 So, far in the first two modules, we have looked at the synthetic approaches to materials. In the first module, we have extensively seen all the chemical synthetic roots which are potential for making materials and module 2. We have worked on the various aspects of thin films, how different materials, inorganic materials can be made. The third module, we will be discussing some of very crucial characterization tools that are inevitable for materials chemistry. And materials chemistry and material synthesis is never adventure without use of proper characterization tools. And therefore, in this module, I am going to highlight about diffraction methods, microscopic methods, spectroscopic methods and thermal analysis methods which can be used as a tool to characterize materials. And I have specially singled out x-ray diffraction measurements as a very important tool which stands very different to other characterization tools. Main reason, there are other characterization methods which are post-synthetic approaches. You make a material and then you try to characterize after you have processed it. But x-ray diffraction is a material not just to characterize what you have synthesized, but during the synthesis itself, it is used as a characterization tool much to the tune of infrared spectroscopy or NMR spectroscopy which is actually used in any chemistry lab to map your synthetic strategy. So, even before you complete your synthesis, you use certain characterization tools to analyze whether you have really made the right measurements. And therefore, I have coined this x-ray diffraction method as a tool to track your synthesis rather than even characterizing the material. And as you would see here, there are different cartoons that I have given in this opening slide. Any material which is crystalline will actually give very beautiful diffraction spots. And this is a particular SEM image which shows a well-ordered crystal lattice. And each spot in this gives you an idea about how the atoms are arranged in a crystal lattice. As you can see here very clearly, this is nothing but a FCC pattern. Each spot in this diffraction pattern talks about a definite arrangement of atoms in a lattice. And that is what you see in this cartoon that there are different planes which has a preferential occupation of a particular atom. And they are periodic in fashion. And how do we go about analyzing and getting different informations about this atomic arrangement or order in a lattice? We have x-ray diffraction as a tool not just in terms of a pattern like this. But we can also try to map it as a wave because x-ray diffraction is nothing but bending of waves. And therefore, when x-ray hits a particular lattice and if it is ordered there will be bending of waves. And this bending of waves can be either constructive or destructive. If it is a constructive interference then you will see a x-ray peak. And if it is a destructive interference you will see no peak. Therefore a constructive interference will give you a x-ray diffraction pattern not necessarily a spot pattern but a diffraction pattern which is more like a wave. So you can easily understand which material or which element gives what sort of a pattern. So this cartoon shows here one of the latest versions of a diffractometer which can be used for getting a x-ray pattern of a particular material. So let us go progressively in this talk to understand what sort of information I can get about x-rays about a lattice or about a material that I am synthesizing. So XRD when I say that means powder x-ray diffraction principally because we are going to deal more with the powder patterns. And XRD can be used first for phase composition of a sample. So when I am starting with say A plus B giving C then your A and B will actually have a characteristic pattern. And as you are heating during the thermal process C is getting formed and we do not know whether C is complete or still some remnant of A and B is present. Therefore you can talk about phase composition and this can also be quantified. So it is a quantitative phase analysis which determines the relative amounts of phases. Sometimes we might start with A plus B we are expecting C but actually it can give C prime or C double prime which are some secondary phases which are not needed and therefore it is easy for us to map even those phases. And then more importantly when we want to analyze and understand what set of a crystal pattern that comes when two samples are heated together what is the nature of crystal symmetry of the third pattern that is the product then you talk in terms of unit cell parameters and what is the lattice symmetry. And we can quantify all this indexing the peak position and we can also look at the lattice parameters that can vary as a function of the substituent ions composition. So different things we can try to harvest from this simple x-ray pattern allowing doping solid solutions strains etc. And this is a big list not only we look at the cell symmetry we also look at the macro strain in a lattice and how we can correlate the strain induced by the crystallites or induced by this poly crystals and we can correlate that to some physical property like resistivity or magnetism or so on. And then we can also look at epitaxy texture or orientation if we are going to make the material in thin film form. Suppose I have a solgial root as we have seen earlier and then I am going to make thin film how can I look at the texture whether it is growing epitaxially or whether it is growing in a oriented way. As I had shown you in the previous modules a chemical approach to thin film is quite different from a physical root to make thin films and we are talking about a very high degree of epitaxy or order growth and in such case how we can use x-ray for mapping that and also other information like peak broadening that can tell us about crystallite size, micro strain and so on. So we will try to revisit some of these aspects as we go through this lecture and I am going to show at least one example of each of this that we are trying to discuss in this talk. Now let us look at the diffractometer in the first place and see what are all the crucial elements in a diffractometer because all these are going to affect our x-ray studies one x-ray tube and the source of x-rays. So what is that to do with my x-ray analysis because the target that you are going to choose will also change the pattern that you are getting. Suppose I use a particular target for producing x-rays and you shift the target then the x-ray pattern will totally be different. So I need to know the goniometer that is the assembly to get this x-rays and then the sample and the sample holder because that is a very essential. Sometimes I will mount the sample but not get any pattern at all principally because the alignment is not correct and then receiving side optics because when you try to use some x-rays then sometimes the target can also show some reflections therefore you need to filter off stray radiations to get the right pattern. So you are talking about receiving side optics and then the detector that counts the number of rays scattered by the sample which gives you a pattern. So all these are essential components and this is a assembly of target and this is how it is chemically defined. Suppose you have x-ray tube which is sealed tube then you can operate the source between 1.8 to 3 kilowatt but if you are going to have a tube or the target which has a rotating anode that is x-ray tube then you can improve on the flux by increasing the operating voltage to 9 to 18 kilowatts. Why is that so? Because when you look here cathode rays are generated from a filament usually it is a tungsten filament that is actually striking on an anode in this case we are talking about copper and x-rays produced and x-ray is actually taken through these windows which are beryllium windows and this is the way x-ray is tapped out. Now when you are heating it continuously x-ray is produced as a result the whole of your target can melt because of continuous bombardment as a result at the rear side you actually have a cooling system and without this cooling system your target will melt down therefore you need a very good chilling unit to cool your anode that is your source for the target but to bring down this melting effects or heating effect apart from using a cooler you can also rotate the target so that it does not really gets localized. So if you are going to do that then you can improve on the wattage so you can play around between 9 to 18 kilowatts. So this is a perfect assembly and we can also see that in a real picture this is how a target looks like and these are your windows and this is a evacuation as you see this is a vacuum sealed therefore this is typically the x-ray target that you are using in a typical diffractometer. Now when you are using a target there are several things that are happening therefore you need to know which ray x-ray you are trying to use. So the wave length of x-ray is determined by the anode of the x-ray source and the typical chemical process that is happening inbound electron is actually knocking out and this is the case that is ejected and therefore some of the outer electrons are actually coming back to the k-shell and that is where the x-ray is produced because x-ray photon is coming out. So the process is actually listed in this cartoon you can actually have a k-beta radiation coming from a x-ray source and that is nothing but the transition from m level to k level or you can have k alpha radiation which is from l to k and within k alpha also you have k alpha 1, k alpha 2 and that is actually seen in the typical x-ray mapping as you would see here for molybdenum alpha copper you can single out the k alpha and k beta. Beta always comes on the left side of the k alpha peak that is higher energy radiation but if you look at the intensity k beta will be slightly lesser compared to k alpha therefore k alpha is the most preferred radiation that you would use. So in any x-ray analysis you would say you have to specify what is your target you can mention this as copper k alpha that means you are talking about a copper a source and this is the radiation that you are using to analyze your material which has a specific lambda and this lambda is unique of the particular target but what happens is that you also get k alpha 2 and k beta or the stray radiations that keep coming therefore you need a required optics and other alignment to block all this extra stuff so that you get a monochromatic source that is called k alpha. So those are essentially part of the assembly of your x-ray diffractometer as you see here this is your x-ray and from x-ray you are actually getting the monochromatic x-ray beam to your sample and then these are the scattered radiation diaphragm which will filter all the unnecessary ones then you have the k beta filter and this is your detector which will finally sense the x-ray the reflection that is coming and what is the principle here you have this measuring circle which will actually go 120 degrees and as the sample angle is changing at different atomic planes you will have the diffraction coming and therefore the measuring angle is typically theta 2 theta combination so your x-ray is incident over the sample at a distance theta or angle theta and then you are getting the diffraction at an angle 2 theta so that is why it is popularly called in powder x-ray diffraction as 2 theta scan so when you say 2 theta scan we are talking about this incident beam which is making an angle theta and then this is measured at 2 theta therefore we measure always as 2 theta scans and that is what we see here. Now as you see here there are spectral contamination in the diffraction patterns so one need to be very careful about those peaks which will actually merge with your peaks so if you are using this x-ray diffractometer you have to be very careful mainly with this k alpha 1 k alpha 2 this is a doublet almost always present and it is very expensive to filter this k alpha 2 but actually k alpha 2 and k alpha 1 they will not be split very much in the lower angles as you can see here this is the split here but at 47 degrees you do not see the splitting much but when you go to higher angles you see the splitting much more clearly for k alpha 1 and k alpha 2 so you got to be careful about the contribution that is coming from k alpha why this is also coming since we are using tungsten filament as the source sometimes on over burning the tungsten lines can also come in the diffractometer therefore we should be very careful to filter off the contributions coming from both k beta of that of the target and also the contribution coming from tungsten filament so this can come as a spectral contaminant in your diffraction patterns and before we go more into the details or the basics of x-ray diffraction I want to tell that in today's diffractometers different targets can be used or x-ray source can be used more popular is copper anode and then we have cobalt anode chromium anode and molybdenum anodes and each of this have a particular k alpha which is to be used in our calculations and we have so far in most of our characterization have used Bearden's data which gives you the k alpha value but in 1997 we have Holzer who has brought about refinements in this data with the much better optics and much better analysis analytical tools that are available therefore these are the refinement datas so typically when we talk about copper k alpha 1 we usually say 1.5405 but you can see here in the fourth and fifth decimal places they do change these are all needed for read well analysis or for more precise analysis of measurements so we need to have this in mind that there are different sources which can be used and I will also tell in one of the slides which anode or which target we need to use copper or cobalt depending on the nature of the sample so it is not always required that you should use only copper we can gamble with other targets typically a diffractometer looks like this this is one of the older version of the diffractometers there are more than six companies which are producing such extra diffractometers this is just to give you an idea how involved this procedure can be and I will also show some of the other ones present generation ones which are much more simpler but with different facilities that are available in a single diffractometer so as you see here this is your x-ray tube that is tower through which x-ray is produced and your sample holder is here mounted here and then you have the receiving slit and your detector and this is all connected to x-ray recorded therefore you can actually get present generation diffractometers not only have a x-ray x-ray machine but they also have computer to record your data so this is the assembly of a diffractometer and the brooker is another company which brings different versions of this x-ray diffractometer there are several versions of diffractometers that are available we have powder we have single crystal only for studying single crystals and presently we also have those which are dedicated use for thin films because the settings for studying thin film patterns are different from powder therefore you need such precise assembly so these are some of the different versions and I will be mostly talking to you about powder diffraction and as you see in this cartoon here you can have tungsten molybdenum copper cobalt iron chromium titanium all this k alphas or L alpha is listed here but what I want to stress here is that if you have iron for example iron k alpha is used for ferrous samples where the iron fluorescence would cause a very high background or you can also use cobalt for ferrous compounds so if I am working with iron oxide or if I am working with ferrite based samples the fluorescence will be very high therefore it is not advisable to use a copper k alpha in those conditions for ferrous samples you always use only cobalt or iron k alpha which is highly recommended but copper is ideal for most diffraction examinations and for thin film analysis also so therefore copper is almost used in many of the laboratories and then you also have molybdenum when low absorption is decided that is with single crystal experiments it is always molybdenum that is usually used and this is again the rear view image of the target that I have been mentioning to you this is copper k alpha target which is used in the instrument and today the version of x-ray diffractometer is much different from the earlier ones as you can see here this is the output that you would get for a typical powder XRD pattern for a complex material and you can see so many peaks are there and it could be as simple as three or four peaks in this whole spectra if it is a highly crystalline and cubic pattern. So, just by looking at a typical 2 theta scan you can guess what sort of crystal symmetry that you are looking for more the patterns more complex the symmetry and therefore just looking at this you can say this should be a monoclinic or a triclinic symmetry. So, number of peaks can also give a quantitative information about what sort of system you are working with and you see there are several menu driven interactive softwares available which can generate the atomic position it can give you the lattice parameter lattice dimension everything can be mapped inside to because such softwares are also available. So, it is very fascinating to use a x-ray diffractometer principally to understand what is the system that you are working with. Now let us go into some of the basics of diffraction and see if I am going to use a x-ray machine what are all the informations that I can look for. Number one as you know we are now looking at a theta 2 theta scan. So, this is what I mean by a 2 theta scan. So, once I get 2 theta values what do I do how do I go from there. So, we have to first understand the basic expression that governs our analysis is nothing but Bragg's law which is n lambda is equal to 2 d sin theta. Now what is this n lambda is equal to 2 d sin theta n in powder x-ray diffraction experiments we always take n to be integer which is 1 because we are looking at the first order reflection n is 1 and the lambda is nothing but your wavelength of your target and this is 2 d sin theta that is actually coming from here this is d and this is your sin theta and this is your sin theta. So, this is actually 2 d sin theta. So, this is what we are measuring. So, n lambda is equal to 2 d sin theta and using this expression we can try to find the interplanar spacing that is nothing but your d this interplanar spacing between 2 adjacent atomic arrangements can be mapped because I know n and I know lambda and I can also know theta from the 2 theta value. So, if I have a peak like this and I have some patterns like this and this is your 2 theta scan this will give me 2 theta value and from there I can find out theta. So, this is how we go about it and first let me start with the featureless curve because this is in reality this is how it is because this is nothing but a x-ray diffraction pattern of glass. Glass is amorphous therefore there is no long range ordering and if you see only a big hump at low angles then that is a very clear indication that it is amorphous in nature. You would not see anything these are all spikes these are not peaks these are spikes. Therefore, what you see here is a featureless noisy curve and that says that it is the material is amorphous or glassy. Now, if you go for single crystal or poly crystals this is how it is if it is a ordered lattice like this then I would get a very sharp pattern as sharp as this and this is for a highly oriented system. So, the peak width or the crystallinity of a particular pattern will be reflected by the shape and size of the x-ray peak. Now, if these lattices are broken into poly crystals as small small crystals then we are actually breaking the long range order and therefore this peak now splits or broadens into this fashion and this B is nothing but your full width at half maxima which gives you idea about the peak broadening and therefore peak broadening has a consequence directly to the size and also shape of your poly crystals. If they are very fine then broadening will become more. So, we are talking about going from a bulk to a very small dimension and typically for that matter nano sized powders will either be amorphous in nature or it will have a very broad peak like this and when there is a broadening you should understand broadening necessarily does not mean it has to be very low sized crystallized or nano sized broadening can also come from several other instrumental problems also. Therefore, we need to be careful where is the origin for this peak broadening. Suppose one peak shows a broad one and the other peak in the same spectrum is showing a thin one then it is not due to the sample but it is due to some alignment problem. But if the sample is truly amorphous or nano in size then all the peaks that are appearing in the pattern will have same broadening then you can be sure that this is truly coming from a nano sized powder. Now what informations we can get number one we can get information about T. T is nothing but the thickness of your crystallite. This is the crystallite that I am talking about and what is the dimension of this crystallite because crystallites are made of very small lattices and therefore I can map what is T. T is given by K into lambda by B cos theta B where K is nothing but a constant that depends on crystallite shape. This is actually taken to be 0.89 and the contribution comes from both broadening and from other factors related to the shape of the crystallite. Lambda we know B is nothing but full width at half maxima so you can actually map your broadening and you can also measure the height and take the full width at the half maxima then that becomes your B and theta B you know that is your bragg angle so you can get T. If T is equal to 20 nanometer then you are saying that your crystallite size is as small as 20 nanometer. So peak broadening is defined by sharers formula which is a very potential information that you can achieve. Now this is how we go about so draw if it is not a very symmetric peak then you need to draw a base line and then fix your peak and then you look at your 2 theta low that is your B here and then your 2 theta B and then you can look at the full width at half maxima. So this is how you go about doing this but word of caution you can resort to sharers formula only if your crystallite size is less than 100 nanometers or 1000 angstrom if it is more it is not good to correlate your X-ray broadening to crystallite size which is not needed because broadening as I told you can come from strain can come from the instrument and also come from size therefore peak broadening can be very very deceptive therefore we should know what we are looking for. So k depends on T and B and this can be evaluated within 20 to 30 percent accuracy at the best. Now when we look at the data analysis we are looking at the plot data that is 2 theta versus counts that is the principle data that you will get and from there you would define what is the bragg angle that is 2 theta so you can get theta then you can calculate D and you can from D you can calculate A and also you can apply sharers formula to the peaks. So these are the basic steps that you would choose when you are handling any data. Now sharers example we can let us take the case of this 400 refraction that is coming from gold foil which appears at 98.25 degrees then we can calculate the crystallite size in that case using the formula which gives you approximately the dimension of your crystallite size to be 120 nanometer and from there you can actually also calculate your B if you know the crystallite size we can try to see the peak broadening but peak broadening is a direct measure of the peak distance itself. We can also take the other example of calculating your interplanar spacing and this is the bragg example that we can talk about. Let us take the small peak that is 38.3 which is index to 111 reflection for gold foil and how do we go about your lambda is known that is from copper and theta is known so your theta will be 38.3 over 2 so your interplanar spacing for your 38.3 will be 2.35 angstrom. So this is how you assign the peak similarly we can do it for 44.5 degrees 64.7 degrees and you can index a pattern. Now crystalline materials are characterized by the orderly periodic arrangement of atoms therefore when the sample is actually rotating you can see that several planes will come into diffraction. So this is one plane and this is one plane specially these two planes are characterized as two zero zero planes this will have exactly half the interplanar spacing as that of your one one zero. So if you have one zero zero plane it will be exactly half of that will be your two zero zero plane. Similarly when the lattice rotates you can bring other planes also into focus for example this is the way you can visualize a two zero zero two two zero plane and this can also give you a particular reflection. So the unit cell is basic repeating unit and parallel planes of atoms intersect the unit cell and are used to define the directions and distances and how do we map this by knowing the lattice parameter we can actually index this to some miller indices as one one one or one zero zero and so on. So these are called miller indices which we can try to index based on the minimum details that we get from your X-ray diffraction pattern. So the atoms in a crystal are in a periodic array and therefore we can try to use this diffraction to understand the long range ordering or the short end ordering that is available or that is present in the crystal lattice. Here is a cartoon that I want to highlight to you this is X-ray diffraction pattern which gives you idea about the different phases of a single material that is present. For example you take the case of T I O 2 and T I O 2 can actually be present in three different phases anatase and rutile which is more predominant and you also have a brocade phase. Now if you take a X-ray map you would see depending on the phases that are present you can also see different patterns that are emerging and the red ones are predominantly the rutile pattern and anatase pattern comes out as green and then the blue ones are indicative of brocade phase. What you should be careful here is that within a short range all these phases are overlapping. So if you are not precisely measuring then you might confuse one phase for the other. So you need to have some idea about all the phases that are possible which will help you in identifying what sort of phases are present. For example even today the greatest challenge for you to understand is the challenge in T I O 2 to crystallize in a preferred symmetry. For example rutile but what happens anatase comes as a major impurity phase. So chemical approaches are there which are used to stabilize only the rutile phase. So the complex can become more confusing if we do not know what are all the different phases that can be present in your given sample. Now we will look in the other few slides how to index or understand what is the repeating x-ray peak and from that what sort of information that I can get. We will see this in the next two slides. Take for example this x-ray pattern where you only see two patterns that are present. In such case what information you can achieve is important. As you would see here this particular peak refers to 1 0 0 and this particular peak refers to 2 0 0. So in that case only those repeating peaks you will get whereas the other miller indices or other crystal planes like 1 1 0 1 1 1 and 2 1 0 these are all absent in this particular reflection. So just by looking at it you can easily trace that when the several peaks are missing only few peaks are represented in your x-ray scan. You can say those belong to a particular class of hkl reflections. So you call this as 1 0 0 when you put within this inverted brackets then you say that this belongs to H 0 0 type of planes. So you will get only 1 0 0 2 0 0 3 0 0 this also talks about the orientation or the texture of your growth. Now if you look for poly crystals for example then in polycrystalline patterns you would get all the reflections 1 0 0 as you see here 1 1 0 1 1 1 2 0 0 all the peaks of different crystal planes are present which you can get in a polycrystalline sample against a single crystal. So in single crystal you would get only a preferred miller indices reflection whereas in polycrystalline sample you will get all the patterns emerging in picture. Now in the earlier days before we got this x y recorder or as you see in present generation everything is appearing on a computer screen in earlier days it was mostly obtained as a photography. So you would see x-ray patterns coming out as a pattern like this and these are nothing but these lines represent the Debye ring or Debye cone which is coming out as a intersection of your detector on this cone which is appearing as this sort of rings. So with respect to the sample these rings can be measured and each of this ring will give you a particular d value interplanar spacing and if you see here the intensity of this also tells which reflection is going to be at its maximum. For example this is a darker shade compared to these peaks therefore they we can say that these peaks are highly intense compared to the other ones. So this peak for example is intense but this peak is less intense so it comes out like this. So this is the way it was mapped and we can also try to measure the distance from the dark spot. So each of this distance can be evaluated using this formula as S 1 or S 2. S 1, S 2 is nothing but the turn it makes with respect to the incoming x-ray. So if you can measure S 1 based on the distance then you can generate the value theta and if you know the value theta then you can calculate for sine square then you can calculate for case kind of sine square theta and from there you can get your Miller indices and also your lattice parameter. So this is the earlier version by which x-ray diffractions were made and those were available only as a photographic film. So you need to make take a x-ray photograph and then you should develop and calculate the distance from the central spot and that is how you measure the interplanar spacings. But today this is all simplified and you can get everything in a single fashion. Just one or two comments about sample preparation it is not always the problem of the x-ray diffractor meter when you do not see anything. Therefore powder preparation is a very very important protocol when you try to look for a very decent x-ray diffraction pattern. Therefore an ideal powder sample preparation means it has to the different orientations should be smooth and equally distributed. If the crystallize in the sample are very large there will not be a smooth distribution of crystal. Therefore there will be too much of noise coming into picture and larger crystallize size and non-random crystallite they can also affect the peak intensity to a larger fashion. So we need to be very careful about how we orient the sample, how we prepare the sample. If the crystallize in the powder sample have plate or needle shape for example. If those are the morphology then you are sure to get a very confusing x-ray pattern and it can be very difficult to get them adopt to random orientations. So you need to look for a top loading where you can press the powder into a holder and somehow try to make a very continuous spread so that you do not miss out on the reflection. So when we have particles with different morphology it becomes increasingly important how you prepare the sample. So we need to go through that and it should also be densely packed therefore care should be taken how you pack the sample and we should also make sure that the samples are ground nicely if you are looking for a polycrystalline one you cannot just take from the furnace and mount it because when you heat any sample at 900 degrees you are actually looking at samples with 100 micron or so. So you got to bring it down so that it is somewhere in the 10 micron range so the diffraction can be uniform. And also you should understand that low angles you can the spread of your beam has to be this big at very low angles whereas at very high angles it can be very small. Therefore when you spread the sample we should make sure that at all angles the incident radiation is falling exactly on the sample and not elsewhere. So these things we need to bear in mind. And just want to mention to you some of the relevance of this XRD analysis as I am progressively mentioning in this lecture there are different ways of using X-rays for characterizing your sample. Strength of the XRD is it is non-destructive quantitative measurements can be made texture can be used limitation is that it cannot identify amorphous materials. So it grows goes really blank therefore we do not have a potential way to characterize amorphous material and your spot size has to be of the order of 50 micron and you do not get any information on the depth profile. So you just get whatever is on the surface you get that. Now there are also several areas where X-ray diffraction has come into prominence relevant industries who use this analysis are from medical to electronic to several range of industries which are using this as a fundamental tool to characterize the sample. I am going to talk in the next few minutes about some specific examples how we can understand X-ray and always X-ray goes in combination with some physical property where you can try to map some reasonable conclusions. For example take the case of cobalt chromium alloy this is a alloy which is a shape memory alloy and this is used in variety of applications including biomedical applications. Question is are structural transitions induced by magnetic transitions because magnetic transition and structural transition can go hand in hand and we can see if you try to prepare cobalt chromium compounds and this is for a 300 degree C anneal because the ash prepared compound shows X-ray amorphous nature and because of X-ray amorphous nature you see this low angle big broadening or hump and if this hump is present at low angles you can be sure that it is just crystallizing and when you heat it only to 300 you can see this HCP phase is crystallizing out in your cobalt chromium sample and if you heat it at 900 degree C you can see different phases coming into picture in this case it is HCP plus FCC that is coming and in this case it is purely HCP HCP and at chromium 40 percent you are getting a FCC phase and this seems to be going hand in hand with the phase diagram that is predicted. But what we see here is that for all the 300 degree sintered samples which is HCP there are certain peaks which are showing a nearly anti ferromagnetic interactions or competing anti ferromagnetic interaction for example this 20 and 30 percent compared to a clear ferromagnetic loop but in this case all are HCP but when you try to heat this to 900 degree C when in this case if it is FCC here HCP plus FCC and in both this cases HCP you can see that there is a different change in the magnetization and so we can directly correlate which phase is responsible for the anti ferromagnetic coupling which phase is giving you a ferromagnetic signal all this can go hand in hand when you try to map your X-ray diffraction pattern. So this becomes very useful to understand how the magnetic transformations affect the structural disorders and how the structural impurities can alter the magnetic signature. So a competing interaction between AFM and ferromagnetism in this cobalt chromium is actually linked to the structural changes that are happening. This is another example that I want to quote which is a cobalt silver and this is nothing but a granular alloy because if you try to put silver into cobalt or cobalt into silver, silver is crystallizing in FCC, cobalt will not actually form alloy rather it is a immiscible alloy and in this what happens cobalt actually forms a cluster like this and therefore it is called a granular magneto resistance system where cobalt does not spread and get mixed with silver rather it isolates in into cobalt nanoparticles. So there can be correlation between the cobalt clusters and the way they orient can affect the electrical conductivity also. So this is actually used as a granular MR system or magneto resistance system this is the ash prepared alloy this is alloy that is sinned annealed at 600 you can see that it is getting crystallized and the ash prepared alloy clearly shows the presence of both cobalt and silver and when you annealed it is actually transforming into a poly crystal. Now what you see here is this is silver and in silver when you try to put cobalt as of this is the X-ray pattern as a function of the atom percent of cobalt and you can clearly see even up to 90 percent atom percent of cobalt that is doped only FCC silver phase is present. What it means is that cobalt even though you dump it with 10 percent the crystallites grow but they are remaining in a amorphous form and all that you can see is only the FCC phase the HCP phase of cobalt does not come into picture but when you annealed the sample of the ash prepared compound then you can see that the cobalt phase is emerging out which means cobalt is crystallizing from a amorphous phase to this one. So you can directly make a correlation between the sort of crystallization process that is going on with any other physical properties and if you actually map this peak which is true for silver and this peak which you are seeing for cobalt now as you see here this 30 peak clearly shows a change in the full with that half maxima and the position as a function of cobalt and this can have a tremendous influence on the properties of this silver cobalt nano alloys. Here again you see for the 600 annealed sample the peak position changes and the full with that half maxima also changes and therefore there is a way to actually interpret the peak broadening. So in this case the peak broadening can come from two situation one is due to strain induced broadening or one is due to crystallized size. Crystallized size is what we get from Schrader's formula where you calculate the peak broadening but one should also understand the peak broadening comes from strain which is nothing but delta 2 theta which is given as 2 theta 2 epsilon tan theta where epsilon is nothing but your strain micro strain and therefore you can actually correlate that strain to the grain size and you can see here very clearly that with the maximum strain is there when the crystallized size it has is at its minimum. So when the crystallized when you go down in the nanometer range what you are inducing is a macro strain which will also affect your MR property and that is what we try to see from this measurements we can actually try to map the dependence of this micro strain to coercivity and to MR also. Another example of cobalt platinum alloy which actually shows this sort of decorations when you try to synthesize you as you see the ash prepared one shows a TM pattern like this but as you show the TM beam it gets crystallized in no time and the ash prepared compounds are clearly showing a amorphous phase but with increasing amount of platinum you can see this hexagonal phase coming for the ash prepared alloy but when you try to heat it at 900 degree C you can see a FCC phase that is forming. What you would expect this to be a HCP is actually getting into a FCC phase even for a platinum 0% composition which means metastable phases can be stabilized when they are nano in size and this can be easily mapped through a high temperature X-ray diffraction. So this is a very unique facility that is available the X-ray diffractometer has a platform which can be used for sintering and where you can easily map a FCC to FCT transformation that is happening this you can clearly see in this peak which is building up as you are heating inside to this is not taken out and then recorded as you are heating you can do a isothermal X-ray and you can see how the phase transformations are occurring and you can see how clearly this FCT peaks are coming this peaks are nothing but the peaks of platinum foil which is used for spreading your stuff but the regions that are of interest is the peak that is growing along this 201 and 112 which clearly shows that a FCC to FCT transformation is occurring and also we can use this for mapping the Teflon or PTFE polymeric films which you can deposit using PED and as you can see here this is for a room temperature deposited film and this is for a 100 degree deposited film 300 degree deposited and at 500 degree annealed film you can see that the peak is lost and we can also make correlations with the SEM pattern which I will skip for now and then I will also show another example where you can try to see how you can track different things that are happening this is alloy where if you take starting materials like cobalt and iron you can end up in a sonochemical process alloy which is stable even at room temperature on oxidation gives a cobalt ferrite. So this can go hand in hand with other experimental techniques which clearly gives you idea about the alloy formation which is actually reported for the first time. Another point that I want to emphasize before I close is that we need to be very careful about the X-ray patterns that we are producing I have rounded it here in this cartoon as log plot because when you try to do single crystal studies if you do it at linear intensity you would see only the peak of silicon being very huge and the system peak will almost be absent. Therefore if you want to really map the epitaxy then you need to plot it in log scale instead of linear intensity only then you will see the comparable values for example here is a situation I have deposited a luteatium oxide on silicon or on YSZ. So in that case very close to the silicon substrate reflection you would see luteatium oxide and YSZ reflections coming. If this is the way it shows then you can say that it is epitaxially growing but then that is not enough because you also see in the log scale several small peaks which are coming. These are not commensurate to your 1 1 1 0 0 peak which are showing 1 0 3 4 4 0 therefore we can although a very impressive TEM is there then you have to understand that it is showing some polycrystalline feature and it is not totally a epitaxy therefore this is very important and the other thing that will also tell whether it is a real epitaxy is nothing but your rocking curve each of this curve we can try to do a rocking curve mode which will give you idea about the width of this rocking curve will tell how good the texture or growth of this films are. So rocking curve is one important accessory in thin films for you to map whether you are growing a textured film and also this is another example where I am trying to code for a organic molecule how this patterns can give useful information in linear intensity versus log intensity scale you can see how the same pattern changes but what is the advantage you can easily map whether any impurity ion is there therefore whenever we record any x-ray pattern we should always look at the log intensity scale to see whether any minute impurities are there for example in this case these are very small peaks does not come into prominence but in a log intensity these are projected much easier therefore we can see whether any secondary phase can come out. Another important one I may not be able to cover in this lecture but then certainly I will be able to cover in future lectures is the phi scan which is used for mapping the orientation or textured growth of your thin film samples. Suppose I have a peak at 38.6 degrees then I can try to see whether it is texturally growing in a single crystal substrate for which phi scan is used I will come to this in the subsequent one and there are other examples also which I may have to skip for want of time in this lecture but just want to tell you that there are three things that are fundamentally used using x-rays one is x-ray radiography in medical applications but x-ray fluorescence is also another avenue where you can quantitatively get to know what how many metals are there or what is the composition of the metal using the same x-ray technique apart from the x-ray crystallography. So as I pointed out to you there are several x-ray powder diffraction features that becomes useful and in this lecture I have basically covered few things to bring it to your focus one is about how this whole thing works and the two important laws that can be verified that is Schroeder formula and Bragg's law the information that you get out of it and try to understand how your crystals are growing and I have told you about how we can use inside to hide temperature diffraction in measurements can be made to understand the phase transition and also the strain effects that can be correlated to other properties and in thin films I also try to show one passing example of how we can map the epitaxial growth. So in the next few lectures we will also look the applications of this x-ray in perspective with other case studies and not only that we will be looking at other spectroscopic tools in this particular module.