Good morning all, welcome to lecture 4 of multi phase flows. Today we will be dealing with something called as scaling analysis. I am sure like most of you would have gone through what scaling analysis is inserted part of your academia. So today we will just go through a systematic approach about how to use scaling to solve certain problems in fluid mechanics. So I will be first going through what the motivation for scaling analysis is and then I will solve a problem which can be solved using two scales and then I will tell you how you can get certain physics out of the problem using one scaling and certain other physics from the other scale. So I will start with the motivation. Scaling is important because first it helps to reduce the parameter space. So by this what I mean is that if you see any fluid mechanic problem, obviously the flow field would depend on the viscosity density, the pressure that is applied, the length scales, the channel wall, how large the diameter of the pipe is and things like that. So what scaling helps us is to reduce the parameters that are affecting the flow. So you can club all the parameters to essentially lesser number of non-dimensional groups. So for example the famous numbers like Reynolds number, Weber number, they all are group of all these individual parameters that affect the problem but they have been clubbed and then essentially you can determine the flow if you know the Reynolds number. So if you know the Reynolds number to be low then you know that it is kind of a creeping flow limit and if the Reynolds number is high you know that it is kind of turbulent. So the first use of scaling is to reduce the parameter space. So it essentially results in obtaining non-dimensional numbers. The second advantage of using scaling is to say when certain physics are important. Like this what I mean is that say for example if you have a fluid flowing in a pipe then you know that if the Reynolds number is low then the viscous forces are important and inertia can be neglected. You know these things, the understanding of physics when you can say that certain forces are not important and certain forces are dominant that comes after like you know scaling the problem appropriately. So we will see the same thing in today's example that we will be looking at. So scaling essentially helps us to find out again non-dimensional numbers using which we can say you know which of the physics can be neglected under what conditions. And the third important point is to assist experimental observations. By this what I mean is that say an experimentalist is you know doing a particular experiment wherein he sees certain physics happening in it. So once you know the problem and then you calculate the non-dimensional number and then you find out what its value is then you can say that you know to explain the physics of whatever is observing you can certain you can neglect certain forces and you know take care only the other forces which are important. For example if he sees something happening in a low Reynolds number regime then you know that inertia is basically not important it is something to do with viscous forces and things like that. So it basically helps experimental observations to be explained correctly. So once you scale the problem correctly you have these advantages that you know makes your life easy. Now I will be just taking you through what the essential steps are involved in scaling a given problem. So these are fundamental steps that you can use for any problem that you will be encountering in fluid mechanics or any other problem for that matter. So this is a systematic approach which you can just apply once you know you get a feel of it. So the first thing is to obviously write down what the governing equations and the boundary conditions or initial conditions are. So any description of physics in mathematical terms would have a governing equation and associated boundary conditions or initial conditions and the governing equations generally are PDs or ODs or something like that. So the second step involves defining certain unspecified scales by which I mean that you know scaling would essentially be you having a governing equation and boundary condition and you making it non-dimensional. So the scale that you choose to non-dimensionalize the equations the reference scales that you are using to non-dimensionalize the equations could be infinitely. You could choose any velocity to make your velocity in the pipe dimensionless because you could divide it with whatever velocity say if the wall is moving with some velocity you could divide it by that velocity to make it non-dimensional or you could even divide it by earth's velocity for that matter even then it would be non-dimensional. But then the point is you want to scale it in such a way that it is easy for you to analyze the problem. So right now we would just say that you know there are certain unspecified scales that we use to non-dimensionalize the above equations. And the third one is something called as unspecified reference scales. So before going into the details of what a reference scale is, what kind of scaling that we are going to use is called as an order of one scaling. By order of one scaling what I mean is that we are going to non-dimensionalize the boundary conditions, the governing equations and things by certain scales you know when you are non-dimensionalizing it you are non-dimensionalizing it in such a way that they become of order one which means that if you have velocity you choose a scale such that you know it changes between zero and order of one. By order of one I mean that it could be of any order of magnitude around one. So it could be varying from 0.1 to 10 but then not more than that. So it is not exactly one it is around one but not orders of magnitude more than higher than one. So you choose scales to make the governing equations, the boundary conditions and the variables and their derivatives of order one. So this is what makes it a unique scaling. So when I said you know you could non-dimensionalize the governing equations with any infinite possibilities of scales you could choose the velocity of earth, you know moon, anything of a track which is going around but then we are choosing a velocity which would make the equations, boundary conditions, initial conditions, everything of order one. So this would essentially from the physics tell you certain unique scales that you can choose. So that is what we will be looking in today's class. So now I come to the third point which is the unspecified reference scales. So unspecified reference scales are those which basically help you to bound the variables between zero and making it order of one. So for example if you have certain things which are not, certain variables in the problem which are not by default going from zero to one. So making it order of one is very easy because you just have to choose a correct scale to make it reach that order of one. So the maximum value that could reach is of order one but the minimum value should be zero you know it should be bounded between zero and it should go to some order of one value. So referencing basically helps you to make the minimum value go to zero. So for example if you have, this is still the third point. So if you still, if you have a slab, a rectangular slab when which heat transfer is happening and you have an equation which governs the temperature in this slab. So you have boundary condition which would say basically tell you there is a hot you know temperature on top and say some cold temperature at the bottom. And the temperature inside this by diffusion is going to only change between Tc and Th. Now if I would have chosen any scale to non-dimensionalize the temperature it would not start from zero because the lowest value which is there is Tc. So it would go from Tc by some Tc scale that temperature scale to Th by temperature scale. So to make it go from zero to order of one we choose a reference scale. So for example in this case wherein you want the temperature, the non-dimensional temperature to vary from zero to order of one you could define your non-dimensional temperature to be T minus Th T minus Tc by Th minus Tc. So what this tells you is that if I hadn't used Tc as my reference then this would not have gone to zero at the bottom all. So it is basically this reference which helps me to make it go from zero to one. So that is what we say when we have the third step as an unspecified reference scale it basically helps you to go from zero to order of one magnitude. The fourth step would be to non-dimensionalize using the scale factors and the reference scales. Once you do this at this step you basically would have your governing equations, boundary conditions, initial conditions, non-dimensionalized and varying from zero to order of one. And then comes the fifth one which basically helps you to retain important terms. So what this means will be clear to you when we do the example that will be following soon. So it basically just helps you once you do the non-dimensionalization using the correct scales and references there would be certain terms which becomes very small so that you can neglect them. So that you can tell that you know for these conditions you don't have to keep certain terms and things like that. So that is what I mean by retaining important terms in the problem. So the first problem that we will be looking today is fluid confined between two infinite plates and the fluid is driven by pressure plus the top wall is moving. So I have the top wall moving with the velocity u, wall and I have a pressure which is also driving the flow. So I have some pressure here P1, some pressure here P2 and there is a pressure drop which is driving the flow along with the motion of the wall. So this problem can be completely solved analytically but then there are two things which is important. So the flow is essentially driven by two forces and it is being restricted by viscosity. The viscosity is the only thing which is offering a resistance to the flow and the thing that is driving the flow is the pressure which is applied plus the motion of the wall. So you can solve this problem completely but then there are certain problems where you wouldn't be able to keep all the physics together. So you would have to solve the problem in two limiting conditions which means that you would have solved the problem when you inherently assume that the motion of the wall is not important. That is one case and the other case would be the motion of the wall is important. So those are the two extreme limiting cases under which we can solve this problem. One wherein you say that it is basically the pressure which is driving the flow and the motion of wall is not that important and the second case is where it is the motion of the wall which is important or at least we are looking at the regions close to the wall where the motion of the wall is the one which is driving the flow. So those are the two cases that we will look today. So there are two cases, case one wherein motion of wall is not important and case two where motion of wall is important. So first we will take case one wherein we are going to solve this problem for the condition where the motion of wall is not important. So I will write down the governing equations for this particular problem. So you have a fluid which is flowing in the x direction and I choose y to be downwards. So this is y equal to 0 the wall and y equal to some h is where my bottom wall is located and this is not moving so the velocity here is 0. So the governing equation for a one dimensional flow, so the flow is only in one dimension in the x direction and we assume that it is steady which means it is not changing with time and we assume that it is fully developed which means it is not dependent on x coordinate. So whatever velocity field is here is the same everywhere along x. So there are two inherent assumptions, we are looking at steady and fully developed one dimensional flow. So the governing equation would be something like this which comes from the Navier-Stokes equation. So this equation is dimensional which means that all of them have their own dimensions. So pressure has a dimension, the lengths have dimensions which are of length. So this is the first step that we looked here wherein we are writing the governing equations and boundary conditions. So since it is a steady state we do not have any initial conditions it is independent of time we are just looking at what is going to happen after all the transients have died down okay. So we have an equation which is like this and then we have two boundary conditions which is u which is the x component of velocity being u w at y equal to 0 and u equals to 0 at y equals to h okay. So this is step one where we have written down the equations and boundary conditions. So step two would be to look at the unspecified reference scales, the unspecified scales which are used to non-dimensionalize the equations and the boundary conditions that was step two.  So it is my y direction scale okay. So this equation can be integrated in the x direction so which means that this term is basically independent of x so it is like a constant. This term can be integrated in x and then you can just put the boundary conditions that the pressure is p2 p1 at x equal to some distance between them being l okay. So when you do that you will get this equation to be where delta p is minus of okay. So that comes by just integrating it in x direction and then putting the limits. So let us say this is my governing equation that I am looking at and the boundary conditions. Now I have got my velocity scales and the length scales written down but they are unspecified that is what I meant by just writing down unspecified scale factors. Now the step three here is to make it referenced to zero. So the variables that we are looking at is u and y, u is already referenced to zero because it is zero at the bottom wall okay and y is also referenced to zero because one of the walls is at y equal to zero. So in this problem we do not have to put any reference scale so step three is basically redundant in this problem. So already referenced already referenced to zero. So yes essentially completed three steps for this particular problem. So the step four is to non-dimensionalize the equation with the given scale factors that we had chosen okay. So I will write it here.    So I am just going to rearrange the terms and then write it down again okay.  So these are my equations and the boundary conditions. So the basic funda was that we want all the variables to be going from zero to order of one okay and in this particular problem the case one this is case one that we are still solving case one is the one that we are looking at where in the motion of wall is not significant okay. So using scaling we are going to find out the conditions under which we can assume that the motion of wall is not significant. So till now I have just you know orally told that you know we are going to look at a case where the motion of wall is not significant but what does it mean mathematically you know under what conditions can you say that the motion of wall is not significant that is going to come out through scaling analysis and that is what we are going to look at today. So till here it is clear right so I just non-dimensionalize my equations using the scales. Now the case where I am looking at where in the motion of wall is not significant. So the velocity is going to be affected by the change in pressure throughout and the viscosity is the one which is resisting the flow okay so you have pressure which is driving and viscosity which is resisting the flow. So the length scale is very much evident from the physics of the problem as well as from the boundary condition here that ys could be chosen as h so that y star goes from zero to one okay. So that is also from the physics because I know that when my pressure is driving the flow that is going to affect the flow throughout the entire domain okay. If it was the case where in the motion of the wall was significant then it is not that evident that the motion of wall is going to pervade throughout the domain okay but a pressure which is driving the flow would be pervading throughout the domain so we can directly take y star to be h okay. So from here you know that ys to be h so from here you know that if I choose ys to be h y star would become one and that is what like order one scaling also would ask you to do. So you know that y star is going from zero to one now so I choose my ys to be h okay. So if I look at this guy here I could choose my velocity scale to be motion of the wall itself uw so I have an option of choosing us to be uw okay. If I do this I am telling that the motion of wall is important because I am going to divide all my velocity throughout the domain by that velocity of wall. So when you choose a scale you should choose a scale so that you want to get the physics also correctly. So right now when I am saying that I am looking at the case where the motion of wall is not significant I am not supposed to be scaling with the motion of the wall. So I won't choose the velocity of wall to be my velocity scale even though I could do that but then if I do that then it means that the motion of wall becomes significant okay because that would always come through the boundary condition. I will never be able to neglect this term if I choose my velocity scale to be uw because if I choose us to be uw at the wall the velocity is always going to be 1 okay. So what I will be doing now is trying to get a velocity scale which is coming from the problem directly. So I will just look at the governing equation here okay and this is the pressured term which was driving the flow and this was the viscous term which was resisting the flow okay. So what I have done is I know what a vis is I put it here okay. I want to look at the case where the pressure is important so I would retain this term okay I can't neglect this term because right now I am looking at the case 1 where in the motion of wall is not significant.  So right now I can just manipulate this to get us is that correct okay I will get us as ?p h2 by l mu okay. So I have two scales for velocity basically because there are two things which are driving the flow the motion is because of the wall being moving and also because the pressure which is driving the flow. So this particular scale the reference scale that we have got here is the one which corresponds to the pressure driving the flow. So because it has a ?p by l so it is the one which corresponds to the velocity scale which is given by pressure driving the flow whereas this particular scale gives you the velocity scale which is coming because of the motion of the wall okay. So in case 1 we will non-dimensionalize the equation using this scale because this is what we are looking at wherein in case 1 the pressure is the one which is important and not the motion of the wall okay. So we will do that here so if I choose us to be given by that ?p h2 by l mu I would see that the first term in the governing equation becomes 1 because we got the velocity scale by making that term as 1. So if you put back velocity scale there you will get that term to go to 1 and you will get ?square u star by ?y star square equals to 0 okay. So this is your governing equation and the boundary condition would be u star being uw by us. So uw as it is and us would be ?p h2 by l mu okay. So this is my velocity at the wall which is at y star equals to 0 and I have the other boundary condition which just means that the wall is not moving at y star equals to 1 because ys was chosen to be h so I have y star equal to 1. So if you look at this particular term here uw by another term here which is us you will see that it is the ratio of two velocities. So the top numerator basically tells you that it is the motion of the wall and this tells you that it is the motion which is driven by the pressure which is imposed on the fluid so this is a non-dimensional number because it is the ratio of two velocities okay. So this can be called as ? we will call this as a non-dimensional number ? which basically is the ratio of two velocities uw by ?p h2 times l mu okay. This is clear so I just took this guy on top and ?p h2 was at the bottom. So this particular number the ? is a non-dimensional number and this is what which tells you when you can you know neglect the motion of the wall and when you cannot neglect the motion of the wall. So if ? is very large which means uw is much high compared to what is the velocity determined by the pressure then it is case two because the motion of wall becomes significant okay when ? is less than one okay that is what corresponds to case one okay which means the motion of wall is comparatively insignificant compared to what is driven by pressure okay. So for case one we basically have that ? is much much less than one okay and this is one because we are looking at an order of scaling one wherein you have everything of order one okay. So this is my equation so I can just replace this boundary condition as ? okay and I can very well solve this problem this is a simple problem which you can just integrate it is actually an ODE in second order so you just integrate and then you can solve for velocity very easily okay. Now we look at the case two we are going to case two you can just see that if you put if you are looking at the extreme case wherein you do not want the wall to be important at all you can just put y u star equal to zero and then you would get a parabolic profile okay but this is possible only because you have scaled it in this way if you had scaled it wrong this would not have been possible you would see that the equations become inconsistent so which we will see in the end. So right now I will look at the case two which basically I am looking at the case where motion of wall is important okay so I have the governing equation to be the same which is my ?p by L was balanced by ? times square u by ? y square okay and the boundary conditions were the same thing again u was uw at y equals to zero and u was zero at y equals to H okay the basic difference is in the choice of scales that we are going to do right now in the previous case we were interested in the motion of wall being insignificant right now we are going to look at the case where the motion of wall is important okay so earlier we had seen that we had two choices of velocity and things like that so we will do something similar so we had the motion of wall and some pressure which is driving the flow okay so what we will be doing is choosing the scales correctly right now so you know that since the motion of wall is important you could directly choose the velocity scale to be given by uw okay so the velocity scale is pretty evident but the length scale is not evident you know the y scale is not very evident because when you are looking at the case where the motion of wall is driving the motion it is not that evident that the motion of wall would permeate throughout the domain you know so there could be just a small region of influence delta only till where the motion of wall is pervading the flow and after that it is the pressure only which is driving the flow okay so we will choose the reference scale for y to be delta which is currently unknown so ys would be delta okay so this is something very important because this is what basically makes your problem different in analysis earlier we had the y scale given directly by H and the velocity was found out from the physics of the problem right now you have velocity scale given by the motion of the wall and the length scale is being found out from the problem so we will just do the same thing that we had done in case one we will non-dimensionalize it using this so delta P by L remains as it is and then we have mu times uw by delta squared and dou square u star by dou y star squared equals to 0 okay and we will just again use we will just bring these terms on to the other side and we will get delta P delta squared by L mu uw plus dou square u star by dou y star squared equals to 0 okay so what was not known to us was delta so we can use again making it order of one to get the value of delta so making that term to go to one we get delta P delta squared by L mu uw equals to 1 and this would give you delta squared to be L mu uw by delta P okay and I could just divide it with H square on either sides to give me delta squared by H squared equals L mu uw by H squared delta P okay so if you see this term which is here there is nothing but the same pi that we had obtained in case one okay so that is exactly same as pi so you could write delta by H to be root of pi okay so the pi which is the non-dimensional number which is the ratio of two velocity scales is not only helping me to find out under what conditions can the motion of wall be neglected it is also giving me the area of influence which is the delta so I know if I can calculate from my experiments if I have an experimental setup wherein I know what the pressure drop is between the two ends of the pipe and I know what the motion of the wall is I can easily calculate what my pi would be because I know what the values are so if I know L mu uw H square delta P for a given experimental conditions I can find out pi and using pi I can determine whether the motion of wall is significant or not significant and using pi I can also find out the fraction of the channel in which the motion of wall is important because delta was the region into which the motion of the wall was important delta by H gives me the fraction of the you know the domain which is being pervaded by the motion of the wall. So that is one important thing and now before finishing I will just and this problem can be easily solved you know solving the problem is not hard it is to understand like you know how to solve it under two different extreme conditions. So before going I will just look at the problem for the condition wherein I would have used the wrong scaling so for example I would look at case one okay wherein the motion of wall was insignificant so I had wall motion insignificant okay so I have my governing equation given by delta P by L plus mu dou square u by dou y square equals to 0 okay so I am going to look at case one now and the boundary conditions where u was uw at y equals to 0 u is 0 at y equals to H yeah. Now what I am going to do is I am going to choose a wrong scale I am going to choose the velocity scale which is u to be uw okay and ys is H okay so I have case one wherein I have purposely chosen the velocity scale to be uw which is not correct because right now I am interested in the case where the motion of wall is insignificant okay so I will just do this and put it up into the governing equation and see what comes up. So we have delta P by L plus mu times uw by H squared coming and then you have dou square u x star by dou y star squared equals to 0 okay and then I rearrange again to get delta P H squared by L mu uw plus dou squared u star by dou y star squared equals to 0 okay and this thing as we had found was nothing but pi right was it pi or is it 1 by pi L u w mu was pi so this term could be replaced by 1 by pi okay so this term was nothing but 1 by pi okay so you have an equation of this form okay and for case one where the motion of wall was insignificant we found that pi is less than less than 1 because pi was nothing but uw by u pressure because that big term which we had is nothing but the velocity scale determined by pressure so this thing for case one is less than one okay so if you put that here then this term is going to blow up so 1 by pi would be something very huge compared to what this term is here this term is of order one because we have non dimensionalized to make it of order one you know so it is no way possible for these two terms to cancel each other and get me zero okay because this guy is of order one and this guy is kind of blowing up so from the final equation that you arrived at you know yourself that you know there is something wrong in the basic assumption that I started you ended up with this equation because of this wrong scaling okay if you had scaled it correctly you would have seen that the this term would be 1 plus dou square u by dou y square in both the cases because in both the cases we chose correct scales so we got two terms which are both but being balanced and both of them are of order one and they could cancel each other but then if you choose a wrong scale the equations themselves will tell you that there is something wrong in the equation and it is not possible for them to cancel okay okay thanks


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Welcome to this material characterization course. In the last class, we started looking at the transmission electron microscopy. I just gave a brief introduction about the technique as well as for the instruments and we realized that the transmission electron microscopy technique involves a lot of diffraction principles and it is good that we have the enough background about the diffraction in the X-ray diffraction section itself. So I hope that you will be able to appreciate this electron diffraction in a similar way without any difficulty. So let me continue the discussion on the instrumentation details about the TEM. So we just started looking at the electron source and the lenses and then basic operations and the types of electron source and so on. So in that we are also looking at some of the details about the other parts and in continuation that we will now look at some more details. So we were just seen that the details of the electromagnetic lens and how it is functioning and all that and today we will discuss about the lenses, apertures and their relation to the resolution. So look at the schematic. What is shown here is there is a specimen, there is an electron beam coming through and then you have the maximum aperture collection angle beta and then you have the limiting diaphragm and then you have the lens and then image is converging. So we are talking about this limiting diaphragm and the apertures. So some of the apertures and the diaphragms appear like this. This is an actual photograph from this textbook and you see that typically they are all metallic discs which where you have the perforation in the middle depending upon the size or the diameter requirement. So typically the diameter can be as small as 10 to 300 micrometer and 25 to 50 micrometer thick. So this is the typical dimension of this kind of apertures and diaphragms and the discs are made up of typically platinum and molybdenum. So one of the objective aperture is shown here, you can see that a small perforation. It varies from model to model and we will look at the actual size of this strip, this is an objective aperture. When we look at the in an electron microscope operations I will just show you what is this four different perforations will do to the image and image contrast and so on. So this is the information about the lenses. So what are they control? What are the aperture and diaphragm functions? To control the collection angles, what is collection angle? This is the beta, so they control that. In objective lenses it controls the resolution of the image formed by the lens, the depth of field and depth of focus also controlled by this. The image contrast, the collection angle of the electron energy loss spectrometer, there also it is being used, the angular resolution of the diffraction pattern. So the apertures and the diaphragms will have all these factors will be involved or it will influence the functions of all these parameters. And also you have the various pumps and you have the diffusion pump and ion pumps and vacuum pump and so on. I will give the actual details when I show the laboratory demonstration and what they do is, so just to give a general comment the advent of high quality digital recording which will remove the need for the film in the camera will do more to improve the quality of the vacuum in the TEM than any advances in pumping technology. So today we completely record all the information in a digital recording system and some of our microscopes still use the plate films and we will look at the details when we go to the laboratory exercise. And coming to the holders, this is how the TEM holder will look like. You can see the details here, so this is a barrel containing specimen controls. This is a oaring seal and the section which is shown in the shaded box is under the vacuum and this is not under the vacuum. So you can see that the specimen will somewhere sit here and then there is a bearing which will sense the I mean the positions of the specimens inside the column. So this is the principle parts of a side entry holder that is held in a goniometer stage. So the specimen is held in a goniometer stage in this orientation wherever we make a side entry holder and you can have different types of holders whether you can have a rotation holder where the sample is will rotate in this fashion and you have the heating holder where you can heat the sample locally to look at the phase transformations and thermal response of a material can be studied thoroughly. And similarly a cooling holder, you can have a quite a bit of a heat treatment can be done and then you have a double tilt holder that means it will tilt in this axis as well as this axis. So that is called a double tilt holder and typically most of the basic version of this equipment will have this single tilt holder which will rotate in this fashion in this axis this is an axis and this rotate in this fashion. So I will show in the lab all this holders how they look like in I mean these are all photographs taken from this textbook but you can I can also show you in our laboratory how this holders are being used or typically you can if you look at the usage rotation holders they are being used to analyze some of the you know orientation effects and then and then crystallography symmetry operation which can be very effectively studied through this holder and then as I said for all the phase transformation studies it can be used and double tilt holder is used especially if you are interested in defect analysis or when you want to obtain a very specific contrast mechanisms or if you are interested in identifying a very specific location and these kind of holders are very useful especially if you want to do a typical analytical work you need a double tilt holder for a normal conventional imaging you can do with the single tilt holder and so on. So this is a brief introduction about the holders and it is not that only a small sample size can be kept and then you can also have this kind of a big samples more than 3 mm specimen just for an information and then you can also simultaneously load the samples in a multi sample holders in a inside the vacuum you can put it in a this kind of a multi sample holder also you can put it in the 2 slot holder and so on. So these are some of the varieties of holders which is available with each of the microscopes. Now how to see electrons see you have to remember that what we are seeing in an electron microscopes it is a beam of electrons our eyes cannot see electrons we have to resort to the phenomenon of cathode luminescence in order to provide an interface between electrons and our eyes. So the cathode luminescence process converts the energy of the electrons that is cathode rays to produce light luminescence as a result any electron display screen emits light in proportion to the intensity of electrons falling on it. The fluorescent screen is coated with a long delay phosphor. So what we have to appreciate here is we only pass the electron beam and which comes out of the sample after the electron beam after comes out of the sample must have interacted with the specimen accordingly the intensity profile will change as I just mentioned in the yesterday's one animation I showed an electron beam pass through a sample the intensity will vary according to the specimen interaction and then that effect can be visualized only when you put it on the fluorescent screen which will again emit a light depending upon the amplitude of the light which which it receives that contrast also will produce we will look at the much more detail about this how the image formation everything in much more detail when we discuss the TM imaging section. So this is only to give you an idea how the electrons are electron beams are made into an image and we should know what KV should you use. So we have a varieties of microscope with different voltages of operating voltages. So you always operate at the maximum available KV unless there is a definite reason to use a lower KV and most obvious reason is beam damage if you recall I just showed in the beginning of the TM lecture I showed some of the images where the specimen get affected by the radiation damage and I also cautioned you that we should not just misinterpret those kind of damages as a characteristic of material. So we have to be very careful with the that is why the appropriate KV need to be chosen if it is a metal or if it is a ceramic if it is a polymer or a biological samples you need to choose an appropriate voltage to examine the samples we will talk about it much more detail when we when we go to the sample preparation section. So you can always operate a 300 KV machine at 100 KV the threshold for a beam damage for most metals is less than 400 KV for lighter or beam sensitive material such as some ceramics and polymers lower voltage may be better. So this comes by an experience it varies with samples to sample. So one has to really judge this with the previous experience and so on. So why do we always prefer a highest KV so there are some of the reasons because the higher the voltage operating voltage or accelerating voltage the gun brightness is better you get the better gun brightness and as we all know that from the de Broglie relation what we have seen yesterday the wavelength is wavelength in shortest when you when your KV is higher the resolution is potentially better. The cross section for inelastic scatter is smaller and the heating effect is smaller. You see we have to remember that when the heating of the sample also will affect your you know characterization purpose because that will that should not induce a new effect into your material or you should not transform your material from the initial stage to some other stage. So the heating is very important so you have to be very careful about the the type of KV you choose before you operate the I mean before you put your sample inside the TEM column to analyze it. So these are all some of the general information about the KV. Then we will talk about very important aspect of again a specimen electro electron beam interaction that is contamination. Vacuum can be a source of contamination particularly residual hydrocarbon from the pump oil which cracked under the electron beam. Carbon is material then deposits on your thinned specimen making it difficult to do a sensible higher resolution imaging or micro analysis. So this we have to be very careful and any material which is being coated on your sample and then whatever you will see as a new feature may not be belong to your specimen at all. So we have to be careful about this. So that is that is exactly the the contamination is always avoided. Contamination also occurs through an airlock with the specimen. It can be minimized by heating the sample above 100 degree in a heating or a cooling the specimen to a liquid nitrogen temperatures. Polymers and biological samples can easily introduce hydrocarbon contaminants as they out gas in the vacuum. So it is sensible to cool the specimen. When you cool the specimen it attracts water vapor which condenses as ice on the surface. So here again the some of the basic idea of contamination is given but then you have to take lot more care while preparing the sample for a TEM analysis. These are all general guidelines within the column but even before even putting the sample inside the TEM column you need to be very extra careful which some of the aspects we will discuss when you prepare when we go to the sample preparation class. I will just show you some of the live examples. Now we will just go to the some of the basic you know instrument and details and its instrumental operation and what you are now seeing is one of the schematic which shows the operation that is called a parallel beam operation. The first one the schematic shown here is you see that you have the C1 lens C1 crossover and C2 lens and then it is falling on the specimen. So which has got some the semi aperture angle is there alpha on the right hand side you see that the beam is made parallel. Why parallel? Because some of your you know diffraction experiments when you do only with the parallel beam you get you will be able to focus the diffraction spot to the sharpest possible. So parallel beam operation is important in a when you do a diffraction analysis. So for that you need to get this condition. So this is done by the insertion of another objective lens here the which is a front focal plane of objective lens you have the another objective lens is there upper objective lens so which is being made into parallel. In the same line you can see another schematic where it shows the how the convergence angle control the parallel beam operation. So for example you see that effect of C2 aperture on the parallel beam a smaller the aperture create more parallel beam you can see that smaller the aperture create more parallel beam you can see that alpha you can have a different alpha will give you a different kind of a convergent beam. And then what you have to understand here is the nomenclature for the lenses C1 and C2 are pertaining to particular system you can have condenser lens 1, condenser lens 2 and then objective lens 1 something like that. So do not worry about this designation of the lenses but it is you have to just see that what the operation of that particular lens and what is the effect of the effect of that particular lens or diaphragm on the probing electromagnetic radiation that is all we are interested. And then you can see that a focused C2 lens eliminates a small area of the specimen with the nonparallel beam suppose if you have the a focused lens then you will have a focused beam here. Here the C2 lens is focused and this is a C2 diaphragm then you are able to get the focused a nonparallel beam. So just to give you an idea inside the column what kind of beam designation or what kind of beam conditions under which the specimens are examined. The convergent beam is a probe we use such a probe and we want to localize the signals coming from this specimen as in micro analysis or a convergent beam also known as a micro or nano diffraction. This is again a very important operations of diffraction. Suppose if you are wanted to obtain a diffraction information from the very localized region for example a small second phase particle you just want a diffraction from only from that particle then you need this convergent beam operation. I will show you the actual diffraction pattern when we discuss the diffraction in TEM in much more details in the following section. So how the convergent beam operation is done this which is being shown as a schematic with the in the ray diagram here. You can see that this left hand side shows how the convergent beam are obtained and here also you can see that how a small probe and a large probe size are controlled by this lens system. Just to give you an idea so you should have the large u by v ratio which promotes the convergent beam of the probe. So this is just shown with the two condenser lenses one is a strong C1 crossover gives a small probe and other is a weak C1 crossover will give a large probe. So how to get the micro probe or a nano probe is it because the controlling the C1 crossover. Now we will just look at some of the alignments of the aperture. So we have just seen what types of apertures and then if they are not aligned properly what is the issue. So these are the some of the schematic which shows that. So you can see that a distorted image of a beam of axis and this is an optic axis this is a viewing screen and the focused image of the beam on axis and then when it is distorted you will see this kind of a configuration of the beam on the screen. So here everything is focused here you can have the focused beam on the axis and the defocused beam on the axis on the this is on the viewing screen. So these two explains how a beam supposed to appear like ideally on the fluorescent screen when you do an alignment setting. So this is just to give you an idea what is that alignment is about. So if the C2 aperture is misaligned under focusing or over focusing the C2 lens causes the image sweep of axis. So it could be under focusing or over focusing from the C2 lens if the C2 lens is aligned the image of the beam remains circular and expands or contracts about the optic axis as the lens is under focused or over focused. So it is completely aligned but you can just under focused and over focused it will just open and close in a symmetric manner. So then we can make sure that the beam is aligned in the column then we are ready to go. So these operations we will see it in the laboratory and very importantly how do we identify whether your beam is having astigmatism. So suppose this is a shape of your beam on the fluorescent screen then you can simply say that there is some issue. So you have this distorted under focused beam and this is a distorted over focused beam and this is supposed to be a circularly focused beam should appear like this and if it deviates from this circularity and then it shows oval shape like this either it could be under focused beam or it could be over focused beam you have to correct it for the astigmatism. So the effect of astigmatism in the illumination system is to distort the image of the image beam elliptically as C2 lenses under focused or over focused. So this is one aspect we have to very important aspect of alignment and this is one of the major part of the operation. So we will now go to the imaging system and I will just play some of the schematic ray diagram which will show what kind of imaging operation one need to carry out in a TEM. So what you are seeing here is the first one is where a diffraction beam will be formed the second one is image will be formed. So I will you see that this is a specimen and there is an objective lens and you have objective aperture and then SAD aperture and then you have the other intermediate lens and then finally it reaches the screen. So what you are to appreciate is when you want to record a diffraction pattern what are you supposed to do?  So I have the objective lens this is an optic axis. So you have objective aperture and SAD aperture suppose if I want to record SAD then objective aperture should be removed from the optic axis that is what shown in the schematic. Suppose if you want to record image your SAD aperture should be out of the optic axis. So you can see that correspondingly how this the intermediate image is being further demagnified and then magnified and finally it reaches the screen and you can see that how the back focal plane again get projected and then how the image formation occurs. So the two important physical operation here one is forming a diffraction pattern one is forming an image a basic thing. We will talk about actual image formation in another better example this is only to show that what kind of physical operation one need to do when you do an imaging TEM imaging. So this is the description of what I just shown to see the diffraction pattern you have to adjust the imaging system lenses so that a back focal plane of the objective lens acts as the object plane for the intermediate lens then the diffraction pattern is projected on the viewing screen. Let us go and see so this is the back focal plane which of the objective lens will act as an image for the intermediate lens then the diffraction pattern is projected on the viewing screen. If you want look at an image instead you read just the intermediate lens so that its object plane is the image plane of the objective lens then the image is projected onto the viewing screen like what I have just shown here. So another important imaging system in a TEM is producing a bright field or a dark field we have seen that in the optical system itself. So you know the basic principle of obtaining a bright field and dark field. So in TEM it is the same thing but the schematic clearly illustrates that how the bright field and dark field imaging are realized. So you have this specimen this is an optic axis and then you have the whatever you get on the screen is given on the 2D projection here. So this is the optic axis and this is also a zero order beam that is transmitted beam and then you have a diffracted spot around this. So when you want to do a bright field image the objective aperture just stays on this transmitted beam and then you will get an image. But on the other hand if you are interested in taking a dark field then you can see that the your aperture is moved to from the optic axis of transmitted beam to one of the diffracted beam. So you can do this dark field imaging on any using any one of this diffracted spot of your interest. So each one will give a different information from a different set of planes from the specimen. So based on that interest you can do a bright field or a dark field and so on. So normally this is done through a beam tilt operation a beam is tilted rather than an objective is aperture is just brought down to this spot. A beam tilt operation will make the beam the diffracted beam come to the center and then aperture is being put on that then you will get the dark field image. So that is the primary information from this slide is you should get an idea a transmitted spot is being used to form a bright field image any one of the diffracted spot is used to form a dark field image. So that is the information from this slide. Now we will look at the other important imaging system in a TEM called STEM scanning transmission electron microscopy imaging. So you have the go through this schematic you have the electron source and then you have the condenser lens. Please recall what we have discussed in a scanning electron microscopy lecture where we had the deflection scan coils. So similar setup is here which will manipulate the electron beam according to the scanning action. We have gone through the scanning action in much more detail in the scanning electron microscopy you just recall those aspects similarly the beam will scan through the samples on the complete surface the only difference between the scanning electron microscopy and this is here the your specimen is transparent but then the scanning action is the same. So you get the signals again you have the detector and then which will correct the signal and so on. Therefore rest all the operations are same except that the specimen is transparent here. So that is one point the right hand side schematic shows how exactly the you know the ray diagram looks like.  So you can see that this is falling on a back focal plane of an objective lens. So you have the scanning the convergent probe for a STEM image formation using two pairs of a scan coils between the C2 lenses and the upper objective pole piece. So this is exact location of the your scan coils between C2 lens and an upper objective pole piece. The probe remains a parallel to the optic axis as it scans. So this is a simple way of putting this transmission as well as scanning system together and you have to just you know you can appreciate that the operations are similar to a scanning electron microscopy with regard to scanning action is concerned. But the difference is the specimen is here a transfer and electron transfer and specimen where in a SEM you have only the surface which is being I mean you gives out all the signals after the scanning. So that is one point you have to remember. So here a principle of forming a scanning image showing how the same scan coils in the microscope controls the beam scan on the specimen and the beam scan on the CRT. Thus no lenses are required to form the image. So it is similar to scanning electron microscopy as I told you before. So how the image formation occurs in a scanning electron microscopy is demonstrated in this. So you have already a knowledge on this so I will skip this. So typically you have the what kind of an image will see through a stem image. This is taken from this textbook again. So you have the bright field image and this is a dark field image. This is called you know annular dark field image and this is a typical diffraction pattern. What you have is suppose if you have the specimen and this is a scanning beam and you have the bright field I mean image can be formed from this transmitted one and this is a diffracted beam. You have ADF is called annular dark field that means suppose if you have this is the diffraction pattern ring pattern an annular ring will collect complete the dark field intensity and completely block the transmitted intensity. Then you get this kind of very interesting image that is called annular dark field and then you have the bright field which is formed with this image in this system. Please remember a scanning transmission electron microscopy is very specifically used for a chemical analysis very useful in chemical analysis and micro analysis or the elemental mapping across the particular location of the material feature and mostly the probe which is being used in the stem is much more smaller as compared to normal TEM operation we will just show you some of the demonstrations about this also. So as an introduction to this course you should know what are all the possible techniques possible in a transmission electron microscopy. In that respect only I just brought the introductory slides like this then we will get into this basic idea when we actually operate the TEM in the lab. So now the another important aspect of TEM operation is a camera length calibration the schematic which shows a basic geometry geometrical relation between the distance between the specimen and the screen and then what you can do with that geometry. So let us see that this is a specimen this is an incident beam suppose this is the back focal plane here and this is a diffracted beam this is 2 theta and this distance is L and then this distance is R this is from the transmitted beam to one of the diffracted beam the distance is R then the relationship what we have is Rd is equal to L lambda. So this is a very important relation we will look at that derivation when we look at the diffraction of the diffraction phenomenon in TEM in much more detail but this relation is very important relation in identifying or indexing the diffraction pattern and the lambda L is kept constant always that is why it is called a camera constant lambda L is a camera constant and this requires some calibration for before you do any analysis your camera length need to be calibrated with a standard sample and then it has to be fixed. So then only you can use this relation for any of your diffraction analysis and so on we will do a demonstration or we will work out some examples also and this is the typical table when one generate after the calibration of the camera constant and I will leave it there we will use this parameter when we do a diffraction analysis you will appreciate this importance of a camera constant why I am showing this slide because when you decide to use this kind of an analysis like if you want to use a camera length and then it has to be calibrated first of all you have to check whatever it is showing in the display in a TEM display whatever the camera constant it shows we have to we should not blindly take it up we have to check whether it is calibrated or not then only you can take that value and use it for the diffraction analysis later so that for that information only I brought this now I slowly move on to the other important aspect in TEM that is a diffraction in TEM before I get into this in a very exhaustive topic in TEM I would like to just recall some of the principles we discussed about diffraction in x-ray cores or in x-ray diffraction lectures see the there is no difference in those principles for whether in terms of you know diffraction condition we talked about reciprocal lattice we talked about evolved sphere concepts and then all this phenomenon whatever we discussed they are all going to be the same in this electron microscopy as well and then another important thing is the you have to just find out what is the fundamental difference between the electron diffraction and an x-ray diffraction you yourself will know now that only the wave length is the difference because with the increasing increasing the acceleration accelerating voltage we will be able to control the lambda that is what we have seen in the beginning of these course so through a de Broglie's relation and in x-ray we have a much higher wavelength so that is one basic fundamental difference otherwise all the diffraction phenomena are same so with that background you will be able to appreciate some of the concepts in TEM also so I will be moving a little bit faster in this lectures I will not spend much time because the most of the concepts are same but I will spend much more time in some of the important diffraction experiments like convergent beam electron diffraction or you have the Kikuchi pattern and so on which are very important diffraction experiments in transmission electron microscope I will spend little more time on that otherwise they are all the same so if you look at the diffraction pattern in TEM you have to just ask few questions suppose if you ask what is it and what can we learn from it why do we see it what determines the scale what determine the distance between the spots or the positions of the lines so something like this if you try to answer these 4 or 5 questions you will see that surprisingly you will get lot of information about the specimen characteristics so some of the related questions is the specimen crystalline if it is crystalline then what are the crystallographic characteristics is the specimen monocrystalline if not what is the grain morphology how large are the grains what is the grain size distribution etc what is the orientation of the specimen of individual grains with respect to electron beam is more than one phase present in the specimen so some of these basic questions related to what I mean I have put some fundamental questions in the previous slide they are all related and you will be able to get all this information from the diffraction so you have to remember in transmission electron microscopy diffraction is more important in fact the whole microscopy operates with the I mean operation lies mostly on the principle of diffraction so you have to give an importance to the diffraction analysis when you really want to use this or exploit this TM so I will I will talk about the importance and much more when I mean I actually give the practical example as well so first look at the typical a sad in TM that means selected area diffraction in TM so what what is shown in this photograph so this is a typical selected area diffraction taken from this textbook once you have chosen the area from which you wish to obtain a diffraction pattern select the required camera length that is the magnification of the diffraction pattern so the camera length is also called you know where whenever you turn this magnification knob when a diffraction mode that camera will I mean the camera length will increase or decrease so this typical diffraction pattern is taken at two different camera length you can see that this is the the orientation of the two patterns are same but only thing is you can see that the distance between the spots are bigger that means this diffraction pattern is taken at one camera length and this diffraction pattern is taken at much little more higher camera length so that is what it is so you have to choose a camera length of your interest that is what it is shown here and then I as I said before you have before we do all this and that your camera length need to be calibrated and then you choose appropriate camera length to do the experiments so diffraction using small probes it is possible to obtain a diffraction from small area in conventional selected area diffraction and approximately parallel electron beam is incident on the specimen the resulting diffraction pattern from a periodic sample consists of an array of sharp sharp spots in the back focal plane of the objective lens so as I introduced using that convergent beam electron diffraction I said we will be able to do a micro probe or a nano probe that means you can make the probe into a micro micron size diameter or a nano size diameter we will also see the the meaning of what I am saying now how what is the meaning of I am seeing a micro micron size beam on the screen or a nano meter size screen beam on the screen what is the physical meaning of it that we will see but then we can obtain a diffraction information using this either a micro probe or a nano probe from a localized region of our interest that is what we are discussing here in a conventional SAD as I just mentioned if when I when I talked about a a convergent beam or a parallel beam I said that a parallel beam operation is important to in order to get a a sharp a diffracted spot so that is what is shown here in a conventional SAD so a parallel electron beam is incident on the specimen where you get a very sharp pattern whereas in a in a small probe a convergent beam has to be used so we will continue this discussion on the diffraction and its effectiveness and also what are the details you are going to get it is very powerful tool or I would say that powerful technique to obtain a most information about the material characteristics we will continue in the next class thank you


Good morning. Welcome to CMC Markets on Friday the 6th of November at the end of what has been a pretty lively week all around. Time to look at the week ahead beginning the 9th of November before we do that. We have the small matter of a US payrolls report to overcome. Obviously at the time of recording this particular video. I don't have side of those numbers so I'll give a little bit of a preview of them. But overall I really don't expect them to change the overall direction of the markets in terms of the price action that we've seen this week. Ultimately it's been a very weak week for the dollar and a very very strong week for global markets. And it's really followed the playbook pretty much that we saw particularly on equity markets in 2016. Because in 2016 we saw weakness into the elections and then we saw rebound post elections. And I think the fact that we've seen such good gains this week rather gives the lie I think to the concerns that an awful lot of people had about what an uncertain outcome the worst possible outcome we heard an awful lot about it in a lead up to the election that the last thing that markets wanted was an outcome that could be contested and that's precisely where we are as I'm recording this video. Both Joe Biden and President Trump remain shy of that 270 majority in the electoral college Joe Biden is around about 17 seat short at 253 with Arizona, Georgia, Pennsylvania and Nevada in the balance. And President Trump is on 214. So, I think in terms of challenging the narrative when it comes to what we've seen this week we're seeing a little bit of weakness in Friday trading not really a surprise when you consider. We're coming up to the weekend it's been a long weekend awful lot of us are probably feeling a little bit tired. The fact is that the outcome is still actually uncertain. President Trump once again reiterated his determination to challenge the outcome of the vote in the various states that they currently still seeing votes counted. He's doubled down on the claims that the election was being stolen, which is a fairly alarming claim to make. And it's a disturbing escalation and potentially. It's against him which I think that it will in the event that he does lose could have significant consequences for the overall political discourse in America over the course of the next four years. Now the most probable outcome still looks like a Democrat win with Joe Biden winning the presidency. There are still nagging doubts though between now and the fifth of January as to whether or not. The final outcome when the final votes accounted and that could come as late as the 12th of November next week particularly in Nevada. When when all is said and done. Still have until the 20th of January until the new US president is sworn in. Yet here we are with equity markets up strongly the NASDAQ up over 8% since the beginning of the week. With all of the concerns that we had leading up to the election and the contested outcome appear to have gone by the wayside now many reasons I think have been in have been espoused how resilient stock markets have been this week despite the current uncertainty. Now obviously central banks, it's one of my favorites that one central banks are more likely to step in with a greater monetary policy activism. Well, that's no surprise. That's just lazy thinking that we're going to be doing that anyway so irrespective of the outcome central banks are always going to be fairly loose in terms of monetary policy. So I don't really think that is a significant surprise to anybody. I think there are a couple of other theories that do make more sense however. First one is a lack of a blue wave, because the Senate is still up for grabs. And the lack of a blue wave is likely to mean steps by the Democrats to rein in the tech giants with more business regulation and higher taxes on the private sector in general is now much less likely. So that's, there's less of a business overhang there.  The Democrats policy manifesto certainly had a higher Texans tax and spending component to it. So the fact that they could well miss out on gaining control of the Senate has to be construed as a as a plus the US business. The other theory is in the absence of an imminent fiscal plan. Due to the political deadlock across Washington DC and Capitol Hill is an easy win for a newly appointed President Biden. And this is again working on the assumption that he wins and will be for him to merely remove or lower the various tariffs that President Trump has imposed on China and the European Union. That could that could institute constitute a much less confrontational approach with respect to the EU in China and act as a significant modest fiscal boost to the US economy. So that I think there's those those two particular last two arguments certainly have some merit and could arguably arguably be used as a reasoning as to why we've seen a significant rebound and equity markets this week. That being said, we're still pretty much in the range that we've been in for several months now, particularly when we look at the FTSE 100 here we can see that it's bounced off the lower line of this channel that I've drawn in and now we're starting to run into a little bit of resistance near the upper line around about 5,935,940 so anywhere near 6000 likely to be a little bit toppy also coincides with coincides with the October highs. If we look consequently at the S&P 500. It's a similar sort of story and actually I've drawn a nice little line through the highs here, which we almost breached in the move up through Thursday, but since then we've come back off those highs there so there is a significant barrier up in and around recent range highs that we saw at the beginning of October. So I'll be paying particular attention to that up a line there to ascertain whether or not this market really has any legs for further gains going forward and I think in the absence of a significant fiscal response I'm going to think is I would argue that it's going to be very very difficult to make the case for a significant significant surge to new highs unless we get some sort of framework, if you like, for a potential fiscal response from a new US administration. If we look at the NASDAQ. It's a similar sort of story. Got the previous record highs up there. Let me just blow that out for you. Just turn that off and get rid of the clutter on the screen. Again, we've got these previous peaks 13th of October. That is likely to be a bit of a barrier going forward. But once again, pretty much since the beginning of September, we've been trading in a sideways range. And I'll likely to continue to do so over the course of the next few weeks and months. The NASDAQ has bounced back the DAX rather the DAX has bounced back very very strongly after falling through the 200 day moving average, but rebounded off this 11,360 area, which highlighted which I highlighted in October as a fairly key support area. If we look at the forum update for this on the 28th of October, I said DAX breaks to the downside below 200 day moving average with potential for a retest of the 11,360 area, which was the April peaks, which is right through here. So once again, resistance suddenly becomes support and also happened to coincide with the previous Fibonacci level of this entire up move here. So we retraced 38.2 from this entire up move from there to there. So again, pretty much in a range for the German DAX. Keep an eye on those chart forums because they are quite useful. If I've got any particular thoughts on a particular asset, I'll jot them down in there with respect to potential future direction for any and where the key levels are for a particular asset. Okay, so I mean that's pretty much where we are in terms of the markets seen a pretty decent rebound over the course of the past few days. I think the really big question that needs to be answered at this point in time is whether or not these gains are sustainable or whether or not we'll continue to chop within the ranges that we've been in over the course of the past few days. It's also been a very, very poor week for the US dollar. That's pretty much borne out by this the CMC markets dollar index. We broke in below the previous lows here, even though we haven't done so on the US dollar index. And the reason that we broke into the downside on the CMC dollar index is because we have a much higher Chinese one component within it. And the Chinese one has outperformed quite significantly. But what's notable about this particular move on the dollar index here is look at this candle here. And I've highlighted this candle for the simple reason is that on the Wednesday, the day of the vote, we saw a significant move higher in the US dollar. But we were not, we were not able to hang on to any of those gains and actually finish the day lower. That's very bearish that suggests to me that there is a potential for an awful lot more downside in the US dollar. Now how that comes about, come about against the euro could come about against the Chinese currency, the Remnambi or the one, whatever you want to call it. Or the pound, for that matter, both very key components of the CMC dollar index. If we look at the Remnambi or the offshore Remnambi, we can see that on this chart here that I've drawn. And that's broken out quite significantly from what looks like a double top. Now if we take this as a double top on the Remnambi and project it down, that brings us back to 648, 645. So taking this move here as a double top projecting it from the breakdown level gives us a move to 649, 648. So in terms of Remnambi strength or one strength, there's quite a bit further to go. So that suggests that we could well see further US dollar weakness over the course of the next few days and weeks. This is a weekly chart that I'm showing you here. I can quickly change it to a daily chart. But nonetheless what it shows us is that there's potential for an awful lot more dollar weakness against the Chinese currency than has been the case previously because of that key breakout point. And if we look at it over a longer time frame, we can see how much the dollar has gained against the one over the course of the Trump presidency. If we go back to 2016 here, we're starting to come back to the levels that we were at the beginning of when Trump took over the White House. So pretty much back to levels where we were in the beginning. It's been a quite a choppy ride. But overall, judging by this chart here, there is potential for further dollar weakness against the Chinese currency going forward. So I'll be keeping a close eye on that, certainly when it comes to the future direction of the US dollar. So now let's look forward to next week and next week is likely to be a little bit quieter. We've had a Fed decision this week, we've had a Bank of England meeting this week. We've had a presidential election this week. And the likelihood is that we may get a clearer idea of where we are next week in terms of the final Electoral College outcome. The big question then will be whether or not the Republicans can hang on to the Senate and that still remains fairly unclear. So at the moment, the president, the position for president is up for grabs, but it looks increasingly like we're going to get President Biden. The bigger question for me over and above the president is the Senate. At the moment it's 4848. So the big question going forward is who gets those remaining two seats. If they go the Republicans way, then we could well see a Republican blocking a blocking strategy within the regulatory. Outlook for BC and capital health. So that is still unknown at the moment. The moment it doesn't look like we could get a blue wave. But at the moment, the outcome for the Senate still remains pretty murky. But at the moment the markets working on the basis working on the premise that a gridlocked government is probably a fairly decent outcome, because it means that politicians can't tinker and do any damage. OK, so let's look forward to the weekend. We've got UK data. We've got Chinese data over the weekend, China trade either Saturday or Sunday. Now, the most recent China trade data for September showed a big improvement. And I would expect that to continue. Finally, the Chinese economy appears to be getting up off the canvas. Obviously, we are now here in Europe in the UK heading into a four week lockdown. Not only here in the UK and England, but also in Germany and France. So economic activity going forward is likely to remain very, very difficult to sustain. That being said, we've seen the Bank of England this week announced another hundred and fifty billion pounds of quantitative easing. And the Chancellor of the Exchequer Issue Soonak has extended the furlough scheme into March next year. So that does offer a little bit of a cushion for the UK economy and more importantly to the UK consumer. And we're going to see how strongly the UK economy bounced back in Q3 in the coming week with the latest first iteration of third quarter GDP. Now, you can argue that this is a rear view mirror stuff and it doesn't really matter. I would argue that it does. OK, it's in the rear view mirror. And ultimately we are in the middle of another lockdown, but it certainly gives an indication as to whether or not there is any momentum behind the rebound that we saw in Q3. Now, we're also getting unemployment data and wages data as well for the UK economy. So it's a fairly, it's a fairly important week for UK data as well as industrial production, manufacturing production and trade data. But the key data, I think, for me is going to be the unemployment numbers away from the GDP numbers. So I'll start with the unemployment numbers, which are out on the 10th. Now, in the most recent set of numbers, we started to see the beginnings of a little bit of a rebound or a little bit of a push higher in the unemployment rate. In the three months to September, this saw a sharp jump from 4.1% to 4.5%. As more employers decided to squeeze down on costs as it became apparent that there would be no V shaped recovery. Now, obviously furloughs helped to disguise some of the harsher damage, I think, in terms of the rise in unemployment and the extension this week until March while welcome is unlikely to have come in time. For a lot of people in vulnerable jobs, given that a lot of a lot of employees had already started to cut back on their headcount. And I think this week's latest jobless numbers are expected to reflect that further with another increase. So I think the monthly jobless claims number is likely to see an increase from what we saw in the last month in September to 7.6 and potentially we could well see a further increase on that number. More importantly, the ILO unemployment rate is expected to push up from 4.5% to 4.8%. So we are slowly seeing the ILO number start to play catch up with the distinct possibility that the three month rate could actually hit 6% or 7% by the end of this year. The ILO unemployment rate that we're seeing in the coming week is up for the three months until September. So we've also already seen a whole host of job losses announced in October, which won't be included in that number. So the real rate is likely to be probably near the jobless claims rate around about 7.6 or even heading towards 8%. And obviously that's not particularly welcome, but certainly I think the extension of the furlough will help to cushion some of the economic shock that could be coming in the UK economy's way as we head into the end of the year. And it's also interesting actually that the furlough extension also covers the end of the Brexit transition period. So there may be a little bit of a longer term thinking going on in the UK government's mind when they decided to make that furlough extension. Maybe they also had the lack of a potential Brexit deal as we head into year end. And they're using the furlough extension to try and cushion some of the potential economic shock there. Doesn't appear to be affecting the pound however. Let's look at the CMC sterling index still looks very much a case of by the dip. So certainly there is an expectation that there will be some form of deal, an EU UK deal, and we're still getting an awful lot of mixed messages. And I think we're likely to continue to do so. The fact of the matter is neither side, given the fact that most of Europe is in a one month lockdown and the UK is also in a one month lockdown. Neither side can afford to walk away at the end of this year without some form of skinny deal. It would be irresponsible in the extreme for both sides not to arrive at some form of arrangement. And that is still my base case that they will fudge something to get to get something over the line at the moment the sticking points still remain fisheries. They still remain the level playing field state aid that sort of thing. We look at cable cable again similar to the sterling rate index very much by the dips on cable. It's a brave trade. I lose count of the number of people who tell me sterling should be large sterling should be at 120 should be at 110. I don't care where it should be. What I care about is what the price action is telling me price action is telling me by the dips by the dips. By the dips until the price action tells you not to. So you basically trade what you see. And what do I see here? I see a succession of higher loads. Now potentially we need to see a break above 132 to take this move that we've been seeing over the course of the past few weeks higher. Good support or 125 and a half 128 and a half even a good support around about 128 and a half. You've got a whole series of loads through here. If we can sustain a move through 132 then we could we'll see a move through to 135. Now what could drive that? It might not be sterling strength. It could be dollar weakness. What we're seeing in terms of euro sterling I think is fairly instructive. If we look at this trend line here. I'm still very much of the opinion that you trade what you see. So at the moment sell rallies on euro sterling. Nice down move here until such times as we break above the 50 and the 100 day moving averages in this trend line here. Then there is significant mileage in basically adopting a sell the rally strategy. There is also resistance through 91. You can see it born out through this peak here and this peak here where I'm drawing where I'm drawing the mouse here. So at the moment euro sterling very much sell the rally until such times as we break above 91. And then we could we'll see a retest of the highs of around 92 20 and the peaks that we saw back in September very much trade what you see. Okay, so what else have we got coming up we've got UK GDP. That's expected to rebound 15.7% so it's not going to reverse all of the damage done in Q2 we saw a contraction of 19.8% in Q2. So to reverse all of that damage you'd need to see at the very least 21 or 22% rebound to undo all of that. So we've seen a modest rebound in Q3. That's unlikely to be replicated in Q4 in Q4 it's going to be damaged limitation. As a result of the lockdown I was seeing in November we've also got German ZEW. Now the German ZEW survey that came out in the October reading with a sharp fall to 56.1. So from from hitting a 20 year peak of 77.4 in September the ZEW fell to a five month low of 56.1. And in November because German economy is pretty much shut down in November we're likely to see another sharp fall with some estimates in the region of around about 40. I wouldn't be surprised it wouldn't surprise me at all to see a much sharper fall than that but that's on the 10th of November German ZEW survey for November investor expectations. They're likely to be bearish even though the DAX has rebounded. EUR a dollar once again heading back towards these peaks here. We look as if we could edge a little bit higher over the course of the next few days on the premise basically that the dollar is likely to remain weak for quite some time to come. And that's borne out by my CMC dollar index chart that does appear to have broken to the downside. Further dollar weakness is likely to prompt a little bit of nervousness amongst ECB policymakers about a stronger euro. And that would presuppose it will probably get further jaw boning from ECB officials about about about the perils of a stronger euro and their ability to hit their inflation target, which is currently at 2% and which they're currently missing by a country mile. So if we get a move back towards <IP_ADDRESS> expected an awful lot more chitchat from European policymakers about talking the euro lower. One thing we have also seen this week is a big jump higher in the gold price. And that's likely to continue to be the case as we head into Q4 we broken towards the upside. That suggests we're probably going to head back towards $2,000 an ounce. We can see that on these two daily candles here we've broken high we broken above the 50 day moving average. We're currently trading around the highs we've tried to go lower on this daily candle. We haven't been able to sustain that move lower currently back where we opened. Obviously the payrolls numbers later later today could well have a big part to play and whether or not we continue to push higher. But overall given the fact that we've broken above this, this series of peaks through here around about 1935 1940, then it's likely that as long as we stay above the 50 day moving average, we could well head back towards the $2,000 an ounce area that we saw all the way back in August. So certainly dollar weakness does appear to be the predominant theme here in the aftermath of the presidential election. Looking ahead, then a while close that let's just open that up again this week, pull that back looking ahead. There are also a number of key earnings announcements that I'm going to be paying particular attention to this week. First of which is house builders person and decided to restore part of the dividend in its numbers earlier this month. The record highs back in February saw the share price half in the lead up to the March lockdown. We have since rebounded and pull back some of that we've seen a number of house builders report over the course of the past couple of weeks looking to restore their dividends. They've got strong order books and they look fairly resilient. More importantly, the construction sector has remained open in this lockdown. So the likelihood is that we could well see further gains for house builders going forward, which you've also got a factor in the prospect that an awful lot of the good news could well already be priced in. What else have we got? We've also got JD Witherspoon's latest numbers as well. And JD Witherspoon nice little pincer movement going on here with respect to this particular chart. Pubs are closed this month apart from takeaways. Obviously been one of the biggest casualties of the pandemic as the hospitality sector. In October, the pub chain posted four year pretext losses of 34.1 million pounds. Now eat out to help out. This is his Q1 numbers. Eat out to help out is likely to have mitigated some of the damage that we've seen in Q1. But we're already seeing job losses being announced even here in the case of JD Witherspoon only last month. Witherspoon announced they'll be cutting 450 jobs from its locations in the various airports around the country. So I think last week's start of new restrictions for this month suggests they won't be the last. So be prepared for more pain here. But keep an eye on those peaks in and around October here. And obviously the lows down here or the line through the lows down here or JD Witherspoon. We've also got ITV. ITVs had a bit of a rough ride of it recently but does appear to have enjoyed a decent rebound from the lows that we saw all the way back in March. Really does need to consolidate this move higher above those peaks that we saw in September. When the company reported its first half numbers in August, total advertising revenue for the period saw a decline of 21% to 671 million. Broadcast revenue also saw a decline of 17% as well with ITV studios. Normally an outperformer seeing a 17% decline to 630 million due to having to pause its production capabilities due to various lockdown restrictions. Now, I think production has restarted but obviously within the confines of the restrictions of the day. We could well see a little bit of a pickup in advertising revenue. We've seen the return of sport to our screens, which will have helped boost ITVs advertising revenues in this quarter. And we'll also be paying particular attention to Britbox revenues there. Hopefully you'll see an improvement there. But I still maintain it's likely to be an uphill struggle for ITV and less advertising revenue shows evidence of a sustained pickup. So you can draw a nice little line through these lows here to try and get an indication of where you could look to pick up any shares on a dip back down towards the downside and certainly in terms of that particular stock. One other thing is Disney. We've also got Disney's fourth quarter numbers. Now, I think Disney is going to be very interesting in terms of Disney Plus. When if we cast your mind back to just over a year ago, when Disney was gearing up for the launch of Disney Plus at the end of last year, they must have had high hopes.  So let's have a quick look at Disney. It's already there. Just pop that in there. Hold that back. Drop that in there. So we're looking at Disney shares recovered. They've recovered a smidgen. But I think the big question is uncutting on it's undercutting on price is one thing I think, you know, in terms of trying to attract subscriptions and it certainly is cheaper. It is the cheaper of Netflix and Amazon Prime and 60 and a half subscriptions would suggest when the company reported in August would suggest that it's still some way to go to compete with Netflix in terms of content depth. And I think that's where it's likely to fall short because while it is some really good content, it doesn't have the depth of content that say Netflix has got and Netflix has just increased its prices. Now, furthermore, I think the decision to charge up to $30 to view its Mulan film may well have been a bit of an own goal as well because $30 is an awful lot unless you're a family to watch a single film you wouldn't even pay that much if you went to the cinema. So it's ability to compete has also taken a huge blow because of the closure of its theme parks, its theme parks or a huge revenue earner. And the fact that they've had to close pretty much most of them for the last six to nine months has blown a massive great big hole in its finance. So companies already announced a loss of 28,000 jobs beginning of October losses are expected to come in around about 72 cents a share. Looking at this particular stock here, have a look at the trend line through the highs here. Draw a line through that. So running into a bit of resistance around about 130, decent support around about 115. If Disney disappoint on the subscriptions front, we could well see a little bit of a tick back down over the course of the next few days. So keep an eye out for beyond meets Q3 numbers Vroom online sale of cars Q3 on the 11th of November Cisco Cisco systems on the 12th of November and Palantir technologies another IPO on the 12th of November. So there is certainly a rich vein of earnings announcements out there. I think the big question I think as we look ahead to the upcoming week is whether or not we get any more clarity on the US presidential election. And if so that should give us a much clearer idea of what the US political landscape is likely to look like over the course of the next four years but I think one thing is certain. It's likely to be a choppy ride it's likely to be a volatile ride.  Thank you very much for listening. It's Michael Houston talking to you from CMC Markets.