 So this afternoon's lecture is going to be on what I've loosely titled, Advanced Sands Methods. This is essentially divided into four different categories and is really talking about methods that go beyond the standard type of sands instrument that we've been talking about so far. So here we're talking about being able to measure larger structures than a typical sands instrument can measure being able to measure surface structures. Looking at how structure evolves with time and also then not working in inverse space for making measurements that are more directly related to real space structures. But at the same time still using small angle scattering. Alright, so if we start with measuring larger structures, we want to be able to configure a sands instrument to measure larger objects, right? So what can we do, thinking back to the lecture I gave yesterday about how we set up sands instruments and what you've had today about doing experiments. What can we do with a sands instrument to allow us to measure larger sizes? Does anybody have any thoughts? What things can we do to measure bigger things? Have a very large sample to detector distance. Yes, that's one option, yep. Any other thoughts? And increasing the Q, it was the lower velocity neutrons. Yeah, so exactly, so using slower, longer wavelength neutrons to get to lower Q values, exactly, yes. And so we essentially therefore have what it amounts to is three different options, right? We can increase the distance for a given beam size. So we set our collimation such that we don't change the actual size of the beam and increase L2, or we can decrease the beam size. So remember we can make the aperture smaller. So that makes the beam size smaller whilst keeping L2 constant, so that gives us a smaller angle as well. Or we can increase the wavelength at some given setting of the instrument. So if we look at this, then we have these three options, right? So we could calculate the required L2 to reach three times 10 to the minus five inverse angstroms using neutrons at a typical high intensity wavelength for a reactor. So four angstroms. We could choose to say, right, we want to get down to a very low Q. So one times 10 to the minus five inverse angstroms, that gets us down to something on the order of 10 microns in size. So what would it take to get to that with a wavelength of four angstroms? And also what would be the minimum accessible Q under circumstances like this, which are perhaps typical of a long sand instrument, if we use a wavelength of 20 angstroms? And so we can calculate these using a fairly straightforward set of combinations. We know how to calculate Q. We know the relationship between the beam size and the distance here and this angle. And that's really the minimum. Essentially, we can take that as a minimum scattering angle, the edge of the beam stop or the edge of the direct beam. And so we can calculate any of these terms given the other components. And what we find, right, if we go ahead and calculate this for these conditions, what we find is that here, if we want to be able to get down to these three times 10 to the minus five inverse angstroms, so this is order of micron in size, using four angstrom neutrons, we end up with an L2 that's 654 meters. That's quite long. And so what might be the problems associated with having such a long secondary flight path? I remember that the primary flight path would be essentially the same, so this will be a 1.2 kilometer long instrument. So aside from building one, can you think of any physics reasons why this might be a problem? Could it be that neutrons like start to deviate a bit from the top? Yes, exactly. Yes. So neutrons have mass and they are moving at normal velocities, so to speak. And so they are affected by gravity. And so the neutrons would actually be, as they're leaving the end of your sample, they're actually mostly traveling in parabolic paths. And so neutrons would basically have hit the floor before they ever got anywhere close to the detector. In fact, on the Long Sands Instrumented ILL D11, just a secondary flight path of only 40 meters, already neutrons at reasonable wavelengths are hitting the bottom of the detector rather than the middle. And so gravity is real and affects neutrons. The other issue is that in order to do this, we end up with a very low flux because of the narrow divergence that we, the narrow angle range that we have to have. So we end up with very few neutrons. So not only do they hit the floor, but not very many of them actually made it to our sample in the first place. In the second case, we can say, well, okay, we need to keep it at 30 meters. So what do we do if we just make the beam size smaller? So this now means that if we go to our optimum setting of matched collimation, 30 plus 30, and having the sample aperture half the size of the source aperture, we end up with a sample aperture of just under one millimeter. And this is very small, right? And so again, we come up against the issue of flux and the number of neutrons that we're able to actually get through our sample. And because we've gone for this matched collimation, we actually lose neutrons as a, you know, the square of the diameter twice, twice. And so we lose an awful lot of neutrons in this. And then we say, well, okay, what's, what could we do if we had a normal sands instrument with a sensibly sized beam? So we have a reasonable number of neutrons, but then we go to the longest reasonable wavelength we might get off a sands instrument. In general, because the flux from the source of neutrons drops off with lambda to the minus five and Maxwell in a Boltzmann distribution, we lose neutrons very quickly. This is somewhat compensated by the fact that the scattered intensity goes roughly as lambda to the three. So we end up with a sort of lambda to the minus two or so change in intensity as we go, so we don't lose as much as we might. But fundamentally, we're still limited by the number of neutrons that come out and 20 Anglons is about the maximum that you can realistically use on any sands instrument. And with a normal sized sands instrument, we simply can't get down to the length scales that we want to get to the Q values we want to get to to get to the large length scales that might be interesting. So you can imagine, for instance, the type of systems I'm talking about here are you want to study emulsion droplets. You want to be able to measure both the structure of the interface and the droplet size distribution. So you need to go into the micrometer range. It's just as an example. And so, so we have, or if you're interested in allies, you want to grain structure size that goes into the micron range. If you're interested in geological samples, they have a lot of structure in the micron range and so on. But this still doesn't get us there and we've had to throw away a lot of neutrons to even not get to the queue queue we wanted to get to. But we do make measurements on these very low Q values and at very larger structures with sands. So, so how do we do it? Well, there are a number of different options. The one of the first ones that was done was actually use lenses to focus the neutron beam. And this allows us to increase the flux for those case where we had a very small beam size, we effectively can multiply up the number of neutrons we get. And the next method that became popular was what we call usands, which is ultra small angle scattering or ultra high resolution small angle neutron scattering depending on how you count it. And this uses a totally different design of instrument to achieve those very small Q values, and you can see this is the method we used to get down to the very lowest Q. And then there's another method that's come along in the last decade or so called V sands, which is since imaginatively for very small angle neutron scattering. And then there's another method of multiplexing beams to allow us to get again increase the flux we get whilst having very small beam sizes. So how do these all work. So one of the nice things about neutrons is the fact that they essentially behave like electromagnetic radiation we can. We can diffract them, refract them, focus them and reflect them. Right. And so we can take lenses that have a made of a material that has a suitable refractive index so suitable scattering intensity. In this case, my knees in fluoride is the is the usually the material of choice. And we can then work out how many lenses we need and where we need to put them. And so for instance, here's an example. We want to focus a tank stop neutrons. It's easier generally to focus longer wavelength neutrons so you pick somewhere where the you still have enough of them. And then we have certain radius of curvature, and then we have a settings, fixed settings for our instrument, and then we can work out how many lenses we need. Unfortunately, unlike light and an actual electromagnetic radiation neutron still interact fairly weekly with materials so the amount we can bend the neutron beam is actually quite small. Using these types of methods. So we end up needing quite a large stack of lenses to be able to focus the beam over these distances. And so actually we end up with a stack of lenses of 36, a third stack of 36 lenses with a focal length of six meters six minute meters. And there are various different calculations you can do to determine exactly for your given configuration of instrument what the lenses are needed. We used it a number of reactor sources to be able to achieve lower Q values, whilst increasing the intensity of the beam. The key thing to note here is the fact that what we're doing in fact is focusing at the sample in this case. We're not focusing on the detector. Okay, so the beam size at the detector is actually not as small as it would be if we didn't have the lenses, but is still smaller than it would be to achieve the same minimum Q. So it's a complicated set of combinations of factors. So another way of getting to lower Q is to use V sands. And essentially what this is is this is a series of pinholes that are aligned such that we get a whole set of independent sand instruments effectively all converging to the same spot on the detector. And so by by doing so we end up multiplying up the number of beams we have, and essentially focusing them in space, so that they all hit the detector at the same point. This actually requires us to have a larger sample than normal to be able to make most of it, but allows us to achieve much higher fluxes than we could for such tiny pinholes. And so in practice what this looks like is you have instead of a single aperture you put in a plate with many apertures on. And you calculate exactly the series of many sets of these apertures you need to prevent crosstalk so that there's only one path for any given set of neutrons. And you also then need a set of lenses to remove to make sure you're removing distortions, some prisms to counteract gravity. And these all need to be nitrogen cooled. And then they eventually can hit the detector in the same place. So this is the instrument at the Helmholtz Center in Berlin which closed in 2019 that did this although it was not very often used. The only instrument currently operating and with with potentially having this setup is the V-sands instrument at NIST. And even then actually they're only operating with converging slits rather than converging pinholes at the moment because aligning these pinholes is extremely difficult. The instrument under development and being built at the Chinese Sipulation Neutron Source will also make use of this method to get to much lower Q. And the SCARDI instrument being built here at ESS will use a similar system but it will actually use slit collimators in a different design to be able to also reach a much smaller Q values. The last example of getting down to really very low Q is a completely different design of instrument. This isn't an add-on to a existing Sands instrument. This is a used Sands instrument and it's what is known as a Bonse Hart type of diffractometer. It's a double crystal diffractometer basically. So what we have is we have the neutrons coming out of the reactor. By the way, can you all see my mouse pointer? Yes. Yes, good. We have the neutrons coming out of the reactor here. They passed through some filters. Remember, we talked about filters the other day. These remove unwanted wavelengths that we don't want for our experiment. We have a curved graphite premonochromator here. So this both focuses the beam and also provides some degree of monochromation. Again, we talked about monochromators. And then here we have a pair of silicon crystals. And these are actually single crystals of silicon about so big that have a channel cut into it and then are made into three blades. And the key point here is that these are all from the same crystal, right? So the crystal planes in all of those blades are perfectly aligned, even if the mechanically the surfaces aren't. So we can cut the the ball of silicon in the right way. So now we would have this silicon 111 crystal plane or another choice to do or something like this, depending upon the wavelength you want. And then so the beam comes in, it hits one part of the monochromator is diffracted. It's another part of the monochromator is diffracted again. It's another part of the monochromator and is diffracted again. And so now through this diffraction, we've done two things. We have selected the wavelength we want very precisely, but also because it's a single crystal and the angular range over which the brag condition is met is very narrow. And so we've not only chosen the wavelength we want very precisely, but we've also chosen the angular spread of the beam very precisely in the in the diffraction plane. We then pass this through our sample, and then we have an analyzer crystal. And if this analyzer crystal and this monochromator crystal are perfectly aligned, then only neutrons that have not been scattered will be diffracted again and reach the detector. What we can then do is we can rotate this crystal by a very small amount and not a few micro radians. And then we now are only neutrons that have been scattered by that angle will now meet the brag condition. And by scanning that analyzer we're now scanning through scattering angle and the scanning through q space. And we can do this with very fine precision and get very, very small angles of measurement. This in fact was the instrument that I used to be responsible for when I worked at this before I, before I came here. And so this means we can now get down to these extremely small q values, as well as going up and overlapping with the measurements we can make with a regular sounds instrument. This sounds fairly wonderful, but there are some caveats one, it's because it's a scanning technique, then time resolved measurements are difficult. Also, the flux of neutrons is very low because we have so narrowly defined the wavelength and divergence. So you remember I mentioned when I was talking about using crystals as monochromators that one of the problems was it really cut down the flux, but it absolutely does here. So a measurement that might take eight hours to make on this instrument for one sample to scan over a relatively from say 10, 3, 10 to the minus five out to 10 to the minus three even not even that 10 to minus two inverse angstroms. And so it's much slower so time resolved measurements are rather out of the question. And the other challenge is that these are channel cut crystals right so they have diffraction in this direction. And so they're narrowing the divergence in this direction, but there's no diffraction in the vertical direction. And so the divergence in the vertical direction is very wide. So in effect, what we're doing here is if you imagine this plot, the circles are constant Q contours. So we're going out here this is a Q value this is a Q value this is a Q value and it's the same, all the way around. You know, the vector changes but the magnitude is the same. So in the given setting of our analyzer we're looking at some Q value in this horizontal direction. And we have very good resolution in this direction right this is due to our diffraction and and beam spread. However, in the other direction we have essentially very poor resolution. You can see that it the resolution is on the order of point one inverse angstroms and that's much much many odds of magnitude higher than what we're measuring. So there's a significant effect on how the data looks on the resolution of the measurement. And so here we have the form factor for a sphere. And this is what the same thing would look like if we measure it on the use and instrument. But we know this. And so when we analyze the data we can take our model, apply this resolution function to it and fit the data directly. So the resolution function for the sands instrument in the same way and and co and co analyze sands and use and state. And so we can still extract information across a very wide Q range, but this has to be born in mind when you're thinking about the analysis of such an instrument. And so we have a lot more slit v sands that also has a slit geometry, which gives this very asymmetric resolution function, which causes some odd effects to the data that you have to take into account when you analyze it. All right. So that's covering all the different ways that we can measure much bigger things out to order 10 microns or so. And then we can actually measure very wide, very wide Q ranges and size ranges indeed. But what if we want to measure surface structures. So, we can actually measure very wide Q ranges and size ranges and deep, but what if we want to measure surface structures. So, in general, sands can provide you with information about the bulk structure in plane, if you set the geometry up correctly, and has quite a strong penetration depth, if you don't restrict the beam size. Whereas reflectometry provides information only in the generally only in the plane perpendicular to the surface. And that is usually limited to a few hundred nanometers of depth of information. And that is usually limited to a few hundred nanometers of depth of information. So how can we measure the in plane structure of thin films? Well, one way is just to make a lot of thin films, right? So get enough material in the beam so that we get a scattering signal. If we, this is fairly common, if you're interested in the in plane structure of films, you make a whole bunch of silicon wafers, put films on all of them, stack them up, put them in the beam, and look at the in plane structure. Right, because then you're just doing a standard transmission measurement just limited to thin films. And this is actually very straightforward, aside from necessarily making films that are the same uniform across each sample, but the problem is here that ideally we have several micron thick films. So that if that's the type of films you're talking about, that's great. But you're really not looking at the near surface region then right you're you're well away from any surface effects once you're into the micron sizes. And you may need many wafers and potentially the background from the substrate can be significant. So here this is where thinking about doing some deterioration schemes and things to enhance the contrast in your sample would end up being necessary if that's possible for the sample. The other thing is to do a reflectometry experiment. In, if you have a two dimensional detector on your reflectometry instruments, then in general you will see scattering that happens off the specular direction, which we refer to very imaginatively as off specular reflectivity. In general, because of the choice of collimation in a reflectometry experiment and so on. What we can do is we can probe sort of micrometer length scale structures in the direction of the beam, right. So, but we get because of the width of the beam we use reflectometry we get no information in the, the y direction, which is along the surface perpendicular to the beam. And so so we can use this off specular structure. And in fact actually this off specular scattering is often assumed to mostly be background signal that you want to subtract from your specular reflectivity and so actually regularly we will use the area next to the specular region a picture like this as a definition of our background signal. But in fact if there is structure there will be information in this. The other option is to do what's known as grazing incident sands or GI sands or g sans depending upon or g sans depending upon your choice of of acronym and language. There are two different regimes, we should sort of we have to sort of consider here. One is what I call true g sans. This is where the incoming neutrons are at an angle below the critical angle, right. So, so here you're essentially in the total reflection regime. And so you only have evanescent wave scattering from the interfacial region. This is extremely weak. The intensity of the waves does decays exponentially through the surface. And this is done really well with x rays. But again because we have many many odds of magnitude fewer neutrons and the neutrons interact more weekly. This means that this evanescent wave is is actually a very weak. It gives a very weak signal and it's very difficult to get anything off this. So more often what we do is we do what we call near surface sands, which often is the bulk of what we call g sans most of the time. Here we bought our incoming neutrons at an angle that's a bit greater than the critical angle. Then we have a refractive way rate wave that is refracted into the surface, and is then scattered from a region below the interface. And then depending on how we set up the equipment we deter and what wave length we choose, then the penetration and scattering volume can be very. This is actually as I said the significant cause of background in reflectometry experiments and is most of what is measured as as off specular scattering as well. So how do we set up these measurements. Well basically what we have to do is we have to take now a pinhole beam. So we narrow the beam in the y direction. So we intentionally take a sands in sands beam, and we inclined it at a small angle, and put and pin it onto the surface of a sample, and then look at the reflected pattern. And now what we have is we have probing in one direction the qi space, which is in this direction in the other direction the reflectometry space. So essentially we can imagine that we have for a given instance we have a specular spot, which is where the direct beam goes, and everything else is off specular scattering either in the one plane or the other. The shape of this pattern, then tells us about the in plane structure. However, the analysis of this is not so simple. We have to deconvolute lots of geometry effects from the sample, and also then come up with a modeling regime to be able to model this, this structure. This can be rather challenging. In fact, the other thing to bear in mind is also that the penetration depth of neutrons is both angle dependent and wavelength dependent. And so by by changing that we, we can either use that to control what what part of the sample we're looking at, or we can just need to know it so that we know what part of the sample we're probing when we're doing our modeling and data analysis. Again, below the angle of total reflection only an evanescent wave penetrates the surface. And so here you can see, as we increase our wavelength, then we become going from being bulk sensitive to being surface sensitive, as we're also looking at different angles. And here's an example of how we can do this, particularly this is might be of interest at ESS using a high intensity time of flight polychromatic beam. We can get over some of the challenges that you face with monochromatic instruments, we will have many more neutrons, and we can make use of the time of flight information to probe multiple depths simultaneously. Here's an example of from the literature of using time of flight grazing instance scattering to look at polymer the structure of polymer nano dot films on the surface. And here, taking different wavelengths allowed to probe different parts of the structure. The real advantage here by for neutrons, because you might say well why can't we just do this with my microscopy or FM or something like this. Well, the answer is that is for looking at buried or magnetic interfaces right so if we have a surface that is a pattern surface underneath another surface then the penetration neutrons allows us to look at that. And we can make use of the magnetic interactions of the neutron to get magnetic information about the surface in plane as well as normal to it. Okay, so we've talked about how to measure smaller structures, how to measure surface structures, and both of these essentially required new types of instrument. Okay, sorry, I didn't there was a question from Jin Shan before I go on to the next one. So, in terms of the depth grade into hydrogen metals I would say it's it's most likely to be either reflectometry, all one of the neutron depth profiling methods that actually aren't so much scattering they rely on looking at things like depth sensitive gamma spectra and things like this. But, but there are good methods I think reflectometry might be a good choice if you can get sufficiently smooth surfaces to be able to measure and depending on whether you want to go beyond maybe 100 nanometers if you if you need deeper information and that becomes a grazing instance problem and then then it gets perhaps more difficult depending on the structure of the metal or alloy. Right. So, what I said before was that we needed specific, mostly specific instrumentation to measure those, those types of structures to measure time dependent structures are some things we can do just with existing sands instruments. But there are some examples where some we can get additional information if we can make designer instruments in a certain way. The simplest time is old sands on the second to minute timescale, or even the subsequent timescale these days is reasonably strong then we can do this with sequential methods so basically just starting off the reaction or the impetus or whatever we want to do to our sample and then just measuring time shots or in the case of event data recording event data over time and slicing it up afterwards into the time slots we want. And an example of of how one can do this is, for instance, this is these measurements that were made on lipid transfer between nano disks. And then what they did was they mixed some deuterated lipid nano disks and some protonated lipid nano disks in a ratio such that when the lipids were perfectly mixed, they would be contrast matched with the solvent. And so what happens over time is that the lipids transfer between the two populations. And so if you just measure the total scattered intensity as a function of time, you get a measure of how fast the lipids are moving back and forth. And as you can see this was done on time scales up to 10 seconds. And because we it was the winner we and because they were just counting total intensity, rather than having to look at the actual scattering pattern. This could get actually quite good. Good signal in short time measurements. As you can see, as we get up to biological towards biological temperatures, the rate becomes so fast that it becomes increasingly difficult to measure. And so here this is where having instruments that have more neutrons and have a setup to measure and even faster time scales would be useful. What you can do are to do things such as standard samples such as stops flow or flow through mixing. So in the case of stopped flow what you do is you rapidly mix in a chamber. And then you can take quick measurements and the mixing time determines the the time of your capture of the measurement. So here you have to do this over and over again in order to build up enough statistics but you can measure whole scattering curves. And so here these were 50 to 100 millisecond measurements that were repeated up to 25 times in order to get enough statistics, but still then using this method you could look at the structural transition of, in this case, mixing two surfactants. So they went from a disk to a physical structure. Another option is if you want to look at reactive systems is to use flow through mixing. Here basically you start them reacting and they pass along a small capillary. And because they're reacting as time goes by, where you look at the sample as it's flowing through also corresponds to reaction time. So if you look close to the mixing chamber, then what you're looking at is short reaction times. If you're looking further away you're looking at longer reaction times and the flow rate can be used to also control exactly where in the reaction time you're looking at. And so these these types of methods can be used to look at short time scale measurements without having to modify the instrument itself you're just changing in both cases here the sample environment you put on the instrument. Another way to do this is for instance to do stroboscopic type measurements where and these are often used with a share so you'll put a rheometer or share cell into the instrument and you will then do put your sample under some sort of share field, stop the share, let it relax and take measurements and you have a triggering system whereby the cycle of the rheometer is linked up to the data collection on the sands instrument. And so you can then again just go through this cycle repeatedly and build up the statistics based upon where exactly in this relaxation curve or excitation curve you were. And this is shown as an example for share but one can do it things like with UV illumination, for instance for light switchable surfactants or polymers. You can turn on a light turn off a light, you can apply electric fields or magnetic fields in similar ways. And look at the response of your system to this by repeatedly going up of course this only works if you have a reversible change and you're interested in that reversibility. However, the minimum time scale that you can measure is limited by the range of wavelengths you have and in the case of a time of flight instrument is limited by the pulse length which gives the range of wavelengths you have. And so there's a for a typical continuous source sands instrument, you have a resolution for these type of cyclical measurements of something on the order of about 50 milliseconds. And so if we. So this is basically just limited by the time it takes different neutron wavelengths to get to the same point on the detector. There was this method invented by Roland Gayler at ILL which he called to san, which is sands for time involved small angle neutron experiments, but also is very similar to the Swedish word for a herbal infusion. Dear me, I'm in the wrong country. And what you do here though is actually you put a chopper at the source, and then you synchronize the chopper with what you're doing to your sample. And what this then means is that neutrons that arrive at the same time were actually scattered at the same time in the sample response curve. It's rather complicated. And actually this type of method to a limited extent can be done automatically at a time of flight instrument because you know when any given wavelength past to the sample because you know where it was at any given time so if you know that the neutron reached your detector at X time, and you know when it started, you know when you sample and so you can know, then find out what state your sample was in when say 10 Armstrong neutrons went through. And this is more or less the same, but with significantly more flexibility in the fact that you can get very high frequencies out of this that you can't get out of a time of flight source. So this technique is available at the ILL and NCNR, and has mostly been applied so far to things like the behavior of ferrofluids, the type of fluids that are used in these fancy adjustable dampers for for expensive cars where by changing the magnetic field you can change the viscosity of the real the real logical properties and the viscosity of the ferrofluid and change its dampener but understanding the critical behavior of these has been done, primarily using reosans. So using to saying there haven't been many other examples of using this because it is generally focused on very high frequency effects. All right, so. So now we've spoken about how we can do time resolve measurements. I want to go on to perhaps what is the most different method so far all of the things we've done look like sands instruments one way or another. This example now where we measure in real space. I'm going to talk now about a technique called spin echo sands. All right, so the ability of a regular pinhole sands instrument allows us to measure in the nanometer to 500 nanometer regime, and we have relatively long instruments and we measure in reciprocal space. So the technique of spin echo sands, which I'll describe in a moment makes you is is able to measure from something like 30 or so nanometers, but goes up well into the range that we're talking about with you sands at 20 micrometers. So much more compact and importantly, one of the things they do is that they give you a scattering curve that is related directly to real space distances is not in reciprocal space. And this can be an advantage in understanding some complex data data sets. All right, so you'll have, you know that some neutrons are affected by magnetic fields. What happens is, is that when we pass them when they travel through a magnetic field, they start to undergo procession. And so, as the neutron passes through the field, it spin starts to process. And so it presented it. So if we have a positive field and a negative field that are essentially the same length and the same field strength. So if we pass them through, we'll process one way and then we'll process back the other way by exactly the same amount. And so the procession the amount of procession is proportional to the field strength and the distance. What we do in small angle scattering, because we don't have a direct single linear beam is we actually use these trapezoidal parallelogram shaped fields. And what we see is if we send one neutron through, it goes through that much, and then it processes back. And it's completely unchanged on the other end, because the unscathed beam gives us this what we call spin echo of zero the angular the difference in the spin between the start and the end condition is zero. And this is independent of height and angle, because of the shape of these beans. If we now put a sample in the beam. And it will now have a different path length in the second magnetic field from in the first one. And so it will come through with a different spin state at the end, then it started with. So the scattering by the sample gives you no complete spin echo and a net precision procession angle. This gives us a very high resolution, even with a divergent beam. So we're sensitive to scattering at about three micro radians, which is, as I mentioned before, similar to the type of precision we can get from a Bonser heart type use and instrument. And so this is now a still Fourier transform scattering, but a different for a transform and gives us the density correlation function. So here we now have a decay curve that is related to the size of the particles. So where the becomes flat is now directly related to the size of the particles. So in this case, we can effectively read off the scale, how big our particles are. So the instrument looks like this, we have a polarizer to polarize our neutron beam to get everything in the same spin state. To start with, we have a magnet to do the field. We have a field stepper to control the field. We have guide fields when they have an analyzer to analyze the spin state when it comes out and a detector. So how does this relate to normal sands? And so essentially, in all cases, what we start with is we start with the distribution of density, a row of R. And in the case of regular sands, we have the square of the amplitude of the Fourier transform, and we end up with intensity as a function of q here. And in C sands, what we have is we have the able correlation function actually goes here, and we end up with what's known as G of Z, which is the C sands function. And they're both related then by their respective transforms to gamma of R, which is the pair distance distribution function, which is the actual real space information. However, here the C sands uses this spin echo length, which means that it is in fact working in real space, real space length, rather than a inverse space length. This technique can be very valuable in cases where you have very dense systems where multiple scattering can be a real problem for C sands techniques. All of our analysis assumes that neutrons are only scattered once when they pass through a sample. If they're scattered more than once in significant quantities, then that can change the scattering curve in a way that's difficult to analyze, or possibly impossible. And so C sands, it can be used often for systems that are subject to multiple scattering that will cause problems for a sands experiment. All of this analysis can actually has been built now into SAS view. So in SAS view you can analyze both sands and C sands in data using the same models. So that may has made life a lot easier for people who want to do C sands experiments. The places you can do this are at the University of Delft reactor where this was invented, and also at ISIS, where the University of Delft group contributed to building two instruments of spec and Larmor, which make use of this method. All right, the last method I want to talk to is about doing Sands with an imaging instrument. And so in Sands what we do is we take a very collimated beam, we pass it through the sample and we look at scattering. In imaging what we do is we take a very divergent beam, shine it on our sample and look at basically take an image on the detector of what has happened to the intensity of the neutrons. It's possible to set up a set of gratings, interference gratings doing what is known as dark field imaging, where essentially by having at these diffraction gratings, we can now and moving them around. We can now do position sensitive small angle scattering of our sample using an imaging detector. And this can allow you for instance to look at the distribution of small angle scattering within your sample which can tell you about the distribution of the nanometer to micrometer length scale structure within a sample. And can be a very powerful technique for certain types of problem. Right, so that overview was really just make you aware of the fact that there are a whole bunch of methods that exist to extend the traditional pinhole Sands measurements to look at structure on much longer length scales short to short time scales and to look at surfaces. These are generally more specialist I mean I said that basically everyone has a Sands instrument at their facility. These types of instruments are very few and far between and require generally much more specialist support and planning than a normal Sands instrument. But if you have the right samples, these can be very powerful and unique methods for obtaining structural information about. So, I'm happy to have any questions. So, what are these time resolved measurements? Yeah. Well, if we do this measurement in the reaction at the process itself, it's like ours. So, what would be optimal. So, so, so long time reaction so long time reactions like that are actually very easy to measure depending on on whether you need very high resolution time in the early phases that say, unless time resolution later. It's very variable but essentially if you went to an instrument that does event mode recording you could just start counting data and measure for the full hour or so. You could choose to slice up the data when you process it into whatever time slices you wanted. Otherwise, if you don't need very tight resolution if you only need say several seconds resolution, you can just make lots and lots of measurements one after the other while the reaction is happening. And that that works fine I've done that on on samples a lot. But it does really mean you need to know a little bit about the reaction rate in upfront to have an idea about what measurement times you should use. Of course you can always measure with very short measurement times now the data together afterwards but that's generally more of a pain and then getting it a little bit optimized style. But those those sort of long times are actually very straightforward to do on a regular science. The reasons we try to sync with on the in-situ diffraction measurement when we charge some metal sample with hydrogen in the beginning so quite fast. I mean, within some minutes, you reach almost a steady state level but then it will take a long time to realize the saturation but I don't know what's optimal. If you want just to follow the very initial period, maybe you have to measure quickly. So so so depending on how quickly quickly is then then measuring on a high intensity, the highest intensity beam you can get with an event recording instrument would give you the best possible time resolution that you could you could choose to have. Another thing you can always do with things that then take a long time to equilibrate is you can wait in between so most instruments have sample changes right so so you can measure measure a sample and then switch to the next one and just, you know, alternate between them looking at at intervals in time you don't have to just keep measuring for those longtime equilibration type measurements. You know you may maybe make some different measurements on some of the samples while the other ones are collaborating over time. So there are there are there are ways to optimize the measurement time that doesn't mean sitting counting for hours on something that isn't isn't changing that fast. But yeah always talk to an instrument scientist they're there they used to those type of measurements very much. Yeah. Yeah. Good. Any other questions. Maybe I missed that you said this, but I was wondering about like spin echo sense. Yes, what kind of systems that would be particularly useful for compared to like regular sense. So the, in general, it's anything where you would want to. So CSANs and UCANs more or less cover the same size range. So, so things like emulsions gels with large scale structure. Geological samples and alloys where you're looking at grain size structure grain structure things like that. You have these very large structures that that can't be measured with regular small angle scattering. And then with CSANs. Depending on the setup you have it can be less sensitive to this multiple scattering problem. So as you increase the size of particles obviously the scattering intensity goes up very rapidly, and you increase the scattering probability. So if it increases then you know you have more and more multiple scattering. And so you get the point where the scattering signal is too strong. So often for you sense measurements we actually have to really dial the contrast down to a level where we can actually make the measurement reliably CSANs is less susceptible to that. And actually CSANs has been used a lot to study things like biological emotions like milk cheese dairy products, and so on. I did some CSANs to look at the structure of very concentrated emulsions and densely packed mixtures of spheres and things like this, we're looking interested in binary sphere mixing. So in general anything where there's length scale structure on those length scales. One nice thing that is now being done on the Larmor instrument at ISIS is that you can do simultaneous sands and CSANs. So they have a setup whereby the CSANs is actually just measured in the beam stop. So you have the center of beam stop measures the CSANs pattern, and then you measure sands all around it. So you can actually on the same sample measure all the way from a few nanometers up to 10 microns. And that's particularly interesting if you have, for instance, structure that's evolving with time. So one of the disadvantages of either CSANs on its own or USANs on its own is the fact that they're much slower. Well CSANs is actually quite fast because it uses the direct beam as well compared to USANs which is slow because it uses a collimated beam. Whereas CSANs can use an uncollimated beam. But normally you would have to move your sample from one to the other. But if you're actually interested in the evolution of structure over time where maybe it's a growth, a nucleation and growth phenomenon or something like this. Then you can look at that with sands plus CSANs. I can think of an example where maybe, for instance, if you're interested in pickering emulsions, right, in particle stabilized emulsions, maybe you're interested in what's happening to the density or amount of stabilizer at the interface over time. And you started off with a very fine emulsion and it's ripening over time. You can look at how that ripening is occurring and look at the distribution of the stabilizer by using contrast variation. But many of these things are things that you would say, well, I can just do that by mostly looking at it. And in fact, whenever people said they wanted to do USANs experiments, one of the things I've asked them is, have you measured it with every other possible technique first? Because this is going to be a real pain to do, including staring at it very hard. Sometimes the eye is great. Exactly, yes. I mean, looking at just how the cloudiness is something you're changing or its turbidity will tell you an awful lot before you even need to do scattering. So it's those type of systems. Systems that aren't necessarily amenable to light scattering is usually the ones that are of the interests where you have very dense opaque systems. Yeah, when neutrons then also are extra helpful maybe. Exactly, yes, exactly. All right. Thank you very much. All right. Well, thank you everybody. I hope you have a good rest of the day and I'll see you in the next couple of days.