 So we have been discussing about quantitative analysis using XPS, quantitative analysis is very popular in XPS in the sense that we can obtain very high quality informations and I have already discussed to you about the way quantitative analysis is done basically when you have multiple elements on the surface layer of a material and if this elements can be represented by i, j and k then I can write down the ratio of ni divided by ni plus nj plus nk is equal to this expression which I have written here basically it is if you look at it properly it is a ratio of i divided by sigma lambda for the specific element divided by the ratio of the same or addition of the ratios of all the elements and by this way we can measure the basically the particular element concentration in the surface layer. So what is needed to be measured is the intensity and I have already told you how intensities are to measure using very nice approach well let us see some of the examples I am going to show you the examples of oxygen metal atomic ratios determine form from the corresponding intensities if you take magnesium oxide first case MgO so it is a palletized powder ratio between oxygen 2s peak divided by oxygen you know metal 2p peak is the concentration is almost 0.95 plus minus 1 as you know 10% is the approximate error in case of the these quantifications and obviously oxygen 1s divided by metal 2s or magnesium 2s is basically almost like 1.1 plus minus 0.1 similarly oxygen 1 is divided by metal 2p is 1 plus minus 0.1 and we can keep on doing this aluminum oxide L2O3 thin plumes silicon dioxide Fe2O3 Cu2O zenoxide molydenum dioxide trioxide and cadmium oxides and these ratios are actually average of 6 measurements and this issues are very reliable so one can actually obtain from the ratios exact you know oxygen to metal amount ratios for the particular oxide. If you compare this XPS measured quantities respect to the electron micropope things will be muscular to you let us talk about silicon and this is silicon 2p so that means it is basically silicon dioxide so XPS gives you 27.3 percentage whether electron micropope gives you 29.3 just differ by 2 atom percentage in different you know wavelengths this is aluminum aluminum you know lab different kind of category so X you can see the values they are very close by not differing much similarly for calcium, potassium, sodium, aluminum and if you look at some of the percentage of the difference is 9% here is about 11% there it is maximum is actually 11.5% so that means XPS gives you reasonably good data in terms of compositions although electron micropope is better but you know electron micropope uses of electron micropope is not easy in the sample has not prepared properly and also electron micropope analysis requires standards which is not the required for XPS so that is why XPS is easier but cost of the instrument for XPS is much higher than the electron probe so that is the advantage. Let us talk about errors as I said error is approximately 10% so II basically the error comes from the intensity measurements so what is the problem there this is basically difficult to separate the intensive photo electrons for the extensive scattered photo electrons which comprise the background that means there are extensive photo electrons which forms a background of the XPS intensity buses you know this binding as a peak so that means there is a background as a this background basically comes from the in extensive photo electrons extensive whether the intensive the peak comes from in intensive photo electron the basic problem is to differentiate between them that means basic problems lies in fitting the background properly because intensity calculation will depend upon how you remove the background and that is why actually error tips in and this error can be approximate to be whatever plus minus 5% is 5 to 10% second important can be I mean upon the Sigma I which is normally calculated from upon these plot which I have shown you and thus that is the and they are it is basically make the error of magnitude is unknown most of the cases lastly error can come from the lambda I estimated error and then I have already shown you how lambda is calculated let me go back yeah these are the lambda I calculated this is the master plot universal curve and obviously measuring this lambda as if there is a small error and then it can lead to error in calculation of the compositions for most importantly this is you need to take care very well otherwise the error can be high Sigma is normally always unknown 9 to 2 we cannot really predict lambda I can be calculated very precisely estimated very precisely so there is no problem there well after giving you some idea about the quantification let me just talk about some other very important issues of XPS most important one is obviously chemical shift in XPS that is why this particular technique is famous for chemical shift means the chemical change of the electronic state or the chemical state you can define when something is some metal is reacting with some oxygen nitrogen or what are other elements together then obviously we need to we can also find out when some reaction is going on whether initial state and final state and we also need to discuss about kumbhans theorem which is very good in analyzing this chemical shift and we can calculate actually this chemical shift using formula finally obviously one is to know the line with a resolution for a particular XPS instruments so let me first discuss about chemical which is very important from the space point of view what is a chemical shift actually chemical shift means change in a binding energy of a core electron of any element T2 change in the chemical bonding of that elements that means when there is a bonding between two elements there is going to be change of the binding energies of the core electrons and this leads to shifting of the peak position in the XPS spectrum I hope this is clear I will make it clear by giving some examples also what it is the quality view of this quality view of this core binding at this are normally determined by what electrostatic interaction or coulombic interaction between the electrons and the nucleus as you know the nucleus a positively charged species electrons are negatively charged species so there is an coulombic interaction between these two so this interaction is what is basically leading to the core binding energies now this can be affected or reduced either by two things one electrostatic stealing of the nucleus charge from other electrons present in the atom that you know if there are other electron in the atoms that can act as shielding barrier between the core electron and the nucleus secondly there is a first factor and there is a predominant factor second factor is the removal or addition of the electronic charge as a result of change in the bonding that will also alter this shielding actually so that means first one is a shielding of the nuclear charge second one is the removal or addition of the electronic charge because of the bonding that can also alter the shielding yes as an extra electron comes that can alter the shielding so these two actually are the you know core binding energies actually dependent on these two factors so whenever we add an electron or remove an electron from the core shells of the atom there is going to be change of the you know charge or change of the binding energies so this bad means if you have withdrawal of electronic charge there is an increase in the binding energy and this is also basically known as oxidation if you take out some electron out of a species is called oxidation and if you add and balance electron charge into it it is called is basically to decrease in bending and this is nothing but reduction okay this is basically can be thought in this way suppose you take a sodium and a chlorine when on the sodium and chlorine reacts and form sodium chloride which is a common salt now how the reaction happens you know very well sodium actually gives away one electron from your outer shell and this same electronic accepted by the chlorine and this process sodium become plus charge and chlorine become negative charge and then these two oppositely charge pcs a get attracted because of a coulombics interaction and forms a bond in this process both the binding energy of sodium and all the binding energy of the binding energy electron sodium and binding energy of the chlorine gets affected and because of these issues we are going to see a chemical shift I hope I made you understand clear now let me give an example in that way let us talk about metal and oxide you know this is how we are talking about metals engineering so it is better talk about metal and oxide let us talk about a simplest possible metallurgists the lithium we have three electrons in its outer cell there are two electrons the 1s orbit and that is one is to and one electrons in the 2s orbit so basically one is to 2s one now that means what if we look at the electron density the 1s to 1s to the two electrons then three electrons so if I if I basically have a plot of intensity versus binding energy you will see this peak for lithium 1s right now what happens when lithium gets oxidized lithium this oxidized it forms like 2o that means two electrons comes from the two lithium charges or two lithium item actually gives a one electron each to the oxygen atom so the oxygen become doubly negatively charged and two lithium ions become singly positively charged and that's how actually the these two opposites are attracted and forms a compound now what is the structure of li2o core shell as 1s to then 2s to then 2s6 okay so 2s6 basically for the oxygen as you know there is no six electrons and 2s but because you have added to a you know for two electrons in oxygen so there are oxygen as four electrons in the two piece yeah two electrons the outer cell so the four electrons four plus to become six so that's leads to change in the binding energy of the core electron of the lithium so that means lithium binding energies gets shifted to the left side and we start seeing lowering of the binding energies and this is due to its increase kidding of the nucleus by 2s conduction the buying energy is higher because li2s it is lost to the oxygen because basically binding energy increases this way not sorry it increases this way there is a Fermi surface energy so binding energy is basically higher because li2s electrons 2s electrons are here there is only one 2s electron there are one 2s to one is two electrons level and 2s one electron 2s level so because these two a single electrons density is lost so there is a change in the shielding of the electrons and this leads to change in the binding energies correct so this can be taught in different little bit different way you know the photo emission actually can be thought of consisting of three steps first is the photon absorption that means except photon comes it get absorbed then this leads to ionization that means when I get absorbed and the electron gets rejected it leads to ionization this is called initial state effects second case second thing is responsible atoms in the creation of photo electron that means ionization has happened how electron has got removed that's why I'm just happen and this leads to increase in a photo electron understand the photo electron comes out with a certain kind of energy now third step can be thought of transport of this photo electrons in the surface and this is what is in the extrinsic effect this is doesn't depend on the you know particular atomic pieces it depends on the surface layer thickness and many other aspects so first is this absorption except except photon get absorbed h nu and this is causes ionization material ionization means removal of the electron from the outer cell or from the core cell rather and this leads to see the second step the photo electron generation and then photo electron moves so therefore final still is one additional positive negative positive charge initial state of BAB and then you have a positive charge attached because of this ionization effect usually chemical ships are thought of as initial state effects initial state means ionization as you see here this is initial state effect state effects relaxations basically is nothing but relaxation process similar to any other relaxation process in this case I don't know whether you can see this is a titanium this is titanium dioxide titanium has 2p 3 by 1 by 2 this is 2p 1 by 2 and this is comes around 460 by electron for binding energy and this is 2p 3 by 2 this is which is basically pin over at a splitting of the two peaks and this comes around 453 so difference between these two is actually 675 667.5 something like that so the the chemical shift for Ti and Ti4 basically charge with dawn when you there is a Ti form Ti2 well yeah let us see what happens in the when this is I am sorry this is 666.75 so this is 6.75 like about now if I form a Ti2 basically I have a change in the state electronic state of titanium form Ti0 to Ti4 plus so the Ti2p half this is 2p half and this is Ti2p3 by 2 you see the distance between these two has reduced to 5.7 electron volt so that means binding energies are the clean orbital splitting of these two P levels P2 and half and P2 3 and half has reduced so the spin order splitting approximately you know constant not a conforming issues like I said chemicals information very powerful tool for functional group and oxidation states so you know this is basically can be thought of a relaxation process which is basically due to ionization of the initial state. Now what is now let us talk about what is the Coopman's theorem after knowing the what is the chemical shift you know Coopman's theorem says the binding energy of an electron is simply the difference between the initial state and the final step that means what is the initial state initial state is the atom with any electrons and final state is atoms with n minus 1 electron or maybe more than one who knows that is n minus 1 electrons ions and plus free electrons so that means in the initial state you have fully you know all the electrons are present in the whatever electron is defined by the atomic number of the element present in the cell and the final state you have removed the electron because of the because of the you know charging because of the ionization effect so you have n minus 1 electron at a suppose one electron has got removed and this extra electron will come as a free photo electron so what is the binding energy change binding energy is basically n e final n minus 1 divided by initial n that is what is basically the equation which is used by Coopman's so if no relaxation followed photo mission there is no relaxation so binding is nothing but the original energy which can be calculated form Hattrick fog theory which is available basically it is a plot of that this relaxation is nothing but electronic rearrangement following the photo emissions please do not get confused to the relaxation of the surface atoms now if I plot experimental binding energy with a calculated binding and just like this if you if you look at carefully this chart they fall on a straight line almost passing to the origin so this are CH4 CH2 to H6 you know C2H4 different kinds of organic compounds up to C4 so one can actually see the experimental binding at this and the and the calculated bandage they are same so that means Coopman's theory predicts what is to be estimated or calculated based on this theory and then measure so this is true so please try to remember this equation when there is an organization this is how we can calculate here we have not considered that free electron we thought this is not no and not any effect because we relax this are the sound if different values typical chemical C1 is values and this are taken from those books as you see here for Hattrick carbon there is CH or CC bonds okay it is binding as is 285 amines this seek nitrogen 286 alcohols has COH or COC both possible 286.5 electron volts flew into carbon it is very important 286 7.8 carbonates has basically CON C00 289 89.6 or CF3 3 more thick fully atom 1 to carbon is 293 to 294 that is this is a very genetic table is available in the literature most values are actually plus minus point to electron ball that is why these measurements says first of oxygen binding energy is basically up a look at carbonyl groups C00 or C00 532 alcohol ether C532 each star here 533 so you one can actually measure this kind of binding energies using XPS well we can actually explain this chemical shift as I said chemicals is very important using charge sphere model it is not very difficult to do for a single atom suppose which has certain number of electrons the electrostatic potential is basically given by Coulomb's law Qv Qv is the you know number of Q charges into electron square divided by RV RV is the distance average radius of valence of electrons Qv is the number of electrons and as we respond so change in the binding energies is obviously change in the average number of like balance electrons is nothing no effect of these two they do not get changed. So if I add the change in the inter atomic potential because of this change in the binding energies then eb becomes bj minus and then this is the plus quantity ? Qv square RV as you see here so bj is the potential of the atom I on j that means when suppose na and cl if na gets one electron removed so because of that is a change in the binding energy now when this na plus charge and this electron is taken by chlorine it comes close to chlorine there is a potential change so one needs to basically use this ? vij along with the change in the binding energies to calculate the exact binding energy of this sodium ion in neighborhood of the chlorine ion that is what actually is calculated to in this model charge pair model now to give you some more examples of chemical shifts that is what make your understanding clear let us suppose carbon 1s in this compound CO I do not exactly remember this is a three fluorine groups one carbonyl group and then there are CH bonds so carbon 1s if you look at it this is this is the typical you know spin orbital spitting and these are the two this s and 2p I think so carbon 1s peak actually has this kind of shapes now if I look at the silicon silicon as pure silicon is here so as you see this is close to almost 0 then silicon f si f si f 2 si f 3 si f 4 so as you keep on you know having more and more fluid ions attached to silicon from 1 to 4 the chemical ships increases so by this way actually one can determine what is the exact state of the atom so if I put the oxidation state versus core electron shift silicon has no oxidation state 0 silicon f 1 has one oxidation state correspond to one core electron shift si f 2 2 si f 3 3 si f 4 is little bit higher than 4 so that means there is a linear relationship between oxygen state and the core level electrons second example I am giving a metallic oxygen iron with Fe2O3 hematite what you are showing is AP 2 1 by 1 2p 1 by 1 as you see metallic iron has binding energies of around 707 whereas iron oxide is a broad peak like this and binding energies of the peak is about 711 so that means there is a change in the other there is a shift towards higher energies as we have told already for metallic iron to the iron oxide let us see another example so in order to give you Fe2O3 and Fe2O3 basically what Fe is three state the plus 3 and always oxygen is plus minus 2 so if I look at this is what is Fe this is Fe3 Fe2 will come somewhere here you can see the small peak Fe2 comes actually in FeO oxide iron oxide so that means we can actually clearly say there is no plus 2 states all the oxygens are actually plus the ironically plus 3 state let us talk about oxygen you know in case of oxides and surface hydration your metal oxide this is oxygen s half so if you look at oxygen one is half if you look at this this is the metal oxide I do not remember what is the metal oxide but if the hydration episode of surface is not oxidation but surface hydration the peak will come very close by this is 530.5 this is 532 binding energies that also can be you know separated out in XPS in this cubic boron nitrate is a very hard material which is used let us see what happens when you do the spectrum before iron the argons iron sputtering and after and sputtering we will show both boron one is fixed if you see this is Pn this is oxide before sputtering there will be some oxides obviously boron oxide but if you sputter you clearly see only nitrate that is why basically sputtering is used now if you do not sputter nitrogen pick what happened I do not know one is this is Bn this is oxide so we do not know this is not a boron nitrogen oxide this is basically boron oxide B2O3 or something if you do the sputtering you just kept to see only the B nitrogen peak cos Pn so that means this is very clear the shift of the compa of the chemical shift of the boron or nitrogen one is peak positions also function of even oxygen presence on a surface so that is can lead to some oxide formation arsenopyrite another example if you look at arsenopyrite you have suppose arsenic iron of sulphide this is what is called arsenopyrite so this can be fitted actually this is done with 100 micron diameter excess part and then we have also showing you arsenic oxide to oxygen state arsenic 2 O3 and arsenic 2 O5 here you see the two peaks one is caused by arsenic as caused by iron and this arsenic 3D actually not arsenic yeah so you have basically splitting and this is distinctly different from these two so arsenic O2O3 so that means in this sample actually have both arsenic sulphide arsenic iron sulphide as well as arsenic oxide O3 O2 as a H2O3 both are present now to not sell after giving you all the examples I just want to show you some in a chart where this can be you know cationally told this is basically 4F7 by 2 binding energies of gold and some gold compounds shown from top to bottom gold actually has a binding as is of 84 if you have gold team compound equatomic its increases 84.5 gold in another compound SN4 85 etium gold what happens it will be I am gold it will be I am gold a u2 again sits very close to a usm cloro auto phosphoric acid phosphoric is basically comes here 85.5 this is again same thing but three ions there is no change in this in the in the positions as you see phosphoric acid phosphene group actually oronite right this comes same place sorry this one decreases here these two are same three oxides change so phosphor phosphene group does not change the electronics you know spining and gs up to F4F7 by 2 but if you change to ring 3 in the phosphene group remaining same it gets increased 87.5 cloro auto phosphene 3 as arsenic decreases similarly iron you know complex compounds also change so that means the force F7 by 2 binding energies can be you know you know used as a marker to determine what kind of gold compounds are prepared or present in the sample that is very clear one can actually use this technique to measure even oxide thickness it is possible let us see what happens for aluminum aluminum has always some aluminum oxides on the surface you cannot remove it so if you look at al2p peaks there will be obviously this is aluminum metal and this aluminum oxide when the oxide thickness about 3.7 high resolution spectrum of aluminum surface the aluminum metal oxide picks own can be used to determine the oxide thickness how it is to be done let us see usually the binding ends of oxide and the metallic pieces are separated by phylectron volts that is when the oxide is very thin less than about 9 nanometers it is possible to distinguish the contributions actually from both oxide and the metal photoelectrons if it is less thick aluminum oxide thickness is normally given by 2.8 log of 1.4 I0 by M plus 1 this I0s Ims are intensities of the peaks of oxide and metal position that means D is for aluminum is given by this formula ln 1 by 1.4 I0 by I m into a plus 1 that is how actually used so I 0 is basically intensity of the you know oxide peak and I am is the intensity of the metal peak so that means if I know intensities these two are the oxide and metal peaks I can put in here and find out the basically the thickness and this is only possible in the thickness is less than 9 nanometers it is more than that then this may not possible to distinguish between these contributions and this fails this is done for many other oxides so in the last actually few minutes I am going to discuss about instrumentation what is done so what I have shown you in the nutshell is basically XPS as a technique and to be used for you know finger printing like you can detect certain elements electronic states of the element present very well and also even we can distinguish between the spin orbital speeding of a particular orbital like 2p or 3p or even Fd orbitals we can distinguish very clearly I have done you that then we can use XPS to measure the compositions very well we have I have shown you how it can be done finally what last few you know 10 15 minutes I have shown you that XPS can actually use to determine the chemical shifts when some reactions happen with 2 pcs like metal and oxide metal and nitride or metal and nitride like Bokkevich boron nitride we can actually determine very very precisely those states last thing that is what I am going to discuss instrumentation instrumentation is very complex let me tell you in the XPS the machine itself a very costly it is about 4 to 5 crores and very few laboratories in India possess this kind of instruments what is the basically electron energy analyzer is basically it is the heart of the instrument is basically electron energy analyzer we have a X-ray source in this instrument in this particular instrument and if this X-rays falls on the sample then as the photo electrons and these photo electrons then are captured or rather then are basically you know captured in different manner and then their energies are measured and this is done by electron energy analyzer the most important one is concentric hemispherical analyzer here you can see here this is R1 R2 there are different concentric you know radius regions are used here R0 R1 R2 R1 is basically natively charged and R2 is also negatively charged by different there is a slit plate here you can see about W1 or W2 depending on that the electrons actually moves in this and then get detected so for an electrons of energy is 0 at s this split slit width ? e by 0 is basically 0.63 by W1 by R0 W1 is basically the width at of this I think this width divided by R0 is this concentric cycle radius half radius sorry constant cycle yeah half this radius or half diameter this is the formula what can actually separate out different ? e values so if you have if you have to have different ?e values you have to either have different W1 or R0 so that is why different R0 as shown here one actually vary the R0 second thing is that is I discussed about this past energies and transfer lens you need to have very high solutions in XPS because binding edge is to be measured can differ by about 0.5 electron volts so that is why we require analyzer with W equal to 1 millimeter and R equal to 1.2 meters you can understand small width by large radius that is that means you know it is convenient to return the energy of the incoming electron so that they have a lower energy as they pass through this analyzer this is what is basically used in a past energies lens system which normally used in this in a particular system it helps us deter the electron energy and also allows us to focus the electron energies you know from the sample to increase the throughput so it retouches the electron energy and also allows us to focus that otherwise you cannot get it absorbed it must be focused so electrons can be focused very easily because the charge particles there is no problem and there are other issues also I am showing you this schematic picture which I obtained but not very good but it can be seen here as you see basically is nothing but this is present in a SCALAP MK2 analyzer you have a metal vacuum vessel sample is here and the X-ray falls like this and gets transferred their electrons for the electrons and then there are different plates there is a aperture here through which electron pass through this is the inner hemisphere this is the outer hemisphere that is what I shown you just now is to hemispheres here in an outer hemisphere R1 and R2 and inside this electron moves and gets detected this is a detector assembly and this is the slit adjuster there is a slit here the slit means this slits this can be adjusted using this this adjuster and that is how it is done so what are the factors we responsible for matter in the electron energy pass energy of the of this system analyze the radius R1 R2 slit with W1 W2 elements in the transfer lens and energy of the photo electrons the transfer lens this is a transfer lens so there are lot of elements which are allowed to focus the electron so that you can pass through the aperture and falls and move inside this hemispherical region well another important thing of the partner instrument is the monochromator XM monochromator is basically monochromator X this is done by Bragg's law as you see here Bragg's law is in lambda to the sin theta if you say aluminum K alpha was 8.3 is a lambda and if you say quartz plates do you become this and theta is this so by using different different plates different crystal plates actually we can monochromatorize we can get exactly the same you know only the aluminum K alpha and not any others K beta or K alpha 2 we can we can do that lastly the photo electron spectra this is actually the whole setup looks like as you see here you have a electron gun electron mean falls XS is generated except falls on a sample okay monochromator XS falls on the crystal that quartz crystal monochromate X3 comes it falls on a sample and the photo electron is generated and then measured in this so this is basically the X3 so thing and this is what is the photo electron generator now one can actually get lots of things obviously one can get this is silicon silicon and carbon peaks one can get odd year also here but we will discuss separately about the odd year electrons and I just want to finish it up using showing that if you saw the past energies as we change the past energy from 10 to 80 electron volts what happens to the particular pieces like PTR polyethylene tetraflate which is used in the bottles this all this plastic bottles are actually made up of this and you can see C1S picks how it gets shifted how it gets affected by this way finally if you say about 80 kilo electron volt pass energies we get a wise nice this the peak positions of the carbon 1s very easily so with this I just close this discussion on the on the XF photo electron spectroscopy in the next class I am going to discuss about the odd years spectroscopy