 Hello everyone. The previous lecture, I discussed the technique, the nuclear analytical technique based on neutrons that is neutron activation analysis and also discussed some of the applications of this technique in different areas. Today, I will discuss another nuclear analytical technique called ion beam analysis technique. As the name suggests in ion beam analysis technique, we use the charge particle beam and the charge particle beam may have different types of reactions with the nuclei in the target and depending upon the type of reaction that are happening, we have different nuclear analytical techniques. So, by this schematic, I will first just introduce what are the techniques that I am going to discuss in this lecture. So, when the low energy ion beam, it could be proton, alpha or even heavier ions, they bombard the target, then there could be backscattering of the projectile. So, the backscattering of the projectile is like rather for backscattering and there is a, as we will discuss in more details, the specific relationship between the backscattered energy and the mass of the isotopes in the target material and therefore, we can identify the elements of the isotopes present in the target and they turn, we can even find out their concentrations in the profile. So, this is a RBS is the, whether for backscattering spectrometry is a very well known ion beam analysis technique in material correct direction. Now, second type of reaction can be that the projectile hits the nucleus and gives a recoil. That means, the atoms target are taken out of the target material. So, they come out of the target material and they can be detected by a suitable detector system. So, the coils which are indicated in the forward angle, the forward requires are detected to tell about the constituent target. So, this is called the elastic recoil detection analysis is purely elastic scattering between the target nuclei and the initial projectile beam. And this also can be used to characterize the different types of materials. There could be another type of, there could be nuclear reactions between the low energy ion beam and the nuclei in the target material. And this nuclear reactions can give rise to the gamma rays. So, the, if you detect the gamma rays by this, from this nuclear reactions, then the analysis based on the nuclear reactions we called are a nuclear reaction analysis. And one of the variants of this is particle induced gamma emission piggy, mostly protons or neutrons are used. So, they are actually similar techniques, but the different will become clear when we discuss each technique in this particular. So, in nutshell, these are the four types of nuclear reactions or different interactions which we will be utilizing in the different nuclear analytical techniques, the RBS, the ARDA, the NRA and piggy. Also, you will see when the the projectile beams interact with the target atoms. They can cause ionization in the atomic systems, like for amplification analysis can take place. And this ionization of the case and electrons will lead to emission of x-rays. So, particle induced x-ray emission, though it involves the atomic orbitals, this also is considered to be an ion beam analysis technique. And mostly people use protons. So, I will not discuss this particular, basically this gives you the composition of the material, different elements will have characteristic x-rays and those x-rays can be detected by suitable detector. And the peak area of the x-ray peaks will tell you the concentration of the particular element in the target material. So, you may have to have standards. And so, it is similar to x-ray fluorescence where you use x-rays to bombard the target material and or even you can use gamma ray or even you can use beta particles. So, x-ray, the emitted x-rays are characteristic of the elements. So, PICC and XRF, these are another other techniques which are used in routine compositional analysis of different types of material. While the ion beam analysis techniques like RBS, ERDA, NRA and PG, they offer much more advantage over simple techniques like PICC and XRF and it will become. So, this is not just a routine analysis, but they involve the detailed analysis of the target material and the processes that one is studying and so on. So, let me first discuss the fundamentals of Rutherford best scattering spectrometry. As the name itself implies, it is based on the Rutherford scattering of the projectile by the nuclei present in the target material. And the two important principles behind this are one is that when a projectile is being backscattered by the target nuclei, there is a precise relationship between the energy of the scattered particle, like the projectile scattered and the mass of the scattering atom. So, basically it is an elastic scattering and as we discussed in the lecture on nuclear reaction, in elastic scattering, the kinetic energy is conserved and it can calculate the energy of the backscattered ion exactly if you know the mass of the projectile target and the initial energy of the the tile as well as the angle theta at which the scattering is going to take place. And so, I have just given an estimate of this RBS. We have a projectile of mass M1 coming number Z1 and having energy E0, bombarding the target material having let us say a particular nucleus you are it is interacting with mass and charge M2 and Z2 and after the scattering the projectile is coming out with energy E1. So, depends on theta equal to let us say 170 or 160 whatever it is we will we will discuss why back angles very shortly. So, you can from the conservation of mass and energy and the conservation of linear momentum set up the equation like we did it in that particular lectures to find out the mass of the the target nucleus E3 if you recollect we had solved that equation for energy E3 of M3 whereas, here we will be determining the mass of M1 itself you will recall M1 plus M2, M3 plus M4 for any nuclear reaction, but here it is elastic scattering. So, it is M1 plus M2 only this one we are trying to it was a energy was E0 here energy is E1 and so this E1 is actually nothing like nothing but E3 you can say and so you can solve this you can that equation was solved and the relationship between E3 and E1 or here E1 and E0 is given by this formula between this contains M1, M2 and theta. So, this term can be clubbed as k. So, the back scattered ion energy is k into E0 and the k is called a kinematic factor it depends simply upon the masses and angles of the projectile target nuclear. So, this tells you so this this is a for a particular value of M2 there is a particular value of k. So, that way you can find out what is the mass of the nucleus which was back scattering the projectile. The second relationship between the probability of scattering of the projectile and the depth of the target and the cross section is given here probability means essentially the cross section. So, the differential cross section this sigma by 2 omega per unit solid angle is given by z1 z2 E square upon 4 E where E is the projectile energy cosec 4 theta by 2. So, you can see here higher the z of the target nuclei has the cross section. So, this will be made more clear that for higher z nuclei the sensitivity is higher cross sections are higher means there will be more events. So, you can then from the determination of the number of particles that are scattered or from the counts in the spectrum of the scattered particle we can find out the concentration of the target nuclei. So, the measurement of the energy of the back scattered particle gives you the mass number and 2 or in the target you identify. So, and from the mass number you can of course identify the elements and from the number of scattered particle. So, number of scattered particle how do you know scattered particle it will be n t sigma i and then you can say. So, this sigma will be this sigma by 2 omega. So, this is the number of particles into t time and so this tells you the concentration of that particular target. Now, let us ask the question why back angles and in fact the RBS is done with the low energy ions energy of the projectile is low because we do not want to introduce any nuclear reaction. So, it is simply Coulomb scattering. So, you need to be below the Coulomb barrier. So, there are no complications because of the nuclear reaction with the target. So, it is a pure Coulomb scattering. So, that energy of the projectile will be kept quite low. Not only that the cross sections for this for back scattering are if you see here cross section for the scattering is 1 upon e square. So, lower the energy higher is the cross section for RBS and therefore we go for low energy ions. So, two aspects why the low energy ions because the cross section is inversion proportional to e square. So, that is e 0. So, lower the energy of the projectile at the sensitivity for the RBS and for sensitivity for detection of the concentration of the elements. So, typically you know people use 2 MeV alpha particle beams. So, you will be below the Coulomb barrier for most of the target to be I. In addition to this you the there should not be any nuclear reaction but that will complicate it will unnecessarily introduce some radioactivity in the sample and so it may become difficult to handle. So, this is the reason for low energy. Second is that mass why back ends. So, back angle is the difference in the particle energy that e 1 back scattered from different masses in the target to be I is maximum at most backward angles. So, if you see here you see here if you put theta. So, essentially you can say d m 2 by d theta the chain in the mass with the angle if you do an exercise and you would find the differences between different masses. Suppose you have got you know cobalt iron nickel different elements to their masses are also different they will add their energy the energy of different masses will be widely spaced at most backward angle. d e 1 by d theta will be maximum at theta equal to 180. But you cannot put theta at 180 degrees because that is the beam path. So, you keep slightly away from 180 maybe 170 160 or so. So, that is the reason for back angle. So, you want to resolve for example, here what I have shown here m 2 different m 2s in the spectrum. So, the chart particle the projectile spectrum if you record in the back angle then you will see here this is low mass higher mass higher mass. So, this gap between these different masses will be maximum at most backward angle. So, you can say the mass resolution is at most backward angle. Otherwise you know at power time they will all merge together the gap will reduce. So, you cannot resolve the if they may start overlapping. Secondly, as I mentioned the cross section are proportional to z square d sigma by d omega proportional to z square of the target elements. And so, higher the atomic number of the nucleus that you are going to investigate higher the sensitivity. Because more events you will get you can see here this is the lower z higher z and still higher gap. So, higher the z higher the counts you will get. So, they are more sensitive. And because of this reason the RBS is ideal for detecting the high Z impurity in a low Z matrix. So, mostly the applications of RBS involve determination of high Z impurities in a low Z matrix. So, you have got a plastic that you want to determine sub impurities metallic impurities or iodine bromine excellent technique for that kind of job. So, there will be several applications. So, that is one determination of depth profiling of high Z impurities in a low Z matrix because of this higher Z being more sensitive and they appear at high energy. So, you can distinguish them from the. And second is the depth profile. You can do depth profiling by RBS technique because the backscattered ion energy will be different depending on the depth from which this can be taken. I will elaborate this more within this cartoon. So, you have a projectile of energy E0 bombarding the target and I have shown a thick target. So, there will be backscattering at every depth of the target. So, from the surface backscattered projectile energy will be K into E0. K is the kinematic factor. So, the energy is well known for the particular M2 you can find out what is the energy because K you can calculate exact K depends upon M1 M2 theta. Now, as the projectile is traveling in the update material it is losing energy and every depth it will get backscattered. So, let us say at a particular depth we say this particular depth energy loss is delta 1 delta E1. So, the energy at this depth will become E0 minus delta E1. So, M2 at this depth will see a projectile coming at E0 minus delta 1 and backscattered from that side. So, you are putting a detector here D. So, the backscattered energy at that point will be K into the kinematic factor into E0 minus delta E1 and again the backscattered ion will lose energy delta E2. So, minus delta. You can exactly calculate what will be the energy of the backscattered ion if it is backscattered from a particular depth in the target material both the kinematics are very well known the energy loss is very well known in a target material you can find out because the stopping powers are known and you can find out the depth. So, that is what is the suppose you know the d by dx you can find out the depth at which the backscattering took place. And so, by recording the spectra of the backscattered particles, tactile particles you can do depth profiling and then you can also get the resolution for impurity concentrations and at what depth they are you can see the depth resolution in RBS delta X depends upon detector resolution at the h m of the peak upon stopping power by dx. So, you can determine the resolution of detector from the normal spectra and then you can do and our stopping powers are known. So, I will just give you some of the examples of RBS. So, you can have RBS in thin target and thick target. So, thin target means the projectile is passing through the target it is not stopped by that. So, you can see here I have shown here some of the RBS spectra using a 4 MEP proton beam at from a we have an accelerator called folded tandem and accelerator. And so, these are the metal files of thorium, holmium, thorium and thorium and their thicknesses are in microns. So, when the particle is going so basically the objective was to see if there is a oxidation of this pyrophoric metal ions on the surface. If there is oxidation there will be surface oxygen on the. So, when the beam is hitting the surface and so both front and back will back together. So, oxygen at the front this is the front and this is back, energy is from the front and low energy is from the back and this is the metal file. So, that you can find out the thickness of the file because you know the DE by DX and we know the energy of the alpha or the projectile and similarly so for thorium, holmium, thorium you can find out the oxygen concentration and the depth of the thickness of the file. So, this is a typical experiment with thin files. If you have a thick target, the thick target means the projectile will stop in the somewhere in the middle somewhere in the target and so the hyzeric impurities will appear at a much higher energy than the there will be a big hump because of the bulk material. So, this is a RBS spectrum of gallium oxide deposited on a thick silicon file. So, on the surface suppose you have got silicon file and you have the gallium oxide on the surface and you see the back scattering. So, the gallium oxide gallium peak will come at much higher energy but the oxygen of gallium will be at much lower energy because the kinematics are dependent on M2 and silicon will be somewhere here and since silicon is very thick the silicon will not appear at the peak but it will appear as a hump, thick edge type thing. So, this is all due to silicon. So, this is due to the thickness of this. Since it is very infinitely long, larger compared to the projectile range you will see a hump or thick target will show a hump. And this is a very interesting experiment of multi-layers. There were several layers deposited of gallium oxide and silicon layers or each layer being of nanometers thick and that could be seen in the RBS spectrum. Of course, if you want to have a higher resolution then you require heavier projectiles like 19 because you require to have a more mass resolution. If you want to have a higher mass resolution or higher resolution you require to have higher ions because the specific powers are high. So, some of the applications of RBS in like this is a polymer inclusion membrane. These membranes are used for separation of metal ions like Cgm and silver from the aqueous solution. So, the constituents are helilose, triacetate, nitrofinal octanthor. This is the bulk material. This is a plasticizer and this is a carrier molecule which will take the Cgm, di-monyl-reptilin-sculptinic acid and this polymer inclusion layer like polymer membranes and you can take up Cgm. So, you want to know whether the Cgm is distributed uniformly or in the sample or not only on the surface. So, that was the experiment. You can see that the file of Cgm in polymer inclusion membrane was studied by IMMG proton being with a current of 3 to 5 nanoamperes and now since proton has got very low stopping power that resolution is only 1 micron but then the thickness of this files are up to 100 microns. So, 1 micron is quite good and this is the fm of the polymer inclusion membrane and you can see here carbon, oxygen, sulphur. So, these are flat that means the thickness the carbon that means the polymer is uniformly distributed and even the RBS spectrum of Cgm shows that Cgm is uniformly distributed in the entire membrane. So, up to 100 micron entire thickness of the membrane the metal ion is distributed. So, the idea was to see whether the plus this carrier molecule sulphur bearing molecule is distributed uniformly in the membrane. Similarly, another experiment was rather for backscatting spectrometry of Cgm diffusion in borospecate class. This borospecate classes are used for immobilization of the high level waste at our department and so you want to have higher resolution. So, we used chlorine 19 beam 6 pnA that resolution was 25 nanometer. So, this is a typical experiment the beam comes from here hit the target and then backscatter chlorine beams are measured by two detectors this is the. So, you have a glass sample and on the surface we have Cgm chloride evaporated then after the evaporation you anneal this sample at different temperatures. So, different temperatures the Cgm will go in that depth and you are studying to what depth it has got diffused. So, this depth profiling of Cgm can be done using RBS and then you analyze to go. So, this is the RBS spectrum and this gives the penetration depth versus Cgm concentration and the analysis of this gives you the diffusion coefficient of Cgm in the glass. These data are useful in subsequent analysis. Another technique is elastic required detection analysis we have not worked on this, but it is also an important technique and which is in fact is complemented rather for backscatting spectrometry because this technique is used for analysis of light elements in a heavier matrix. RBS we use heavier elements in lighter matrix this ERDA lighter elements in heavier matrix and why it is so? If you recollect the kinematic equation for elastic scattering the energy of recoil we can say E2 is divided by 2 energy projectile energy into M1 M2 upon M1 M2 square or theta and so the projectile mass if projectile you need to have you are detecting the required power direction. So, if you have a heavier projectile mass all the requires will come in the power direction it will give you a bigger peak the energy of the center of mass will be more and so all the requires come in the forward peak. So, you detect put the detector in the forward angle and detect their spectrum by delta e telescope. So, you use delta e telescope thin delta e silica detector and thick silicon or you can use a delta e of based on gas and the stopping power is given by and z square by e into the electron density of the medium. Since you are putting the sample detector in the forward angle let us say 15, 20 degree or 30 degree if you have to show the target may be thick because the heavier heavy ion beam will not travel much. So, what you want to do you put the target in a glancing position. So, small angle may be 15 degree or so and so the this is called a glancing position at forward angle you measure the. So, the heavy ion beam is not passing through the target, but it may be appearing from it is the requires coming from different depths in the So, why heavy ions because we want the higher required energies and which will appear at the forward angles and why low angles because with heavy ion cell projectiles requires will appear at the forward angles only. The requires will come in the forward angle only if you have a heavier mass. So, ERDA essentially is used to detect low jet impurities in a hyzer matrix. Typically like you have 1 MV per nucleon chlorine. So, 35 MV chlorine beam and you have a thick detector and thin detector and keep the angle at 15 degree or so. So, I will just quickly give you two applications of elastic required detection analysis. One of them is so, ERDA is essentially used for low jet input detection hydrogen helium lithium carbon oxygen in a hyzer matrix and this most of the time you know these hyzer matrices are high technology materials like porous silicon, diamond like carbon films, silicon nitride etc. And if you have a very thin target like micron thick or even less then you can use it in the transmission mode means this geometry you do not need to put in the glancing angle beam can pass through this. So, we have an iodine 127 beam of 140 MVB you are determining the impurities in the molybdenum foil of 100 nagram per centimeter square. So, you can put detector at forward angle and now you will get the spectra due to different impurities like carbon oxygen in the form of narrow peaks and this is the iodine elastically scattered from molybdenum. So, this is not of interest and you have the molybdenum peak the molybdenum requires you will get and so, they were essentially wanted to see what is the what is the impurity. So, it was basically carbon impurity and the carbon content was found to be 75 percent of the molecule. So, they are they are used in like nucleotide experiment we have a metal file and you want to know what is the impurity in the target. Normally the ERDA is studied in reflection mode because you have a you would have thick target and you will be it is like micron thick side. So, you would like to know what are the elements present as a control there. So, one of the examples I am giving you the silicon nitride it is a very very technically important material because of high hardness wood creep resistance high wear resistance hard material low coefficient of thermal expansion chemically resistant and increased metallic mechanical strength and fans applications in automotive industry bearing cutting tools etc. So, one of the studies were that that glancing angle they study the the requires from the target what is the target silicon and silicon nitride on a silicon substrate you have a thick silicon and on which you sputter or evaporate and you make a layer of silicon nitride you can do even ion sputtering. And so, under this position so, glancing angle and forward angle you will see the spectrum. So, the thickness of this silicon nitride was actually very thin it was about 12 nanometers 12 nanometer thick silicon nitride and the composition is not known because you may be depositioning by ion sputtering. But you can see here the you can get a flat concentration of nitrogen and silicon here that is the bulk silicon and you will see some impurities these impurities are seen here low depth impurities. And from the ratio of the nitrogen and silicon count this is silicon they could find out that it is a Si 3 and 4 silicon nitride Si 3 and 4 with the depth resolution of 2 nanometer. So, as I was mentioning you know this ERDA is basically used in specific cases where you are looking for a particular information. It is not just routine analytical technique but it is used in whenever you want a specific information about the material that you have developed. So, that is all I have to say in the next lecture I will take the other two techniques in nuclear preparation analysis and particle induced gamma emission. Thank you very much.