Hello everyone, in today's class on advanced characterization techniques, we are going to study a few things about properties of neutron radiation and neutron sources. Up till now in this course or rather this module of the course, we have been dealing with mostly X-ray diffraction and electron diffraction, but now we are going to look at a different class of radiation that is neutron diffraction. So all of us are aware what exactly are neutrons. So we know that neutrons are essentially subatomic particles which are there sitting in the nucleus along with the protons. These particles are characterized with no charge and have mass which is equal to 1.675 into 10 to the power minus 27 kg. We are also aware that this mass of neutron is slightly higher than that of protons. Now in addition to the mass, neutrons are also characterized with a spin of half and nuclear magnetic dipole moment of 1.913 times that of a nuclear magneton which is approximately equal to about 5.05 into 10 to the power minus 27 joule per tesla. So having said that, we know that neutron as such is a very different subatomic particle when compared to proton and an electron. Now with the exception of hydrogen one, all atoms consist of neutrons and protons. In fact the neutrons bind the protons together in the nucleus because the protons with all their positive charges have a tendency of repelling each other. The neutrons actually act as glue that holds all the protons together in the nucleus. Having said that, we are also aware that for the same atom we can have a situation wherein the number of neutrons are different in the nucleus and such kind of atoms are actually known as isotopes. One of the classical example of an isotope is the carbon 12 and carbon 14 isotope wherein we know that the carbon 12 isotope is actually characterized by 6 protons and 6 neutrons. While the carbon 14 isotope that we are having has 6 protons but in this case we have 8 neutrons. So moving ahead, we also know that the bound neutrons in the nucleus are absolutely unstable. However the unbound neutrons which are just not associated with the nucleus are highly unstable. Well what exactly I mean when I say that they are unstable? Well the neutrons undergo what is known as beta decay. What happens in a beta decay is that a neutron gets transformed into a proton, an electron and an electron anti-neutrinole. Let us not get into nuclear physics but for the time being and assume or rather understand that it is not possible to have unbound neutrons as a source for carrying out diffraction or neutron scattering experiments. Therefore another important point that needs to be noted that all this dissociation or decay mechanism that I told ensures that the lifetime of the neutrons is only about 15 minutes and therefore it is necessary to produce neutrons as and when required. Coming back how to produce neutrons? Well we can always produce them using nuclear fission as well as nuclear fusion. I am not going to talk much about fusion and fusion but let us talk about neutrons as a particle. We know that neutrons are subatomic particles and quantum mechanically they show wave particle behavior. So for a neutron travelling at a particular velocity we can always assign a particular wavelength and treat it as a wave with that particular wavelength according to the deep Broglie wavelength criteria. Now the beauty about neutrons as a source for carrying out diffraction or scattering is essentially that the velocity at which the neutrons travel when combined with their mass essentially ensures that the kind of wavelength that we are going to get is of the order of hang strong which falls in the range of that of x-rays and this is what ensures that we can use neutrons for carrying out diffraction experiments where also the inter atomic or rather inter planar distances are of the order of few angstroms. But when compared to x-rays neutrons offer much better penetration depth and that is essentially because neutrons essentially interact with the nucleus of that. Now if you look and consider atom the nucleus occupies a much smaller region compared to the entire at size of the atom because most of the region is occupied by the electron cloud having said that this ensures that the neutrons have a much better penetration depth compared to x-rays and it can be as high as a few millimeter in materials with high density. As I had already mentioned this is essentially due to the fact that neutrons see or rather feel only the nucleus and not the electron crowd. So they travel essentially through a very open structure compared to x-rays or electron that see or rather interact with the electron cloud. The same philosophy or the same concept is shown over here in this figure. So if you look at a free surface over here and consist and consider it comprises of all these atoms with the dark spot at the center being the nucleus and the electron cloud surrounding it. You see that the neutrons actually interact with the nucleus and it can undergo diffraction or scattering. While the x-rays interact with the outer electrons and it undergoes x-ray scattering or diffraction. Therefore we can assume that the probability of x-rays interacting with an atom is much higher than that of a neutron and therefore the penetration depth of neutrons is much higher than that of x-rays. Having said that neutrons also have a tendency to interact with the dipole mind you we had talked that you know neutrons have a particular spin and a magnetic dipole moment associated with it and therefore the neutrons can interact with free electrons that also have a dipole moment and this dipole-dipole interaction can give us information about magnetic scattering or diffraction. I will like to bring to your notice that neutron diffraction is probably one of the most sophisticated technique that can give us some information about the magnetic structure of the material. Having said that let us try to understand how exactly diffraction takes place when neutrons are used as a source. Well the concept is exactly similar to that of x-rays. Only thing is instead of x-rays getting bounced off from the outer part of the atom we have neutrons which get bounced off or rather reflected from the nucleus of the atom. Therefore we get a interference pattern very similar to that of x-rays or electrons. The diffraction theory for x-rays and electrons can be easily extended to that of neutrons and therefore the scattering and diffraction principles that we employ for x-rays and electrons can be borrowed one to one for neutrons also. This actually ensures that Bragg's law is valid for neutron diffraction and that we can carry out all the x-ray diffraction and scattering techniques that we talked about using neutrons. However as I had already mentioned one of the best property of neutrons that is on offer which is not there for electrons and x-rays is that they can give us information about the magnetic structure. Now this information is not given either by x-rays or electrons but neutrons can offer us information regarding the magnetic structure of the material under consideration in addition to the crystal structure. So now when it comes to generation of neutrons so we had talked how we generate x-rays different ways of generating x-rays similarly neutrons also can be generated in different ways. Essentially we have to draw off the neutrons from the nucleus of the atom and this can be done using a fission reactor. In a fission reactor we use a neutron source like radio isotope californium 252. Now this releases neutrons which are bombarded on a U-235 nuclei. This leads to fission of the uranium nuclei and release of neutrons. Now with the use of proper moderator we can control the number of neutrons that are released and this can act as a continuous source of neutrons. Another important way of producing neutrons is using what is known as a spallation source in which case we use synchrotron to accelerate protons to very high energy of the order of giga electron volt range and focus this beam on depleted uranium target or these days the most favored target is tantalum which ensures that neutrons actually fall off or rather fall off from this material that is from uranium target or tantalum target giving a pulsed source of neutrons. I would like to mention that a fission reactor can be used for producing nuclear fuel and therefore in most countries it is generally not used for academic activities. However a spallation source is more appropriate and most of the time is used regularly. However one of the biggest problem with spallation source is that it produces a lot of radioactive waste that means that comes from the target material. So once the accelerated protons hit the uranium or tantalum target and gives out neutrons the left over material is highly radioactive. So this is one of the drawbacks of the spallation source but having said that depending on the kind of energy that we have we can have neutrons into different neutrons can be classified into different regimes. So if you look at hot neutrons, hot neutrons are moderated at 2000 degree centigrade. They have energy range of about 0.1 to 0.5 electron volt wavelength of about 0.3 to 1 angstrom and travel at a velocity of 10000 meter per second. There are thermal neutrons which are moderated at about 40 degree centigrade. They have energy range of the order of 0.01 to 0.1 electron volt wavelength of the order of 1 to 4 angstrom and travel at a velocity of 2000 meter per second. Mind you I hope you have noticed that the thermal neutrons probably are the most important neutrons because look at the wavelength. Their wavelength is of the order of x-rays that we use in a laboratory. Having said that look at the energy level that we are having. The energy level is of the order of one tenth to one hundredth of an electron volt that is in the range of a few milli electron volt. In order to produce the same wavelength if you remember you are using a voltage of the order of kilo electron volt when it came to x-rays. So I hope this point is very well taken that we can get the same wavelength of neutrons at a much lower energy level. Now there are also what are known as cold neutrons. So these cold neutrons are actually moderated at 2000 degree centigrade and they have energy which is lower than 0.01 electron volt and a wavelength of the order of 0 to 40 angstrom and travel at a speed of 200 meter per second. So most of the cases that we will talk mostly will focus since we are keeping x-rays and electrons as our focus I will talk mostly about thermal neutrons which form in the same range as that of our x-rays. So from all these sources how what is the kind of spectrum like what is the kind of neutrons that we get? Do we get neutrons of same frequency and energy or a different energy? Well like x-rays also we get you know we have continuous spectrum and we have a characteristic peak not here for neutron. In case of neutrons if you look at the intensity versus wavelength plot we see that the neutrons follow a Maxwell distribution which is being depicted over here. Most of the times we do not need a wide range of energy distribution and therefore we use monochromators to you know choose only a wavelength of our interest and use it for further use. Now one of the most important part like which we had talked about during x-ray as well as electron diffraction is actually the scattering cross section. The scattering cross section essentially defines the probability of scattering event between neutrons and nucleus for a plane wave ikz a scattered wave which is f of theta and phi and is multiplied with e raised to the power ikr by r. Now this gives us the scattering probability right if you remember this is exactly similar to what we had for x-rays and this term f of theta phi is nothing but equivalent to the structure factor that we had used in case of x-rays. So the differential cross section if you are about to calculate is d sigma by d omega which is nothing but proportional to square of the structure factor. Now this is nothing but you know the intensity that we get you remember in x-rays we had also talked about this is just a change in terminology but in case of x-rays we had this intensity proportional to the f square. Now if you go for integral cross section which is nothing but you know you integrate this differential cross section so which is sigma is equal to integral d sigma of d omega by d omega this d omega is the solid angle we will talk about it in a later slide but this essentially gives us a measure of effective surface area seen by impinging particles. So the affected area presented by nucleus to an incident neutron is actually represented in terms of a bar which is nothing but a unit of area and one bar is equal to 10 into minus 27 meter square having said that another important point that needs to be noted is that once the neutrons are traveling and they interact with matter they are going to get attenuated that means their velocity is going to change and therefore the attenuation is given as exponential minus n sigma t where n is the number of atoms per unit volume and t is the thickness. So the cross sectional is proportional to the square of structure factor now this is very important in determining the intensity of the diffracted beam. Coming back again the reason we are talking so much about neutron cross section is actually because of the wave nature and particle nature. So here you know neutrons can also be considered as particle nature while in case of x-rays we just ensured that you know intensity is proportional to the structure the square of the structure factor. Having said that this will be more clear with this drawing over here wherein you see we have incident neutrons which are coming over here and this is the target we see that how the neutrons get diffracted in a particular direction. So if at all we have a neutron flux of phi which is nothing but the number of neutron per unit area per time and the sigma is the total number of neutrons scattered per second per for incident flux of phi. So our d sigma by d omega where d omega is the solid angle that is covering is actually the number of neutrons scattered per second into d omega and this is for phi d phi isn't it and therefore our d sigma by d phi is nothing but the number of neutrons scattered per second into d omega in a energy range of about dE. So we see that we have incident and what is the probability of neutrons getting diffracted so this is nothing but the fraction of neutrons that are getting diffracted in a particular direction omega. So this is nothing but your neutron cross section and this is absolutely proportional or rather directly proportional to the square of the structure factor. So let us talk as I had already mentioned that you know the neutrons actually interact with the nucleus of the atom and not with the electron crowd. So if you look at the nucleus you know that there is a nuclear force associated with the nucleus. Now the range of the nuclear force is very small and of the order of few centimeters. We are also aware that the kind of wavelength that we are using for neutrons is of the order of few angstroms. Therefore we have a situation where the wavelength of the neutrons is much much larger than the range of the nuclear force. Therefore the energy of the neutron is much much lower than the energy of the nucleus and this ensures that there is no energy transfer between neutron and nucleus. This actually ensures that once you have a neutron interacting with a nucleus it does not lose its energy and therefore all the scattering and diffraction phenomena that are occurring are essentially elastic. The wavelength as I had already mentioned is actually decided by the velocity because lambda is equal to h divided by the momentum which is nothing but mv. So the velocity of the neutrons does not change. However their angle the d omega part right in the last slide we had talked about may change. So the scattering is far from nuclear resonance and there is no absorption of neutrons in during interaction of a neutron with the nucleus of an atom. A schematic diagram of the same is shown over here where we have this incident beam of planar neutron beam right and here we see that the number of neutrons per area ds per second after scattering is vds phi scattering square. This is again your wave equation which is squared that gives you the intensity ds is the area and v is the velocity. So at the end of the day we end up getting equal to va square d omega where d omega is the angle it is not been shown over here but see it is a solid angle right and a you know that the scattered circular wave as equation of minus a by r e raise to the power ikr right. So now the number of incident neutrons per unit area ds which is your phi right is nothing but v psi incident square which is nothing but equal to v and the cross section d sigma by d omega is equal to a square right. So depending on the scattered circular wave amplitude okay we are going to get the d sigma by d omega and as you can see the total scattered neutron is nothing but in a solid angle right once you integrate you get 4 pi a square right this is where this term is very similar to that of the surface area of the sphere okay so we are considering all spherical waves. So the point is I would like to repeat again that the neutron cross section is actually proportional to the square of the amplitude right like this is what we got even for x raise only thing is we are trying to derive it in a slightly different way because here we are going instead of having a wave approximation we are trying to explain the same thing using a particle approximation having said that at the end of the day we end up getting the same solution right. So in x raise or for that matter in electrons right like electrons we talked about coherent scattering and coherent scattering. So the actual scattering length right for neutrons with the nucleus is actually given say by a i which is nothing but a plus delta a i now this the delta a i essentially indicates a random component right so the random component of scattering vector contributes to incoherent scattering. So the contribution of a this summation of a or other bracket of a actually corresponds to elastic while this delta a i corresponds to in elastic scattering. Now the information about collective motion and relative position of the nuclei is given by coherent scattering so this is very similar to what we are having right like where your atoms are sitting that means where your nuclei are sitting and where your neutrons are getting interacted are interacting with this with the nucleus and getting scattered. So this is because of coherent scattering however we also know we have seen this Debye-Waller like term that you know at only at 0 Kelvin all the atoms are sitting at their own place in the unit cell in fact at any temperature other than 0 they are actually vibrating right. So we actually get a motion of individual nucleus and that actually leads to incoherent scattering. Now this contributes actually to this delta a i term. Now this term is slightly different than the Debye-Waller term because that is taken care of but any small perturbation in the nucleus is actually captured using incoherent scattering. To just give you an example I will mention that you have cross sections associated with both coherent as well as incoherent scattering having said that a classical example is that of a hydrogen which has a very low coherent scattering cross section and therefore cannot be detected using normal coherent scattering neutron experiments. However it has very nice or rather very high incoherent scattering cross section therefore if you want to study diffraction experiments mostly hydrogen is replaced with deuterium which has a very good rather a very high elastic or rather coherent scattering cross section but has very poor incoherent scattering cross section. So this way you can see that we can use different kind of scattering events namely coherent and incoherent to detect the presence of a particular element or rather to be more precise a particular isotope in neutron scattering or diffraction. Mind you if you want to study diffraction where we need to carry out which corresponds to coherent scattering we have to use material or like we will get better signal for deuterium. Therefore people who work on ice most of which is H2O solid H2O actually replace hydrogen with deuterium to carry out neutron diffraction studies to determine the crystallographic texture while if some if you are more interested in studying the spectroscopic aspect of it we can always use hydrogen having said that another important aspect with neutron diffraction if you remember for x-ray diffraction which x-ray diffraction does not have to offer is the scattering cross section. So if you remember we had the scattering cross section or rather the intensity was proportional to f square in case of x-rays and f was nothing but it was your atomic number. So it is not possible to differentiate between two elements which are very close to each other in the periodic table. However look what happens when we look at neutron cross section which is given over here in terms of scattering length we see that two atoms or like two elements which are very close to each other have very different right you see aluminum and chlorine they have quite a different scattering cross section this essentially ensures that we can easily separate out these two elements which are very close in periodic table using neutron diffraction. At the same time we also see that we get information about the magnetic cross section also so you see here we have nickel 62 here and we have another nickel so the scattering cross section for nickel and the magnetic cross section they are two different so we can actually find out where our nickel atom is sitting and where the magnetic moment is sitting right ditto for cobalt and you see here for different isotopes of nickel you see the huge amount of difference in the scattering cross section. Now this information is offered only and only by neutron diffraction the similar information is presented in a very nice way over here so we can see here the x-ray relative scattering length we see hydrogen is small carbon as it moves as a function of z. However when we look at neutron we see that there is no one to one correspondence between z that is atomic number and the scattering length okay and see we can easily separate out between adjoining elements. Taking forward our comparison between neutrons and x-rays we have seen that neutrons actually behave like particle and wave while x-rays are actually electromagnetic wave. Now neutrons have a mass associated with it while x-rays have no mass associated with them neutrons have a spin of half while x-rays have a spin of one or they have a magnetic dipole moment while x-rays have no magnetic dipole moment the neutrons actually interact with the nucleus while the x-rays interact the electron cloud. Now neutrons are scattering power independent of 2 theta which has been shown over here so you see what happens the intensity versus sin theta well it is almost a straight line well it is always a straight line because it is not dependent on the angle while when we talk about x-rays we know that this value decreases remember we had seen this f versus sin theta value how it was decreasing it started from z and it was reducing continuously as a function of theta not so for neutrons. Now neutrons with their kind of energy they have and since they interact only with the neutrons have very low absorption while x-rays get absorbed a lot but there is a problem since neutron interaction is weak we need large amount of sample while with x-rays we can live with small amount of sample. Now in neutrons the neighbors as well as isotopes can be easily discriminated while for x-rays the neighbors isotopes there is no way we can see isotopes neighbors the discrimination is very very difficult. The detection of light element is very difficult in x-rays while it can be done on a routine basis in neutrons. One of the biggest USBs of neutrons is that it can be used to determine the magnetic structure while no magnetic structure information is obtained from x-ray diffraction as we had already seen that the neutron is a very weak source or rather a very weak probe but this is not a disadvantage because a weaker probe ensures that the kind of interaction that we are seeing is not because of an artifact or any change in the state of the matter that we are studying. I would like to mention that the x-rays are intense source and by the when I say intense I am not really talking about synchrotron but even a normal x-ray laboratory source is almost 1000 times brighter than a neutron source. Having said that you should always remember that neutron source are not available every at every place and in fact they are very there are hardly a few places in the world while x-ray sources and x-ray diffractometers are available at every university and therefore can be used on a day to day basis. Just to show you the but having said that you know it is not like x-rays are good and neutrons are bad. In fact these two techniques are completely complementary to each other and this particular slide kind of encompasses the basic you know complementary nature of both the techniques. So look at different elements we have shown different elements over here and see how the neutron cross section and the x-ray cross section varies. So you see that materials with high x-ray cross section have low neutron cross section. Therefore you can see that if there is a situation where we have material with high x-ray cross section and high neutron cross section at the same time we can always use x-ray and neutron diffraction or scattering technique to complement and get complete information from the sample under investigation. Now just to compile what are the advantages of neutrons over x-rays well both of them have comparable wavelength in the angstrom level. However the energy of neutrons is much lower. The neutron lower energy as I had already mentioned ensures that there is no harm to the sample there is no damage to the sample. The interaction of neutrons with the sample is more of that of a what happens you know ping-pong ball like which gets trash from one place to the other while in case of x-rays the x-ray photon is like a cannon ball which is going through the structure. Neutron diffraction therefore can predict where atoms are that is the nuclei are and what they do this is something that x-rays cannot tell x-rays just tell us where the atoms are but they do not tell where the nuclei are and therefore atomic structure and dynamics can be estimated directly mind you only using neutrons. The dynamics part come because neutron diffraction not only tells us where the atoms or rather the nuclei are but also what they are doing fine. So this is one of the biggest advantage of neutron diffraction you know that neutrons scattering cross section varies randomly like we had seen those curves that you know it is not dependent on z. Now this ensures that we can easily differentiate close elements in the periodic table at the same time we also have this ability to differentiate between isotopes the different isotopes of the same element using neutrons x-rays have no capability to differentiate between the isotopes. As we had seen neutrons offer a very weak probe and therefore it gives us a very better signal though the signal is very weak and it takes some time to collect and amplify the signal the weak probe actually ensures that no damage is caused to the material under investigation. More importantly no damage is caused to the structure of the material under consideration. We have seen that neutrons have higher penetration depth and they are very very useful for getting bulk properties. Many a times if our grain size is very large if the grain size is very large x-rays cannot penetrate and they cannot give us complete information about the kind of phases and say for that matter preferred orientation that is present in a material. This is where neutron diffraction becomes very very important and this is something that can be done only with neutron diffraction. So whenever it comes to getting statistically relevant data for a normal you know diffraction data we can always use neutron diffraction. The biggest advantage and which I am reiterating again and again for neutrons is that they give information about the magnetic structure. Neutrons are essentially neutral particles with spin of half and have a magnetic dipole that interacts with the magnetic dipole of outermost electrons in an atom. This ensures that we can determine not only the crystallographic as well as but also the magnetic crystal structure of the material under investigation. Now this is one of the best advantage of neutron compared to that of x-rays. Now talking about instrumentation now this is some slide that we had already seen we saw that this was for x-rays. So we had you know a source incident beam optics a sample a diffracted beam optics and a detector. We have something similar not exactly the same but something very similar for neutrons. We will try to see how actually we have instruments for carrying out neutron diffraction. So let us start with the source. So as we had seen earlier like we have a reactor as a source for neutron diffraction for producing neutrons the reactor is a continuous source and which is shown over here so you see intensity you see there is a constant intensity right peak intensity is limited by cooling capability in nuclear reactors you see the intensity is quite low. However if you have a spellation source which we had talked about earlier it is a pulse source we see here instead of having a continuous energy level we do get pulses right this is as a function of time and here the intensity of the pulses is much higher because of better cooling control okay. But having said that we know that we do not get a continuous spectrum but the intensity is nevertheless higher. Now for the continuous spectrum right this is very similar to what we have for x-rays and once you put a monochromator we can use a normal diffractometer for continuous source and do the same kind of study that we did for x-ray diffraction. However if you are using a pulse source mind you we have to use a time of light measurement wherein we measure the time taken by the neutrons to travel the same distance mind you once the neutrons get scattered at different angles after interacting with the material they are going to take different time to reach the detector and this can be used to measure the diffraction rather the scattering angle and intensity using time of light measurement right in time of light we know that the velocity or rather the mass of the neutrons is the same their velocity is also the same but depending on the angle of scattering they are going to take different times to reach the detector. So this technique is actually known as time of light technique this technique is very fast and however we need very high flux for it. Now this diffractometer data acquisition analysis is very simple and very well suited for magnetic studies and gives us a very good resolution at low angles. However at high angles we do not have any other choice but to go for time of light measurements. So just to talk about you know we talked about the optics so let us talk about the optics we have seen the source now we have what are known as neutron guides. Now what the neutrons guide do essentially they reduce the beam delivery losses and ensure that the electron the neutrons are traveling in a particular direction right then we also have what are known as neutron choppers. Now these neutron choppers actually are rotating mechanical discs with openings that actually control the initial velocity of the neutrons. Remember that we have to this initial velocity of the neutrons when I say actually ensures that you are getting neutrons in a particular energy range that is what we are aiming at right so this is what we want then all this neutron that is incident that interacts with the sample and then we have a detector which requires the time required for a neutron of a particular energy to reach the detector right the scattering angle is related to position of the neutron detector. Now talking in details we know that in X-ray optics also to get a wavelength of a very radiation of particular wavelength we use what are known as monochromators for neutrons also we use mosaic monochromators which are nothing but asymmetrically cut single crystals these ensures that neutrons with only a particular wavelength are able to pass through okay similarly the neutron guides actually reflect the neutrons right then reflect the neutrons and thereby kind of reduces the path that is available for the neutrons to travel these comprises of glass plates with about 150 nanometer of nickel coating. So the neutrons which are incident get reflected and are guided to a particular region the chopper as I had mentioned comprises of rotating mechanical devices that block neutrons of various energy and allow only neutrons with very low bandwidth to pass right so we had seen that there is a Maxwell distribution of the Maxwell distribution we allow only a small path to pass using chopper there are certain investigations where in we need polarized neutrons right for doing magnetic study. So in that case we use a flipper now how does a flipper work I will show in the next slide but keep in mind which is shown over here so you see here we have neutrons which are having both kinds of spin right plus half and minus half now we have a substrate which is essentially silicon and a magnetic film coating on it right so you can have iron or niobium and we see that all the neutrons which are incident on it get polarized right so only one direction so you have neutrons coming in two opposite directions all of them going in one particular direction. Now the single layer can be replaced with multi layer and we can get multi layer mirrors or super mirrors to get highly polarized neutron source these are actually very important for carrying out magnetic structure determination having said that another most important part of neutron diffraction is actually the detector most often the most common detector is the helium ion detector which comprises of a gas field detector we also use semiconductor detectors as well as scintillator detectors for analyzing neutrons I have shown a few schematic of the cold neutron chopper spectrometer at Oak Ridge National Laboratory to just give you a feel for things and here you can see that we have a Fermi chopper let us not talk about it but it is like more of a chopper that you know controls the kind of wavelengths which are going in we have a bandwidth chopper then we have shielding this is your nuclear guide and here you see here is where our sample is and these are all your detectors so these are pretty big and you see this the entire source to sample right so if this is your source over here to sample this distance is huge 36.2 meter and everything all of this is shielded and all this you can see that why very high angles we can get information using the spallation source. Having talked so much about neutrons let us now sum up with why at all neutrons are important and for this you have to go to the energy momentum space diagram and here we see that this is our energy and momentum diagram or reciprocal space and angular velocity diagram right and here we see that for different amount of you know Q and our energy this is you mean you can also plot it as your R versus T right R is the you know spatial distance and T is the time we see that neutrons scattering you see there are various other techniques we see Raman scattering over here right it is giving us some information about the time and the time related stuff and the distance related stuff about what is happening at a atomic level so you see Raman scattering gives us a very small information which is even better than what we getting using NMR or certain other techniques like dielectric spectroscopy or infrared spectroscopy that is shown over here but look at neutrons you see neutrons gives us a lot of information see in elastic neutrons scattering right because of back scattering right uses a lot of information similarly here we have small angle neutrons scattering and ultra small angle neutrons scattering so we see when we compare at the Q omega right the Q omega plot for different materials for the structure of different materials we see that neutrons neutrons offer the ability to probe and cover the maximum region in the Q omega space and therefore neutrons are very important source for carrying out material characterization I hope you appreciate the importance of neutrons in materials characterization in the next class which is also the last class of this module we will talk about small angle neutrons scattering and wind it up thank you.


Okay, welcome to Intro to AP Computer Science for new AP teachers. In this video, I'm going to talk about static methods, and they are obviously very important. So first topic is what is a static method, talk about the basic structure, making sure the students understand the difference between what a method call is versus a method definition. Now they've seen method calls before in the strings unit, or also in the math class, math dot square roots, string dot life, for example. But now we're going to actually be writing our own methods and definitions. And again, they should be somewhat familiar with the idea of sending values and returning values from what I just mentioned. But here we really need to hammer it home and to show how all the different little pieces of the puzzle fit together and how, you know, what you send has to match with what you return. Talking about the idea of a signature, because there are quite a few, not quite a few, but you'll see questions on the AP exam, especially in the multiple choice. And I'll say, well, which of these methods is possible based on the signature, you have to understand, you know, how signatures work. And then overloading, which is, of course, multiple, you know, same function name, different signature, which is what I was just talking about, then have an idea for an introductory exercise that you can use with students. So what is a static method? So a static method is a method that belongs to a class as opposed to an object. So this, it's a bit of a hard concept to explain, just because, you know, classes are a bit more abstract. But, you know, as you know, like, so for example, let's say I have a student class, and one of the examples I'll use is what we can have a static attribute, like number of students. And so we look at a student, student has an age, student has a grade, but the number of students is not related to that student personally. That's, you know, that student adds to that attribute in this particular case, but it's not an attribute of that student of an individual student. It's an attribute of them as a collection, as a collective. So that's kind of how I kind of think about it is it belongs to the class, not individual. So it's just one thing, not multiple. So again, it's a little ephemeral, that one. Again, it's just static methods are a way of organizing code to make it reusable, and to make it just easier to update and to maintain. And typically, well, a static method is either called directly from within the same class or called using dot notation from within another class. And again, we've seen this, we've seen math dot square root, for example, would be an example of a static method that belongs to the class, in this case, math. The basic structure, again, we see public, static, void, and not always void, but public static, and which is the return type, the name of the method, and then whatever arguments go to that method. So we have a choice between public and private, we have a choice between, well, in this case, it's static or not static, if it's not static, it's not a static method, go figure. And the return type is what type of value does it return void means it doesn't return type. Then we have our method name, which again follows the same naming conventions as what camel case in this case, then whatever the arguments are, these are the values that we are sending that we can send to that particular method. So the method call versus the method definition. So we have to first define the method. What's nice about Java is it doesn't matter if you define it afterwards or define it before, because in the compilation process from source code, the byte code, it just kind of, you know, fixes all that for you. Other languages that order is a bit more important. So the method definition goes outside of the main method. So that's important. So make sure that, you know, the students closed the main method and then the next, you know, these static methods come afterwards. Typically, I put it afterwards. And the method call comes in inside another method, usually the main method, but a static method can call a static method, which could call another static method. This is not uncommon. But for most of the programs that we do in AP computer science, typically, you're calling from inside the main method, although you will see a few, you know, exceptions to that. Sending values. So we can send values to methods. And as I mentioned, we've seen this before with math dot square root. So in this case, we're sending the value 25.0 to the static method sqrt. And the number and type of value sent must match what you see in the definition. So if we were to look at the dot square root method definition in Java, so I don't know if we could find that, we would see in there double something because it accepts a double returning values. We have a choice whether or not to return a value. We can also return objects. I should have mentioned that we can also send objects. But at this point, the only type of object they really know is a, well, I guess now we did the person object. So, but typically speaking, you're sending values and then later you start sending a bit more object type stuff. And technically it's an object reference, which is something that should be brought up either sooner or later. So you can see in this example, double x equals math dot square root 25.0. So the value that we're sending is 25.0. And we're returning, of course, it'd be 5.0, which would then be assigned to x, which is also a double. In Java, only one value or object can be returned. So that could be a collection though. But like for example, Python, you can return multiple values, which is kind of cool. But yeah, Java, you can't do that. So your Python students, they're coming from Python might be like, hey, why can't we do this? Because that's just the way it is. The signature. You'll see the concept of the signature. And again, it's important because there are multiple choice questions on the AP exam, where this isn't this is important. So let's say you have an example here, you see on the screen at the bottom, you have a string string int. And then the trying to send a string and int string, it's not going to work. So the signature refers to the number type and order of values in the method definition. So this example, public static double double x, a lot of doubles there. So the signature here would just be a single double. But yeah, you could have a signature like so first, last, first name, last name, age. So in this case, string string int. And what I tell my students to do, when they're taking the test is just a little bit of a shortcut is to write the signature like this. So capital S, capital S, and I.  So I for integer D for double and B for Boolean, capital S for string. And if there's another type, they would use a capital capital letter for that. That way they can just say, okay, this is a SSI, but this one is an SIS. I can't use that. Overloading. This is important concept as well. It's kind of related to what we just saw. So if you have a signature, you know, so it's two methods with the same name, but different signatures. So based on the values that are sent, each, the method that's called is changes. So for example, you know, public static, double it, public static, double it, double x. So you can see here, we have an int as our signature. And here we have a double. So which method is called depends on the type of value sent. So if I send an integer, it's going to call this method. If I send a double, it's going to call this method. You can do a lot of interesting stuff with that, especially with constructors when you get to that later. And for my introductory exercise, this is what I actually tend to do before I explain all these things. Or we can do it after as well. So what I do is I have four, four students as volunteers. I have them stand, you know, spread out in front of the board and above each student, I write, you know, void print 42, and get the answer void print double, you know, so each student represents one of these methods. And then I'll take some paper and or many white board effect on these days when I have one, and write a number on it. And I give it to a student, I say, okay, you know, you choose which method to call. But if it takes, for example, in this case, if you call this one, then you have to, you have to actually physically take the white board over, or physically take that piece of paper over and give it to that student, and then go sit back down. Now, in the case where there's a return type, that student at the board has to then either take a little white board or a piece of paper and walk it over physically to that other student.  And the person catches it, hey, here's an eight. You know, so they just really visualize that process of passing values around the program, you know, at least in the real world. So moving those numbers or tennis ball, whatever adaptation you want to do, it could be a little, you know, a little frisbee or something, depending on how safe your students are. My students are pretty safe. So a tennis ball works or even a ping pong ball, if you're worried about injuries.  And they're, they're visually seeing it and also a little bit of physical activity. It's nice to get the students out of their chairs when you can, especially in a coding course. That's how I, that's how I introduce these concepts with the students and practice them. So topics today were what is a static method? We looked at the basic structure, and again, make sure to emphasize the difference between the method call and the method definition, sending and returning values. Again, this is one of the things that kind of confuses students. A lot of times they'll, they'll call it, but they won't assign the return value to variable. And then that value is lost. You see that a lot. And then the idea of a signature and based on the signature, we can create multiple overloaded methods. So one same name, different signature, and depending on this values that are sent, that determines which one is called. And then finally, we saw the little example, introductory exercise. It's a nice fun one. It takes a few minutes. But the students will will remember that one because it's kind of active. That's the end of this one. Thanks for watching.