Ethan is right that the demo does not map on to the anomalous scattering normally encountered. I think this might be because the damping is inappropriate - which is (at least in retrospect!) why I thought it was for a non damped case and asked whether anyone knew of a better example for a damped oscillator.
Firstly I want to make clear (for those who believe I am stuck in the 19th century) that I believe the theory involving quantisation of the electromagnetic field for x-ray scattering works splendidly. It gives results in agreement with the classical treatment regarding the electron as a driven oscillator. The agreement between the two is verging on beautiful. The problem with the quantum approach is when one tries to give an account of what happens to a photon before it has been detected. People get tied up in knots. Concepts such as the phase (or amplitude) of a photon are problematic. If a photon has a certain energy known with a high degree of "certainty" then its timing (and therefore any phase) will have a high degree of uncertainty. Similarly I don't think its amplitude can be defined unless the photon is confined (doing this lead to a Nobel prize a few years ago). In contrast, the classical approach via a damped oscillator lends itself to a mechanical simulation and should help understand what is happening.
The classical description for scattering can be found in many places e.g.
http://oldwww.iucr.org/iucr-top/comm/cteach/pamphlets/8/node2.html.
This handles the absorption of energy as well as the excitation produced by the incident field.
The mechanical simulation attempts to show both amplitude and phase changes across resonance and this is what is required. The phase changes should correspond to the effect of changes in f' and f'' on the scattered wave. A 180 degree phase change for scattering from a free electron is expected. Whether the charge is positive or negative the charge will oscillate to produce a wave opposing the incident one. As John Helliwell pointed out this also happens at reflection from a surface (the refractive index change at a surface is just some sum of the scattering factors of the components). I think the damping factor (k) is rather low in the simulation so one gets a large change in amplitude, presumably similar to the strong resonance of lanthanides. The phase at resonance seems to be correct although I am not sure whether it should be 90 or 270 degree. So, we have a peak corresponding to f'' which increases to a maximum and then decreases with opposite slope. The f' equivalent would be expected to follow the slope (by the Kramers Kronig relationship) giving a change in sign on either side of the resonance. This corresponds for example to Fig. 8.2 in Elements of Modern X-ray physics by Jens Als-Nielsen and Des McMorrow and is what appears to be the case in the simulation. In other words the simulation corresponds to that for a classical driven damped oscillator with certain parameters.
Despite this, I too am not entirely happy about the simulation. The damping seems to correspond to a strong resonance and this is not the normal case. Control of the damping factor is therefore required. Finer steps for the frequency changes would be good. Finally, it is difficult to see the exact phase changes - I would like to see little graphs for the amplitude of the driver and oscillator with time so the phase shifts can be seen more clearly.
The reason I would like to see this is that I believe a demonstration of this type would give crystallographers an intuitive understanding of the physical principles behind anomalous scattering. If such a demonstration is not available, the IUCr should clearly give a large teaching type grant to someone who comes up with the best proposal to construct a machine to meet the requirements in the previous paragraph.
Colin
-----Original Message-----
From: Ethan A Merritt [mailto:[log in to unmask]]
Sent: 06 November 2015 18:38
To: Nave, Colin (DLSLtd,RAL,LSCI)
Cc: ccp4bb
Subject: Re: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] Diffraction as a Single-Photon Process; was RE: [ccp4bb] Twinning Question
On Thursday, 05 November, 2015 23:32:09 [log in to unmask]" target="_blank">http:[log in to unmask] wrote:
> For scattering from a single electron isn't there a 180 degree phase
> change between the incident and scattered wave?
I don't see how to fit that into the context of diffraction from a crystal.
It gets right back to the original confusion that arises when mixing descriptions of single-particle events with wave-like interactions.
Would your scattered photon count up all the electrons in the crystal and choose a phase based on whether the count was even or odd?
> The spring demo shows this when the driver frequency is higher than the resonant frequency. I think the strong resonance in the spring demo corresponds to a strong white line. For the real component of the dispersive correction there will then be a change of sign across the white line as in the demo.
I am coming around to the view that the demo nicely demonstrates that transfer of energy from the driver to the resonant object occurs only as a certain frequency, but is not designed in such a way that it maps onto a model for anomalous scattering. There is nothing in the demo that corresponds to a scattered photon. The "phase" in narration is the phase of the induced resonance relative to the driver. But what we are interested in is the phase of the scattered photon relative to that of the incident photon, something that is not represented by
any component of the demo that I can think of.
And the effect that it does show, the transfer of energy at the resonance frequency, is most directly analogous to the generation of X-ray fluorescence (incoherent scatter) rather than a coherent scattering event. You could remove the drive motor from the demo at that point and the oscillating weight would remain in an excited state.
For the purpose of showing how excitation and scattering depends on the input wavelength/frequency, maybe videos like these are more useful:
https://www.youtube.com/watch?v=gNooDfVH30g
https://www.youtube.com/watch?v=nCeoYN9exL0
Ethan
> The damped driven oscillator is a common method used to describe x-ray scattering around resonance. However, I doubt whether the demo corresponds in detail to this. I am also unsure about the degree of damping in the demo (need another knob on the control box for this) but assume that the driving force, amplitude of oscillation and damping all balance out to give a steady state. As you imply, more frequency points would be useful.
>
> Colin
>
>
> From: Ethan Merritt [mailto:[log in to unmask]]
> Sent: 05 November 2015 17:33
> To: Nave, Colin (DLSLtd,RAL,LSCI)
> Cc: ccp4bb
> Subject: Re: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] Diffraction as a Single-Photon Process; was RE: [ccp4bb] Twinning Question
>
>
> On Thursday, 05 November 2015 11:51:49 AM [log in to unmask]<mailto:[log in to unmask]> wrote:
>
> > Ethan
>
> > My understanding is that one would have to have separate springs for each electron in the atom. Only some would be at resonance for a particular driving frequency. One would apply some sum for the total scattering of the atom.
>
>
>
> Sure. The problem is that the phase in the physical demonstration does not match up
>
> with the phase seen for anomalous scattering even when considered one electron at a time.
>
>
>
> In anomalous scattering the f' term is maximum negative exactly at the resonance point.
>
> So far as I can see, that strong negative component "flips the phase" so that the
>
> 180° phase shift is seen at (or very near) to the resonance frequency. As the
>
> frequency increases from there, the f' term returns to near 0 and the f" term
>
> reaches its maximum. This corresponds more or less to a 90° phase shift as the
>
> imaginary component dominates over the real component. At even higher frequency
>
> the f" term also decays toward zero and the phase gradually returns to the original
>
> value. Thus the sequence of phase values is just plain different in the anomalous
>
> scattering case and the motor-driven-spring oscillator case.
>
>
>
> So as the frequency increases, the physical demo highlights an induced phase
>
> below -> edge -> above -> high
>
> 0 -> 90 -> 180
>
> Whereas anomalous scattering shows
>
> 0 -> 180 -> 90 -> 0
>
>
>
> If I were to show this video while teaching, and a student asked me to explain
>
> in more detail how it relates to anomalous scattering, I'd be flummoxed.
>
>
>
> I am inclined to think the narration in the video is simply wrong, or at least
>
> misleads the viewer to an incorrect conclusion. The caption on YouTube doesn't help.
>
> It's not that the phase is locked at 0 below and 180 above the resonance point;
>
> it's just that far from resonance point the input and output phases are decoupled.
>
> The camera happened to catch times at which the driver and the suspended object
>
> were "in phase" or "out of phase" and the narrator pointed that out, but neither
>
> state is a general phenomenon. I think. But maybe I'm confused.
>
>
>
> Ethan
>
>
>
>
>
> > Of course this is trying to give some physical description for the electromagnetic field when I was complaining about a similar thing for quantum mechanics. A nice article by Freeman Dyson illustrates the difficulty of doing this for both approaches.
>
> > http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf
>
> >
>
> > Colin
>
> > -----Original Message-----
>
> > From: Ethan A Merritt [mailto:[log in to unmask]]
>
> > Sent: 04 November 2015 21:59
>
> > To: Nave, Colin (DLSLtd,RAL,LSCI)
>
> > Cc: ccp4bb
>
> > Subject: Re: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] Diffraction as a Single-Photon Process; was RE: [ccp4bb] Twinning Question
>
> >
>
> > On Wednesday, 04 November, 2015 09:48:13 Colin Nave wrote:
>
> > > Domenico
>
> > > Thanks for the kind words!
>
> > >
>
> > > I still don't like descriptions such as " Therefore, the anomalous scattered photon will still be able to resonate with another anomalous scatterer within the crystal" This is an attempt to describe what happens to a photon before it has been observed and is therefore an attempt to interpret Quantum Mechanics. As Feynman said about his formulation - it is ""merely a mathematical description, not an attempt to describe a real process that we can measure. Niels Bohr "brainwashed an entire generation of physicist into believing that the whole job was done 50 years ago" as Murray Gell-Mann said. This might be a bit unfair but most physicists accepted the Copenhagen interpretation and concentrated on carrying out the necessary calculations from which we have all benefitted. Quantum Mechanics works but treat the physical descriptions of the processes with scepticism.
>
> >
>
> > > Regarding anomalous scattering I like the classical analogy in terms
>
> > > of a damped driven oscillator. There is a good video of this sort of thing at https://www.youtube.com/watch?v=aZNnwQ8HJHU , for a non damped case showing the phase changes near resonance.
>
> >
>
> > I like the video, but it leaves me scratching my head a bit.
>
> > One comes away from it expecting that there will be a 180° change in the phase of every Bragg reflection just from choosing a "long" or "short" wavelength x-ray source. [Or to be more precise a 180° change in the contribution of the anomalous scattering atoms to every Bragg reflection].
>
> >
>
> > I realize that if the phase were to flip for all atoms then by Babinet's principle the same underlying structure should be recoverable with either choice of phases, but does this really happen? Anyhow, that would not apply when only a subset of atoms in the structure have an absorption edge that is spanned to the two wavelengths in question. So does this demo really match up to what happens in an X-ray experiment?
>
> >
>
> > Ethan
>
> >
>
> > > A bit of damping is probably apparent but if anyone knows of a better example for a damped oscillator I would be interested.
>
> > >
>
> > > Colin
>
> > >
>
> > >
>
> > > -----Original Message-----
>
> > > From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
>
> > > Dom Bellini
>
> > > Sent: 03 November 2015 18:05
>
> > > To: ccp4bb
>
> > > Subject: Re: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] Diffraction as a
>
> > > Single-Photon Process; was RE: [ccp4bb] Twinning Question
>
> > >
>
> > > Dear All,
>
> > >
>
> > >
>
> > >
>
> > > Sorry for bringing back this old topic but I think I might have an explanation to satisfy the original query, which I believe was not conclusively put to rest in the end.
>
> > >
>
> > >
>
> > >
>
> > > I think the problem that me and the original poster, Jacob, were having was that we were confusing energy with amplitude (at least I did). I.e., anomalous scattering affects/reduces the amplitude of the atomic form factor (or structure factor in case of a crystal), but not the energy (or wavelength) of the scattered photon, which is the same as that of the incident photon. Therefore, the anomalous scattered photon will still be able to resonate with another anomalous scatterer within the crystal, without breaking any conservation of energy theory. Since anomalous scattering is an elastic effect, if one accepts the explanation model of "photon interfering with itself" and "mini-waves" in the case without resonators, then this model could be equally valid even in the presence of more than one anomalous scatterer.
>
> > >
>
> > >
>
> > >
>
> > > I would like to thank Colin Nave to make me realize that I was mixing up anomalous scattering with inelastic scattering. I am pretty sure I had it clear while doing my PhD many moons ago.
>
> > >
>
> > >
>
> > >
>
> > > I hope I understood correctly the original question and that this explanation to the query might make some sense to other people as well, rather than just me :-).
>
> > >
>
> > >
>
> > >
>
> > > Best,
>
> > >
>
> > >
>
> > >
>
> > > and sorry again for bringing this back,
>
> > >
>
> > >
>
> > >
>
> > > D
>
> > >
>
> > >
>
> > >
>
> > >
>
> > > ________________________________
>
> > > From: CCP4 bulletin board [[log in to unmask]] on behalf of
>
> > > [log in to unmask]<mailto:[log in to unmask]> [[log in to unmask]]
>
> > > Sent: 31 August 2015 14:12
>
> > > To: ccp4bb
>
> > > Subject: [ccp4bb] AW: [ccp4bb] AW: [ccp4bb] Diffraction as a
>
> > > Single-Photon Process; was RE: [ccp4bb] Twinning Question
>
> > >
>
> > > Dear Jacob,
>
> > >
>
> > > You are not the only one who does not believe in quantum mechanics. Albert Einstein was probably the most famous non-believer.
>
> > >
>
> > > I agree with you that since we observe interference and diffraction patterns, there must occur interference somewhere. Although Niels Bohr claimed that you cannot say anything about a quantum system between two measurements, my strong feeling is that we see interference between the different superimposed quantum states. This is for me the truly spooky part of quantum mechanics: instead of a single foton, as long as we do not measure, there can be hundreds of fotons haunting our crystal. However, the moment we switch on the light, we find only one. The position of this foton will have been influenced by all other spooky fotons.
>
> > >
>
> > > I do not see how quantum mechanics would not conserve energy, but would be interested to learn.
>
> > >
>
> > > HS
>
> > >
>
> > >
>
> > > Von: Keller, Jacob [mailto:[log in to unmask]]
>
> > > Gesendet: Montag, 31. August 2015 13:06
>
> > > An: Schreuder, Herman R&D/DE; [log in to unmask]<mailto:[log in to unmask]>
>
> > > Betreff: RE: [ccp4bb] AW: [ccp4bb] Diffraction as a Single-Photon
>
> > > Process; was RE: [ccp4bb] Twinning Question
>
> > >
>
> > > >This means that when a foton at the same moment interacts with 100 scatterers (or resonators), there are 100 or more different states and in each state the foton interacts with a different scatterer. In each state, one foton interacts with only one scatterer. The moment the measurement is made, we find only one discrete foton, corresponding to one of these states. The distribution of the states, and therefore the possible outcomes, depend on the presence of all scatters/resonators within coherent range.
>
> > >
>
> > > Then I don't see how interference or diffraction patterns can occur without resorting to what others have said, which I don't understand really: that interference is not really happening at all, but something else with spooky probability distributions which don't need to subscribe to conservation of energy.
>
> > >
>
> > > JPK
>
> > >
>
> > >
>
> > > Von: CCP4 bulletin board [mailto:[log in to unmask]] Im Auftrag von
>
> > > Keller, Jacob
>
> > > Gesendet: Donnerstag, 20. August 2015 20:42
>
> > > An: [log in to unmask]<mailto:[log in to unmask]<mailto:[log in to unmask]:[log in to unmask]>>
>
> > > Betreff: Re: [ccp4bb] Diffraction as a Single-Photon Process; was RE:
>
> > > [ccp4bb] Twinning Question
>
> > >
>
> > > What I don't understand is how a single photon, which I thought by definition was an indivisible quantum of energy, can be split up arbitrarily amongst a number of scatterers into these "mini-waves." Doesn't that self-contradict QM's concept of quanta?
>
> > >
>
> > > One might say that somehow there are two energy-related characteristics to the photon:
>
> > >
>
> > > 1. the actual amount of total energy in the photon, and then
>
> > >
>
> > > 2. the "type" or "color" or "frequency" of the photon's energy.
>
> > >
>
> > > If you will allow me this dichotomy, then I can understand how it can be distributed to different atoms-small portions of energy of the same "color" are distributed to all of the resonators. One would also have to presuppose another thing, that the resonators themselves are able to accept packets of energy of size 1/n, as long as it's of a certain color. The problem is, however, that allowing photons and resonators to do these things violates what I thought was the central tenet of QM, that there are indivisibles known as quanta.
>
> > >
>
> > > Maybe, then, one can just drop the bit about there being quanta, or at least put a star by it?
>
> > >
>
> > > JPK
>
> > >
>
> > >
>
> > > From: [log in to unmask]<mailto:[log in to unmask]<mailto:[log in to unmask]:[log in to unmask]>>
>
> > > [mailto:[log in to unmask]]
>
> > > Sent: Thursday, August 20, 2015 2:03 PM
>
> > > To: Keller, Jacob; [log in to unmask]<mailto:[log in to unmask]<mailto:[log in to unmask]:[log in to unmask]>>
>
> > > Subject: RE: [ccp4bb] Diffraction as a Single-Photon Process; was RE:
>
> > > [ccp4bb] Twinning Question
>
> > >
>
> > > Valid questions.
>
> > >
>
> > > The phenomenon of resonance needs some explanation here, in terms we can imagine:
>
> > >
>
> > > Take first the normal case: let all the n resonating electrons gain 1/n in energy from the disappearing photon. These n resonating electrons emit partial waves or whatever you want to call them totaling n*1/n in energy, which recombines into the new photon. But what happens when the phases lead to extinction? Where does the energy go? Well, it just does not happen, it won't get scattered in THAT direction. So in the probabilistic picture again, IF a photon does gets elastically scattered, then it WILL appear again. WHERE it might appear, is given by its probability distribution, aka the Fs. No contradiction here, although I fully admit that the mini-wave picture results from the need to explain, in experience-accessible terms, a non-experienceable process. That is the QM conundrum, but not a contradiction.
>
> > >
>
> > > Now the anomalous (n.b.: not inelastic!) case: In this case the net effect is a change in the fs and thus Fs, and again all it does is change the probability distribution accordingly and above picture holds. But wait - where does the X-ray fluorescence come from, and if the photon uses all its energy to kick a photoelectron out, how can it reappear? It does not. The unlucky photon that generated the photoelectron is DEAD, otherwise we violate energy conservation. That photoelectron then causes either fluorescence via outer to core transitions or can be directly measured in case it manages to escape, or make Auger electrons, whatever satisfies energy conservation. The lucky photons, passing close to absorption energy, experience only the change in scattering factor. If you look at the theoretical QM calculations for absorption spectra (Cromer Lieberman etc.), you see that the dispersion curves actually show a singularity at precisely the orbital excitation energy. That absorption curve is again simply a probability function for photon death at a given energy. In solids, this curve can be more complicated and have more detail, but still the same.
>
> > >
>
> > > So, you cannot simultaneously measure diffraction and fluorescence of one and the same photon. The fluorescence scan does not come from the anomalously but elastically scattered photons. It comes from the absorbed dead ones. There is no difference between the normal and anomalous 'miniwave' picture other than a change in fs and Fs.
>
> > >
>
> > > Radiation damage, btw, is just a process cascade caused by that photon death.
>
> > >
>
> > > I abstain from digressing into inelastic/incoherent processes.
>
> > >
>
> > > Best, BR
>
> > >
>
> > > From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
>
> > > Keller, Jacob
>
> > > Sent: Thursday, August 20, 2015 9:48 AM
>
> > > To: [log in to unmask]<mailto:[log in to unmask]<mailto:[log in to unmask]:[log in to unmask]>>
>
> > > Subject: [ccp4bb] Diffraction as a Single-Photon Process; was RE:
>
> > > [ccp4bb] Twinning Question
>
> > >
>
> > > Do you have any explanation of how a single photon, which contains x amount of energy, can cause multiple electrons (at least 1000's!) in anomalously-scattering atoms to resonate at that energy?
>
> > >
>
> > > We don't find that the presence of different numbers of resonant scatterers requires x-rays of different energy; so why, if the energy is being divided into different numbers of resonators, does the same energy of x-rays work?
>
> > >
>
> > > I believe that BR's book says that the photon disappears or annihilates briefly, then re-emerges. This must be true, then, across thousands of electrons at once, both normal and anomalous?
>
> > >
>
> > > Jacob
>
> > >
>
> > >
>
> > > From: Edwin Pozharski [mailto:[log in to unmask]]
>
> > > Sent: Thursday, August 20, 2015 9:36 AM
>
> > > To: Keller, Jacob
>
> > > Subject: Re: [ccp4bb] Twinning Question
>
> > >
>
> > > typo indeed. The point, of course, stands - with older sources there are *no* photons inside the crystal for over 99% of the time. (Notice that diffraction pattern is still present, Bragg's law satisfied, etc)) X-ray diffraction is, for all intents and purposes, a single photon experiment. Even with the brightest and most coherent sources, when you could have multiple photons within a large crystal, these are still separated in space by a distance that is at least 100x the coherence length. Thus, X-ray photons do not interact with each other (and even if they would, it's still does not make them a wave, just good ole photons that due to their high spatial density would have detectable probability to engage in multi-photon events).
>
> > >
>
> > >
>
> > > On Wed, Aug 19, 2015 at 5:13 PM, Keller, Jacob <[log in to unmask]<mailto:[log in to unmask]<mailto:[log in to unmask]:[log in to unmask]>>> wrote:
>
> > > >Also, if your X-ray source is not exactly the brightest synchrotron, you are probably looking at ~10^9 photons/sec at best (I am estimating here that it would take at least 15-20 minutes of data collection using early 2000s "RAxisIV" in-house system to get diffraction image of intensity similar to 0.5s exposure at 12-2). That is one photon every nanosecond. Let's continue to ignore the fact that most photons just fly through. A photon zips through a 1mm crystal in about 3fs. Think about this - at a moderate intensity home source (and I can go to sealed tubes), the process of crystal illumination by X-rays is more like single photons flying through with about 300x long pauses between events. To scale this, imagine that a single photon spends a whole second inside a crystal, probing it's electron density. You would then have to wait five minutes for the next photon to arrive.
>
> > > I was re-thinking through this, and I think one of these numbers is wrong, viz, "A photon zips through a 1mm crystal in about 3fs." The speed of light is 3x10^8 m/s, so this leads to ~3.3 ps for a 1 mm path, and not 3 fs, a difference of ~10^6. Maybe it was just a typo? Anyway, it may not make a huge difference, since this would still make for an average of ~1 photon in the crystal at a time, assuming a high flux of 10^12 photons per second. But of course there would be some Poisson statistics involved, and there would be several photons a significant part of the time.
>
> > > Also, I wonder about relativistic effects: in the famous train-in-tunnel thought experiment, a large train can fit in a short tunnel if it's going close to the speed of light. Is this applicable here, such that many photons are in some sense in the crystal at once? Or maybe this is a red herring.
>
> > > But, to change topics a bit: part of the reason I am wondering about this is anomalous scattering. Since the resonance energy of an atom is a fixed amount, how can one photon provide that energy simultaneously to the requisite number (at least thousands, I would think) of resonant scatterers? Something's very funny here.
>
> > > Or, come to think of it, perhaps resonant scattering is no worse than normal scattering: if the energy is divided up between the all the normally-scattering electrons, you even have a problem with the one-photon picture, since the emerging radiation is still of the same energy. You want to have everything being scattered with a certain energy, but you also want all the scatterers to scatter. The concept of "energy" seems to get strange. Does one then need two terms, in which "energy" is just a characteristic of radiation, like a color, and then there is some other attribute like "probabilistic intensity," which describes how much "photon" is there?
>
> > > It is striking to me how much depth these everyday occurrences really have when one starts wondering about them.
>
> > > Jacob
>
> > >
>
> > >
>
> > >
>
> > >
>
> > --
>
> > Ethan A Merritt
>
> > Biomolecular Structure Center, K-428 Health Sciences Bldg
>
> > MS 357742, University of Washington, Seattle 98195-7742
>
> >
>
> >
>
>
>
> --
>
> mail: Biomolecular Structure Center, K-428 Health Sciences Bldg
>
> MS 357742, University of Washington, Seattle 98195-7742
>
>
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
MS 357742, University of Washington, Seattle 98195-7742
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