 Hello everyone in today's class on advanced characterization techniques we are going to try and learn something about extended X-ray absorption fine structure as well as surface extended X-ray absorption fine structure and near edge X-ray absorption fine structures. In the last couple of classes we have been talking about diffraction as well as scattering of X-rays as well as electrons, but in today's class we are going to focus on how we can use X-rays for getting spectroscopic information and therefore chemical information from the material or substance under consideration. So as you can see over here there are two different techniques namely the extended X-ray absorption fine structures, the same technique with a different geometry known as surface extended X-ray absorption fine structure and near edge X-ray absorption fine structure which are put together as X-ray absorption spectroscopy. So in today's class we will just get acquainted with these techniques I would like to mention that both the techniques namely the extended X-ray absorption fine structures as well as the near edge X-ray absorption fine structures is based on similar principle however they differ in the regime of operation in terms of energy. So let us go back and see what exactly we have understood earlier in the course of our earlier lectures. So all of us know and which are something that I emphasized that extended X-ray absorption fine structures is essentially a spectroscopic technique and it gives us information about the chemical composition however unlike techniques like EDS that is energy dispersive spectroscopy EX-AFS gives us information at the angstrom level about the chemical content or the chemical environment of a particular atom under consideration. It is based on the same X-ray absorption edge which we had touched upon in our second class while you are understanding the instrumentation involved in X-ray diffraction. So just to recollect it again here you can see a normal spectrum as a function of wavelength for say something like copper target here in you see how we get the absorption for a nickel filter and here you see that the absorption essentially increases with the increase in wavelength. However at a particular wavelength there is a sudden drop in the intensity and this occurs because of absorption. So our today's technique EX-AFS essentially focuses on this kind of a phenomena this absorption edge that we are seeing in the figure discussed over here. So we know that how does X-ray interact with matter we had talked about elastic interaction which leads to diffraction. Now the diffraction can be either wide angle X-ray scattering which we carry out on a routine basis in laboratories or it can be according to small angle X-ray scattering which we had touched upon in the third and the fourth lecture. At the same time in elastic scattering that leads to Compton scattering which is studied using the X-ray Raman effect was also touched upon in a earlier lecture by my colleague. However what we are going to talk today about essentially is X-ray absorption. So here in you can see that there is a decrease in intensity of the X-ray as it passes through a material. So the extent to which this decrease in intensity occurs depends on the absorption coefficient mu which essentially decides the extent to which intensity of energy beam is reduced as it passes through a material. The absorption edge that we had seen earlier is essentially a sharp discontinuity in absorption spectrum of X-ray when energy of photon correspond to energy of a shell of the atom. Now we are going to talk about it in the next slide but let me just you know kind of put it mathematically the how absorption can be quantified. So if the incident beam is of the intensity I0 passes through a material with thickness of X the amount of attenuation that occurs is actually to the power minus mu by X where mu is the absorption coefficient and therefore the intensity after passing through the material gets modulated as I is equal to I0 e raise to minus mu by X. If we incorporate the density of the material we can get I is equal to I0 e raise to minus mu by rho into rho X this is particularly important when we are considering mixture of various material and we can take the weighted average of the absorption coefficient as well as the density generally it has been found out that the relationship between mu and rho is not only wavelength dependent but also atomic number dependent. Now on the right hand side we can again see the similar curve what we had seen earlier where we have a critical energy WK for ejection of K electrons from nickel and this corresponds to a steep drop in the intensity and leads to absorption of the X-rays of the copper X-rays what we had seen in the earlier case. Having said that what are the kinds of interactions that can occur when a particular photon wavelength is incident on a material. So for X-ray photon of energy H nu is incident and has sufficient energy it can knock off an inertial electron. In order to do that the energy of the X-ray photon has to be greater than the binding energy of the electron. Once this electron is knocked off from the inertial it can go and become a part of the continuum. There are other possible scenarios that can also occur having said that if the electron from the inertial is knocked off and goes to the continuum we can get a transition from outer shell to the inertial and this transition is accompanied with a release of another photon which has a wavelength that is different from the incident photon. This phenomena is known as fluorescence and we can also use the fluorescent photon to uniquely characterize the material under or rather the element under consideration. Another possibility is that in case this inertial electron is knocked off we can also have a release of another OJ electron from the outer shells in order to accommodate this phenomena. So all this including the fluorescent photon as well as the OJ electron or the photo electron will essentially characterize the element under consideration. If we can uniquely identify and correlate either the photo electron the OJ electron or the fluorescent photon with a particular element we can get chemical information about the same. Now this is this philosophy is used in a variety of spectroscopy technique and X-ray absorption spectroscopy which comprises of extended X-ray absorption fine structures as well as near edge X-ray absorption fine structure which is also known as Zanes is no exception. This is this these techniques is a comprise of modulation of X-ray absorption coefficients at or near the absorption edge. So here again let us go back and have a look so this is where we have an absorption edge and here you can see the wavelength. So how and therefore the frequency is also and you can see that what all modulation occurs near the absorption edge is what is used as a finger print for the presence of a particular element using in these techniques. So let us look how exactly the pattern looks like. So if you recollect this is how the absorption edge looks like so in this case since it is energy you see we are going this way here is the absorption edge and again it goes on increasing but decreasing energy. However you notice if you are the modulations which can be seen in this pattern here again I would like to point that the technique Zanes X-ray absorption near edge structures are found very close to this particular absorption edge while extended X-ray absorption fine structures as the name suggests is far away therefore extended right. So all of them these modulations which are far off are essentially known as extended absorption fine edge structures. Now to emphasize that whenever we talk about absorption edges it has to be specific. So if you want to study a particular element you have to focus a particular edge. Now this point is made clear in the spectrum shown over here. So here again we see that indeed we are having two absorption edges the L3 absorption edge of lead and the L3 absorption edge of bismuth. So in the present scenario we are focusing on the L3 absorption edge of lead the region which is very near to this edge essentially comprises of Zanes spectra while the region far away comprises of extended X-ray absorption fine structure. So this transition or this differentiation between X-abs and Zanes is a bit arbitrary though there are ways of kind of quantifying it as a thumb of rule generally it is considered that at a wavelength of the or energy of the order of 100 electron volt from the absorption edge Zanes is valid while beyond say 50 to 100 electron volts extended X-ray absorption fine structure are valid. So as I had mentioned X-abs starts from 50 to 1000 electron volt from the absorption edge. If you appreciate that at with increasing the energy we see that there is the oscillations that we are getting essentially die out having said that absorption of X-ray photon is actually accommodated by emission of photo electron. Now this photo electron unlike in the normal case tends to behave like a wave right like this is the basis of wave particle duality wherein you see that our sub sub atomic particles can also behave as wave having said that these the wave form because of the photo electron actually interacts with the neighboring atoms and therefore they get scattered from there not only that there is an interference between outgoing as well as back scattered photo electron wave and this leads to interference. Now this is something that we had talked about time and again right like we have the X-rays which are going they meet in phase there is constructive interference if they meet out of phase there is destructive interference. So something very similar to it is happening however this is happening very locally and at the atomic level and these modulations are essentially seen in the Zanes or for that matter X-abs spectra and this essentially contributes to all the oscillations that we are seeing over here. So all these oscillations that come we will have a better figure later in the class but the situation is very similar to what has been shown in the figure. So here we see we have our essentially atom which is actually emitting electron waves. So you see the electron waves are going the moment they interact with another atom what actually happens is they are back reflected right they are back scattered and once these propagating and these back reflected the interfere right the interfere and depending on that we get if there is constructive interference high intensity and if there is destructive interference we get low intensity and this leads to essentially the oscillations that we saw in the X-abs spectrum. So what kind of interaction that can take place what I showed in the earlier figure is a very simplistic assumption and here each and every atom is essentially just reflecting the waves in nice spherical form. However this may not be true there are various kinds of interaction that may occur. So here we have some possible scattering or multiple scattering events have been figured out over here. So here in the first case we see a single scattering path right so like you the electron wave is scattering from the red atom to say the green atom and it is getting reflected from the green back to the red right while in this case we have a double scattering path which is shown over here okay and we get mostly for forward scattering angle of close to 180 degrees. Similarly there is also quadrilateral triple scattering path and also triangular triple scattering path. I am not going to go in details but I hope you appreciate that depending on the kind of interaction we are having all the mode of oscillation is of the pattern is going to vary. Now having said that we can always find out what kind of interaction is going to occur between the two at neighboring atoms and what do we expect to get as a output more about it later but remember that for a given atom the kind of interaction that takes place depends on its neighborhood. Now this is the very genesis of the X-ray absorption spectroscopy technique wherein we can get really information about the atomic neighborhood of a particular atom or particular element under consideration because remember in this case we are focusing only at the absorption edge of one particular element like we can see over here. So you focus on one particular element and you see the modulations for that particular element so we see that okay if I have led somewhere what is the neighborhood of red of lead okay so this is how it works out now moving ahead as I had read as I had mentioned X-ray gives information about the neighboring atoms not only that it tells us what is the approximate atomic number because remember at the end of the day the scattering tendency of the atoms is essentially dependent on their structure factor and which you are quite aware varies as a function of the atomic number. Having said that another important point that is very relevant is the distance between the two atoms if you remember whenever we talk about interference what really matters is we are essentially going from the real space to reciprocal space so the same kind of thing happens over here and depending on the distance we are going to see whether we get constructive interference so all this information we do get using X-abs however it is highly modulated having said that one of the biggest advantage that we have with X-abs is that it works very well for crystalline as well as amorphous materials while our X-rays particularly when we talk about diffraction gives us very little information about amorphous material at the same time X-abs can also be used for studying solids, glasses, liquids and even gas having said that one of the biggest advantage of X-abs is in studying in situ processes that occur in different class of materials however X-abs is not really as common as other spectroscopy technique right EDS and the main reason for that is we need tunable X-rays to capture a particular edge I hope you appreciate that whenever I showed the earlier images we were going at a particular value of the absorption edge and this means we need a source for X-ray which can gives us energy over a particular range and this not only that we also need energy resolution which is very good of the order of 10 power minus 4 volt in 1 volt and therefore most likely and in most cases we have to use a synchrotron source for carrying out X-abs study having said that the main driving force for carrying out X-abs is to study light elements like carbon, oxygen and nitrogen now these elements cannot be very well studied using conventional spectroscopic technique having said that we talked about different kind of interactions that occur namely the electron the free electron that is given out once a photon energy is absorbed you also talk that you know there can be a fluorescent X-ray that can come off and there can also be an all J electron so all these signals can be used in X-abs in one way or the other to get some information about the localized chemical composition having said that X-abs is generally used in transmission as well as fluorescent mode to get the relevant information a general instrument that wherein we can carry out X-abs is shown over here and you can see that we have a beam coming out from synchrotron however we need a double crystal monochromator to get a particular range of energy and we need a incident flux monitor to see what is the intensity of the incident X-rays then it has to interact with our sample if it is working in transmission mode you can see that the synchrotron beam passes right through the sample and we have a transmitted flux monitor which monitors the intensity after the X-rays have passed through the sample at the same time we also have a fluorescence detector to see what all kind of fluorescent photons or fluorescent X-ray that we are getting so having said that you I hope you appreciate that we can get information about the chemical environment in a particular material either using the fluorescent signal or the transmission signal point that is to be noted here is that in the transmitted signal the frequency of the incident and the transmitted wave remains the same while in fluorescence there is a change in the intensity of the not only the there is change in the frequency of the incident photon having said that for detecting the intensity of the X-rays we essentially use ionization chambers other detectors like photo diodes photo multipliers as well as solid state energy dispersive detectors as well as wavelength dispersive detectors which we had touched upon earlier in this module as well as I am sure it must have been covered in the in the earlier part of this course by my colleague but most likely what we use in case of extended X-ray absorption fine structures are ionization chambers as they provide high flux and wide energy range. Now that we have gone so you see how simple we have a very simple exact technique right the instrumentation part has got nothing exotic however one of the most important criteria is the synchro availability of synchrotron having said that you see with such a simple instrumentation there are there is a strong capability to carry out in situ experiments so we can vary temperature pressure doping as well as orientation and concentration in a solution and study how the chemical composition is of the material under consideration is changing as a function of external stimuli another important thing that I have that I have not mentioned yet is that there is ability for us to get the synchrotron and use a polarized property of X-ray and if you have polarized wave of synchrotron or X-rays we can see get sufficient information about the orientation this orientation I mean like the kind of bonds that we are having between A and B so by X-Affs you can know that you know A is surrounded by B but if you use polarized X-rays we can not only know that you know E is surrounded by B or C but also at what angle it is aligned with respect to A this is particularly important for deciding the chemical bonding between the two species. So as we had already discussed X-Affs what we do excite the core electron to higher unoccupied or continuum state now for this we need energy tunable source of X-ray photon to illuminate the sample for instance if I am having a compound say A, B, C, D and I want to study what is the neighborhood of say A and A or B then I should be in a position to tune my energy to the absorption edge of A, B, C or D having said that another important point is that what all we are getting what all pattern we are getting it is not just the absorption edge as the name suggests this is extended X-ray absorption fine structure so we should have the ability to provide photons with energy of few hundreds of electron volt below the absorption edge and up to few thousands of electron volt beyond the absorption edge. So there is a strong energy dependence of the absorption spectrum and we should be in a position to control the energy and therefore we have to use a synchrotron which gives us energy resolution of 10 power minus 4 volt in about 10 volt. So as we can see the X-abs data is characterized by a step function centered at binding energy broadened by measurement resolution lifetime of core hole and monotoleically decreases with energy remember what all we are getting is happening at the absorption edge so let us go back and just look at the absorption edge so if you go to the absorption edge this is where you knock off an electron from the inertial and then there are these interaction between the electron wave right and this interaction leads to the oscillations that we are getting. So in order to get that this there is a lot of superimposition of the signals because there is not just one scattering event there is easily a situation wherein you can get multiple scattering and therefore this makes analysis of the data slightly complicated. However a very simple governing equation is given over here so here you see the chi of k is essentially summation n of j which is nothing but the number of atoms which are surrounding a particular atom or element under consideration the fjk exponential minus 2k square by sigma square is essentially the disorder term which actually decreases in intensity with the number of oscillations and there is a electron inelastic scattering term so here you see we have a scattering term which essentially comes from elastic scattering and here we have the inelastic scattering term which actually determines the interference right so we have to see how much interference is occurring okay so this elastics electron inelastic scattering term is this one the second exponential the first exponential over here is actually the elastic scattering right like which dampens and this interference term essentially decides what kind of an oscillation pattern that we are going to get. As you can see from this equation the period of oscillations increases with the increase in frequency having said that also there is an increase in the period of oscillation with increasing r where r is the distance between the atoms under considerations and also the intensity chi e actually increases as we have more and more j assuming that or more and more atoms assuming that all of them are scattering in phase okay so now let us go and see how exactly XF's data looks like so you see here this is again our energy versus absorption coefficient and you see the same thing we do see that instead of getting a sharp drop we do see a few modulations over here this does not show a lot of information however once you convert it to chi k k cube versus k we see that there are lot of oscillations I will tell you the reason why we are multiplying with k cube and I hope you appreciate that essentially it is done to actually see the oscillations at higher value of energy as we move away from the energy from the absorption peak we see that there is a lot of damping effect. So in order to see the oscillations if we plot chi of k versus k cube we do see all the oscillations now another important thing is this k is essentially in the reciprocal space so that is why you see over here we have the angstrom inverse right now this information can be taken back and plotted in the real space and we do get this as a function of r which is nothing but the distance actual distance between the atoms under considerations and this shows the intensity right so this is what we are going to try and match when exactly we take the data so now I am going to show you some things about how exactly we do XF's data analysis having said that I should mention that you know we use well developed software at different synchrotron sources and one such software is IFFIT which is used at University of Chicago now these are available for free and what you can do is you can take and try to analyze what all data we are getting from different synchrotron sources so you see over here this is what we have this is what the kind of data that we get fine which is nothing but mu of E versus the electron versus the energy right so this mu of E comprises of both the things right for your Zane's data which is very close to the absorption edge right which is shown over here and which we can separate and the data which is far off from the absorption edge but even before we do that once you get a signal the first and the foremost thing that we do is to subtract the background and this is what has been shown over here so we subtract the pre-edge background and then we normalize it we can also separate the Zane's or region which is very close so you see we have gone almost up to 100 electron volt and said that you know up to 100 electron volts I have Zane's and beyond that I have X-ray absorption fine edge structures you continue with that and after doing all our pre-edge subtraction we carry out post edge subtraction and here you see the kind of oscillations that we are getting quite a few bit of oscillations now what we do is we take the same part after subtracting the background and our chi of k versus the k and you see this is the actual data that we get after doing entire background correction as we had seen earlier in order to see or in kind of modulate and see the oscillations we can plot chi of k versus k square into k square versus k and here you see how we get the modulated oscillations and they are easily visible now all these modulations correspond to a particular interference occurring between two atoms okay so now if you see this is how it looks like we had plotted chi of k versus k now the same information can be taken back and plotted in real space so now you see we have chi of r versus r and this r is in angstrom and here you see we are seeing some characteristic peaks having said that if you remember this chi of r that we are having as well as r itself the Fourier transform of chi of r it has a real part and a imaginary part so we have tried to match the real part and we do indeed see that you know the red one shows that okay there is a good match having said that please note that you know there is the intensity is dying off at higher values of r and once we plot you know k square versus chi of k versus k you see that you know all the oscillations are visible and we can see that there is a good match though it is not visible over here having said that once we get our chi of r versus r we can go back in literature and actually find out what corresponds to which peak corresponds to what so this is just like jcpds or icdd where we have a database so here we can see that this peak which we get between 1 and 1.5 angstrom essentially corresponds to feo while between 2 to 3 actually corresponds to fe and fe so by doing like this we can see that we can fit in all different kinds of peaks and get individual contribution from individual for that matter here iron iron and iron oxide peaks not only in real but also the reciprocal space I hope with this analysis it is very clear that we can identify not only what all atoms are present in the neighborhood but also at what distance they are present and therefore this technique uses information about the chemical surrounding at the angstrom level here again I have just mentioned to you that we can carry out various test in situ like heating as well as applying pressure so just to show you what kind of effect we have if we apply temperature we see that there is a continuous decrease with increasing temperature so these are some practical limitations that we have but remember the kind of oscillations all these corresponds to all these oscillations actually correspond to the interference between the waves that are being you know scattered from the surrounding atoms and you see that as we increase the temperature there is a decrease in the oscillations okay another important parameter this chi of k I hope you remember like if we start if you go back to the first curve we see in this case we have mu of e which is nothing but your distribution and here I have swiftly shifted and I did not mention what exactly is chi of e but let me just write that chi of e is nothing but mu of e minus mu okay I have gone on the wrong side let me just do it over here so let me say that this my chi of e is equal to mu of e minus mu 0 of e so this is nothing but the differential term okay of mu 0 okay so this is what we have done over here okay so having said that what all we have talked about up till now is the basic right the basic physics for doing extended x-ray absorption fine structures and I hope you appreciate that we are talking about very thin samples mostly I mentioned that you know we have a sample large enough so that the x-rays are able to pass through it however there are instances when we are looking at surface phenomena and there that is where grazing incidence is very important and if we carry out the same x-ray absorption fine structures in grazing incidence mode it is known as surface enhanced x-f's or se x-a f's now the biggest advantage that we have is that we can irradiate a region extending from nanometer to millimeter range just by changing the angle of incidence having said that we can also use the same concept of detecting either the reflectant beam or the fluorescence or even low energy electron namely the auge electrons to get some information about the chemical environment of a particular element under consideration as I had already mentioned that the original equation of x-f's breaks down at lower k where we have this near edge x-ray absorption fine structures at in this energy range actually what happens is there are multiple scattering events and the dynamical calculations have to be incorporated now these are two involved and as such Zanes rather Zanes or near edge x-ray absorption fine structures is actually used only as a fingerprint technique by which I mean that if you see a particular you know peaks in the Zanes spectra we can say that okay this particular element is present however the quantitative analysis of this technique has not developed till date. However the Zanes use a lot of qualitative information about the coordination chemistry molecular orbitals band structure as well as various multiple scattering events that can occur in a material having said that I hope you have you appreciate that we can get excellent short range order information about chemical environment using x-ray absorption spectroscopy we can also use this technique to study crystalline amorphous as a materials as well as liquids however synchrotron radiation is almost always necessary for carrying out x-ray absorption spectroscopy another important disadvantage that we have is though we know the chemical composition or the chemical surrounding we have absolutely no idea about the oxidation states and the theory that is involved for understanding x-f's as well as Zanes is pretty complicated and this complicates the use of this technique in getting some information with high fidelity thank you