 So we are going to discuss about the EBSD today so I will discuss first the EBSD principles and then I will tell you how the integration of the EBSD with computer has changed the analysis of the EBSD patterns and then also the related aspects during the study of the deformation behavior in the texture study of materials and finally I will show you how the EBSD actually is done in the real microscope. EBSD has a long history as we look into the papers about 90 years back in 1928 Kikuchi from Japan first time observed Kikuchi patterns the Kikuchi lines and although it has been reported that he did not observe actually he postulated that there will be possibility of formation of Kikuchi lines in the electron diffraction patterns and in fact Kikuchi went on later on when TM was discovered and it has observed this lines to exist and they are basically due to the enelastic scattering of electrons then after about another 26 years in 1954 black reflected Kikuchi lines were observed in TM by Alam then in 1969 to 1979 saw a huge change in the in the ACM techniques of EBSD three different types of diffraction patterns were detected one is the SACP that is select area channeling pattern the one which I have discussed in the last class where in fact 10 micrometer resolution was obtained by joy at all at Oxford University and at Bristol University Digny et al or Digny and others actually I found out the coastal diffraction patterns with a practical image resolution of 20 micron finally EBSD came with one micron practical resolution by venerable set all at Sussex University again from England 1980 to 1984 saw extensive uses of computer in indexing EBSD patterns and then from 1990 onwards we have fully automated EBSD systems with half transformation possible again major contribution came from in a set of PL in a set of coastal and race and from 2000 onwards that is in the 21st century we have very fast automatic pattern analysis systems obviously I have not listed the the improvement in camera resolution and camera activities in this EBSD so now it is possible to have high-resolution EBSD in fact people are doing in-city use the experiments which we will discuss and it is even possible to have high current EBSD so I will not be will discuss all of them I will discuss some of these during this lecture let us first look at the basic theory of EBSD as you know the electrons from a source like tungsten filament or lab 6 filament or FEG in ACM the accelerated at a very high voltage 20 30 40 may be 60 kilo volts depends on the microscope and allowed to fall on the sample surface so therefore because of this interaction of the sample the electrons will undergo scattering one of the effect of this interaction is scattering and the scattering actually can create a point source of electron with all possible trajectories within the material let me show you example suppose this is a material and we have electron and once the electron falls on the sample you can see it is going to create a point source here and from where the electrons actually can move in different directions in the crystalline materials you have the atomic planes and these crystal planes can actually cause diffraction provided Bragg's law is satisfied so therefore in crystalline material if you have number of crystal planes sitting on the inside the in the material and the electron falls and they can also actually get scattered but in some cases if the crystal planes are actually oriented properly with respect to the electron beam so that Bragg's law can be satisfied we can have diffractions and as I said in the last class these if we change the beam orientation we can have the channeling of electron baxial electrons at the same time the scattering of baxial electrons inside the crystals and this can give rise to black and white lines and these are actually basically kibbutz lines so this is basically the reason for origin of the EBSG the scattering or rather Bragg's law dominated or determined scattering of the electrons in the material so therefore as you know all of you know because you have done the preliminary course on the the the calculation the Bragg's law EBSG occurs due to basically Bragg's diffraction and we know Bragg's law is given by 2 design the regular n lambda everyone in this course will have idea about this particular equation which Bragg's Henry Bragg and William Bragg they discover long back and as you know that if the electron beams with a certain wavelength falls when lambda falls on a atomic plane of passing D it can get scattered by the Bragg's law with an angle theta satisfying 2 design theta equal to n lambda where n is basically order of reflection normally it is 1 in case of X-ray but in in case of electron refraction it can be more than 1 so therefore whenever the electron beams are getting scattered by the lattice planes if they satisfy the Bragg's law then there will be diffraction and then we will be able to detail the diffraction by using camera we will have the EBSG patterns that is the basically things so if we want to go in detail of that scattering from a single lattice plane so if you look at it that we know that each lattice plane what is can be indexed by hkl by Miller Babelius index of Miller indices gives rise to two diffraction cones let us see that how it is operates so as suppose you have a crystal like this which basically cubic is shown like that and suppose this is the 110 plane in a cube and then if I have electron means falling on this plane and then they are getting diffracted so this diffracted we will create a cone of intense electrons these are all can be easily borrowed from the X-ray diffraction anyone who have studied X-ray diffraction we know that even in X-ray diffraction camera also we have cones of reflections coming out because of the diffraction from a single crystals and then if you have a phosphor screen we can detect these lines with these lines actually called kikuchi lines so this is basically from a single lattice planes now you have multiple crystal per unit crystal in a sample so therefore there will be different kinds of patterns or different orientation of the kikuchi bands will come different from the different planes of the crystals and then we can get actually a complexity pattern so for ACM electron wavelengths basically they are much larger than the TM the opening cone angles are found to be close to 180 degrees this cone angle which is coming many times has been found to be 180 degrees very large because wavelength is even larger here so 2d sin ? and then ? if ? is large then ? will be large because sin ? is proportional to ? now obviously one can look at the scattering from the 3 lattice planes and suppose you have a one we have just basically 20 kV electron beam striking a sample which still take to 65 to 75 degrees degrees with respect to the beam and then we can think of like this suppose this is silicon unit cell again we have a basically diamond cubic structure electron being falling on this it can get scattered different planes will scatter and form these kikuchi lines which is shown in this picture here and then on the phosphor screen the crystal structure at the point of incident of diffract the electron beam according to Bragg's law and each lattice planes basically you can look at it each lattice plane 110 or 100 type they are giving rise to two sets of basically cones one set is this other set is this so whenever these two sets hits the phosphor screen they leads to two lines and these two lines actually call the kikuchi lines so we can we are basically terming this as a kikuchi lines basically we are naming them by the scientist called kikuchi so in actual sense this is taken from J. Hesling actual sense we can actually see this kikuchi lines during the experimentations if we have a camera put inside the ACM so if you see this is a sample which is tilted with respect to the beam at about with respect to the normal as a plane with at about 65 to 75 the Celsius and then the electron means falling like this this is basically schematic obviously one cannot image the electron beam by using normal camera electron means invisible so and then it generates this cone this cone actually has two two cones actually so they fall on this first of skin and screen produces two lines on the on the screen so this is the origin of the kikuchi patterns or diffraction patterns and in a two dimensional plane as I have shown here this is a crystal this basically creates this lines and bands and this bands as you will see the axis or meeting points this meeting points are called zone axis in the literature because they are like different roads coming from different places and meeting at certain points we know that there are junctions so these are actually called zone axis there is one here they are therefore there are many more one there actually so one can actually index the zone axis using proper index scheme again using backslope well that is very what is called general one so that we can get a very nice defraction pattern but at the same time one must understand that all the backslope electron which are falling on the sample they may not produce the scattering which will be detected by the skin so therefore there will be as only a small proportion of the electrons arriving at the phosphor schemes are diffracted so bulk of these electron beams are not diffracted they will undergo multiple diffraction and then getting absorb into the material or may be coming out but then they will not contribute to this kikuchi bands so therefore a pattern is always superimposed with the back on a background is just like x-ray fraction pattern x-ray fraction pattern you have a background intensity coming from Bremstal and are the peaks is a coming from the scattering due to bags okay so therefore this background needs to be subtracted otherwise we do not get a very nice pattern these are all actually done in a computer nowadays so one can look at in fact the backgrounds defraction can be subtraction can be done same way like any radiations and this is done here you can see that backgrounds are like this with respect to this this is very small intensity although but still it has to be subtracted then to get often a very nice EBSD pattern not only that as I said in the beginning of the lecture with the advent of computer only fast computers this technique has taken a big lead in the material science research activities so images which are obtained or patterns which are obtained from the EBSD camera they need to be processed and as you see the unprocessed EBSD pattern is in fact does not contain much information so normally we take in several EBSD patterns on a particular case so if we select a point on the material and take several EBSD patterns from that and then we just integrate them once you integrate them signal to noise ratio improves and then we correct the background intensity so that the brand contrast increases and many cases image are compressed so get even better clarity of the bands so these are all routinely done in the computer one is do not bother about it while doing the experimentations but you must know that these are required to obtain a good quality EBSD pattern now as I said zones or zone axis just several two or three slides before zone is nothing but a phase or planes in a crystal with parallel intersections that is what is shown here you can see that there are phases which are actually have a parallel intersections and zone axis is the common direction of the intersection obviously so if I have a several planes there will be one direction which will can which will be contained in all the planes that is actually called zone axis so in wherever the EBSD patterns or EBSD bands or QG bands that will meet in the EBSD pattern they actually can be defined as a zone axis and can be indexed using a proper scheme just to show you that as I said these are actually zone axis which are actually taken from germanium sin crystal at 20 kilovol acceleration and you can see that these are the actually zone axis marked here by red and they can be indexed which I am going to discuss after sometime so this these zone axis are actually carry information about the orientation of the crystals in the geometrical plane and material so when this on the grains well that is actually done using half transformations half transformation provide a suitable technique actually for deriving the parameters of a straight line and that is actually bands positions in the EBSD patterns let us see how it is done basically EBSD pattern is nothing but XY plot as we look at it there are two dimensional XY plot so what we do is that we convert this XY into rho theta plot okay so if suppose we have three zone axis one two three or three bands other on the EBSD pattern then the X is given by this one the horizontal variable and vertical one is basically Y axis and then you can see that rho is connected to X and Y and theta which is given by at the top of the this picture X cos theta plus Y sin theta equal to rho so we can convert this information from XY space to the huge half space that is rho theta space and we can get these bands for they are called huge bands half bands actually so lines in the patterns I can be converted into spots in the half surface and this is again done routinely by computers we do not need to do anything in the real material as this problem you go to the EBSD setup so the computational power is so much that this are done routinely in fact our online processing is possible also so basically real information which is gathered can be at the same time processed in the same computer by transforming this information from this XY space to half space and then once you do this we have you have to detect the bands okay and these bands are detected by using indexing scheme oh that is what is called EBSD pattern recognitions so we is the EBSD patterns can be recognized or indexed using several schemes so as you know EBSD pattern obviously are unique to your specific crystal orientations even if I know the crystal structure of the material apparently it is basically depends on the how the crystal is oriented in the space or the grain is oriented in the space so this is a very unique thing about this so dependent orientation just like in a TM diffraction pattern diffraction events actually depends on the orientation of a crystal in the plane in the space same thing actually is true for here by resolution is poorer here at the same time you can actually have much largest as what is called area can be analyzed in a ACM as compared to TM because thin area is very small in a TM sample but in ACM you have a large area which can be analyzed pattern is controlled by the crystal structure obviously structure means space group symmetry lattice parameter and precise compositions if it is an alloy one is known the precise composition within each pattern the specific bands or the spare of cones of diffraction represent the spacing of the specific lattice planes as we have already told you when we are discussing with the Bragg's law then EBSD pattern recognition compare this patterns of the bands with at loss which are prepared for the so many years of experimentations to index the crystal orientation required so therefore this is again just like extended fraction pattern analysis we have the extended fraction taking from a sample and then you compare with the at last which is available in the literature if there is a new crystal then we cannot index so we have to go by again by standard process of first doing the crystal structure of the material lattice parameter and other things to index it and then this information will go to the at loss just like the ICDT database in xc diffraction this also a database so that can be used to the what is called index EBSD pattern this all databases all given to each and every software which are used in a EBSD analysis so along with the software database are available this is just like a was manual it is fully automated now as I just now discussed and can be used to index so VSD patterns let us see that this is taken from pyrites pyrites is nothing but a ph2 what can take metal also but I am showing you as you see there is a zone axis here there in fact there one there one so many this your next is there the zone axis there many okay so basically this is the major zone axis where the many many many lines are many many bands are meeting now unique for the crystal orientation obviously and the composition for the pyrites can be more than 100% 100 degrees for total crystal positions that is you can basically obtain for large angle of diffraction and special resolution is nowadays can be obtained of less than one micron possible and some pertinent details can also be obtained let me let us show you that a diffraction pattern for specific planes so therefore this one is basically band so width of the band is basically one by displacing of the of the crystal of the particular plane of the crystal this is the first word diffraction pattern okay as you see here this lines and this is basically second word diffraction the blue lines which are shown on the screen the actually second order diffraction the yellow ones actually first word diffraction just like in a TM diffraction pattern your first order second order third order or first order in higher order diffraction patterns so and this is a major pole axis as I just told because there are so many lines and meeting and their points the bands are meeting at this point and this is what is called holds high order laway zones rings they are basically same like in seabed or converging in electronic diffraction patterns in a combination of the fraction pattern you can get zero order liaison then first order second order or zero order and higher order liaisons so this is a zero order and this is a first order so that is basically way to read the EBSD pattern now to give you some other example so this is the original pattern of some crystal and now it can be either manually index or auto index so auto indexing is done like this the way I shown you first the bands are marked by different lines and then they are indexed this is again computer done by computer as you see this is hexagonal crystal okay this is in fact Bismuth so the different lines can be easily marked so in every cases you see one inside there are two lines outside the two lines this is the first order this is the second order diffraction lines or QC bands and this is a major zone axis here this is another major zone axis and there are some minor zone axis also possible this is another major six zone axis here so this can be easily compared so origin pattern will be matching with this then we are sure that we have done the indexing properly so to index we require many things not only the crystallographic information you need the SCM geometry that is beam energy specimen detector position and also orientation of the detector how the it is oriented respect to the crystal usually which is these are all fixed per ACM beam energy sometime can be changed but specimen is also fixed by the user and detector position are fixed so only thing which you change which you can change actually beam energy and this will change the wavelength of the diffraction beam crystallography as I said just now crystallography is very important because you need to know the sample crystallography clearly sample that is the lattice parameter space group all these things are required to be known and they are actually input for any kind of crystal and diffraction characteristics to be also known that is relative to the diffraction intensities must be known this all obtained all all given in the ACPDS or ICD databases of the any crystals so but I will show you some example how it is to be done and it can be calculated as I said so let us see how we can create that we can create this data so first let us suppose you have a crystal like aluminium which is a common metal you know it has a crystal structure and with the lattice parameters like ABC is 0.0 0.405 nanometers and alpha beta gamma this is gamma gamma is basically 90 degrees and the symmetry also to be can be obtained is a cubic the lower group is M3M space group is 225 or F3 bar M face center M3 bar M and unit cell symmetry indices there are 4 atomic positions we know that so let us see the atomic positions there aluminium sits at 0.00 that is occupancy 1 and the aluminium again sits at the face center 0.5 0.5 1 also 0.5 0.5 0 sorry that is occupancy 1 and you can have 0.5 0.5 occupancy 1 and 0.5 0.5 0 occupancy 1 so you know everything about the crystal by knowing all these stuffs the lattice parameter symmetry and the atomic positions that is all we need to calculate the XA diffraction pattern also so how to do to increase the ABC pattern you must know the relative intensity as I said that is of the bands or gives you bands or reflections in the patterns just like XA diffraction pattern you need to know the relative intensity of the diffraction peaks same thing done here so and most approachable use is the kinetic diffraction theory which is very complex let me tell you in fact in TM probably it has been discussed to you but many cases it may not be discussed to you in that case there is no choice of then going back to the books and learn it kind of a diffraction theory is what is called routinely discussed in the TM books and this model actually calculate the structure factor for each of these HKL planes how it is done when the intensity is basically square of the structure factor related to structure factor okay it is basically square of that and HFHKL is given by sigma G equal G goes to 1 to N FG FG is basically the atomic scattering factor in exponential minus twice pi I H dot XG K plus K dot YG plus I dot JD where HKL is the plane indices and XYZ are the lattice the atomic positions this is the N is the number of atoms as you know and FG is basically a scattering factor for each apartment which can be obtained from the any database and lattice planes and atomic positions already told you so how do I create it aluminium so let us do that we know that for whether 111 therefore 111 planes so this spacing is 2.338 with intensity coming to be 100% because 111 is the most dense atomically dense plane so therefore it will have the largest intensity coming defections in coming from this plane followed by 200 again it has there are three such planes with a 69.4% intensity and so on one can actually go on calculating this for many many large now planes and if you see we need to do that this are routinely done obviously for aluminium is very easy for other things other crystals complex crystal is not in easy one needs to be used computers to do that so manually doing is very difficult but aluminium manually this can be all calculated well that is actually way this crystal databases are created and then these are used to index the EBSD the the bands in the EBSD patterns and then obtained index those patterns to obtain the crystallographic orientations so once we know the orientation of the each crystal what do I do with it that is what is the basically important aspects one needs to know well as you know suppose in a crystal there are many grains I can draw this grains here like this in a material okay so if you have so many grains and I was know that the definition from the grain tells us that each of these has separate separate orientations so what you need to know is from EBSD is that once you put the electron beams on this crystal on this grain we can obtain the orientation of this crystal or the grain per easily by doing all these kinds of indexing these patterns from this grain similarly I go to the next crystal or next grain and do the same analysis and then this and then this and then this so on and once you do all this analysis we can store this information how the crystals are oriented with respect to the physical space XYZ and then once you know that we can basically do this orientation contrast imaging so we can plot this data on a micro graph to obtain the orientation information of the grains is grain so that is actually called orientation contrast imaging so that means the contrast of this image will vary depending on the orientation of the each grain of the crystal so in a polycrystalline sample where suppose this is to talk about the emission signal orient how it is dependent on the crystal orientation in a polycrystalline sample you have different different grains one is this this is another one another one this and the planes are oriented different and each of these grains and now if we have electrons falling on each this suppose this particular grain and then we can obtain the orientations just by doing this so we can basically give a grayscale image contrast on this okay based on whatever way we define a grayscale and then we can obtain from this we can make it darker depending the orientation of this crystal and this is again can be done this way this way so that is how when actually obtained this grayscale level it depends on the penetration and the emission also emission means how much basket or the diffraction is coming out from this crystal and detected by the camera so that is how actually this is this is very simple this is the simplest possible way of representing this you know orientation images on a crystal on the in on the EBSD patterns are amazed from a large sample is done I am showing you let me show you some image electron beam is basically scanned in any scanning electron microscope and sample is tilted so rather than positioning the beam on a point on a EBSD because we are scanning the beam so you put the different position a beam on the different position of the sample and there will be sports card electrons with intensity determinate penetrations and crystal orientation obviously and they are emitted towards the EBSD detector and this these signals are detected by silicon devices or the camera which is basically Peltier cooled camera and and attached to the EBSD detector and this is how it is done so once you have all this information we can plot it you can see this is a very large area this is only 100 micron so that means this is approximately 10 times of that so 1000 micron is this length and this is approximately about 6600 micron very large area scan and we can see different grayscale contrast on the image so each of these actually showing the orientation of the quasi grains on this on the sample so this is you can see that this grain is darker so that means this is oriented very preferably with respect to the so and this gain is wider and there are lots of dots they actually that means they are actually not contributing to the any information to the EBSD pattern so that means the first cut of electrons orientation contrast image of variation in crystal orientations the counter variation is only here qualitatively so you can do that so let me just tell you that how this is done in automated or compromised system computer control movement of the electron beam across a sample can be done if it is the cat pattern can be captured from each point and that is what is shown so you can basically go to each point and capture the EBSD pattern and this is the pattern from one indexes pattern by using a pattern recognizing software and then soft as either crystal orientations in three only angles 515253 and a phase information per pattern to a database for analysis so I am not going to discuss about how this oil angles are determined this is again not possible in the short span of time but one is to know also the important to run this manual visual check for solution before even we do this analysis because computer is a basically black box whatever goes in is comes out so if you put garbage in little garbage will come out so one must actually run one must actually see visually these patterns and be sure about it what you are saying is what you are obtaining and then do this indexing in a computer this is again taken from one our sample this is the grain orientation image okay and you can see this is 0 to 1 pole figure okay and you can see there is a predominant texture that is why these things are looking black those of you have little bit knowledge about texture you can understand and these grains can be shown to be oriented along different zone axis actually this red is actually close to 0 0 1 and blue is actually close to 1 1 1 and the magenta is close to 0 1 1 so therefore one can actually see the different orientation and obtain this inverse pole figure and then find out the where this when majority orientation coming into picture I can see largest cluster is coming here which is at a different angle almost like 90 degrees from the pole and some of these are coming at along 1 1 1 okay this is close to 1 1 1 those of you know little bit of this will understand so therefore we can obtain the majority crystal orientation from these images which is very nice and the inverse pole figure of this will be this image so you must have little bit about how to generate this pole figures and how to study this pole figures and then one can actually obviously obtained this kind of maps as you say this is 1 1 1 this is 1 1 0 this is 0 0 1 and this is actually called rolling direction transfer direction is a very standard in a texture I am not going to discuss deeply in our texture in today's lecture so that can be done so using EBSD routinely people nowadays study the structure of the material texture means how in a multiple grain material crystals are oriented if there is the orientations of the crystals are haphazard then there is no texture is orientation of the crystals are happening in a particular direction predominantly then we call this a texture material so that can be obtained and depending on people can actually go on doing research on different kinds of materials because nowadays we know that the original crystals play so much important roles in dictating the material behavior that is why texture material is coming into picture so with this actually I close and I am going to show you some example in the next lecture of texture analysis how they can be used really to obtain information of the crystal orientations and also to obtain the how the processing parameters can change these crystal orientations and this can be used for the day to day applications also very advanced applications so which I am going to do in the next class.