fetishes?) for filling tables and specifying
units has made everyone so insecure as to doubt even the fundmental notions
of set theory and of the cardinality of sets.
There is the axiomatic definition of integers by Peano's axioms, and
then there is Cantor's definition of the cardinality of sets where the
cardinal number of a set A is the class of all the sets B that can be put in
one-to-one correspondence with A. One can then show that integers are a
particular case of cardinal numbers: the cardinal number associated to the
integer 0 is the class of all sets having no members (e.g. the void set);
the cardinal number associated to the integer 1 is the class of all sets in
one-to-one correspondence with the set {0}; and given a cardinal number
associated to the integer m, one can get that associated to the successor of
m by considering the class of sets obtained by taking the disjoint union of
each of the sets in the class defining that cardinal and of {0}. Cardinals
are more powerful than integers because they can be infinite, and even
transfinite.
With this in mind, you can say that you have the same number of apples
as of oranges if you can associate one apple to each orange and vice-versa.
The set of apples and that of oranges have the same cardinal, and that
cardinal is uniquely associated to an integer, the number of both apples
and oranges. You cannot add apples and oranges, but you can add the integers
to which the cardinals of the two sets are associated, to get the cardinal
of a set to which both apples and oranges belong, e.g. of that of (pieces
of) fruit.
Marc was correct in pointing out the anonymity of numbers used to
count things, i.e. of cardinal numbers: this anonymisation is produced by
the process of forgetting what things are, as long as you can put them in
one-to-one correspondence with each other. So indeed, the unit of a count
is the integer 1, i.e. the cardinal of the set {0}. Of course, if we say
that f=7.8 this is not an integer; but the next chapter of any book on set
theory would explain how one progresses from integers to rational and real
numbers.
I apologise for this non-CCP4 answer to the initial question!
With best wishes,
Gerard.
--
On Sat, Feb 27, 2010 at 11:49:25AM +0100, marc.schi...@epfl.ch wrote:
Quoting Dale Tronrud det...@uoxray.uoregon.edu:
P.S. to respond out-of-band to Dr. Schiltz: On the US flag I see 7 red
stripes,
6 white stripes, and 50 stars. If I state I see 7 I have conveyed
no
useful information.
Yes, but cast in a mathematical equations one would write :
Number of red stripes = 7
Number of white stripes = 6
Number of stars = 50
i.e. without units
one would not write :
Number = 7 red stripes
Number = 6 white stripes
Number = 50 stars
Marc
--
===
* *
* Gerard Bricogne g...@globalphasing.com *
* *
* Global Phasing Ltd. *
* Sheraton House, Castle Park Tel: +44-(0)1223-353033 *
* Cambridge CB3 0AX, UK Fax: +44-(0)1223-366889 *
* *
===
Re: [ccp4bb] units of f0, f', f''
I'm not aware that anyone has suggested the notation rho e/Å^3. I think you misunderstood my point, I certainly didn't mean to imply that anyone had suggested or used that notation, quite the opposite in fact. My point was that you said that you use the term 'electron density' to define two different things either at the same time or on different occasions, but that to resolve the ambiguity you use labels such as 'e/Å^3' or 'sigma/Å^3' attached to the values. My point was that if I needed to use these quantities in equations then the rules of algebra require that distinguishable symbols (e.g. rho and rho') be assigned, otherwise I would be forced into the highly undesirable situation of labelling the symbols with their units in the equations in the way you describe in order to distinguish them. Then in my 'Notation' section my definitions of rho rho' would need to be different in some way, again in order to distinguish them: I could not simply call both of them 'electron density' as you appear to be doing. The question of whether your units of electron density are '1/Å^3' or 'e/Å^3' clearly comes down to definition, nothing more. If we can't agree on the definition then we are surely not going to agree on the units! Actually we don't need to agree on the definition: as long as I know what precisely your set of definitions is, I can make the appropriate adjustments to my units you can do the same if you know my definitions; it just makes life so much easier if we can agree to use the same definitions! Again it comes down to the importance of having a 'Notation' section so everyone knows exactly what the definitions in use are. My definition of electron density is number of electrons per unit volume which I happen to find convenient and for which the appropriate units are '1/Å^3'. In order for your choice of units 'e/Å^3' to be appropriate then your definition would have to be electric charge per unit volume, then you need to include the conversion factor 'e' (charge on the electron) in order to convert from my number of electrons to your electric charge, otherwise your values will all be very small (around 10^-19 in SI units). I would prefer to call this quantity electric charge density since electron density to me implies density of electrons not density of charge. I just happen to think that it's easier to avoid conversion factors unless they're essential. Exactly the same thing of course happens with the scattering factor: I'm using what I believe is the standard definition (i.e. the one given in International Tables), namely the ratio of scattered amplitude to that for a free electron which clearly must be unitless. So I would say 'f = 10' or whatever. I take it that you would say 'f = 10e'. Assuming that to be the case, then it means you must be using a different definition consistent with the inclusion of the conversion factor 'e', namely that the scattering factor is the equivalent point electric charge, i.e. the point charge that would scatter the same X-ray amplitude as the atom. I've not seen the scattering factor defined in that way before: it's somewhat more convoluted than the standard definition but still usable. The question remains of course - why would you not want to stick to the standard definitions? BTW I assume your 'sigma/Å^3' was a slip and you intended to write just 'sigma' since sigma(rho) must have the same units as rho (being its RMS value), i.e. 1/Å^3, so in your second kind of e.d. map rho/sigma(rho) is dimensionless (and therefore unitless). However since rho and sigma(rho) have identical units I don't see how their ratio rho/sigma(rho) can have units of 'sigma', as you seem to imply if I've understood correctly? What I'm more concerned about is when you assign a numerical value to a quantity. Take the equation E=MC^2. The equation is true regardless of how you measure your energy, mass, and speed. It is when you say that M = 42 that it becomes important to unambiguously label 42 with its units. It is when you are given a mass equal to 42 newtons, the speed of light in furlongs/fortnight, and asked to calculate the energy in calories that you have to track your units carefully and perform all the proper conversions to calculate the number of calories. I can only agree with you there, but I never suggested or implied that a mass value (or speed or energy) should be given without the appropriate units specification, or that one should not take great care to track the units conversions. Actually many equations in crystallography are not as friendly as this one since they have conversion factors built into their standard formulations. With the conversion factor built in you are then restricted to use the units that were assumed. The example of this that I usually use is the presence of the factor of 1/V in the Fourier synthesis equation. It is there only because our
Re: [ccp4bb] units of f0, f', f''
Hi all, Usually density means mass divided by volume. The mass of an electron is known. Then it will be no arguments. Maia Ian Tickle wrote: I'm not aware that anyone has suggested the notation rho e/Å^3. I think you misunderstood my point, I certainly didn't mean to imply that anyone had suggested or used that notation, quite the opposite in fact. My point was that you said that you use the term 'electron density' to define two different things either at the same time or on different occasions, but that to resolve the ambiguity you use labels such as 'e/Å^3' or 'sigma/Å^3' attached to the values. My point was that if I needed to use these quantities in equations then the rules of algebra require that distinguishable symbols (e.g. rho and rho') be assigned, otherwise I would be forced into the highly undesirable situation of labelling the symbols with their units in the equations in the way you describe in order to distinguish them. Then in my 'Notation' section my definitions of rho rho' would need to be different in some way, again in order to distinguish them: I could not simply call both of them 'electron density' as you appear to be doing. The question of whether your units of electron density are '1/Å^3' or 'e/Å^3' clearly comes down to definition, nothing more. If we can't agree on the definition then we are surely not going to agree on the units! Actually we don't need to agree on the definition: as long as I know what precisely your set of definitions is, I can make the appropriate adjustments to my units you can do the same if you know my definitions; it just makes life so much easier if we can agree to use the same definitions! Again it comes down to the importance of having a 'Notation' section so everyone knows exactly what the definitions in use are. My definition of electron density is number of electrons per unit volume which I happen to find convenient and for which the appropriate units are '1/Å^3'. In order for your choice of units 'e/Å^3' to be appropriate then your definition would have to be electric charge per unit volume, then you need to include the conversion factor 'e' (charge ! on the electron) in order to convert from my number of electrons to your electric charge, otherwise your values will all be very small (around 10^-19 in SI units). I would prefer to call this quantity electric charge density since electron density to me implies density of electrons not density of charge. I just happen to think that it's easier to avoid conversion factors unless they're essential. Exactly the same thing of course happens with the scattering factor: I'm using what I believe is the standard definition (i.e. the one given in International Tables), namely the ratio of scattered amplitude to that for a free electron which clearly must be unitless. So I would say 'f = 10' or whatever. I take it that you would say 'f = 10e'. Assuming that to be the case, then it means you must be using a different definition consistent with the inclusion of the conversion factor 'e', namely that the scattering factor is the equivalent point electric charge, i.e. the point charge that would scatter the same X-ray amplitude as the atom. I've not seen the scattering factor defined in that way before: it's somewhat more convoluted than the standard definition but still usable. The question remains of course - why would you not want to stick to the standard definitions? BTW I assume your 'sigma/Å^3' was a slip and you intended to write just 'sigma' since sigma(rho) must have the same units as rho (being its RMS value), i.e. 1/Å^3, so in your second kind of e.d. map rho/sigma(rho) is dimensionless (and therefore unitless). However since rho and sigma(rho) have identical units I don't see how their ratio rho/sigma(rho) can have units of 'sigma', as you seem to imply if I've understood correctly? What I'm more concerned about is when you assign a numerical value to a quantity. Take the equation E=MC^2. The equation is true regardless of how you measure your energy, mass, and speed. It is when you say that M = 42 that it becomes important to unambiguously label 42 with its units. It is when you are given a mass equal to 42 newtons, the speed of light in furlongs/fortnight, and asked to calculate the energy in calories that you have to track your units carefully and perform all the proper conversions to calculate the number of calories. I can only agree with you there, but I never suggested or implied that a mass value (or speed or energy) should be given without the appropriate units specification, or that one should not take great care to track the units conversions. Actually many equations in crystallography are not as friendly as this one since they have conversion factors built into their standard formulations. With the conversion factor built in you are then restricted to use the units that were assumed.
Re: [ccp4bb] units of f0, f', f''
Depends on in what units you want to get your electron density in, or what scattering objects (electrons) you integrate over for the SF formula. Since the exponent is dimensionless in the SF formula, and the FT commonly is electron density, electrons (not negative charge) has to be somewhere in the SF formula. If fo is in electrons, then f' and f have to be units of electrons as well. The f' component reduces the real part scattering, it is negative (in electron units, again not in charge). BR -Original Message- From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Tim Gruene Sent: Thursday, February 25, 2010 11:25 PM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] units of f0, f', f'' Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A
Re: [ccp4bb] units of f0, f', f''
Hi Tim, Maybe it's too early in the day for me, but why can't electrons be a unit? You seem to be confusing physical (in-)divisibility of an entity with the symbolic use of fractions of that entity in calculations. We can speak of the average number of cows per acre of land without having to cut up cows into small pieces (although I love a good steak as much as the next person - and probably a lot more than that), or the average number of people on a plane without having to remove some limbs of a particular person to represent that number (although amputation of my legs would make my journeys a lot more comfortable in terms of legroom). --dvd Disclaimer: this answer does not involve any (mention of) CCP4 software. Mea culpa. On Fri, 26 Feb 2010, Tim Gruene wrote: Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A Best wishes, --Gerard ** Gerard J. Kleywegt Dept. of Cell Molecular Biology University of Uppsala Biomedical Centre Box 596 SE-751 24 Uppsala SWEDEN http://xray.bmc.uu.se/gerard/ mailto:ger...@xray.bmc.uu.se ** The opinions in this message are fictional. Any similarity to actual opinions, living or dead, is purely coincidental. **
Re: [ccp4bb] units of f0, f', f''
Dear CCP4BBers, I believe the answer to this question is that the correct unit for the scattering factor is actually length (the square root of the scattering cross section), i.e. it is strictly the scattering length. In the dim and distant past I did some neutron diffraction, and scattering factors here are typically expressed in cm (not very SI I know). In ND the factors vary oddly with atomic number so you have to use the correct units. In X-ray diffraction it goes with the number of electrons (which are all the same after all) so it was convenient to define scattering factors as a ratio by dividing by the scattering length of hydrogen, so f for hydrogen (i.e. one electron) becomes one, rather than a length in cm. f, f' etc. then become dimensionless quantities, and the maps come out effectively in e/A**2 (whereas they are really in scattering density). In ND, of course, you cannot do this and the maps are in units of scattering density. Simon Phillips --- | Simon E.V. Phillips | --- | Director, Research Complex at Harwell (RCaH)| | Diamond Light Source Ltd| | Diamond House | | Chilton | | Didcot | | Oxon OX11 0DE | | United Kingdom | | Email: simon.phill...@diamond.ac.uk | | Tel: +44 (0)1235 778946 | |+44 (0)1235 778431 (sec) | |+44 (0)7884 436011 (mobile) | | www.mrc.ac.uk/OurResearch/ResourcesforScientists/ResearchComplex| --- | Astbury Centre for Structural Molecular Biology | | Institute of Molecular and Cellular Biology | | University of LEEDS | | LEEDS LS2 9JT | | United Kingdom | | Email: s.e.v.phill...@leeds.ac.uk | | Tel: +44 (0)113 343 3027 | | WWW: http://www.astbury.leeds.ac.uk/People/staffpage.php?StaffID=SEVP | --- -Original Message- From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Bernhard Rupp Sent: 26 February 2010 08:46 To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] units of f0, f', f'' Depends on in what units you want to get your electron density in, or what scattering objects (electrons) you integrate over for the SF formula. Since the exponent is dimensionless in the SF formula, and the FT commonly is electron density, electrons (not negative charge) has to be somewhere in the SF formula. If fo is in electrons, then f' and f have to be units of electrons as well. The f' component reduces the real part scattering, it is negative (in electron units, again not in charge). BR -Original Message- From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Tim Gruene Sent: Thursday, February 25, 2010 11:25 PM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] units of f0, f', f'' Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A
Re: [ccp4bb] units of f0, f', f''
Dear all, Gerard Kleywegt, Bernhard Rupp and also John Helliwell explained to me that the unit of f' and friends is indeed meant to be electrons as in the elementary particle and not electrons as charge unit as in eV. Personally I find this very irritating and such things should be avoided - the formulae wouldn't change by using e (as in charge) as unit and adding a minus-sign. I should remember that a charge density map has negated signs compared to an electron density map. But I admit this is my personal view and might start a lengthy discussion about units as - if I remember correctly - we had on this board not long ago. It's just like my disliking that negative charge seems red for chemists and positive charge seems blue. Cheers, Tim On Fri, Feb 26, 2010 at 10:01:45AM +0100, Gerard DVD Kleywegt wrote: Hi Tim, Maybe it's too early in the day for me, but why can't electrons be a unit? You seem to be confusing physical (in-)divisibility of an entity with the symbolic use of fractions of that entity in calculations. We can speak of the average number of cows per acre of land without having to cut up cows into small pieces (although I love a good steak as much as the next person - and probably a lot more than that), or the average number of people on a plane without having to remove some limbs of a particular person to represent that number (although amputation of my legs would make my journeys a lot more comfortable in terms of legroom). --dvd Disclaimer: this answer does not involve any (mention of) CCP4 software. Mea culpa. On Fri, 26 Feb 2010, Tim Gruene wrote: Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A Best wishes, --Gerard ** Gerard J. Kleywegt Dept. of Cell Molecular Biology University of Uppsala Biomedical Centre Box 596 SE-751 24 Uppsala SWEDEN http://xray.bmc.uu.se/gerard/ mailto:ger...@xray.bmc.uu.se ** The opinions in this message are fictional. Any similarity to actual opinions, living or dead, is purely coincidental. ** -- -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A signature.asc Description: Digital signature
Re: [ccp4bb] units of f0, f', f''
... and positive difference density should be red not green :-) Phil On 26 Feb 2010, at 09:22, Tim Gruene wrote: Dear all, Gerard Kleywegt, Bernhard Rupp and also John Helliwell explained to me that the unit of f' and friends is indeed meant to be electrons as in the elementary particle and not electrons as charge unit as in eV. Personally I find this very irritating and such things should be avoided - the formulae wouldn't change by using e (as in charge) as unit and adding a minus-sign. I should remember that a charge density map has negated signs compared to an electron density map. But I admit this is my personal view and might start a lengthy discussion about units as - if I remember correctly - we had on this board not long ago. It's just like my disliking that negative charge seems red for chemists and positive charge seems blue. Cheers, Tim On Fri, Feb 26, 2010 at 10:01:45AM +0100, Gerard DVD Kleywegt wrote: Hi Tim, Maybe it's too early in the day for me, but why can't electrons be a unit? You seem to be confusing physical (in-)divisibility of an entity with the symbolic use of fractions of that entity in calculations. We can speak of the average number of cows per acre of land without having to cut up cows into small pieces (although I love a good steak as much as the next person - and probably a lot more than that), or the average number of people on a plane without having to remove some limbs of a particular person to represent that number (although amputation of my legs would make my journeys a lot more comfortable in terms of legroom). --dvd Disclaimer: this answer does not involve any (mention of) CCP4 software. Mea culpa. On Fri, 26 Feb 2010, Tim Gruene wrote: Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A Best wishes, --Gerard ** Gerard J. Kleywegt Dept. of Cell Molecular Biology University of Uppsala Biomedical Centre Box 596 SE-751 24 Uppsala SWEDEN http://xray.bmc.uu.se/gerard/ mailto:ger...@xray.bmc.uu.se ** The opinions in this message are fictional. Any similarity to actual opinions, living or dead, is purely coincidental. ** -- -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A
Re: [ccp4bb] units of f0, f', f''
These quantities are components of the total structure factor, and therefore must have the same units as the overall structure factor. The definition of a structure factor is the ratio between the scattered amplitude from some structure of interest and the amplitude scattered by a single electron. The structure can be an atom, a protein, or even an entire crystal. In this way, we separate the contribution of the molecular structure from all the other factors of scattering (like polarization and Lorentz factors). This definition heralds back to Hartree (1925) Philos. Mag. 50, 289-306, which was the first time the term structure factor appeared in the English literature. Although Debye Scherrer (1918) Physik. Zeit. 19, 474-483 probably deserve credit for coining the term (in German), something very similar to a structure factor (without the modern name) appeared as a variable f in Darwin's original paper on scattering theory: Darwin, C. G. (1914) Philos. Mag. 27, 315-333. It was immediately after measuring the resolution dependence of f that Debye amazingly and immediately realized that we were going to have to accept quantum theory (Debye (1915). Ann. Phys. 351, 809-823). Anyway, the structure factor is a ratio, and therefore is technically a dimensionless quantity, but even a dimensionless quantity has a unit in that there is some situation where the structure factor is equal to unity (1.0). This unit is when the object of interest scatters just as much as one of Thomson's classical electrons would (Thomson, (1906); Woolfson, (1997) Ch. 2). So, it is convenient to describe structure factors in terms of how many electrons it would take to produce the same signal. Hence, the unit of structure factor is the electron, but probably better denoted as the electron equivalent to avoid the present confusion. For example, the F values calculated by SFALL or REFMAC have units of electron equivalents per unit cell. Again, a dimensionless quantity, but far more informative when the unit is spelled out. Abbreviations are great, but not when taken to the point where they introduce ambiguity. I see nothing wrong with using a particle or other physical object as a unit as long as the meaning is made clear. After all, until recently the unit of meter was a metal stick they had in France. And the unit of mass is still a lump of metal which weighs exactly 1.0 kg. This object is slowly oxidizing, and that means that the mass of everything else in the universe is actually decreasing (by definition). Which could perhaps account for recent observations that the expansion rate of the universe is accelerating (Riess et al. (1998) Astro. J. 116, 1009). I'm sure Ian and Mark will have more to say about this... -James Holton MAD Scientist Tim Gruene wrote: Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A
Re: [ccp4bb] units of f0, f', f''
Tim Gruene wrote: It's just like my disliking that negative charge seems red for chemists and positive charge seems blue It is perhaps interesting that one CAN trap electrons in an optically clear matrix by irradiating a flash-cooled sample of 25% glycerol (with a touch of NaOH to keep the pH up). The species that results is called the solvated electron (e^-subaq/sub) and it is a deep blue color: http://bl831.als.lbl.gov/~jamesh/pickup/blue_stuff.gif Of course, this is viewed in transmission, so the electrons are actually absorbing in the red. ;) -James Holton MAD Scientist
Re: [ccp4bb] units of f0, f', f''
James Holton wrote: Anyway, the structure factor is a ratio, and therefore is technically a dimensionless quantity, but even a dimensionless quantity has a unit Like the index of refraction, which is also a ratio and therefore a dimensionless quantity whose unit is...what again ? -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] units of f0, f', f''
I would only re-iterate my observation (see our previous discussion about the 'units' of angles) concerning the importance in any document (including e-mails!) to have a Notation section where all quantities in use are rigorously defined. The definitions can be as wordy as you like, since they only appear once per quantity per document, or I suppose you could reference the Notation section in another document if you really wanted to save space. However you do it, all quantities absolutely must be defined somewhere once and once only. Then you can refer to the quantity as many times as you like in the body of the paper with the appropriate units (if any) and there's no possibility of ambiguity. If anyone is unclear about your meaning they just have to refer back to your definition. Problems with units often stem from an unambiguous definition. So following my own advice: NOTATION Notation f0: atomic scattering factor for normal scattering, defined as the ratio of scattered amplitude to that for a free electron. /NOTATION The word 'ratio' gives the game away: f0 is dimensionless and therefore unitless, it's just a pure number. It doesn't have dimensions of electric charge or length or anything else, and it doesn't have units of electrons, it's just a pure number. If anyone is uncertain about what this number refers to, they have only to refer to the above definition, there's no possibility of ambiguity through abbreviation. Note that every quantity that has dimensions has units and vice-versa, you can't have one without the other. What may appear in some cases to be units are actually just shorthand for scale factors that are pure numbers: here's the definition of some scale factors in common use: radian = 1 pi = ratio of circumference/diameter of any circle degree = pi/180 If you really must you can say that the scale factor for f0 is 'e', so then you can say 'f0 = 10e', but then you have to define 'e': 'e=1', in which case 'f0 = 10' so you're really no better off. Cheers -- Ian -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton Sent: 26 February 2010 15:04 To: Tim Gruene Cc: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] units of f0, f', f'' These quantities are components of the total structure factor, and therefore must have the same units as the overall structure factor. The definition of a structure factor is the ratio between the scattered amplitude from some structure of interest and the amplitude scattered by a single electron. The structure can be an atom, a protein, or even an entire crystal. In this way, we separate the contribution of the molecular structure from all the other factors of scattering (like polarization and Lorentz factors). This definition heralds back to Hartree (1925) Philos. Mag. 50, 289-306, which was the first time the term structure factor appeared in the English literature. Although Debye Scherrer (1918) Physik. Zeit. 19, 474-483 probably deserve credit for coining the term (in German), something very similar to a structure factor (without the modern name) appeared as a variable f in Darwin's original paper on scattering theory: Darwin, C. G. (1914) Philos. Mag. 27, 315-333. It was immediately after measuring the resolution dependence of f that Debye amazingly and immediately realized that we were going to have to accept quantum theory (Debye (1915). Ann. Phys. 351, 809-823). Anyway, the structure factor is a ratio, and therefore is technically a dimensionless quantity, but even a dimensionless quantity has a unit in that there is some situation where the structure factor is equal to unity (1.0). This unit is when the object of interest scatters just as much as one of Thomson's classical electrons would (Thomson, (1906); Woolfson, (1997) Ch. 2). So, it is convenient to describe structure factors in terms of how many electrons it would take to produce the same signal. Hence, the unit of structure factor is the electron, but probably better denoted as the electron equivalent to avoid the present confusion. For example, the F values calculated by SFALL or REFMAC have units of electron equivalents per unit cell. Again, a dimensionless quantity, but far more informative when the unit is spelled out. Abbreviations are great, but not when taken to the point where they introduce ambiguity. I see nothing wrong with using a particle or other physical object as a unit as long as the meaning is made clear. After all, until recently the unit of meter was a metal stick they had in France. And the unit of mass is still a lump of metal which weighs exactly 1.0 kg. This object is slowly oxidizing, and that means that the mass of everything else in the universe is actually decreasing (by definition). Which could perhaps account for recent observations that the expansion rate of the universe is accelerating (Riess et al. (1998
Re: [ccp4bb] units of f0, f', f''
Sorry, of course I meant to say: Problems with units often stem from an *ambiguous* definition.! I. -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of Ian Tickle Sent: 26 February 2010 17:18 To: James Holton; Tim Gruene Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] units of f0, f', f'' I would only re-iterate my observation (see our previous discussion about the 'units' of angles) concerning the importance in any document (including e-mails!) to have a Notation section where all quantities in use are rigorously defined. The definitions can be as wordy as you like, since they only appear once per quantity per document, or I suppose you could reference the Notation section in another document if you really wanted to save space. However you do it, all quantities absolutely must be defined somewhere once and once only. Then you can refer to the quantity as many times as you like in the body of the paper with the appropriate units (if any) and there's no possibility of ambiguity. If anyone is unclear about your meaning they just have to refer back to your definition. Problems with units often stem from an unambiguous definition. So following my own advice: NOTATION Notation f0: atomic scattering factor for normal scattering, defined as the ratio of scattered amplitude to that for a free electron. /NOTATION The word 'ratio' gives the game away: f0 is dimensionless and therefore unitless, it's just a pure number. It doesn't have dimensions of electric charge or length or anything else, and it doesn't have units of electrons, it's just a pure number. If anyone is uncertain about what this number refers to, they have only to refer to the above definition, there's no possibility of ambiguity through abbreviation. Note that every quantity that has dimensions has units and vice-versa, you can't have one without the other. What may appear in some cases to be units are actually just shorthand for scale factors that are pure numbers: here's the definition of some scale factors in common use: radian = 1 pi = ratio of circumference/diameter of any circle degree = pi/180 If you really must you can say that the scale factor for f0 is 'e', so then you can say 'f0 = 10e', but then you have to define 'e': 'e=1', in which case 'f0 = 10' so you're really no better off. Cheers -- Ian -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton Sent: 26 February 2010 15:04 To: Tim Gruene Cc: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] units of f0, f', f'' These quantities are components of the total structure factor, and therefore must have the same units as the overall structure factor. The definition of a structure factor is the ratio between the scattered amplitude from some structure of interest and the amplitude scattered by a single electron. The structure can be an atom, a protein, or even an entire crystal. In this way, we separate the contribution of the molecular structure from all the other factors of scattering (like polarization and Lorentz factors). This definition heralds back to Hartree (1925) Philos. Mag. 50, 289-306, which was the first time the term structure factor appeared in the English literature. Although Debye Scherrer (1918) Physik. Zeit. 19, 474-483 probably deserve credit for coining the term (in German), something very similar to a structure factor (without the modern name) appeared as a variable f in Darwin's original paper on scattering theory: Darwin, C. G. (1914) Philos. Mag. 27, 315-333. It was immediately after measuring the resolution dependence of f that Debye amazingly and immediately realized that we were going to have to accept quantum theory (Debye (1915). Ann. Phys. 351, 809-823). Anyway, the structure factor is a ratio, and therefore is technically a dimensionless quantity, but even a dimensionless quantity has a unit in that there is some situation where the structure factor is equal to unity (1.0). This unit is when the object of interest scatters just as much as one of Thomson's classical electrons would (Thomson, (1906); Woolfson, (1997) Ch. 2). So, it is convenient to describe structure factors in terms of how many electrons it would take to produce the same signal. Hence, the unit of structure factor is the electron, but probably better denoted as the electron equivalent to avoid the present confusion. For example, the F values calculated by SFALL or REFMAC have units of electron equivalents per unit cell. Again, a dimensionless quantity, but far more informative when the unit is spelled out. Abbreviations are great, but not when taken to the point where they introduce ambiguity. I see nothing wrong with using a particle or other physical object as a unit as long
Re: [ccp4bb] units of f0, f', f''
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
Re: [ccp4bb] units of f0, f', f''
Electron density has the same units as f/V, i.e. Angstroem^-3 (and of course dimensions L^-3). Again if you insist, you can have units 'e*Angstroem^-3' as long as you define somewhere the dimensionless scale factor 'e'=1, but again it doesn't get you anywhere. One should avoid attempting to infer definitions of quantities from their names, sometimes it works sometimes it doesn't: what matters is the formal definition, in this case electron density is defined as 'number of electrons per unit volume'. Again 'number of electrons' is just a pure number just like 'number of apples' (I'm assuming that 'number' here is not restricted to integers): it has nothing to do with the concept of 'electron' (or 'apple'), except insofar that electrons and apples are concepts to which the operation of counting can meaningfully be applied. I. -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of Bernhard Rupp Sent: 26 February 2010 18:39 To: Ian Tickle; CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] units of f0, f', f'' 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 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] units of f0, f', f''
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 b...@ruppweb.org: 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
Re: [ccp4bb] units of f0, f', f''
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. We put units in our discussion of numbers because it aids in our ability to communicate meaning to one another. Yes, electrons 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. 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 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. 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 marc.schi...@epfl.ch 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 b...@ruppweb.org: 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
Re: [ccp4bb] units of f0, f', f''
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
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.
The problem obviously arises here because of the ambiguity of using the same
name ('electron density') to define two different quantities simultaneously.
You'll recall I pointed out that Problems with units often stem from an
ambiguous definition! Let's suppose you were writing equations involving both
of these quantities, and let's say 'electron density' = 'rho'. Then you might
write in a computer program the perfectly valid statement:
rho = rho/sigma
where the 'rho' on each side means different things. However this is certainly
not valid as an algebraic statement as it stands (where sigma may take any
value). Note that it is not the usual practice to carry the units with the
variables in the equations in the way you suggest in order to allow you to
distinguish them (it would make the equations pretty unreadable!), so the units
are actually irrelevant are far as equations are concerned. So you would have
to write something like:
rho' = rho/sigma
then the ambiguity is resolved. Moreover you would now need to define rho and
rho' in a way that the reader would be able to distinguish them, for example
you might say rho = electron density = number of electrons/Angstroem^3 and
rho' = electron density Z-score = rho/sigma(rho). So now you have not only
been forced to distinguish the variable names, you also have had to distinguish
them in their definitions, hence it should no longer be necessary to
distinguish them by labelling their units.
Now of course labelling things in a computer output in order to distinguish
things that might be confused is quite a different issue from distinguishing
things in equations, for one thing you're free to write anything you want in
your own program, but equations have to obey the rules of algebra. I don't
know what was the context that gave rise to the original question but I think
it's quite likely to have been the equation f = f0 + f' + if, in which case
one needs to be careful to avoid ambiguous definitions.
Cheers
-- Ian
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Re: [ccp4bb] units of f0, f', f''
How many apples do you have? 1, 2, 3... this is unitless. If using apple as currency, the answer will be that apple is unit. Unit is a concept for information exchange. If f stands alone, no one cares the unit. Electron is the currency atoms used to communicate with X-ray, its unit is ELECTRON. Lijun On Feb 26, 2010, at 2:04 PM, marc.schi...@epfl.ch 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 b...@ruppweb.org: 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 Lijun Liu Cardiovascular Research Institute University of California, San Francisco 1700 4th Street, Box 2532 San Francisco, CA 94158 Phone: (415)514-2836
Re: [ccp4bb] units of f0, f', f''
On Friday 26 February 2010, Lijun Liu wrote: Electron is the currency atoms used to communicate with X-ray, its unit is ELECTRON. Ah! That explains the problems I've been having with some of my crystals this past year. Collateral damage from the devaluation of currencies everywhere. Complicated by the issuance of unfavorable f terms whose utility was based on imaginary currency. Ethan
Re: [ccp4bb] units of f0, f', f''
Ian Tickle wrote:
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
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.
The problem obviously arises here because of the ambiguity of using the
same name ('electron density') to define two different quantities
simultaneously. You'll recall I pointed out that Problems with units
often stem from an ambiguous definition! Let's suppose you were writing
equations involving both of these quantities, and let's say 'electron
density' = 'rho'. Then you might write in a computer program the perfectly
valid statement:
rho = rho/sigma
where the 'rho' on each side means different things. However this is
certainly not valid as an algebraic statement as it stands (where sigma may
take any value). Note that it is not the usual practice to carry the units
with the variables in the equations in the way you suggest in order to
allow you to distinguish them (it would make the equations pretty
I'm not aware that anyone has suggested the notation rho e/Å^3.
What I'm more concerned about is when you assign a numerical value to
a quantity. Take the equation E=MC^2. The equation is true regardless
of how you measure your energy, mass, and speed. It is when you say
that M = 42 that it becomes important to unambiguously label 42 with
its units. It is when you are given a mass equal to 42 newtons, the
speed of light in furlongs/fortnight, and asked to calculate the energy
in calories that you have to track your units carefully and perform all
the proper conversions to calculate the number of calories.
Actually many equations in crystallography are not as friendly as
this one since they have conversion factors built into their standard
formulations. With the conversion factor built in you are then
restricted to use the units that were assumed. The example of this
that I usually use is the presence of the factor of 1/V in the Fourier
synthesis equation. It is there only because our convention is to
measure scattering in e/Unit Cell and electron density in e/Å^3. The
factor of 1/V is simply the conversion factor that changes these units.
Mathematicians use the same units in reciprocal and real space and do
not have this term in their Fourier synthesis equation.
Since the conventional forms of the equations in our field often
have conversion factors built in (e.g. 1/V or 2 Pi radians/cycle),
we have to worry about the units of the variables in ways that pure
physics people usually don't. When calculating structure factors from
coordinates we can't just say that x is the x coordinate of an atom,
we have to specify that this x is measured in fractional coordinates.
The way we write the equation forces us to use this particular
coordinate system in a way that E=MC^2 does not.
unreadable!), so the units are actually irrelevant are far as equations are
concerned. So you would have to write something like:
rho' = rho/sigma
then the ambiguity is resolved. Moreover you would now need to define
rho and rho' in a way that the reader would be able to distinguish them,
for example you might say rho = electron density = number of
electrons/Angstroem^3 and rho' = electron density Z-score = rho/sigma(rho).
So now you have not only been forced to distinguish the variable names,
you also have had to distinguish them in their definitions, hence it
should no longer be necessary to distinguish them by labelling their units.
Now of course labelling things in a computer output in order to distinguish
things that might be confused is quite a different issue from distinguishing
things in equations, for one thing you're free to write anything you want in
your own program, but equations have to obey the rules of algebra. I don't
know what was the context that gave rise to the original question but I think
it's quite likely to have been the equation f = f0 + f' + if, in which case
one needs to be careful to avoid ambiguous definitions.
Which is exactly what I've been advocating. I'm glad we have reached
agreement.
Dale Tronrud
P.S. to respond out-of-band to Dr. Schiltz: On the US flag I see 7 red
stripes,
6 white stripes, and 50 stars. If I state I see 7 I have conveyed no
useful information.
Cheers
-- Ian
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This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com
[ccp4bb] units of f0, f', f''
Dear all, I just stumbled across the question about what is the unit of f' and f''. The first couple of hits from ixquick.com claim it was e^-. Since e^- is not a unit but symbolises an elemtary particle (of which fractions are considered non-existent), I was wondering whether the unit of f, f', and f'' is actually e (a positive charge!) and the value of f^0 of Fe at its K-edge was actually 26e or -26e - see e.g. Table 1 in http://www.ccp4.ac.uk/courses/proceedings/1997/j_smith/main.html Cheers, Tim -- Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A signature.asc Description: Digital signature
