 So, now I have come to a very important part of a neutron spectrometer known as monochromators. As you can see in this diagram above that as I showed you earlier there is a collimator in the beam path in pile collimator and then it is followed by a monochromator. This monochromator actually this is a polychromatic beam which is falling on the monochromator what goes out is a monochromatic beam monochromatic coat within coats how good monochromatic beam it is that I'll discuss now and this whole circle you see this is the monochromator drum at the center of this monochromator drum is the monochromator and this spectrometer was the design by BN Brock house is triple axis beam you can rotate the monochromator and the whole spectrometer rotates around it including the sample including the analyzer and including the detector. Now so by rotating the monochromator you can choose a different lambda the sample is here and the sample scatters the beam now there are options you have got an analyzer if you have an analyzer in the beam path then you can also keeping the rest of the things fixed you can rotate the analyzer and you can do an analysis of the scattered beams energy before it goes to a detector. I must mention that neutron detectors cannot distinguish energy of neutron because neutron has to be converted to some other radiation before it is detected and I just show that you have choices of having a position sensitive detector or a end-on detector this we'll discuss later but the fact is if I take out the analyzer part then I have a situation where I have the sample which has scattered the beam but after the beam I have not put any analyzer so I have an incident beam in an elastic scattering so either you can end on detectors as I showed you this is not the way it is actually earlier days a single detector moves from one position to another to another and that is how the scattered beam is monitored and counted and it takes longer time so today we have got something called position sensitive detector these red straight lines so the beauty is that with these detectors you know at which point the detector has hit and once you know the point doing the distance from the sample you can find out the angle of scattering so in one shot you can collect the data unlike the previous case where you do end on collecting collecting data over time serially so this is sort of a parallel processing all the data at the same time so as I told you that this is elastic but the more generally you have got three axis monochromotor sample analyzer three axis that's what it was called a triple axis spectrometer so we have a triple axis spectrometer where the first you have the monochromotor axis followed by the sample axis followed by the analyzer axis triple axis spectrometer this is what was done by BN Brockhouse and he got Nobel Prize for his studies on because this is for inlass scattering experiment because you know the energy of the incoming beam and after analyzer you know the this is decided to the k prime outgoing and these also tells me of what energy finally prime k prime so this is the measurement which I to discuss to earlier this is what due to sigma d omega d e is for inlass scattering which goes on which is done for getting the dynamical processes in the system at various time scales but if I take out the last leg and if it is just a sample and followed by a detector now the detector earlier this was rotated serially as I told you with an end on position at different times it rotated around the sample today we have position sensitive detectors so the need of rotation goes away and this is the typical detector to measure d sigma d omega so this is for structure work structure at various length scales and these are also integration equals a integration over sq omega d omega so this is gives you i q zero instantaneous picture I hope you remember when I discussed the correlations for various kinds of correlations in case of neutron scattering so now we have reached an important point where we have reached the monochromators so now I have to discuss wow how to monochromatize the beam very simple answer the monochromatization is not a difficult task you know that we use 2d sin theta equal to n lambda on the maxillian spectrum and we choose a particular wavelength for experiments and of course here I have shown typical neutron scattering setup monochromator you can also use a filter instead of a monochromator you can use a filter where I use a filtered beam for a low resolution experiment and then you can look at the analyzer and look at the detector so this is also one possible configuration I want to show you so this collimator and then filter does the filtering of neutron beams as I showed you like beryllium filter filters out the low energy neutrons or you can even use a monochromator beam monochromator which chooses one particular wavelength which is usually done most of the experiments and I will come to them later when I specifically discuss the various facilities so this is what you have so now you use crystal to monochromatize the typical monochromators that are used by Lister or some of them copper beryllium pg or pyrolytic graphite is very common germanium single crystal silicon they easily available we also have magnetic monochromators this oyster alive is a monochromator come polarizer so not only monochromatizes the neutron beam it also chooses one particular polarization of the neutron beam I will complete later how it does I just want to put it here in the list of the monochromators now the angle and the plane that we choose depends on the wavelength that's clear because I have to get 2d sin theta equal to lambda and I need to choose the right d to get the lambda that I need for my experiment now should we use perfect single crystals now I have drawn it to vertical blocks you see if I use a perfect single crystal a perfect single crystal means you have one very specific plane which satisfies 2d sin theta equal to lambda so it gives out only a narrow slice of the neutron beam so suddenly it gives a monochromatic beam but you also have the added requirement that you need neutrons because already your neutron beams as I told you down by a factor of 10 to the power 7 to 10 to the power 8 as it came out from the reactor beam line now you are monochromatizing it but then you have a competing interest you need a monochromatic beam but you also need a large number of neutrons to do your experiments so how to have that dual purposes of so what we do need actually I need a larger slice of this beam so what I mean to say if I put a single crystal this is a maxillian which has come out from the reactor if I use a perfect single crystal I have a perfect so almost like a delta function in energy which will be scattered out by the beam only this much of neutron beams I will have but what I need actually more number of neutrons so that means I have I need a E plus minus D E delta E but of course immediately the question comes immediately my lambda becomes undefined lambda plus minus delta lambda because delta I will add to the uncertainty of the wavelength yes I'm ready to accept uncertainty at the cost of at the cost of resolution well I also need more number of neutrons so every experiment is a design where you have a compromise between resolution and intensity so I want intensity I also want to have resolution reasonably good so I have to make a compromise between these two by taking a larger slice of beam but how do I take a larger slice of beam from the maxillian that is a question and that is done by that is done by a mosaic crystal so I tried to show you how a mosaic crystal works a mosaic a single crystal will have a narrow beam going in and just one beam going out a mosaic crystal is one which has got crystallites which are perfect in themselves these are the crystallized various colors you see this blue red yellow these are the crystallites but now they are slightly oriented with respect to each other so the way it can be done actually you take a perfect crystal and you can hot press it that means you take it to a higher temperature and then press it and then it will introduce grain in the system there will be grain boundaries and you can have slightly misoriented uh note my words slightly misoriented crystallize in that case when the beam comes false if I take a single polychromatic beam with a single direction the outgoing beam because some of them will scatter at a lower angle some of them will scatter them at a higher angle and you have a range of angles and a range of lambda in the outgoing beam which is desirable so we use mosaic crystal and hot pressure technique similarly we can also use bent single crystals I'll come to that so I just show you that if you have a flat perfect crystal in that case a 2 dhkl sin theta is equal to lambda you have only a parallel outgoing beam of single wavelength in a mosaic crystal you have a parallel beam coming but since there is some angular variation in the planes that are offered to the incoming beam please remember this is a polychromatic beam so the angle becomes slightly different when sin theta theta becomes slightly different you choose another lambda from the beam at slightly different angle so you have got excuse me is around 20 to 30 arc millis 30 arc millis half a degree so you have got a resolution compromise but you gain in intensity using a mosaic crystal another way of increasing this angular width is to use a perfect crystal but to bend it now you see if this is a bent crystal look at it from left to right the parallel beam falls here here the angle of incidence is small here the angle of incidence is large so it focuses the beam it's true it's like a mirror it is like a elliptic mirror which focuses the beam but it also gives you larger spread in lambda that means more intensity that means it makes some compromise on the resolution to give me intensity so instead of flat perfect crystal I will tend to use either mosaic crystals or bent perfect crystals both of these help me to gain in intensity at the cost of so if it is a perfect single crystal you have only one angle going out perfect and from this polychromatic beam this beam is polychromatic the direction has been fixed by your in the solar collimator but now direction is fixed but there are many energies I want to choose one it chooses only one which I don't want because it is too narrow just one so now I have a mosaic crystal as I showed you in case of mosaic crystal there are lots of small crystallites inside this so this beam is polychromatic directional this direction becomes slightly uncertain so I have this gives me a delta lambda a larger slice from this from this max volume so my number gets enhanced I make some compromise on the wavelength resolution and also on the d resolution because when I'm doing brag diffraction your delta d by d is the subject of interest for us how good we can resolve our d spacing and that depends on not only delta e it also depends on delta theta also I can use a bent crystal when I put a parallel beam on a bent crystal you can see the angle here is small and the angle here is large so you have got a focusing effect large angle and the divergence increases for the beam and again it gives you a delta e desirable delta e so these are the tricks for the mosaic crystal that one uses to improve the intensity in the beam at the cost of resolution so I have now I am just showing you photo of a very fine germanium crystal slices are used you can see this photograph it will make you some I show you this because this will give you some idea this height is almost 20 25 centimeters and each point there was stuck a single crystal which is bent so basically here this curvature that you see is in the vertical plane that means in the vertical plane it is curved like this and you can see that the beam gets reflected onto the samples and it focuses the beam so it makes the beam size smaller it makes a compromise on the angle and now in the and as I told you with the here the resolution is not compromised because you are doing the focusing in the vertical plane but you are doing the experiment in the horizontal plane so you gain in intensity using these germanium crystals but you get high resolution data in the horizontal plane so this is this large beam because neutron beam is large you want to use a smaller sample size that's often the need because it is very difficult to grow large quantity of samples especially if the samples are novel and you need to get data from them then this is one way which is being done this is in UK also I will show you open Australia in the reactor here these are hot press germanium so they have been made a vertical stack of this germanium each one has hot press that means they have a lot of mosaic spread in them so first you make the vertical focusing so you reduce the size of the beam and then there is mosaic spread so you also have delta lambda you get more intensity so this is in opal australia they have this hot press germanium monochromators and there as I showed you that this is a horizontally and vertically focusing monochromators all these sizes are typically 15 to 20 centimeters the large assemblies ultimately the beam size can be as low as 1 centimeter square you can see that they're actively controlled double focusing monochromators consisting of an area of 315 pyrodynamic graphite crystals this is at NIST USA so monochromators possibly a single most very important component in our beam path so now let me come to the fact that we I talked to you about beam tailoring inside the reactor and the target after the beam tailoring how they are transported out so I talked about beam holes beam lines and the guides and after we have brought them to the beam I talked to you about various collimeters and filters that are put in the beam path and at the end I have talked to you about how you get a monochromatic slice from a polychromatic beam using these techniques in the next lecture I will discuss with you the role of detector and monitor counters in neutron experiments and then we will get into real experiments with our samples