 Hello, today's lecture I will be introducing you to scattering for mesoscopic world. The mesoscopic world I have going from microscopic world which I have been discussing till now with you to mesoscopic world. So the microscopic world or the crystallographic nature of the crystallographic samples and also liquid and amorphous samples were small r correlations. In brief that is what I was looking for either through brach diffraction or through liquid and amorphous diffractions. So from there now I am moving on to world where I actually play with the resolution and I try to see things which are typically 1 nanometer which is 10 angstrom to 100 nanometer length scale. So this is the mesoscopic world. There is a lot of interest to understand structure at this length scale. Mostly people talk about inhomogeneities and come to it when I deal with specific examples and this is done by small angle neutron scattering. When it is a small angle neutron scattering possibly I am a little wrong because it is actually small q neutron scattering but in the popular parlance small angle neutron scattering is accepted and sans. That is a very well known technique and today any major neutron source will have not one but several of these instruments. But even before I start the subject proper I have a responsibility because last time I promised you that I will tell you briefly about single crystal neutron diffraction and also some references. So in case of single crystal neutron diffraction please note that this is how the sample table looks like because as I showed you earlier that when it is a powder crystal from the sample at a certain angle you have a Debye-Shearer cone, Debye-Shearer cone and my detector I showed even with photographs for simple extra diffraction cuts a piece of it of this cone as intensity and from there I can get the dispacing even in case of position sensitive detector based instrument that I showed you I take a horizontal plane in which I have these detectors in case of liquid and amorphous I can cover I cover a larger angle in case of crystallographic samples I cover slightly lesser angle and get peaks in this detector plane it is intensity versus Q. Here because it is a single crystal now I don't have a Debye-Shearer cone but what I have is a evolved sphere and whenever my scattering vector I showed you touches I mean the sphere touches and there is a reflection whenever Q is equal to G or K, K prime, K minus K prime equal to G in this three-dimensional wall so there will be reflected beam in that direction. So here that means my sample will send the reflected beam to 4 pi solid angles and not in a plane because this is a single crystal. So what we do actually we have a Goniometer which is known as a four circle Goniometer on the sample table without giving you too much of details this is the Goniometer its role is to the four circles are the rotation of the entire table rotation of the sample and around two axis we know that by rotating it through Eulerian angles I can bring the reflected beam from anywhere in 4 pi direction down to the horizontal axis on which the detector is rotating it is here the detector is rotating around the sample so this four circle Goniometer's role is to bring the reflection down to the plane of the detector because the detector is heavy and it is not possible to cover all four per angle or move it along the horizontal axis in a vertical direction so this is the trick we play by using a Goniometer. So in this case as I told you earlier that we can study single crystals but more importantly in case of neutron we can study hydrogen as single crystals which is very important because hydrogen has a large scattering cross section but you may question that I told you earlier that hydrogen is an incoherent scatter coherent scatter incoherent scatter so it will only give a background true and hydrogen has a small coherent scattering but in this case because it is a single crystal your reflected beam is extremely narrow and very sharp a realization of true delta function because it is so narrow and sharp I don't have to care about the background under the delta function peak because I have very large intensity in the beam and that's why unlike powder diffraction I can easily use hydrogenous single crystals and hydrogen bonding is one of the most popular topics in single crystal neutron diffraction hydrogenous samples so we can and also because the reflected beam is extremely narrow so to capture the beam on the detector I don't go very far I come close when I come close I compromise on delta theta because it is such a narrow beam I need to capture it on a detector and I add a delta theta that is for the detector and I can't use too many examples but just I show you this is the kind of structures we can get but most importantly we can have ab initio initio structural solution different from what we did for powders where we did read well refinement in case of read well refinement we start with a structure and keep on refining it so that my experimental results matches with the model here we don't have to go for any model we can find out the hydrogen bonding and the entire structure of the single crystal from an ab initio way so this is the difference and I will stop for single crystal diffraction from here moreover last time I discussed you with you the results from amorphous and liquid solids so I will not get into the discussion but in the last lecture I missed the references which I have put here and this is the data from sandals in ISIS spallation neutron source at Rutherford Appleton Laboratory UK and also this is the data from Dhruva where this is the HQ the total structure factor which helped us to get molecular clusters so not only we have the amorphous structure but we also have these molecular clusters inside the liquid which is possibly one of the unique results of this experiment and I missed the reference so this is the reference for the same with this much now let me dive into small angle neutron scattering or sands now as I told you the mesoscopic world is studied using sands so here are just some examples I have taken from some reference so you can use polymers complex fluid means this structure shows actually something called micelle where the molecule has got a head which is possibly here it is hydrophilic and a tail which is hydrophobic and when you put these are called surfactant molecules when you put them in a solvent they form this kind of structure and you can study rather you can get information about this kind of structures using sands techniques it is extremely useful for biological samples even at larger length scale and also in material science like precipitates like precipitates so metallurgies are also interested in biology, chemistry and of course physics so all communities they find this technique very useful and I am going to talk to you about this technique today so also this is from a Japanese website for the biological samples they are mentioned various things like biomembranes and right up to microorganisms you can study with small angle neutron scattering or sands now onwards I will use the word sands but remember in your mind that what I am talking is actually small and cute scattering now with that so we are using it to study mesoscopic size inhomogeneity is in a media please remember inhomogeneity so what I mean is that you have a matrix some kind of matrix it can be liquids or it can be a solid and you have an inhomogeneity which have got different scattering length density please note the term SLD I have forgotten about the microscopic structure of the medium I am talking in terms of density and not in terms of atomic positions which I did till now using powders in liquid and amorphous systems in single crystals I was talking about atomic positions and trying to solve it now I am talking about scattering length density okay so and the so why is scattering length density so let me just come down to what I taught you in lecture 3 or 4 so the real space correlation function is G of R which is a Fourier transform of I of Q that we measure so I measure it but their Fourier transform each other and when I talked about model fitting when I talked about reverse Monte Carlo my target was to go from here to the real space but what does quantum mechanics tell us I will use the uncertainty principle so we are talking about in an experiment a Q which is 4 pi by lambda sin theta this is the momentum transfer is a wave vector transform momentum transfer is h cross Q and now we know from uncertainty principle that delta P delta R must be delta than equal to h by 4 pi but delta is nothing but h cross delta Q and delta R and then delta R is greater than or of the order of I might be missing some of the numerical numbers 1 by delta Q so your inherent resolution dictated by the quantum mechanics or rather by uncertainty principle is the resolution I will call it the resolution resolution resolution resolution in real space to be more precise depends on 1 by delta Q now what is the delta Q is it the Q resolution of my experiment no you are doing a Fourier transform over the entire Q values that you have used in the experiment so your delta Q is Q max Q max because this is the range over which you do your Fourier transform so when we talk about Q max I am sorry I am clean Q max or Q M then please see that I so far I have been talking about smaller and smaller units structure atoms and because they are opposite inversely proportional to each other I was talking about larger and larger values in Q if you remember when I talked about crystal refraction from powder samples I went to Q equal to typically around 10 angstrom inverse would have loved to go further but fact is that here we do a refinement so 10 to 12 angstrom inverse is good enough when we have a very crude model and not a crystallographic model in case of liquid and amorphous system then I went up to 15 angstrom inverse in river or if I talk about rather for deproton laboratory as pollution neutron source I talked about 50 angstrom inverse so I went to such large values because I might attempt direct Fourier inversion and large Q is required now I have gone in the other direction so now I want to do experiment at low values of Q so low values of Q is possible one is by going to low angles or by going to long wavelengths both of them give us small values of Q and that is why this is called small angle neutron scattering because I go to small angle I also go to larger wavelength and that Q max dictates how much is the resolution so now let me take various diffraction techniques we have small angle neutron scattering we have small angle extra scattering we have light scattering so I have given typical wavelength actually here the range will be 3000 angstrom not angstrom angstrom to 7000 angstrom that's for light extra you know copper k alpha is 1.54 angstrom so I have written typically 1 angstrom I can put to softer extremes certainly small angle neutron scattering the typical wavelengths use 5 angstrom every technique has its plus and minuses for example light scattering you can see because lambda is very very large so 1 by lambda if I put Q is very very small actually 1000 will give me 0.001 angstrom but typical number but the fact is that in case of light this is a plus point so you can see and when it is such a small Q I can see very large objects smaller the Q larger object that I am studying larger the Q smaller the length skill that I am putting so I can see very large objects but here the most important thing is the light demands transparency you can do light scattering unless your medium is transparent the solutions are fine small angle extra scattering very fine but if you take say 1.54 angstrom copper k alpha radiation that will have a penetration depth of typically say tens of micron if you go to softer excess say 100 angstrom excess it's possible in this one in our other cat in the earth it does have facility for soft excess but they will have even less penetration depth in case of small angle neutron scattering one you can do to longer and longer wavelength penetration is not a problem so you can use a solution of typical say fractions of a millimeter thickness neutrons will easily penetrate we decide the thickness of the sample to the extent we can do we can see single scattering vertical scattering is a nuisance for scattering experiments and so we can typically we use around 5 angstrom so here I must mention to you that when I want to use long wavelength neutrons the fact is that earlier I discussed with you in the general field that my intensity as a function of energy so as an energy goes up lambda goes down so lambda comes in this direction and as it goes in this direction I have a maximum now if I want to go to longer wavelength then I need to it is better if I can modify the spectrum using a cold neutron source cold neutron source cold neutron source is a cold moderator kept inside the reactor that re-thermalizes this flux to lower energies the area remains more or less same maybe slightly less but you see an increase in the number of neutrons with longer wavelength because for small angle neutron scattering we need longer wavelength neutrons so like I talked to earlier when liquid and amorphous system when I needed to go to very large q values I went to very short lambda and a spallation neutron source an ideal place to do such experiments because they are the neutrons are inherently produced with very high energy similarly for cold neutron sources because it's a reactor and we use a cryogenic moderator inside the reactor we have better cold neutrons and small angle neutrons scattering are restrained in reactor based sources