 So I stopped with an example of simultaneous minimization of chi-square for nickel titanium bilion film and I justified the use of genetic algorithm for such minimization. I will now take you for a tour through the various instruments available for such experiments. Let me just show you the instrument that we have at Dhruva at Trombay India. So this is the guide tube where the neutrons are coming flowing down the guide tube if I may say so in this direction. And I had shown you earlier there is a small-angle machine, two small-angle instruments on this guide. At this gap we have what is known as a PNR or polarized neutron reflectometer. This is the whole instrument is kept inside a shielding pit because as I told you earlier that reflected intensity falls as 1 by Q to the power 4 with angle. That means it falls very rapidly reflected intensity. And we need to minimize the background at the detector to the extent possible. For this instrument I will quickly show you this is the instrument. So here is a closer look. So the guide neutrons are flowing down in this direction. We have got a silicon monochromator sitting at the guide path which diverges the beam in this direction. And by S1 and S2 I mean two collimeters, two slits which make a collimator to collimate the beam to few walk seconds because we need to have a narrow beam for reflectivity experiment. And there is a super mirror polarizer here. I will shortly narrate to what is a super mirror and how it works as a super mirror polarizer. This instrument is meant for a vertical sample. So there is a magnetic field here. These are the pole shoes for the permanent magnet and the sample is vertical. And here there is a position-sensitive detector. So we reach the detector after an analyzer which at the moment we don't use, we don't analyze the beam reflected by the sample. And this position-sensitive detector arrays the reflected beam on it as per channel. So it looks somewhat like this. I have just shown you this point. Each experimental point at Q space or it is as per angle, but each point is actually an integration over such an intensity profile on the position-sensitive detector. And so each point is an integration over such values of reflected intensity after subtracting the background. So we also take the background as channel-wise on the PhD after closing down the sample with a cadmium sleeve. Cadmium is a strong neutron absorber, so we don't allow anything to come from the sample onto the detector and then we do the background measurements. So that tells me how many neutrons are there, stray neutrons are there in the guide hall. It's much smaller than what we have in the reactor hall and we have given the specifications here. At the moment these specifications have slightly changed. The wavelength we have gone up to 3 angstrom. It's a COA-efficient titanium-zirconium super mirror. We also have a non-polarized super mirror. The detector is a linear helium-3 detector. And we have got a DC flipper, neutron beam flipper with an efficiency of 92%. And we have a 2 kilo Gauss permanent field on the sample to magnetize the sample. Usually thin fields have low saturation magnetization in their hysteresis loops, if I may show you hysteresis loops. And generally we expect for magnetic moment density, we should saturate the thin film so that the magnetization is aligned in one direction and we can measure the magnetic moment density from a magnetized sample. Now this is a schematic of the same instrument. So the guide gives a monochromator, gives a beam out. Then there's a polarizer, non-polarizer super mirror. So it can polarize the beam. Then there's a DC flipper. So I can get one particular polarization after reflection from the super mirror. And then after that I can flip it to 180 degree away. So on the sample I can have either up or down polarization neutrons which is either parallel or anti-parallel to the magnetization in the sample. This analyzer super mirror we generally don't use because of intensity restriction. Our source in Drouwer is a low intensity source. So often it is not used. What we get from such experiment is magnetic moment density. If I do polarization analysis after the sample, then we can get the magnetic structure. I will give you an example later. The position sensitive detector allows me to look at the specular reflectivity. It can also help me to collect data in off-specular mode if I look at the structure of the peaks that I showed you here. And then I can also get off-specular intensity. That's an advantage of using the position sensitive detector. But otherwise this instrument is a step scan instrument, step scan. It is not unlike what I showed you earlier for the diffraction instrument that you collect the data in one shot. Here the sample is rotated around the beam in theta direction. And if this is the position sensitive detector normal to the beam, the reflected intensity moves channel-wise on the detector. And each integrated peak is one intensity in the reflectivity profile, one intensity in the reflectivity profile. So it's a step scan instrument, but the use of PSD helps us to collect off-specular data. I will use some examples later. I just now talked about a neutron super mirror. What is a neutron super mirror? Now I will explain to you what is a neutron super mirror. Let us consider, let's magnetize nickel film. So as I told you earlier that for positive and negative direction of a neutron beam, it sees different potentials for plus and minus neutrons, so different critical angles. For a single film, if I consider theta, then we have two different critical angles. And theta critical angle is given by root over lambda root over pi B coherent plus minus B magnetic. Sorry, I am mistaken, by pi, root B coherent plus minus B magnetic by pi, we have two critical angles. This is for a single film. Now then there is an idea that if I have a bilayer of a magnetic and non-magnetic materials, then let us say I have got a periodic bilayer of let us say nickel and silicon. Nickel is magnetic, silicon is non-magnetic, it's a periodic bilayer. In that case, apart from the critical angle for nickel, I will also have a Bragg peak depending on the periodicity. At a Q value, which is commensurate with D spacing because twice pi by D nickel plus D silicon will tell us where this Bragg peak will be. Now this is a periodic bilayer with one periodicity. Now the interesting thing is that if I can keep changing the periodicity, that means when I am depositing this multi-layer film, I keep changing the periodicity by changing the thickness of nickel and silicon layers. So let us say here for here it is D1, here it is D2, then it is D3. I continuously keep changing. So I might consider this. This is also periodic bilayer with varying thickness. Now when I use a varying thickness, then the Q value or the angle for the Bragg peak keeps shifting. And if I keep on going to thicker and thicker film, this Bragg peak will go to lower and lower theta. So with the multi-layer with varying thickness, I have got a number of Bragg peaks and as I keep on increasing the thickness from a certain value to a certain other D1 to D2, both for nickel and silicon, the Bragg peak position keeps varying and ultimately what I get is intensity versus theta I will put. If nickel was falling somewhere here, now because of these overlapping Bragg peaks, because they are finite films, overlapping Bragg peaks have extended the critical angle. And that's why it is called a super mirror. A nickel film possibly will reflect, total external reflection will take place up to a certain angle. This angle is extended by using a periodic bilayer with varying thickness. Now this is possible because neutron is transparent. Most media are transparent to neutrons. So neutrons can penetrate deeply and I can get a structure like this. So this is a neutron super mirror. Now the next step, now neutron super mirror is consisting of magnetic and non-magnetic materials and I can magnetize the mirror and then this same intensity pattern, either theta or q, if this is for positive then for negative the critical angle can be low. So now this intensity tells me that the positive or up neutron because it sees a larger v because this is twice pi h squared by m rho b coherent plus bm. This critical angle for magnetic one will be large and now it is a varying thickness periodic bilayer. So plus will have a large critical angle and minus will have a smaller critical angle and this is the angle. So if I use an angle to reflect the neutron beam which is between theta c if I may call it plus and theta c minus, then this let us say this angle then at this angle this neutron doesn't get reflected. The negative neutron has got a reflectivity zero whereas here the reflectivity is almost one. So that means by reflection of an unpolarized beam at an angle between these two it will give me a polarized beam reflected and the transmitted beam will be other polarization. So this is not only reflecting the neutron beam it is also polarizing the neutron beam and this is called a super mirror polarizer. So I started describing to you how neutron reflective reflection takes place and now I show a device based on the principle of reflection which can polarize a neutron beam and these super mirror polarizers are commercial items available and used heavily for various neutron instrumentation only that I will be showing you that we have used. Let me just show you the reflectivity profile obtained from this source of m equal to 4 iron silicon super mirror. Now what is m equal to 4? Usually super mirrors I will write it as Sn are compared with nickel critical angle. Nickel has a critical angle 6 arc minutes per angstrom. What does it mean? As I showed you the critical angle is greatly proportional to if I as I wrote earlier that critical angle is proportional to lambda. So that means and this and nickel has critical angle 6 arc minutes per angstrom. So that means if I have a one angstrom neutron the critical will be 6 arc minutes. If I have a 4 angstrom neutron the critical angle will be 24 arc minutes. So this is what means by 6 arc minutes per angstrom and now this mirror is m equal to 4. That means this has a critical angle for all wavelength which is 4 times that of nickel. That means if I use a 4 angstrom neutron on this super mirror the critical angle will be 24 into 4 that is 96 arc minutes. That means 1 degree and 36 arc minutes 1 and half degree. So this is the reflectivity plot of course this in linear range because to show that where the other reflectivity minus falls to 0. So this is reflectivity curve this is the m value given. So you can see this m equal to 4 the reflectivity intensity for one polarization is almost 80% not exactly 180%. So that is good enough if I reflect I get 80% of the beam reflected but because the minus neutrons the down neutrons their reflectivity is falling over here. Any angle in this range in this range for reflecting my neutrons will give me a polarized beam and the polarization efficiency is also plotted is almost 99%. So I will get a 99% polarized neutron beam of up neutrons if I use a reflection angle which is qz value between these two and qz equal to 4 pi by lambda sin theta. So I can calculate the theta for this this will as I showed you that for it can go up to one and half degrees and that's why it's called a super mirror. And these are commercially available iron silicon super mirror the reflectivity plot is from this source. So we use neutron super mirrors heavily for all our instruments. So now I give you the schematic I showed you the schematic of the reflectometer at Dhruva. Now I show you the typical general reflectivity reflectometer designs at ISIS this is from the source. So you have a source and the slits collimate the beam there is a monitor and again there is a position sensitive detector arresting the beam because this is a polychromatic source. So in one setting I can get a large range of q and I also mentioned that if I go by time of flight plot I would like to mention to you that the reflectivity profile if I measure it as a function of time of flight intensity. Suppose I am taking talking about the single field then it will look somewhat like this. The other key is the oscillation because time of flight large means this is large lambda and large lambda is small q. So this is just the mirror image or rather if I look at a reflectivity plot in a reactor source the same thing will look like this intensity versus q. So if this one is viewed from the backside of the page if I could if you can go to the back of the board you will get this pattern this is just for information. The intensity reflected intensity in a time of flight plot will look like this and in q plot in the reactor this is a reactor this is a spallation source they look a mirror image of each other in reflectivity profile.