 In this lecture, we will continue about what we learnt on the transmission electron microscopy as we had realized that our we are making electrons being transparent to the particular material that that is how the term comes out that it is a transmission electron microscopy because we are utilizing electrons to transmit them through the material through my specimen and then understanding what is happening at much more at the microscopic or the nanoscopic level that is the term transmission electron microscopy. So, in earlier class we had in the earlier lecture, we had learnt how we can utilize electrons in terms of how we can form an image or how we can really achieve a diffraction pattern by focusing them particular either at intermediate image plane or at back focal plane. If we are forming a diffraction pattern at the back focal plane, what we get finally is nothing but an image and if you are forming we are keeping our aperture at the image plane, what we get is finally a diffraction pattern. So, there is essentially couple of features which are required for imaging. So, we can see that there are certain key features which are required for imaging that we require at least 3, 4 or 5 imaging lenses that are needed in addition to the two condenser lenses and for most imaging systems, we keep aperture just after the objective lens because once we have we are forming our image plane as well as the back focal plane behind it beneath that particular level. So, that is the reason we want to keep an aperture just after the objective lens. So, that we can form we can selectively choose what we want to really form whether a diffraction pattern or an image. So, we need to have an aperture. So, we can select we can selectively place where the incident beam or the transmit beam is passing through or whether we are able to whether we want to get a bright field image or a dark field image and this part has to has not to be under stated, but objective lens is the most important lens because this is the one which defines the resolution. So, whatever we are forming the all the information from a specimen is now being collected by the objective lens. So, that is the reason objective lens is the one which will decide the overall resolution of a particular imaging system and it a more than that it is it is where it is collecting all the information from the specimen and the clarity of that particular image at the objective lens that will essentially decide how the diffraction pattern will form or how the particular image will form and that becomes very critical in defining a defining the resolution. So, objective lens we have objective lens after that we keep our aperture. So, whatever image which was passing through the objective lens that gets accumulated at a particular plane that can be a back focal plane or an or the image plane and once we keep our aperture there the information which has been collected by the objective lens that only can pass through forward to produce the next image. So, that is the reason we keep that objective lens is the most critical component of the whole electromagnetic lenses and that defines the resolution of the whole microscope itself. And again the aperture which is being placed after the objective lens it is also a very essential because it not only it is not only admitting the primary beam, but it also allowing the diffracted beam also into the optical system. So, what we are getting we are getting two sets one thing is the transmitted beam itself we are allowing it to pass through. So, for that we are we admit the primary beam to pass through the particular aperture at the same time we can also use the diffracted beam to also pass through the aperture in case we want to produce a dark field image. So, that is the key feature of imaging first of all if you are allowing a transmitted beam to pass through we can form something called a bright field and if you allow a diffraction diffracted ray to pass through we can form something called a dark field. So, so interplay of all those things we can play play around and we can form the form a particular image. So, in this thing we directly know that we require certain lenses certain magnetic lenses which will allow the formation of a nice electron beam a collimated electron beam and of well accelerated electrons which can be which can now become transparent to the specimen. Once it has passed through it passes through the through the specimen collects the information and then goes to the objective lens. So, the image or the diffraction pattern which is being formed by the objective lens that decides the overall resolution of the transmission electron microscope. So, that becomes the most critical component in the TEM because that is one which decides the resolution. So, once we have that we allow the beam to pass through forward and now we pass it through certain apertures it can be either the back focal plane or the or at the image plane to yield the final diffraction pattern or the image itself. So, this is how we can form form form a bright field image we allow the transmitted beam to pass through and once it strikes a strike the particular sample. Then we have the objective lens out here once it is passing through objective lens we have the aperture as we stated earlier. So, we allow this is the back focal plane as a back focal plane we allow only the transmitted beam to pass through and then final what we achieve is nothing but a bright field image. So, in this particular place where we have the back focal plane it is the intermediate plane where we get the diffraction pattern. So, in this case we are we are keeping the aperture so that we can allow only the transmitted beam to pass through. So, let me highlight it with some other color so that we can show it. So, we allow only this particular portion to pass through everything else is nothing but it is basically cross drop it we do not allow this one to pass through at all. So, the aperture has to be of particular diameter or of particular size that it allows only the transmitted beam to pass through. We can also allow a certain region also to pass through we can also allow central beam plus some other spots also to pass through the aperture, but in in case when we want to once we want to form a bright field image we allow only this particular portion where the only transmitted beam is let through the aperture. So, we have this aperture and this is my this is our transmitted beam after interacting with the sample it passes through the objective lens and then we are allowing only the aperture which allows only the direct beam to pass through. So, in this case what we are seeing is that so we so we keep the aperture in the back focal plane this is nothing but the back focal plane where we are forming our diffraction pattern intermediate diffraction pattern. So, we keep the aperture in this particular location at the back focal plane and now our objective lens and which is the plane the beam which is passed through the objective lens in this aperture we allow only the transmitted beam to pass through. So, this is my transmitted beam and we allow only transmitted beam to pass through and so the image which which is being resulted some of the beam is now getting blocked the diffracted beam which was diffracted that is getting blocked. So, there is a weakening of the direct beam itself, but now this weak beam only results my final image. So, in this case what happens is we see that the heavy atoms though those are enriched and the crystalline areas they appear dark because what is happening is the crystalline areas which have diffracted they appear dark and then other other other heavy atoms they also tend to absorb the electron beam. So, they also appear much darker. So, brighter regions appear much more the thinner regions appear much more brighter. So, coming to a contrast of it in the previous case when we use when we are utilizing the bright field our field the overall area around a particular feature appears very bright and only it is those features which tend to diffract the electron beam. So, my features will appear dark, my field appears bright that is the that is how we get the name of bright field that my field is bright whereas, my features are darker. Now, coming to the contrast of it I have something called dark field imaging in this case the direct beam is blocked by the aperture whereas, one of the one of the diffracted beam the diffracted beam is allowed to pass through the objective aperture. So, what we have now here is we have our transmitted beam whereas, we see it once it passes through objective lens the information which is being carried from the specimen it is now getting blocked. So, I do not allow my transmitted beam to pass through at all rather I take one of the diffracted beams in this case I was I had some diffraction. So, this particular spot which corresponds to the one out here. So, I let only one of the diffracted spots to pass through and from that I allow only a transmitted only one of the diffracted spots to create the image. So, once I am letting only the one of the diffracted beam to to form an image I get because my direct beam is now being stopped I cannot the features the field around it becomes very very dark because I only have a very weak beam which is giving me the overall image. So, what happens here is that the information which is coming here is coming only from the only from the particular plane or any particular crystallites which have given rise to this diffracted spot. So, only those features will tend to appear bright because we are able to capture that diffracted beam. So, that is what is happening here in the dark field imaging our field is totally dark my features appear very very bright because in this particular case in the dark field imaging I catch the beam which has which has been diffracted from a particular feature. So, that is the reason my feature will tend to appear brighter whereas my field will appear dark that is the reason we call it the dark field imaging where where where in this case we are blocking the transmitted beam and we are allowing only the diffracted beam to pass through. So, that is what we are seeing here that we are allowing this diffracted beam to pass through and form an image. So, that is what is giving rise to the dark field imaging and in this particular case we can get information it can be from the planar defects it can be stacking faults or even we can get some particle sizes and this happens because the beam is already interactive with the specimen and that is how what we get is a dark field image. So, we had a particular aperture which was at the at one of the diffracted beam spots and we allow this particular diffracted beam spot to pass the information further in terms of forming the image. So, in this case we are blocking the direct beam and we are allowing only a diffracted beam to pass through the objective aperture and this is again the back focal plane where we are forming the back focal plane where we are forming the intermediate diffraction pattern and now this goes on to form the final image and that gives me the information specifically from the region which has diffracted this particular spot and that that can come out other form some planar defects it can come out from stacking faults or it can even come from the particles as well. So, this is the information what I can get from the dark field. This case I have an advantage that I can specifically pinpoint that this diffraction spot is coming from which particular location. So, all those crystalline regions which were which were diffracting this transmitted beam all those which were responsible for the diffraction will tend to appear very bright in this particular imaging. So, I can exactly pinpoint that the what is the overall orientation of a particular grains just by choosing my just by seeing my or analyzing my diffraction pattern. So, I can select a particular spot and I can say this grain belongs to so and so category. So, what will be the orientation of those particular planes just by indexing the diffraction pattern that is the beauty of this dark field imaging that we can find out the orientation of those particular grains which are leading to the diffraction of a particular particular beam. So, in bright field image what I can get I can get some orientation contrast because depending on if I have particularly aligned I have some aligned crystals they will tend to diffract the light. So, in this case the if anything is oriented almost parallel to the incident beam they will tend to diffract. So, if I have a particular crystal which tends to diffract the beam and in this case you know the theta is approximately 0 to 1 degree which is very very low. So, even when they are very almost parallel to the zone axis. So, my incident beam itself becomes a zone axis. So, if I have any particular grains which are oriented in this particular direction they will tend to appear much more darker. So, I get some dark contrast because of the orientation additionally I can also get some thickness contrast it happens that the areas which are closer to the edge they are they appear much more brighter. It happens because if I have some region which is much more much more thinner less electrons are being absorbed in this particular regime. So, I get very bright image when the specimen is very thin whereas most of the electrons they get absorbed by the thicker regions because they are interacting with the material it is very harder for them to get completely transmitted. So, those regions which are far from the edge they tend to appear much more darker. So, in overall we can see that for the for a bright field image we are allowing only the transmitted beam to pass through and all my region all my field appears very very bright. So, if I have certain grain boundaries they will appear dark whereas most of the regions they will appear bright. So, I have bright background whereas my features will be dark such as grain boundaries will appear darker or any other particular inclusion they might also appear darker because they are diffracting the light my dislocations will appear very dark because they are diffracting the light diffracting the beam. So, in this case in the bright field imaging we can get orientation contrast that can arise from just by the orientation of a particular grain if they are oriented approximately parallel then they will tend to diffract the beam because they will satisfy the Bragg's law and the incident beam itself becomes the zone axis for those particular crystals. And secondly I can also get some thickness contrast which arises because the when I have very thin edge very thin material electrons can pass through very easily. So, they can generate very high intensity of the signal whereas if I have particular material which is very thick then electrons find it hard to interact and pass through the material. So, information what we are getting after the electron beam is passed through the material I tend to get a very dark image. So, that is how it can also arise the thickness contrast can arise like that. And secondly in the bright field imaging all my features tend to appear very dark because they tend to diffract the light. So, my dislocations grain boundaries inclusion they tend to appear they appear very dark whereas my overall field appears very bright because I let the transmitted beam to pass through that is the idea about bright field image I can get overall field of how the sample is what is approximately grain size and all such things I can find out from the bright field imaging how the distribution of the dislocations or may be say precipitates in a particular matrix. So, that gives an overall idea using the bright field imaging how the distribution of faces is or how the dislocations are there what is overall grain size and all such things. Now, coming to the dark field imaging it happens that in the bright field image I get certain features which may not be so distinctly observed. So, in case I might have some features like this grain boundaries all those things can be like this in a bright field, but once I come to dark field I might realize that one of the grains which were which was appearing to be single grain might have some different orientations. So, might be one grain was oriented differently and then that feature is coming out to be very bright because that one is responsible for the particular diffraction. So, if I choose a particular diffraction spot say my diffraction pattern was appearing more like this with the central beam this is the central beam. So, I had probably one of the spots which is giving me everything else will appear dark whereas only one of the portions will appear bright. So, this one is the dark field imaging, but from that I can clearly distinguish that this particular crystallite is oriented in a very in a manner that it is satisfying the Bragg's law. So, only this particular grain this particular diffraction spot is arising only from this particular crystallite because it is oriented favorably to the transmitted beam. So, once as soon as my transmitted beam is coming it gets diffracted by this particular regime to give me a diffraction spot. So, I can clearly say that this is not it is that this region is not a it is not a complete grain it is probably subdivided into two sub grains and this sub grain is giving me the parallel diffraction spot because it is oriented to certain direction. So, and those micro crystals which are appearing brighter and those are the one which are diffracting the beam into the aperture which are the opening. So, if you go back and we can see that that the we were allowing all the beams transmitted beam diffracted beam. So, we are stopping the transmitted beam and we were allowing one of the diffracted beams to pass through and this brightening is result of the portion of that particular beam which has now been diffracted into the aperture because that diffracted beam once it falls into the aperture that results the formation of the final image. So, this particular crystallite is responsible for creating that final image. So, that is the reason this particular crystallite starts appearing brighter. This tells us one more thing that initially we are seeing two crystals. In this case we are seeing single crystal, but now in the dark field now we are seeing those as two different crystals. So, only a portion of that has is appearing bright it means that only that particular portion is the crystallite which has a perfect orientation of a particular plane. So, that has that clearly distinguish that this particular grain is not a single grain, but it is a it has more than one grain present in it. And again in the dark field like once you have weak beam sometimes what happens we allow only the transmitted beam to we allow only the transmitted beam to pass through. So, what happens because of that that certain features they tend to get dissolved into the background which is very very wide. So, I had I might have certain very features which are very bright here some features out here some features out here, but it might happen that certain pattern of dislocations or any certain features they get dissolved into the background just because just because that it is very poor contrast because my central beam has passed through. So, it will result a very very brightening of the overall phase brightening of the field. So, in that particular case some of the grains which should have been appeared very brightly. Now, because my overall background is overall background is so wider that this particular feature basically hides away, but in the dark field I can exactly pinpoint my this region by choosing that particular diffraction spot which is responsible for creating this particular portion this particular feature then I can select I can just highlight only this particular part. So, once I can highlight from this part I can get much more clarity because my background is totally dark and now this feature only is bright. So, the contrast I am getting from a bright feature and the dark dark field it can provide me very nice information about this particular feature. I might even see how this particular dislocations how they were nicely oriented. So, I can get some information from that as well in case I had particular stacking fault is there and a substructure in the stacking fault that part also I can see very clearly in the dark field imaging. So, that is the beauty of dark field imaging I can create a better contrast because I allow only a very weak portion which was a very which was forming one of the diffracted beams. It means the contribution from that particular feature was very very low, but it is resulting only a small diffraction spot. So, now I can trap that particular feature through a particular diffracted beam and I can learn more about that particular feature. It can be a dislocation it can be a small feature it can be a nicely oriented grain it can also be a twin boundary or it can even be a stacking fault. So, that is the beauty of the dark field imaging that I can get a very nice or improved contrast through the dark field imaging. Whereas, it might result a very poor contrast because of the weak beam in the bright field and coming to the high resolution TEM I can form lattice fringes I can even result something called a lattice fringing I can image each and every the parallel planes which are responsible for forming a particular plane. In this case I use a larger objective aperture. So, what I allow I allow a transmitted beam I had my sample somewhere here and then that thing as taken the information to the objective lens this is my objective lens and then we have the plane the back focal plane which allows not only the directed beam, but also couple of the diffracted beams. So, in this case I allow many of the diffracted portions as well as the transmitted beam to pass through and form in lattice image this results because of the interference of the diffracted beam with the direct beam. So, I can get some phase contrast as well. So, what is happening here is we are getting the creating the interference of the diffracted beam with the direct beam to result a phase contrast. So, in this case what I am what we are doing we are allowing the central beam to pass through we are also letting the diffracted beams to pass through the aperture. So, in this case our aperture size is much bigger that it is allowing both the diffracted beam as well as the transmitted beam to pass through the aperture. So, this is the diffraction pattern and we are allowing more than one spots to pass through and the interference between those two beams will result the lattice fringe imaging. At the same time for creating a high resolution I need to I need to have a particular t m which is a resolution which is sufficiently high enough. So, the point resolution of the microscope has to be very very high. So, that it can really image at the same time we need to have a proper orientation of a zone axis. If my zone axis is not properly oriented I might not get all the fringes or the lattice fringes. So, that so I need to have the sample properly oriented. So, that I have a particular orientation and that can be imaged through the high resolution t m. So, again if my resolution is sufficiently high enough I can see individual row of atoms. So, in that case I can even analyze the atomic structure for a particular specimen just by seeing it under the high resolution t m. That is what h r t m is high resolution t m. So, I can form an image I can see individual row of atoms just by this particular imaging pattern. So, once I want to get a high resolution t m I am more interested in getting the lattice fringe image. So, in this particular case I let the transmitted beam to pass through as well as the diffraction beams to pass through and the interference of both will result the lattice fringe and this load lattice fringe is nothing but the array of the row of atoms which are parallel to one another those form those are forming certain planes of a particular crystal and all those rows of atoms I can really see individual kind of I can see individual rows of atoms which are perpendicular to the plane as well row of atoms which are spread by a certain distance through the lattice fringing which are which are which are being formed using this particular technique. And in this case I need to have a very high resolution of t m. So, that I can separate out the lattice fringes, but contrary to that it is not always necessary that I always need to have a high resolution to get a lattice fringe imaging. I can even get the lattice fringe imaging even when I do not have a very high resolution. So, high resolution does not always mean that I need to have a lattice fringe imaging. I can even see grain boundaries which are a couple of angstroms in width through the high resolution t m. So, high resolution t m is I can I should be able to resolve couple of angstroms may be less than an angstrom by this particular technique that is called high resolution. And the term of a lattice fringing is something different as compared to the high resolution t m, but again the t m is not free from the aberrations. So, in this case particular case we have something called spherical aberration chromatic aberration and again astigmatism. So, what is happening here is in the spherical aberration I am getting more of a barreling. Again this is the most important of the objective lens in t m is the objective lens in the t m because that is the one which is responsible for collecting the information and forming an image. So, once I have something sphericity being introduced into the particular imaging it is again not good. So, I need to avoid the spherical aberration because the lenses they have to be focusing everything at a particular location. In case I do not focus the image at one particular plane at one particular plane then it will tend to make the image look more spherical that part I want to avoid. And second thing is the chromatic aberration because though we have the high tension supply which are much more stabbler like 1 in 10 to power 6 volts will like there will be a variation of 1 in 10 to power 6 volts. So, that is the high tension supply is generally much more stable, but once the electron is passing through a particular material it will tend to have some variation in energy and that is the one which causes much more chromatic aberration. It means that energies of different wavelengths will tend to focus at different regimes they would not focus all at one single point. So, that causes that the lower wavelengths may tend to focus much earlier as longer wavelength will tend to focus at much larger distances. So, that will not focus everything at one single spot and that causes the chromatic aberration. And then again we have astigmatism that means the beam which is basically traveling on the horizontally and the one which is traveling vertically they again would not tend to focus at a single point. It is because the way the lenses are designed so it might happen that lenses are much more stronger at certain points and they will tend to focus at different lengths. So, that thing is called astigmatism that my vertical and my horizontal scales they do not match up properly. That happens because the non uniform magnetic field which is present in the path of electrons and we can again correct it using a stigmator, but again with all these aberrations it is more like using a coke bottle for a magnifying lens. So, even the best electromagnetic lenses can be thought of that much manner. So, it means that so much aberration is already existent at that particular scale and if we can translate it to what we see it means we can be called legally blind. So, if our lenses are as good as our eyes and then we have the best electromagnetic lenses which are available still which will be legally blind we would not be able to see anything. That is the overall feature of this particular TEM that they have spherical aberrations chromatic aberrations astigmatism and these create so much problem that we cannot so if we can scale it up to over eyes will be totally blind. But these cannot be some of them cannot be avoided they can be corrected. So, we have certain features of some corrected lenses which are which have come recently to the market. So, this is what is happening in the case of spherical aberration that we have a point source that starts forming an image. So, at this particular point once we the same exact kind of circularity or the length how much they have travelled for a particular plane we have total spherical aberration of 0. So, we will form the same image at this particular plane, but at any other location at any other location say at the red this particular red line mass spherical aberration may not be 0. So, because we want the wave fronts all the wave fronts which are arising from particular point to be spherically distorted we do not want that to happen. So, the point has to be image as a they will be basically imaging as a disc and we will have certain regime because some things are getting focus much earlier some things they get focus much later. So, we have a ring which is showing the plane of least confusion and again once we come to the Gaussian image plane around here the image is completely distorted and it is showing very large feature. Again these all features are much more elongated in this particular direction angular angle wise, but again we can see that this is this region is causing the minimum confusion. So, this is the one where we want to keep our particular aperture to finally, image it further and this this diameter comes out to be C s b cube where b is the half semi angle and C s is the constant again we are do saying that that we are exaggerating this image in the angular dimension because these angles are limited to couple of degrees less than 0 to 1 degree. So, still we are exaggerating it to that particular level to show what is happening exactly because we want the wave fronts to travel exactly the same distance. So, in order to avoid the distortion of a particular image similarly, we have spherical aberration it is giving rise to the region of minimum confusion and that thing comes from this particular thing what we discussed earlier. Then we can also have chromatic aberration and that chroma chroma means color. So, we have wavelengths of different wavelengths. So, even when the two wavelengths they are starting from the same point the wavelengths which are much smaller they tend to focus much earlier because they have very high energy whereas, for the longer wavelengths they tend to focus somewhere else. So, again we have some regime of minimum confusion. So, we can get that chromatic aberration also can be very much prominent in terms of deteriorating the image. So, in spherical aberration we have again the wave fronts are not matching properly and the chromatic aberration our wavelengths are not matching properly that is the reason they create differences and where they focus on and again we have some lenses which are available which have been corrected for the spherical aberration because now we can create certain electromagnetic lenses which can tend to form fields which are much more regular or much more uniform either at the center or at the same time at the corners. Because, once we have a particular electromagnetic lenses they are located on this side. So, once the electron is passing through there it will observe much more stronger field once it is near the particular electromagnetic field whereas, once it is very near to the center of the core it will experience a little lesser field. So, that is the reason it tends to go much more forward in terms of focusing because these will get bent to a little lesser degree as compared to the electrons which are at the periphery. So, the bending will be much more higher near the particular electromagnetic lenses whereas, it will be much more similar at the center part of the particular lens. So, that starts giving rise to the spherical aberration and the chromatic aberration it arises because of the interaction of the electron with the material itself. Some of them get inelastically scattered inelastically absorbed and they start losing the energy which can be to the order of 15 to 25 e v. So, that starts giving rise to the chromatic aberration and further again it is due to the non-niformity of the electromagnetic electromagnetic lenses my axis symmetry is lost. So, what is happening is my x and y which is the x my x direction which is the vertical direction and my horizontal direction is the y. So, my horizontal direction and my vertical direction they do not tend to focus at the same point. So, I am seeing here my horizontal portion it is getting focus as some particular point whereas, my vertical direction is getting focus that some other point. So, again I get this again I get certain area which is the least least confusion, but again I am getting a distortion of the image along this particular point. That is arising because of the because of the non-niformity of the lens in itself. So, that part also I can really observe out here. Again the astigmatism cannot be prevented, but it can only be corrected and later on I can also get something called thickness fringes. And we learnt earlier that once you have very thin specimen most of the electrons are getting transmitted, but once you have a thicker portions my electron beam will start getting absorbed by that particular by that particular material and it will start rendering a much more darker image. So, I am getting much more brighter portions which are much thinner regions whereas, I am getting very nice information or very huge information from the point where I have I am getting very my thick regions are giving me much more absorption of the electrons and I am getting a very dark image. But there is something called thickness fringes that thing can arise because initially I have a direct beam and I have some diffracted beam. So, what is happening is at certain point because of the thickness I can start getting a feature that my diffracted beam is exactly opposite in phase as compared to the direct beam. So, emergence of my direct beam and the diffracted beam because of thickness my diffracted beam has gone out of phase as compared to the transmitted beam or the direct beam. So, my diffracted beam it has gone completely reverse in terms of phase with respect to the direct beam. So, what I get finally is 0 intensities at this point total cancellation at certain thickness level because initially I had a direct beam my direct beam was in phase with it. So, I get some reinforcement as soon as the thickness starts changing the phase starts changing. So, once the phase is changing what is happening is at the edge I had very bright intensity as soon as I start getting into the material I start getting some point where I am getting cancellation of my cancellation of the direct beam with the diffracted beam there I start getting some dark fringes. So, I had certain overall I had a bright field image, but because of the change in the thickness part I start getting a phase difference and from the phase difference I start getting something which is completely deleting my incident beam or the direct beam and I start getting some dark fringes. It is happening here is my direct beam is getting completely annihilated by the diffracted beam and then again I start getting something in much more in phase because once it has cleared this particular portion it will it will be completely like this completely opposite. So, I will get complete annihilation where I am getting no intensity and soon I will start getting some shift in the diffracted beam. So, again I start getting some more brighter region then again it starts reducing in the intensity and again I come back to the dark fringe then again my intensity starts increasing then again I drop down and I get again dark fringes. So, that is what that is how the thickness fringes come using this particular electron the interaction of the direct beam with the diffracted beam. So, in this particular case when I have thickness fringes or contours what is happening is I have a two beam situation. So, I have a diffracted beam and a direct beam and they tend to go periodic because the phase difference is arising with respect to the thickness. So, depending on how much what is the overall thickness of the particular crystal I tend to get the overall interference of those two beam and I get something which is much more periodic in nature. So, I can see that the intensities they keep gradually from high to low to again back to high or from low to high to back to low. So, that is what is happening in case I had a hole out here. So, then because of thickness I start getting certain fringes. So, my intensity was my intensity has gone has dropped down to this particular level to 0 then again it starts increasing then again it drops down. So, again it starts increasing again it drops down once my phase is exactly negated by that. So, if I see it from the top what I see is my hole was here. So, I start getting some dark fringes. So, ideally once I make my T M sample I have I generally make the sample by creating a hole in the center. So, what we can see is wherever we have we have hole and we have thicken of a thicken of a sample to cause this particular diffracted the particular interference between the direct beam and the diffracted beam. What we can see is certain dark fringes. So, what is happening is what is happening is all this fringes correspond to the same thickness. So, all this fringes are nothing but similar thicknesses. So, initially I had a hole which was much more brighter then I had the intensity going down to 0. So, I get a dark particular dark circle or field around it and that that signifies that I have a particular material which is a similar thickness. Then again around this particular regime I see the intensity. So, if I had particular particular feature like this and then one more like this. So, out here when this region is where we have a constant thickness or the nearby similar thickness around this particular regime though which is over which has gone which has become totally dark. Then what is happening is the region nearby I am getting increase in intensity again the intensity decreases then again I have a region which is a which is a similar thickness. So, those similar thickness regimes are given by certain fringes and that thing that thing is the thickness fringes or the contours. So, these contours are called thickness contours and that we can visualize from the intensities. So, I can we can see the intensities out here. So, with the maximum intensity we can I am getting a particular dark particular dark point. So, in terms of that so that that is giving the thickness fringes. So, advantage of this one is basically this one tells me what are the regions where I can where I can see where I can say that the thickness of the sample is same in all those locations and again what is happening is again I am seeing some difference in the intensities out here. So, again this region will again have the similar intensity similar thickness. So, this particular regime and they have a similar thickness and then this particular contour it has a similar thickness. The contours which is inside and the contour which is outside they will have a different thickness. So, the single contour it means that they will have a same thickness. One more thing which can arise in this particular case is something called a bend contour and the bend contours can arise from a very soft sample. During the sample preparation if you can induce enough stresses into the material then what happens is some of the planes can really bend while we are preparing the sample. So, that sample preparations can also induce some sort of a defect which is called a bend contour. So, what is happening here is we take a particular crystal which was supposed to be straighter. This particular orientation or this particular set of planes was supposed to be straight horizontal, but what is happening here is because of the sample preparation we are inducing some stress into the material through which there is bending of this particular planes and once the particular planes are being bent then once the transmitted beam strikes on to the sample some planes they are oriented perfectly because even less than 1 degree can yield a diffraction of that particular plane. So, once we add planes which were oriented parallel and they can get tilted by a degree or so and that will lead to the satisfaction that can even satisfy the Bragg's law at certain point it might start satisfying the Bragg's law and so that beam which is supposed to pass through will get now diffracted. So, what I will get is the beam which is supposed to get diffracted the beam which is supposed to pass through is now getting diffracted. So, this point I get a very low intensity. So, I get a 0 intensity beam here as well some other location which was bent in the negative direction. Now, there also the beam instead of passing through it is now diffracted. So, here I will get one more diffracted beam. So, what is happening here is I am devoid of any intensity out here as well as I am devoid of any intensity here. So, I get something called two black lines and appears of those two black lines in the Breitfeld image is the reasoning that we get we are getting a bending in the sample and that is that is in the bent contour. So, this is this is a particular feature which is which says that the sample was not prepared properly. So, in this in the in a particular Breitfeld imaging what we start getting is a two pair of dark lines and a pair of dark lines can arise anywhere in the Breitfeld and those are doing nothing but they are spoiling our observation and that is the example of the bent contours. That clearly tells us that our sample preparation was not good and that is the reason it also spoils the overall imaging in the Breitfeld because now the place which is supposed to pass through the light they become obstacles and they are tending to diffract the light and the transmitted beam which is supposed to pass through is not getting diffracted. So, the overall region which was very very bright that is now being devoid of a particular beam. So, the transmitted beam. So, that particular portion appears dark. So, the overall intensity of the beam has gotten has gone down and that results me a dark spot or the dark line. So, continuous flow of that particular thing gives me a dark line and that that is nothing but a bent contour. Secondly, we can also get something called Kouji lines. It might happen that the transmitted beam gets somehow in elastically scattered. So, I can get some incoherent elastically scattered electrons. So, those are not in basically phase with the transmitted beam and they can now get diffracted by the certain planes. So, I had some elastically scattered electrons and now those are getting diffracted by certain planes. So, I had some energy of the beam which is lost some energy by some scattering and now that particular beam is getting diffracted. So, diffraction of that we can clearly see that that beam is which was supposed to pass through is now getting diffracted. So, I will get a set of two lines which is the excess line the line which has gotten diffracted and the line which was supposed to get transmitted but did not. So, I get now pair of bright line which is the excess line and one line which is devoid. So, I get one dark line. So, what essentially I am getting I am getting essentially a pair of bright line and a dark line. So, that is what is called a Kikuchi line that we have a transmitted electron beam which was in elastically scattered somehow and then instead of passing it through the material it gets diffracted and one gets the diffracted beam becomes excess line and the beam which was supposed to get transmitted which did not pass through will result a dark line. So, overall I get a pair of dark line and bright line in the Kikuchi line. So, I get a particular Kikuchi line which is a which is an which is a excess or energy higher higher energy or which is much more brighter and a deficient line which is a darker line. But one thing one thing which we can really see here is that they are highly dependent on the orientation of this particular crystal crystal planes. They are also called crystallographic markers because once we are getting a diffraction pattern they form railroad. So, even with a here and there a little bit of change in the orientation of the crystal still we will get will get diffraction spot at the same location, but that is not true with the Kikuchi lines. In Kikuchi lines we can exactly orient them in a particular manner so that they can get diffracted from all the particular symmetry. So, they can they can maintain the symmetry of the crystal if they are getting diffracted from 1 1 1 we can exactly trace where the 1 1 1 plane is going through what kind of orientation the kind of symmetry which 1 1 1 has the 3 fold we can clearly see in the Kikuchi lines as well. So, the the causal cones they behave as though they are rigidly fixed to the diffracting plane and they are fixed to the crystal and, but Kikuchi lines once we even till the particular till the particular material they will also tend to move out. So, so position and the density of the diffraction spot they change very little in the diffraction pattern, but Kikuchi lines they move along with the tilting of the particular crystal. So, they are very sensitive to the even to the very small tilts and that is the reason they are called crystallographic markers. So, in this Kikuchi lines we how do we are forming it forming it is we are allowing that in this case in electrically scattered beam it gets diffracted. So, we get a bright line and in this case we get a dark line where the beam was supposed to get transmitted and they are dependent on the orientation of the planes only. So, the lines which are appearing now here are here are highly dependent on the orientation of particular planes that is the reason they are called crystallographic markers and they are very sensitive to even small tilts. Whereas, my diffraction spots the resulting from the interaction of my wall sphere with the rail rods not really with the points, but with the rail rods which are resulting from the from the atoms at the in the reciprocal lattice. So, still even when I tilt my particular wall sphere or my crystal a little bit my diffraction spots will appear at the same location. So, they will get affected, but my Kikuchi lines they are so dependent on the crystal orientation that they will they will change their position with the small tilt in the in the crystal again. So, this is the way with the with the Kikuchi lines. So, we in this particular thing we can really see that how Kikuchi lines are important in terms of tracing a particular plane how they are following and we can also it also maintain the symmetry of a particular crystal as well. So, in this lecture we learnt about the bright field image and the dark field image that we once we have once we have a particular back focal plane if we allow only the transfer beam to pass through we get something called a bright field image and that is very essential in terms of overall characterizing if how the distribution of faces what is the overall grain size and all such things, but once we allow only the diffracted beam to pass through we can highlight we can produce a very high contrast image and we can also see particular feature which is dislocation or a grain boundary or even some stacking faults or some some other things some precipitate or any preferably oriented grains as well and we can get much more detailed information from that particular dark field image because my field is totally dark. So, I can see much more clearly how much feature is behaving. So, that part we can see from the dark field image and then again then again we learnt about how the thickness fringes are arising and what kind of aberrations are there. So, we learnt about how what kind of difference aberrations are inherent in a T M such as spherical aberration chromatic aberration or astigmatism. So, how and how they result and again we learnt about the thickness fringes or the bend contours or even the equation lines. So, that is all I have for the today's lecture. Thank you.