 In normal plastic deformation, the force I take aluminum at room temperature or copper or you know the ductile materials, then typically I get a elongation of about few tens of percent. But, there is a phenomena known as structural super plasticity, in which case I can get elongations in tension up to more than 300 percent and there are even reports of getting about 2000 percent elongation. That means, this is really a drastic effect and as we shall see later that in nano crystalline solids or bulk nano crystalline materials, we expect that this effect is going to be enhanced. Typically super plastic deformation takes place when the temperature is high, when the grain size is less than about 10 microns. That means, we are not really talking about nano scale grain size, but we are talking about micron scale grain size. The grains if they are equiaxed it helps and especially so if they remain so during and after deformation and the grain boundaries are glycyl. That means they are not pinned and typically that means that we have a large fraction of high angle grain boundaries. So, these factors tend to promote super plastic deformation in materials. So, to summarize these factors, it is typically more than about 0.5 T m which is we call that close to a recrystallization temperature. The grain size is in the micron scale, the grains are equiaxed and we have a large fraction of glycyl grain boundaries. Presence of a second phase of similar strength to the matrix reduces the cavitation during deformation and this in which also can inhibit grain growth at elevated temperature and this helps in obtaining super plastic deformation. Because even though I may start with an micron size grains if during deformation because we are at high temperature there is a tendency for grain growth. Then what happens is that we are going to have large size grains and this would inhibit super plastic deformation or further plastic deformation. Typical alloys which are found to have super plasticity or are aluminum 33 percent copper, zinc 22 percent aluminum alloys. Many super plastic compositions are close to the eutectic or the eutectoid points. That means having a eutectic or eutectoid composition helps in super plastic deformation and typically super plastic deformation is diffusion controlled and this diffusion can be either lattice diffusion or can be grain boundary diffusion. So, here briefly we have summarized some of the aspects which contributes to super plastic deformation and they include material parameters, they include process parameters, material parameters include their composition, the kind of grains we have got, the grain size, the process parameter obviously includes temperatures and we shall see that it is usually low strain rate which actually promotes super plastic deformation. And if you look at typical materials and you plot a stress versus strain rate curve, then you would notice that log of stress versus strain rate and of course, you could plus normal stress or you could actually plot shear stresses shows a sigmoidal behavior. And this is typical of many, many materials though not all materials and such a log stress versus strain rate plot shows three regions region 1, 2 and 3. In region 1 and 3 typically the strain rate sensitivity is small of course, the way of obtaining such a curve would be to do a experiment at a certain strain rate and find a stress for a given strain a fixed strain. And then I would like to plot the result of such many, many experiments in the form of a log strain rate versus stress curve. And if I do so, this is now result of many experiments, I would notice that there are three regimes, the region 1 where the strain rate sensitivity is small, region 3 where there is an again strain rate sensitivity is small, but in the intermediate regime. But there is a region 2 where actually the strain rate sensitivity is high, this region 2 is often refer to the as the super plastic regime and here in we actually get the maximum elongation. And we also have to note that the x axis being log strain rate, these region 1 corresponds to low strain rates, region 2 corresponds to intermediate strain rates and region 3 corresponds to high strain rates. Then in normal materials suppose I employ very high strain rates, then I would expect that there is going to be a reduction in a phenomenon like super plasticity. The mechanism, underlying mechanism between these regions also change and the kind of sensitivity to purity of the sample also change. For instance in region 1, the sample is sample purity plays a important role, it is very sensitive to sample purity. While in region 2, the sample purity and grain size are not, the material is not that sensitive to that. When I am saying sensitive, it implies that there is a dependence, but it is not sensitive. In region 3 for instance, again the material is not that sensitive, it becomes again sensitive to the purity of the sample. Now, the underlying mechanism for instance could be grain boundary diffusion as in the case of the region 1. It could be predominantly grain boundary sliding and this grain boundary sliding is of course, accommodated by dislocation activity and also some amount of diffusion. But that is region 2 mechanism, while in region 3, inter granular dislocation process with these dislocation interacting with the grain boundaries is expected to play an important role in the deformation of the material. Therefore, if you look at to summarize this slide, therefore I am looking at a plastic deformation of a super plastic material and I know that the governing equation is now at constant strain and temperature. That means, it is a high temperature behavior of the material I am plotting here. That means, I can write stress as a strain rate power m, where m is the strain rate sensitivity and in the highest, if the strain rate sensitivity is high, then I get long super plastic elongation, large percentage elongation and this is the middle region in the curve. Now, a very related kind of a phenomena to super plasticity is a phenomena known as creep. In creep 2, sometimes we get long elongations, but the essential difference between, if you look at even the mechanisms, often the mechanism between super plasticity and creep are very similar. Therefore, we can think of creep and super plasticity being as related phenomena and typically these are again low strain rate phenomena. They are usually typically high temperature phenomena, but the important difference being in creep, we can think of as damage accumulation leading to the failure of the sample, while in super plasticity extended plastic deformation can be achieved. That means, accumulation of damage leading to failure is delayed in super plastic deformation. So, what is creep? Creep is permanent deformation of the material at constant low. Previously, we had seen the uniaxial tension test. In uniaxial tension test, we know that to cause further plastic deformation or to cause further even elastic deformation, we need to increase the load. That means, this deformation with increasing load, but here in creep actually the whole test is carried out at constant load or sometimes at constant stress and you slowly progressively accumulate strain, but at constant stress or load. And this with therefore, a typical result of such a creep experiment will be a plot of time versus strain. So, you are accumulating strain with time and therefore, you have a what is known as a creep curve. And this as I pointed out is an high temperature phenomena, but we have to remember now we are talking about homologous temperature. That means, I the relevant temperature is nothing but T by T m and if I am close to the recrystallization temperature or above it, then I would expect phenomena like creep becoming very important. Therefore, if you look at lead, lead is even room temperature is high temperature. Therefore, if you hang a load on lead wire, then actually lead will creep at room temperature. Normally, increased plastic deformation takes place with increasing load, but in creep plastic deformation takes place at constant load. So, this is the basic definition of creep and this has to be kept in mind. And creep rates become appreciable only above about 0.4 or 0.5 T m. Mechanisms of creep in crystalline materials is different from that in amorphous materials. And for now, we will restrict ourselves to creep in crystalline materials, because in amorphous materials typically you have the mechanism of creep could be very similar to what you call viscous flow or Newtonian flow. While in crystalline materials, we will see there are many, many mechanisms which can contribute to creep and we will have a next slide which will actually give a broad overview of these mechanisms. It is important to note that at temperatures where creep is appreciable, various other material process may also become active. And these of course, may contribute to creep. They may what you call lead to failure. They may actually what you may corrupt your creep data, but it is important to note that high temperature is the region of what you may call all kind of thermally activated process taking place. Like this could be oxidation, this could be precipitate coarsening, this could be recrystallization etcetera. And therefore, when there are parallely many, many process taking place, it becomes what you call complicated or difficult to deconvilue the pure effects of creep. These are these other effects which can come in like oxidation which could actually corrupt your data. Creep experiments as I pointed out are conducted either at constant load or constant stress. And creep can be classified based on either phenomology, that means the kind of constitutive behavior in which case you would call them power law creep or Harvard on creep. Some of these names come in, but here we will focus on the mechanistic classification of creep which is we will of course, consider in the slide after this. But first we will take up as I pointed out what happens when I load a material at constant load of course, and plot the strain with respect to time. So, similar to the case of super plasticity of course, there the axis for very, very different there it was a plot of log strain rate versus log stress, but here I am plotting time versus strain. And you get what you might call the three regions of creep. So, a time strain curve is the creep curve and you typically observe three regions region one region two and region three. Initially of course, when you have subject a material to a load you will get some elastic deformation which is the initial strain epsilon naught, but with time this strain grows and therefore, you get a creep curve. In region one the creep rate decreases with time you can see that the slope is downward sloping. That means that the creep rate decreases with time and the effect of work hardening is more than recovery. That means that here the work hardening is contributing to the increase in the strength of the material which is actually leading to a decreasing creep rate. In region two there this is called the region of minimum creep rate and typically you can consider that as a constant rate of creep, because you can think of this as a linear portion in the curve and therefore, you can think of as a constant creep rate. That means that here the work hardening and recovery are approximately balanced. That means whatever strength you are gaining by work hardening is sort of lost by the recovery processes. And therefore, you are having a constant creep rate. In region three which is the region leading finally, of course if you want to draw it to a region where finally, fracture takes place where in cavitation other damage accumulate to such an extent that the material actually fails. Then you would notice that this region three could be absent or delayed in constant stress stress. So, if you are doing a constant stress stress this region may not be observed and if you do a constant load stress you may actually observe this. Here in the necking of the specimen starts and many as I pointed out failure process like cavitation etcetera set in and finally, this is a region where you would not like to operate your material in because it is turning towards failure. Now you can study the effect of stress and the effect of temperature on creep and it is notice that of course, if you load a material with increase and increasing stress it or in more and more load then you would see that the initial elongation increases. So, you have an initial elongation which is increasing which is now the elastic elongation with more stress. Additionally you would notice for a given time suppose I draw a time axis here with increasing stress you would actually obtain and higher amount of strain which is what is expected that means the material is going to fail in a shorter period of time. Suppose this is my failure line then actually the material would fail at shorter time when you increase the stress which is what is of course, common sense expected. On the other hand effect of temperature is very much similar to the effect of stress and here in a game you would notice that you have an increased initial elongation. Of course, the reason for this initial elongation is that the elastic modulus actually decreases with an increasing temperature though this is not very very sensitive to temperature increase, but definitely there at least a 10 percent reduction in elastic modulus is seen when you heat a material from room temperature to say it is melting point. Therefore, this decreased modulus would imply that my initial elongation is going to increase though it is a smaller effect than stress for instance on the initial elongation and similar to the effect of stress you would notice that for a given time for instance I draw the curve for a given time. That means in an increased temperature test actually I would have an increased strain that means strain would increase at a constant time if you increase the temperature. That means creep is going to proceed faster and which also implies that your specimen is going to fail soon. So, this is a brief overview of super plasticity and creep and later on we will actually get back to understanding that why these kind of creep and super plasticity is expected in the case of nano materials and of course, we will also address the question how far the expectations are fulfilled. Now, what are the creep mechanisms which can give rise to failure? There are three kinds of mechanisms which are important the dislocation related mechanisms the diffusion related mechanisms and grain boundary sliding mechanisms. Later on we will see that when you go to nano scale materials the deformation mechanism would actually change switch from slip to grain boundary sliding. Therefore, you can see that why creep would is expected to become important in nano scale or nano grain sized materials. When you are talking about dislocation related mechanisms there are three important phenomena one is cross slip one is climb and other is glide. And as we know that glide requires climb requires higher temperatures because that involves vacancy diffusion and here I am talking about climb of edge dislocations. Then glide can also become more and more thermally activated therefore, at high temperature this is also glide is also going to get predominant. Diffusional mechanisms on the other hand can involve either grain boundary diffusion or lattice diffusion. And as it is obvious in a fine grain material the grain boundary diffusion is going to become more and more important. And grain boundary diffusion phenomena for creep is called cobalt creep wherein the grain boundary diffusion is controlling the creep phenomena. And wherever the lattice diffusion is controlling the creep phenomena it is known as the nabarro haring creep. Additionally diffusion at the core of this location which is called pipe diffusion can also influence creep. And the diffusion rate through the core of a edge dislocation is more because that is a region of free volume. Though we should notice very important thing that when you are talking about lattice diffusion though and if I want to write the diffusivity for these three phenomena I can write down the diffusivity of pipe being greater than the diffusivity of grain boundary diffusion which is greater than the diffusivity of lattice diffusion. But this does not imply automatically that the amount of matter transported by pipe diffusion is going to be more than the grain boundary diffusion because the cross sections of these is different. And typically in a normal material you will notice that dislocation cross section for pipe is the smallest followed by grain boundary followed by lattice. So in normal materials you would notice that it is lattice diffusion which is going to sort of be prominent at normal grain sizes and normal temperatures. But then at different rates of different strain rates and different temperatures other phenomena can also become important especially in nano crystalline materials. And there it is important note like in the case of creep super plus we point out and creep we point out there are accompanying mechanisms which cannot be ignored like dynamic recrystallization which play an important role. And finally so we just to summarize this slide there are three kinds of important mechanisms which we need to enlist those contributing to creep. One is dislocation related mechanisms wherein you have dislocation phenomena like cross slip of screw dislocations climb of edge dislocations and glide of screw and edge dislocations. Diffusional mechanisms like grain boundary diffusion dislocation core diffusion which is called pipe diffusion lattice diffusion and also interface reaction controlled diffusional flow. Finally of course grain boundary sliding is also an important mechanism which can contribute to creep. Now we will highlight a few points regarding these various mechanisms cross slip is typically predominant in low temperature of creep wherein screw dislocations can cross slip by thermal activation and give rise to plastic strain as a function of time. So essentially if you are working at low temperature and you are studying creep then this would be an important mechanism to consider. Edge dislocation piled up against obstacles and suppose you are talking about dislocation climb edge dislocation piled up again obstacle can climb to another slip plane parallel to it and cause plastic deformation which means that as a function of time you are going to get strain. So here we are talking about edge dislocations and for now I will schematically show it as being piled up at some kind of an obstacle and this is on this slip plane. Now at low temperatures this will get this will remain stuck but at high temperature this can actually climb this dislocation to a parallel slip plane and continue to move. This implies I can actually get plastic deformation from those dislocations which had become a cell at low temperature. And in this case obviously the rate controlling step is going to be the diffusion of vacancies because climb is possible only by diffusion of vacancies. And the other way of looking at it is that the atoms at the core atomic row which was here at the core of the dislocation or near the core of the dislocation actually diffuses out that means the dislocation climb by one height. In grain boundary sliding if you look at it at low temperatures the grain boundaries are considered stronger than the crystal interior and impede the motion of dislocation. This is what we know from normal and this we have this in some sense is a reflection of what we have always known as the hall patch effect. At higher temperature the grain boundary being a high energy region become actually weaker than the crystal interior and often some time this even described as the sort of a melting of the grain boundary at high temperatures. And this temperature where there is a crossover where in the grain boundary becomes weaker than the grain interior or the crystal interior is called equicohesive temperature. And therefore, at high temperatures the grain boundaries can actually slide past one another to cost plastic deformation. So, inherently at high temperature there can be a switch in the mechanism of plastic deformation. And this we will see is not only happening at high temperatures, but an equivalent way is actually reducing the grain size wherein we will observe a similar kind of an effect in nano crystalline materials. In diffusional creep and we have already seen the two names we associated the Nabarro-Haring creep and the Coble creep. In response to the applied stress vacancies preferentially move such that the specimen axis which is along the stress axis actually grows. And in effect what happens is that so there is a diffusion of vacancies from the direction of tensile stress to the direction perpendicular the phase at perpendicular which leads to a net elongation in the specimen that means I get this elongation purely by diffusional. Therefore, you can have creep that means strain accumulating as a function of time. And again like the case of the dislocation client this whole process is controlled by diffusion of vacancies, but obviously it is needless to say for this mechanism to operate we do not requires dislocation. Dislocations are not required for purely diffusional creep. However, if you want climb mechanism for creep to take place there has to be diffusional flow. So, just to summarize this slide in diffusional creep purely diffusion that means diffusion of vacancies from the phase at which is been loaded here for some loading here to the phase at which is perpendicular. So, above diffusional flow of vacancies in other words I can think of it as matter being transported along the opposite direction. So, this is the direction of transport of matter and this implies that I am going to get an elongation purely by diffusional flow that means the material is going to progressively get longer in this direction. And of course, these are all exaggerated views. So, the material gets longer in this direction the direction of the tensile axis. And therefore, you can have accumulation of strain with time typically there is a map called the creep mechanism map which puts together data from very many experiments. And tries to identify regions of various mechanisms which are operative and typically such a map would have a homologous temperature with normalize stress. There are other axis also possible in a creep mechanism map, but I have just chosen one as an illustrative example wherein I plot homologous temperature or of course, natural temperature with shear stress or normal stress. And I would notice for instance this is a creep mechanism map for polycrystalline nickel. And you can notice that the grain size is large it is of the order of 0.1 millimeter. I can see that there are various regions wherein different mechanisms operative like of course, at high stress values plasticity. So, this is the line above this is the dividing line above which you will have plastic deformation which is the normal plastic deformation you expect that means this is not typically a region of creep. And of course, that even higher stresses you have the ideal shear strength of the material, but if you look at the high temperature regime and the low stress regime which is the region below this plasticity regime you have for instance the region where you can have power law creep you can have region which is wherein the diffusional flow creep is taking place. And at very high temperatures you have lattice diffusion dominated creep, but at lower temperatures you have the grain boundary diffusion dominated creep. And there is a whole region which is marked in grade which is the region of what you might call dynamic recrystallization. Therefore, I can put together data from various experiments and I can identify mechanisms and such a map is called the creep mechanism map. And such maps are very very useful if I have to understand the creep phenomenon. Now, let us switch to the topic to a different topic wherein we will talk about testing of nano materials and nano structures. So, far we have of course, talked about some basics regarding plastic deformation we have talked about super plastic deformation creep etcetera, but one important thing we have to remember is that inherently bulk materials there are very standardized testing procedures over decades and they have been standardized. And therefore, we know how to do tests on these bulk materials we know how to interpret the data, but when it comes to testing nano structures and nano materials there are very important issues which is still being addressed. Often in many cases there are no standard procedures like the ASTM available for testing such materials. And therefore, two things become important how do I test these nano materials and second thing how do I interpret the data I get from each one of these tests. Like for instance suppose I had a thin film then I may do a hardness test on a thin film on the other hand I may have a nano wire I may do a tensile test or some kind of a nano tensile test on a nano wire. How can I compare these two data is an important question and still of course, science is grappling with some of these questions and trying to correlate the results. So, let us address some of the important issues involved in testing nano structures and nano materials. And see how we can get around understanding the results of such tests. The testing procedure for determining the mechanical barrier of nano crystalline materials is expected to differ that that used for bulk materials this is needless to say. And this is due to the small size of the nano structure like there are some structures we have already noticed they do not have any bulk counterpart at all. Like for instance I am talking about a carbon nano tube it does not have a bulk counterpart at all. Suppose I want to test a nano pillar then I may not be able to grow that nano pillar into large sizes in the form or with the properties I am looking for and therefore, they exist only in the nanoscale. Secondly the amount of material available for me available for testing could be very very small. Like for instance suppose I have nano layers obtained by molecular beam epitaxy typically you will have these nano layers in the nano a few tens of nanometers at best going to sub micron regime. But typically this molecular beam epitaxy such a slow process that we do not make bulk materials out of MBE. And the problem gets even more complicated if this nano structure or a nano crystal is a part of the larger hybrid. That means suppose I have a lead nano crystal embedded in an aluminum matrix and we have already seen that we could produce such a material. But actually melt spinning lead along with aluminum then it becomes challenging for me to determine the properties of this lead nano crystal. Suppose I am interested in the melting point of this lead nano crystal or I am interested in the for instance in the modulus of this lead nano crystal. And I want to isolate the property of this lead nano crystal from the matrix. That means now it is embedded in a matrix and therefore, I may not be able to separate out the properties which are coming from interface and embedding effects from the pure material properties. So, this is an interesting problem as we have seen that a freestanding crystal if you approach the nano side always going to melt at a lower temperature. That means there is going to be a depression in the melting point. But an embedded nano crystal as we have seen in some cases based on the interface energy can actually you can observe super heating. Therefore, it becomes difficult to separate out the effects. What is coming from the nano crystal or the embedded nano structure and what is coming from the what you call embedding material or the matrix around it. The processing route can play a very very important in determining the properties. For instance I may have materials obtained by powder consolidation, mechanical milling, high pressure torsion etcetera. Each one of these process the kind of defects introduced in the material. The kind of amount of material produced by these materials the amount the shape of the particles produced by these processing routes each one of them is going to be different. And this often produces variations in the properties of the materials. Like for instance the porosity could be higher even I produce using powder compaction. While dislocation density could be high when I do it by mechanical milling or high pressure torsion. That hence it becomes actually difficult to compare the properties across sizes and processing routes. So, this is an important challenge in studying bulk nano structured materials that on one hand I do not have sufficient nano material available for my testing. But then every material cannot be produced by every processing route. And therefore, I have a variation in properties coming as which is in a hand from the processing route itself. Therefore, it becomes difficult to find a way of generalizing the behavior at the nano scale. And to give an example suppose I have a electro deposited nickel it showed a ductility for about 100 percent. That means a very good ductile material while the same nickel if produced by powder compaction had a very little ductility of 3 percent. And in both cases the grain size was seen to be identical of about 10 nano Therefore, my processing conditions or processing parameters or the processing route is now going to affect the properties that nano material I produce. And this becomes an important challenge that how do I compare now for instance an electro deposited nickel with a nickel produced for instance by powder compaction. So, this is an important challenge in the study and determination of the properties of nano structures and nano materials. And even when you are talking about a single carbon nanotube it is obviously not easy to isolate a single carbon nanotube make sure it is a defect free carbon nanotube. Then actually if I want to produce for instance and frequency through it or try to study stensile strength it becomes actually a challenge when you are actually operating at the nano scale where you need to isolate the carbon nanotube put it between say two contacts and maybe I want to measure its conductivity. And in the process also I make sure that I am measuring the inherent conductivity of the nanotube and I am getting rid of all the contact effects etcetera. Hence to summarize the issues associated with the evaluation of mechanical properties of nano structures and nano materials we have a problem of small size or limited quantity. We have a problem of separation of the property of the entity in question from the support or substrate. And we know that many nano structures cannot be obtained in a support free fashion that means suppose I am wanting to produce a 5 nanometer thin film typically I would grow it on a substrate a glass substrate on an ITO substrate or I may grow it on a sapphire substrate. And therefore, there is a substrate embedding which is going to determine some of the properties I have a problem of the small quantity of sample in many cases. And therefore, the small quantity of sample implies that there is an abundance of hardness data and very little of tensile data on these material. While in bulk materials it is very easy to make a tensile dog bone or one of the specimen tension specimens and actually find out the tensile data. Then there are artifacts introduced in the processing route and we will have a few little more things to say about the artifacts which are induced by the processing route. And hence how these artifacts can be controlled therefore, I am now not seeing the property of the that means I can obtain the inherent property of the material and not that arising from the artifacts. And there is an additional problem in bulk nano structure materials is the uncertainty in the grain size measure. Many research reports would actually report an average grain size, but not report the grain size distribution. And this grain size distribution could be very large that means that there could be a variation of about 50 percent around the mean grain size. Suppose the person says that the average grain size is 50 nanometer what actually could be the scenario is that the grain size could vary from about 20 nanometer to about 80 or 90 nanometer. So it is so what the property I am seeing is of a polycrystalline aggregate with very different many different grain sizes rather than as mono dispersed grain sizes. And obviously when you go to very small grain sizes you will use certain technique and some cases the study could be transmission electron microscopy in which case I am sampling a very little volume of the material. And therefore, I do not have a bulk estimate on the grain size that means grain size variation is not well studied or well characterized. And this is often the case which much of the reports in literature as well. Therefore, I have many many problems associated with you know testing nano materials and get trying to get a true property of the nano material. Now that implies that I have to find ways of synthesizing bulk samples. And of course, when I mean bulk samples I am talking about materials like bulk nano structured materials. And I am not really referring to I cannot make a bulk counterpart of a nano tube. So, that I can test the sample easily and I can so variation in sample quality can lead to altered properties which are not inherent to just the reduced grain size. And this is very very important as you have seen. Therefore, we know how to produce bulk nano structured materials which can yield good samples for conventional kind of a testing. So, this is an important problem we are talking about. And there are two popular techniques for producing bulk nano structured materials. And these are consolidation of powders and by severe plastic deformation techniques. So, these are techniques which have become popular in the last 20 years wherein I am people are addressing the question that how do I produce these bulk nano structured materials such that I can put it to some of the common test which like tensile testing or hardness testing such that I am able to obtain the properties inherent properties of the material easily. The problem with consolidation of powders is that it can lead to a high level of porosity in the final sample. And this has led to the popularity of SPD technique because as you know powder metallurgy and powder material science has been around for quite some time. And very many important materials like tungsten etcetera are produced actually by powder consolidation. But then when it comes to nano scale this porosity can actually play havoc with the properties. And therefore, people are worried about or trying to develop very many SPD techniques. In severe plastic deformation techniques is interesting to note that plastic deformation is leading to a decrease in grain size. So, the automatically by plastic deformation you are actually getting a reduction in the grain size. So, this is with progressive deformation and here the technique is called severe because typically the in a technique like equi-channel angular pressing what you do is that you have a channel of a certain cross section. So, you have a channel and of course, this is you can have an angle of bend and this angle can be as severe as 90 degrees. And you extrude a material through this and actually you can do multiple passes you can send a material through this put it back again put it back again. So, you can accumulate strain and since the channel diameter is or the cross sectional area is constant you call it an equi-channeler. And because of this angle you call it the equi-channeler angular pressing and by getting this kind of a repeated plastic deformation you are accumulating strain in the material and this can lead to reduction in grain size. There are other equivalent techniques like high pressure torsion and which has been used to produce nano crystalline silicon with about 20 nanometer grain size, accumulative roll bonding, multiposs coin forging and repeated corrugation and straightening. So, there are very many severe plastic deformation techniques which have been used to produce nano crystalline materials. Typically, the grain size produced by these techniques of the order of 100 nanometers and it is usually difficult to go down to even smaller grain sizes when you are using some of these severe plastic deformation techniques. Needless to say when you produce a material with severe plastic deformation you are going to have a often a very high dislocation density. Even you are suppose a typical grain size about 200 nanometers you are going to have very high dislocation density. There is going to be a large what you call variation in grain size around the mean, but on the other hand the problem with consolidated powders is that you are going to have porosity problem. So, we will now take up some common features of these SPD techniques some advantages and disadvantages. Though we are trying to identify some of the common features but we should note that technique to technique there obviously, variations and this variations could be important for a given material. All these can produce bulk samples that are practically free of contamination and porosity. Both strength and ductility increase with increasing strain that means, we are decreasing the grain size with increasing strain and additionally we are increasing the strength of the material and it is ductility. So, this is a beautiful thing to be doing. In pure materials like copper, iron, titanium the grain size can be reduced to about 100 nanometers and typically the grain size range could be from what 5 to 100 nanometers. That means, there is a large grain size variation even in a given sample and it is sometimes very difficult to decrease the grain size below 100 nanometers using some of these techniques. The important thing is that at very small grain sizes when the grain size starts reduce grain boundary sliding and grain rotation may start to take place. So, that means the mechanism of deformations which is and we will see what is the reason behind this in some of the coming slides. There are lot of nano distortion to the lattice and there is a high elastic strain in the final product which have produced using the severe plastic deformation techniques. The end product which is the say for instance I may use some 5 passes or 10 passes using a severe plastic deformation technique. A range of grain sizes following some kind of a log normal plot may exist. The smallest grains with d of less than about 15 nanometer may have no dislocations in them. That means they have become dislocation free. The intermediate size grains may have a large dislocation density and even larger grains may actually be divided into sub grain boundaries. And when I mean sub grain boundaries, we mean a low angle grain boundary which is actually you know if you follow the Reed Shockley model consists of an array of dislocations. Therefore, when I am talking therefore you can see the one of the problems associated with severe plastic deformation straight away. That now there is a log normal distribution of grains and there is a range of grain sizes within and the structure of each one of these grains the microstructure is different. The smallest grains are practically dislocation free. The intermediate size grains have a large dislocation density while even larger grains are actually divided into sub grain boundaries. So, this variation is an important thing. And therefore, whenever I am using such a sample for determining the property, I have to remember that I have I cannot say this is a single function of a single grain size. It is actually a distribution of grain sizes and obviously needless to say this these techniques do not work well with brittle materials like ceramics and inter metallics which are usually expected to be brittle. Next we try to understand the grain boundaries in nano crystals. Now, so far we have seen that we are talking about reduction in grains. We have also seen that grain boundaries are expected to play an important role when you go down to smaller and smaller sizes not only grain boundaries, but triple lines and also quadruple junctions. So, these volume fraction of these increase and we have seen that they play an important role in determining the density of the material especially below 20 nano meter crystallite size. We have already seen that how the elastic modulus could change purely arising from the presence of these grain boundaries triple lines and quadruple junctions, but we have an important question to arise ask ourselves are grain boundaries in nano crystals different from their bulk counterparts. So, we will try to understand this question and when we ask the question what is a grain boundary? We said that it is a region wherein the atomic positions are in deviation with respect to the bulk or the crystal region. And therefore, we even assumed a thickness for the grain boundary to be of the order of nano meter. So, in other words in some sense in terms of the disturbance to the atomic positions even the grain boundary itself was a nano structure, but now we will take up the important question of can are there really grain boundaries of that thickness. And so to ask ourselves that question that are grain boundaries in nano crystals any different from that in bulk crystals. We have already seen that grain boundaries and interfaces can comprise about 50 percent of the volume fraction of a nano structure material when the grain size comes down to very small size like about 5 nanometers. But so far studies have shown that in many cases the grain boundaries in nano structure material seems similar to that bulk counterparts. So, this is a very important finding that even though we are talking about a grain boundary in a nano structured material their overall character in other words the thickness you can talk about the disturbance their structure the perhaps the models I would use to describe these kind of grain boundaries in nano crystal. They seem to be very similar to their bulk counterpart this is a very important observation. In a lot of investigations have been undertaken in this area to understand grain boundaries in nano structured materials. We will just consider couple of examples here to understand how they can be similar how they can be different. For instance if you look at titanium palladium nano structured thin films you see that both sharp and disordered grain boundaries are seen along with disordered triple junctions. So, that means that there are the sharp grain boundaries which are very similar to the bulk counterpart, but they are also grain boundaries showing considerable disorder and this characterization was done by transmission electron microscopy. The region of disorder at the grain boundaries was about 0.5 nanometers. So, this is in the same order as the thickness we assume previously for a grain boundary. And the most common model used to explain grain boundaries and the triple lines are what is known as the disclination model because disclination is then is associated with the rotations. And therefore, typically people use either for large angle grain boundaries they use a disclination model to understand grain boundaries. This aspect we will skip now, because the we have already seen how with the volume fraction of grain boundaries what is the fraction of triple lines etcetera. Now, to summarize this slide we note that there could be disturbance there could be differences in the grain boundary structure with respect to the bulk in very specific examples like the titanium and palladium nano structured films, but even there there were grain boundaries which were very very similar to their bulk counterparts. And in normal grain boundaries and nano crystalline grain boundaries there is a region of disorder which can be thought of the order of about 0.5 nanometer or of order of 1 nanometer. But next we will take up an important example where in the grain boundary is truly a nano structure in its own right and that is the case of the inter granular glassy film. We know that grain boundaries are regions where order from one grain changes to another grain. And grain boundaries already we have seen can have some degree of disorder, but if you look at older literature below 19 before 1950s people even assume that grain boundaries in normal materials are like amorphous grain boundaries. But more and more observations are shown that it is not true that grain boundaries are not not disordered in a sense of amorphous. And therefore, there are even structural unit models of grain boundaries, but these inter granular glassy materials are special class or international inter granular glassy films are a special class of grain boundaries which are observed in specific material. This is not universal, but there are in specific materials found under specific processing conditions like you find them in silicon nitride, alumina, strontium titanate etcetera in which in these materials there is a thin layer of glassy material of constant thickness of about 1 to 2 nanometer. It is a very special boundaries found in very special materials. And the thickness if you look at this high resolution lattice fringe image at the bottom there is a region below where in you find a region which is about 1 to 2 nanometer. This is a thickness and this is the nano scale structure. So, in other words this amorphous like region or a glassy material the reason why it is called glassy and we do not call it a glass because its structure the glass the structure of this inter granular glassy film is different from the bulk glass which can be formed from a similar kind of a material found in a for instance a triple pocket which could be down the grain boundary. So, if you have a triple pocket between three grains then suppose these are IGFs inter granular glassy films then this triple pocket glass is akin to the bulk glass while these IGFs have a structure which is glassy. In other words there is some partial order close to the boundaries and these are self regulating in their composition. And therefore, they are a different kind of a structure compared to the bulk glass. And they are in themselves a nano structure wherein the grain size happens to be in the micro scale. So, they are in their own right a nano structure or a nano structure in a bulk material. These IGFs are characterized by nearly constant thickness and it is basically independent of the orientation of the bounding grain except for special misorientations which are called the CSL misorientations. You would find that the orientation does not determine the thickness of the glassy film, but it is definitely depend on the composition of the ceramic. And this glassy film itself sometimes becomes a self regulating in its composition that means suppose you put more and more calcium then it only retains a certain amount of calcium in the IGF region. And the remaining calcium would actually go into the triple pocket where there is glass. The IGF is resistant to crystallization and is thought to represent some kind of an equilibrium configuration. So, this is a very important kind of a structure which is some kind of an equilibrium configuration. The presence of the IGF along with its structure plays an important role in determining the properties of the ceramic as a whole. So, this nano structure though it is a small volume fraction of the entire ceramic, but it plays a profound role in determining the property of the ceramic as a whole. Suppose I tested this ceramic and the impact then it is likely that the cracks would actually propagate in a granular mode, inter granular mode and the crack would grow along these grey these IGF. And typically it has even molecular dynamic simulations have shown that the crack would tend to propagate along the interface between the glass and the ceramic or between the IGF and the ceramic. So, even though this is a small volume fraction of the material its effect on the creep properties of the material the fracture toughness etcetera becomes profound. And therefore, it is important to study these IGFs in their own right. And the example shown here it is actually a high resolution micrograph for a lattice fringe image from a Lutetium magnesium dot silicon nitride sample. Where in the grains have hexagonal shape and the IGF is of about the thickness of about 1.5 nanometers. Now we have talked about various aspects like superplasticity creep etcetera. And we also said that the role of grain boundary the role of diffusion etcetera is going to be more and more when you go down to the nano scale. So, the next question the obvious question is that what kind of a mechanical behavior should I expect in nano materials. Of course, the next question we will ask after this is that having made these expectations that we are going to see in a nano material how far are some of these expectations actually observed in nano material. And in what cases we find that the expectations are not fulfilled if you assume that the scaling laws are valid at the small length scales in the scale of nano materials. Then I would expect that the strength at low temperatures to increase as a sizes of the grain at decrease. That means we know that from the hall patch relation which will come to little more detail soon that these yield stress varies as is proportional to 1 by d power half. And that means that very small grain sizes that you would actually expect the strength to become very high. But then this increase in strength cannot go on forever, because you know that the ultimate limit is of course, the theoretical shear strength which means that at some small grain size you would expect the hall patch relation to actually break down. So, this is one important thing would naturally expect that at very small grain sizes the hall patch relation would break down. That means the sigma y versus d plot d per minus half plot which is going to be a straight line is going to break down. At we also expect that there is going to be low strength at high temperatures and we expect creep mechanisms to become operative. And for instance if you look at the strain rate for cobalt creep it goes as d power minus 3. And because of the short diffusion parts I would expect because in nano structure material there is lot of interface diffusion and the path length required for diffusion will become smaller. Therefore, I would expect that creep like mechanisms would become operative when you go down to small grain sizes. And we have said that creep in some sense is a counterpart of super plasticity. And therefore, I would also expect super plastic deformation to take place which is usually observed at high temperatures and low strain rates to actually occur at lower temperatures and higher strain rates. That means now when I go down to nano structure materials I would expect that I would be able to get super plasticity at lower temperatures. Previously we said that it is going to be about 0.5 T m or more, but then now we would expect that it takes place at lower temperatures. And typically creep and super plasticity strain rates are of the order of about 10 power minus 4 or smaller. So, can I get super plasticity at much higher strain rates like 10 power 0 or 10 power minus 1. And I also expect this higher creep rate to take place by grain boundary diffusion mechanism at lower temperatures. So, the lower temperature part is a constant as we discussed before. And, but then I would expect that the mechanism will switch say for instance from bulk diffusion to grain boundary diffusion. This is another thing I would expect when I go down to nano scale. Additionally we have seen this and I just to reiterate what we have seen before with decreasing grain size I would expect a switch in mechanism for plastic deformation from slip to twinning. And in other words with decreasing grain size the crossover from slip to twinning is postponed to larger strains and twinning may be suppressed for very small grain sizes. So, this is what I expect. So, if I talk about deformation of nano materials if we should notice that deformation in nano structured materials seem to occur predominantly by dislocations at interfaces and not by bulk dislocation. And I am talking about a grain size for instance of the order of about 30 nanometer or less. We have already seen that when I am talking about large grain sizes more than 100 nanometers. There are dislocations and there is dislocation activity that implies dislocation related slip can give me plastic deformation. But when I go down to very small grain sizes about of the order of 30 nanometers then it seems that dislocations at interfaces which have a bugger's vector smaller than the lattice dislocations. And these seem to play an important role in the deformation of the nano material. And in TM experiments done they observed that mobile dislocations are actually absent when the grain sizes below about 30 nanometer. So, this is an important switch in the mechanism when you go down to very small grain sizes. In brittle materials like ceramics at small grain sizes grain boundary sliding may is it seem to be a predominant mechanism for plastic deformation. But having seen this in many cases we expected that the nano crystalline counterpart would actually have a higher ductility than the bulk grain size material. But this is not seen in all the cases and in many cases we see that the nano crystalline sample showed poor ductility than their micro crystalline counterparts. So, this is an important observation that it is not always that the nano crystalline counterpart is going to have higher ductility in higher strength. But many cases they have poorer ductility than their micro crystalline counterparts. Some of the important things we observed regarding mechanism is the paucity of dislocation within the grain which we already seen that in a previous slide that when you go down to a very small grain size of less than about 15 nanometer typically less than about 30 nanometer. We see that there is they are not many dislocations within the grain and additionally it is actually difficult to generate dislocations or multiplied dislocations. Because for a mechanism like the frank read source to operate which you already seen the strength or the stress required goes as 1 by L. And as the L decreases now the grain size decreases that means that we may actually exceed the theoretical strength before operating an actually a source like a frank read source. Therefore, when I go down to small scale materials to reiterate the deformation mechanism is expected to change from bulk what you call the dislocations present in the crystal leading to deformation to interface dislocations playing a prime predominant role and also grain boundary sliding what you call playing an important role. Additionally, multiplication of dislocations that means increase in dislocation density also seems difficult in nano crystalline material. We have been talking about the phenomena of grain size and strength and we said that the important relation governing the strength and the dependence of strength on grain size is known as the Hall-Petsch relationship which is given which you already encountered before, but we reiterate here to be as sigma y goes as sigma i plus k by root of d. Now sigma y is the yield stress of the material sigma i is the in stress to move a dislocation in a single crystal. Now, this is something like the inner and lattice resistance k is the locking parameter and is a measure of the relative hardening contribution of the grain boundaries and d is the grain diameter. And this Hall-Petsch relationship is some kind of an empirical relationship which is true for polycrystalline materials and wide variety of materials studied over a range of grain sizes have seem to be obeying this rule which is called the Hall-Petsch relationship. Now, the relation states that the grain size decreases at the strength of the crystal I mean as you reduce the grain size the strength of the crystal is going to increase. And typically the reason behind this is given by a mechanism known as the dislocation pile up at the grain boundary model. So, this is a typical classical model called the dislocation pile up model which means that grain boundary stops the dislocation then further dislocations are piled up at the grain boundary. And this pile up increases the stress on the grain boundary and this can lead to further slip initiation on a neighboring grain suppose this is green one then you can initiate slip in. In other words you effectively have a stress amplification by this pile up and you also see that there is an increasing strength because of the impediment cost to the motion of dislocations by the grain boundary. But the important point to note is that in many many studies they could actually not observe a pile up and therefore, there are alternate theories which have been proposed to understand the Hall-Petcher relationship. And but we do not want to go into the details of the theory, but we note for now that across a size of grains in the micron scale to the even larger sizes and sub micron sizes across very many materials this Hall-Petcher relationship is found to be true. And this is essentially coming from the fact that the grain boundary is an impediment to the motion of free motion of dislocations. And it additionally it is found that hardness also seem to follow relationship similar to that for yield stress in the case of very many materials. In other words I can write instead of sigma y I can write the hardness of the material and still it will have a 1 by root d kind of a dependence on the grain size the hardness. And as I pointed out that that means if I go to smaller and smaller grain sizes then I would obtain a harder and harder material or a material with higher and higher yield stress and it has been found that in nano crystalline copper the grain size over 6 nanometers is about 5 times harder than a material with about 15 micron meter grain size. And if you talk about the yield stress of nano phase palladium which is about 5 times harder than the bulk material with the grain size of about 100 micrometer. So all these effects typically are understood in terms of difficulty in creating dislocations and barrier to dislocation motion in this nano grain size material. So we have seen that this strength increases with decreasing grain size. We also noted that we cannot keep on increasing the size with decreasing grain size because some point of time we are going to exceed the theoretical strength of the material. And also we noted that now because the grain size is so small that actually it does not support it is too small to actually support the pile up. Therefore, even if you look at the pile up mechanism or use a fact that now you are going to have very high strength or we find that actually we cannot multiply dislocations like a by a frank read mechanism at these small sizes. We expect that the hall pitch relationship is actually going to fail and this failure is typically occurs at very small grain sizes of the order of about 10 nanometer. But if you want to look at the broader picture what is that what is that we expect then when you go down to very small sizes and now I am talking about very small sizes less than of about say about 25 nanometer or so. So when you are going down to these small grain sizes and I am now talking about reduction in grain size from micron size grain size to about 50 nanometer grain size we do expect that the hall pitch relationship is going to be altered. So what are the ways in which this can be altered number one is that of course that you may actually have an altered hardening. That means that the material tends to get harder and harder, but the rate of hardening actually is reducing. So that means I can actually have an altered hardening. So this is the red line here. So even though that means that the d power half relationship breaks down, but the material is still getting harder with decreasing grain sizes. So this also cannot go on forever as we pointed out, but this can at least take place in a small regime close after between of less than about 25 nanometer. The other possibility is that there is no hardening that means the materials hardness tends to remain constant with grain size as you go down below 25 nanometer. The third possibility which is also seen in some kind of materials though it must be said that this is not been verified for a large class of materials or it has not been verified without much scattering data. In other words there is considerable scattering data whenever they try to do measurements at these small grain sizes. And again to point out the difficulty associated with this nanoscale materials that it is very difficult to obtain mono disperse of grain sizes. And also we not only want mono disperse grain sizes, we do not want grain sizes grains which are having very high aspect ratio. We want more equiaxed kind of grains so that our results are interpretable. Therefore, getting such kind of specimens is very difficult and therefore there is a large scattering data, but it has been seen that not only can you have altered hardening, you can have no hardening with decreasing grain size, but interestingly you can have something known as the inverse hall patch effect which means that there is a softening with grain size. And this data has been accumulated by studying experiments performed on materials like copper, nickel, iron and titanium. And this figure you are seeing below is actually a compilation of data of many such experiments. And therefore, it is very interesting to note that when you reduce the grain size below about 25 nanometers, you have three kinds of possibilities. Some materials show some kind of one effect, some other materials were different effect, but then the most important effect you can see is that actually you may observe something known as the inverse hall patch effect, where in actually the material softens with decreasing grain size. So, this is a very interesting effect which has no counterpart or the bulk analog which is especially observed in very small grain size materials. And we have already observed that in nanostructured materials, the dislocation needed for deformation may be absent that means or they may be sessile, and new ones are prevented from forming. And if you look at test performed on materials with poor ductility like intermetallics and ceramics, the results of possible increase in ductility by grain size reductions are contradictory. That means that there are materials where in still lot more research has to be done, lot more investigations have to be done to actually determine that by with decreasing grain size do I get additional ductility, what is exactly the mechanism of ductility which is giving rise to I mean the reason behind the ductility etcetera. So, even from the previous graph I showed you that there is a little positive of data, there is scatter in the data, and there are issues related as I pointed out right from porosity to the method of manufacture of or method of synthesis of these specimens. Therefore, still more work has to be done, but definitely there are very interesting effects when you go down to nano scale which includes the inverse hall patch effect observed in poly crystalline materials. And a precise what you might call a definition or a precise understanding of these kind of materials can only arise, when we take into account not only the grain size, but we also take into account the grain size distribution, the grain orientation distribution, and additionally the grain shape which is also going to play an important role in determining the deformation characteristics of nanostructured materials.