 we had previously seen that when we use a composite structure or a hybrid then we can get beneficial properties which are neither found in neither the one of the components which go on to make the hybrid or the composite. Additionally we had seen that how a poly crystalline material can be thought of as a composite of grain boundaries, the crystal, the triple line junctions and quadruple junctions and we are also made a calculation on the upper bound and lower bound on the elastic modulus when we use this concept to understand poly crystalline materials especially at the nano scale. We had also seen the relationship known as the Hall-Petcher relationship in which we had described the increase in yield stress with decreasing grain size and we had seen that the relationship if you plot sigma y versus d power minus half then you will find the linear relationship. We had also pointed out that it is actually the grain boundaries which are responsible for such a relationship and one of the common models used to understand this Hall-Petcher effect is known as the dislocation pile up model. We had also noted in that context that actually that this model though it is a popular model that often electron microscopic evidence is not available in support of this model even though this kind of a behavior is seen in a wide class of materials across large variations in grain size. But we had also noted that when we go down to very small grain sizes actually the Hall-Petcher relationship breaks down which is what is expected and we noted that there could be a regime in a below about 20 nanometer grain size wherein you could have an altered strengthening but with decreasing grain size we could have a no strengthening with decreasing grain size or we could also have what you might call an inverse Hall-Petcher effect which is a absolutely no concept which is coming basically in the grain size being in the below about 20 nanometer which is especially new for nano crystalline materials. Now we will consider an hybrid and we will also explore the possibility of the applicability of Hall-Petcher relationship in nano laminates and particulate composites. Nano laminates are hybrids with layer spacing of a few nanometer a schematic is shown below in which you have two materials and in the example considered one material could be nickel another material could be copper of course you could take a void variety of materials for instance you could have a germanium layer followed by a germanium silicon solid solution layer you could have a gallium arsenide layer and a indium gallium arsenide layer but anyhow you can form a bi layer which is basically a 2D nano crystal and you can stack them one on top of the other to obtain a laminate structure. The two layers could actually be coherent with each other they may be incoherent or they could also be semi coherent and in the process you actually have a long periodicity or you have a periodicity in the z direction so this is my z direction the important point to note is that of course this is my layer period that is this is my unit cell parameter along the z direction now this implies there are two lens scales in this problem one lens scale is related to the lattice parameters of each one of these crystals and suppose I am talking about nickel and copper then the lattice parameters of the individual components is one lens scale in the problem the second lens scale is of course the individual layer periods and if I take them to be equal then I need to talk about the periodicity along the z direction which I just described which is an additional lattice parameter in the structure. Now such a structure can be called a super lattice because now and it is a super lattice in the z direction and the reason that you tend to form such kind of composites is because you get additional benefits which are not found in either one of those individual components. Now in the case of nickel and copper if I make a nano laminate that means the periodicity is of the order of 10s or 20 or 30 nanometers then it is found that the nano laminate form from two soft metals like nickel and copper nickel and copper both are fcc that implies that the pearl stress in these structures is small and they easily plastically deform then this nano laminate can have a strength of the order of a few gpa that means we are approaching the theoretical shear strength which is of the order of g by 2 pi in nano laminates this is a very beautiful and strange effect that means that we are getting very high strength in these nano laminates while each one of those components nickel and copper actually are very soft metals. In titanium nitride, niobium nitride by multi layers that means one layer is titanium nitride the other layer is niobium nitride we can have a hardness value approaching that of about 50 gpa and if you note the hardness of individual layers like the titanium nitride and niobium nitride that is much lesser than this value of 50 gpa. The important point to note in this context is that not only are we getting this kind of a hardening effect but suppose I study the hardening effect as a function of the bilayer period and for now I assume that the individual layers made up of either titanium nitride or niobium nitride or in the nickel copper system either made of nickel and copper are equal thickness I do not vary that thickness I keep it constant but then I vary the overall periodicity or the layer thickness. Then if I plot a log of the bilayer period versus the tensile strength and often in such systems either you measure the tensile strength or you may even measure the hardness then you find an approximately linear relationship with a plot showing a slope of about point minus point five this is like a hall patch behavior that means that now if I am plotting log bilayer period versus the log of the tensile strength I find an approximately linear plot which shows a slope of minus point five which means that we are seeing a effect which is very similar to the hall patch effect. That means that in the hall patch relationship we originally pointed out that typically you plot yield stress and yield stress follows this relationship we had extended to say that even hardness follows this relationship now we are saying not only is the grain size d which follows this relationship but could actually be a bilayer period in a nano laminate or in a laminate structure. So, this is a very interesting effect and if you dwell a little deeper about this nickel copper super lattices you would notice that in a decreasing bilayer period up to about 20 nanometer leads to an increase in the yield stress in the tension test further decrease in bilayer period leads to a decrease in the strength the peak strength corresponds to about one dislocation per year. So, this linear trend is of course followed in a certain regime as I pointed out and would not be followed in a very large period, but the interesting thing is that the peak strength corresponds to about one dislocation per layer and of course, we will soon see how what is the mechanism which has been attributed to this kind of a strengthening to summarize this slide. We can not only have nano scale materials but we can have nano hybrids in which case the two components forming the composite or the hybrid structure are of both of the nano scale. In this case the individual layers for instance of nickel and copper are in the nano scale and not only that this kind of a nano laminate actually shows very high strength even though it may be made of materials which are actually soft like nickel and copper. And this can approach almost theoretical shear strength of the material and that means the yield stress could be of the order of gigapascals. And additionally you also observe whole pitch kind of a behavior in a certain grain size or a bi layer period regime. Now, the hardening is such multi layers and super lattices have been explained using a number of concepts. We just list them here we do not go into the details of some of these because some of these are still debated upon which is the correct mechanism which is the dominant mechanism in one kind of a system vis-a-vis correct kind of mechanism in other system. But some of these we list here and we may make a few additional comments. They are talking about increase in barrier strengthening which is giving rise to this kind of an extraordinary strength in the nano scale. There is expected to be some kind of a coherency between the two layers. Suppose I am talking about two layers this is my layer A and this is my layer B. So, it is expected that this interface between layer A and layer B could be an coherent interface that means it is an epitaxial relationship between this A and B layers and which gives rise to certain coherency stresses. And these coherency stresses are going to modify your local stress state which is coming from an externally applied shear stress or a tensile stress. It is also assumed that if this bi layer period becomes large and if you start with what you might call a coherent system then it will no longer remain coherent for large thickness and in fact you may obtain misfit dislocations decorating the interface. So, typically you could have certain decoration of misfit dislocation along the interfaces which implies that the system is partially coherent and this misfit dislocation would impede the motion and this misfit dislocation as we have noted before is a structural dislocation. It is not a statistically stored dislocation in the bulk of the crystal and such a misfit dislocation would tend to give rise to certain hardening effect which is seen which could attribute to the additional hardness of such a material in the nano scale. Additionally, there is the concept of the dislocation image force which we have encountered before and this is due to the discontinuity in the elastic modulus at the interfaces. A few words may be necessary here because this is not the classical image force because in the classical image force we have noted before that you have a free surface and there is a force which is attractive force towards the free surface. Now we can extend this concept of an image force in this case of course I can make a image construction and therefore, the attractive force between the two is called the image force. But I can extend this and this kind of force is called a configurational force because this is coming not because of an individual mass particle being attracted to an individual mass particle, but because of the configuration of the entire system and such a configurational force can also exist between for instance a harder material and a softer material. And if I put a dislocation in a harder material it will be attracted towards the softer material and this is I am talking about elastically harder or softer. So, if I have harder material and the dislocation sits in the harder material and there is an interface with the softer material then the dislocation may feel a force towards the softer material and this kind of a configurational force can of course loosely be called an image force even though we should understand that actually now I cannot have an image construction because this is not valid anymore this is not a free surface this is a softer material nevertheless the dislocation will feel a configurational force towards a softer interface because now the energy of the system would tend to decrease as a dislocation is position closer and closer to the softer material. That means that such kind of effects also seem to play an important role in their strengthening of these bilayers and they have also been attributed to give some effect some additional effect to the hardening which is seen in this bilayers which we have seen approaches that almost theoretical shear strength of the material. And additionally of course some common mechanisms which are observed in the case of large grain size materials like dislocation pile up and bowing of dislocation which is like the aura 1 bowing are also observed. But now we have to note that this can only occur at larger bilayer bilayer periods that means that in smaller bilayer periods we already noted that there is not enough space for a mechanism like a frank read mechanism or aura 1 bowing mechanism to operate. And we have already seen that in when you talk about a really small periodicity then the whole region can only support only one dislocation per layer. That means that it is not possible to have put multiple dislocations of course when I am talking about multiple dislocations I am talking in the thickness direction. So, there could be of course many dislocations in the and of course I am schematically showing here in the direction of the x or y. But in the z direction which is perpendicular or the direction of the periodicity of the laminate there you do not expect more than one dislocation. And of course you could have even smaller sizes when the system becomes completely dislocation free. In other words no dislocations are supported in the bulk of the two crystals which make up the super lattice. So, we see that in nano laminates we can obtain very high strength and this is to understand this we have to invoke a mechanism which is now thickness dependent it is not independent of thickness. And therefore if you go from larger bilayer periods to smaller bilayer periods a mechanism may switch to a normal what you call dislocation pile up or bowing mechanism to other kind of mechanisms which are operative like we just know saw the image force mechanisms etcetera at very small bilayer periods. Like we make a nano composite between as a laminate composite we can also make nano composites the usual way which is the particulate nano composites. And here in also we have of course we see lot of beneficial effects of putting nano particles in a bulk matrix that means the relevant nano entity in this whole system is the reinforcement that means I could actually have a polycrystalline material. And the grain size of this polycrystalline material is in that could be in a micron scale or tens or even hundreds of microns that means this is not the relevant nano scale dimension. But then I could put particles inside here which are used as reinforcement and for now I will draw schematically these particles as spherical particles though there is no reason to believe they have to be spherical. And these particles could also be precipitates and this nano scale dispersion of the second phase in a bulk first phase can actually give rise to a tremendous increase in strength as shown in some of these examples here. We have already of course talked in detail about the presentation hardening system wherein you have precipitates of the scale of 1 to about 100 nanometers. And we will not repeat it here, but which is the case of the Duralumin which is the presentation hardening system. But we will take up other examples like nano sized molybdenum in a volume fraction about 5 to 20 percent which is from the usual small volume fraction to a reasonable volume fraction. When it is dispersed in a micrometer grain sized alumina that means the grain size of alumina is no longer than nano scale it is only the molybdenum reinforcement which is in the nano scale there is constable improvement in hardness fracture strength and toughness. So, you see that the properties are overall enhanced by putting a nano sized molybdenum in a alumina which and you know that alumina is a ceramic that means that it is prone to brittle fracture. And its fracture toughness is expected to be small therefore, there is a tremendous reason to add these kind of particles which would give you an increase in fracture strength and also in the increase in toughness. And toughness being the energy absorbed before fracture takes place nano sized silicon carbide dispersions again we are talking about silicon carbide in the nano scale of about 200 nanometers in the same matrix which is the alumina matrix also leads to an increase in fracture strength by a factor of 3. So, this is very very important because alumina as you know as being a ceramic being an oxide it is in a stable state. So, it is prone to it is resistant to some of those usual things which metals are not resistant like corrosion etcetera. And it has a good elastic modulus as well, but the problem with ceramics as you know they are very intolerant to cracks in other words they have a poor fracture toughness. So, by adding silicon carbide dispersions in nano scale you can get increase in strength factor of about fracture strength of about factor of 3 which is a pretty good increase. The high temperature mechanical properties are also pretty good and you know typically these ceramics are do find applications in high temperature and this would be a good thing to add actually silicon carbide. The decrease in hardness with increasing temperature which is what you expect because now you can have thermally activated motion of dislocations. In other words in normal alumina at room temperature the strength is very high because dislocations are not that glissile the pulse stress is very large. But then when you go to high temperature some of these will start showing plasticity because now you can have thermally activated slip and also other mechanisms like green boundary sliding may start to take place. And therefore, this softening effect is significantly reduced when you use an alumina silicon carbide composite rather than a monolithic alumina. That means you have benefits on all fronts you have benefit in the fracture toughness you have benefits in the high temperature strength and also in the case of a moldenum in alumina you actually have an increase in hardness and toughness also. Therefore, it makes sense now to actually make some of these composites with reinforcements in the nano scale. And we have already seen one example where in carbon nanotubes has been used for reinforcement of alumina and we have seen that typically these are multi world carbon nanotubes and by doing so you can actually get a benefit in strength there as well. So, to summarize these slides we have of course individual nano structures which themselves so very good properties, but then we also have composites and hybrids where in what is one in relevant entities in the nano scale which can also give us improvement in the properties. Next we take up the issue of creep in nano materials we had earlier talked about creep as a general phenomena. And we had also talked about various kind of creep mechanisms and we had talked about issues which will be highlighted when we go down to the nano scale. We said that some of these mechanisms of creep for instance when we talk about these diffusion of mechanisms when we talk about issues like climb we said that when you go to nano scale all these effects will be enhanced and therefore, you would expect certain what you call creep rates to be high. Additionally we also noted one of the important mechanisms of creep is this grain boundary sliding and if you go down to a and we noted that for grain boundary sliding in some sense we have to cross the equicohesive temperature. Decreasing the grain size in some sense is like increasing the temperature and therefore, even at low temperature we said we would expect some kind of a what you might call a behavior like a increased creep rate means we noted that we would expect in nano structures in nano materials high creep rates and that too at lower temperature. So, this is what we had expected we had anticipated now we will actually see how much of this is actually true when you are talking about creep of nano materials. And we will see in this case that in some systems we do expect what our expectations were, but in many other systems we not only do not see what our expectations were, but we can even see effects opposite to the that what we had expected. So, if you talk about two important systems like nano crystalline palladium and copper which have been pretty well investigated and you can clearly see in these cases the grain sizes of the order of 40 or 20 nanometer which is extremely small. In this system there seem to be no increase in creep rate as compared to the micron sized counter parts. So, this is pretty startling that we did expect that we would have increased creep rate when you go down to nano sizes, but there were there was no increase creep rate of course, when we are comparing and micron sized grain we are using the same temperature as for the comparisons. And more surprisingly in some temperature regimes even a lower creep derivatives observed in the case of palladium. So, this is in direct contradiction of our expectations which where we thought that there is going to be enhanced creep rate. And therefore, this is extremely surprising in the case of nano crystalline materials and the creep behavior. Studies on copper in the grain when here we are talking about a small distribution of grain size which is 10 to 25 nanometer and palladium about 35 to 55 nanometers. And here in the 40 nanometers can be thought of an average in the regime between 35 and 55. That means again at the heart of the mechanism we have to keep in our mind that though there might be an average grain size reported in literature, but there is always a spread in grain sizes and more the statistical data we get we will actually find out what is the true distribution of grain size. And T m in these structures showed there is a porosity in the sample. That means there was some damage there was some and the question of course arises that was this damage accumulated during the testing time or was it effect of the prior porosity in the sample. So, this is an important question I do not think the authors investigated that part creep in and then the creep study was done in two temperature regimes one in the low temperature regime of about 0.24 to 0.33 T m and one in the medium temperature regime it is about 0.33 to about 0.5 T m. And in this case there was low creep rate and low grain growth. And in the case of the high or medium temperature regime the creep rate was decreasing even after long testing time and more importantly there was grain growth. That means that if I have grain growth I mean essentially changing the microstructure of the sample. And here we are not talking about a small grain growth we are talking about a grain growth where in the grain size increased by a factor of 4 or more. And this we are talking about the average grain size which implies that the microstructure is continuously changing maybe there is also porosity in the sample which is increasing. And therefore, it is difficult to characterize creep in many of the nano crystalline materials. Because I cannot understand if this decrease creep rate is occurring because of the nano crystalline effect or is it occurring because of the increase in grain size which is taking place during the testing. And therefore, these are very serious issues associated with creep testing in materials that often we do see porosity often we see lot of grain growth. And therefore, it is difficult to separate out the effect which is coming purely from the nano size grains vis-a-vis the changing parameters structural parameters as the test is being conducted. Now, the below is shown for instance the studies on this copper material which is has a grain size in the range of about 10 to 25 nanometers. And in this plot we have the instantaneous strain which is the elastic strain initially has been removed. And the initial creep regions of the curve also excluded in the plot. And if you observe this there are you see that at lower temperature of course, the overall creep strain at a given temperature suppose I take a temperature like a time for about 10 hours in 10 hours at a lower temperature of course, you are accumulate lower strain at a higher temperature accumulate higher strain which is what is expected. But additionally you notice that the creep strains are continuously building up even after a long hours of testing. To summarize this slide in copper the creep rates in the nano crystalline sample was comparable to the micro one size grain size sample. But in palladium nano crystalline sample actually we could see certain lower creep rate at certain temperature regimes. So, this is what this was extremely surprising as in the case of creep of nano materials. But this is of course, as I pointed out in the case of testing of nano crystalline materials even in cases where we are able to control the artifacts. The artifacts includes porosity in the initial sample artifacts include grain growth which you just talked about. Even when we are able to account for some of these effects there is no universality. That means in some cases you do observe a decrease creep rate, some cases you do not you observe a similar creep rate to the micro crystalline counter parts. But there are other examples where in the creep rate increased with a decrease in grain size in the nano scale regime that in this was an alloy of nickel and phosphorous. The creep rate of 30 nanometer grain size material was higher than the 250 nanometer grain size material. That means by decreasing the grain size and of course, both these grain size are in the nano scale. One is 250 nanometers and one is 30 nanometers there is an increase in the creep rate. So, we have seen that all three possibilities exist on reduction of the grain size. Of course, the comparisons are slightly different because in the first case we had compared in the case of copper. We had compared the nano grain size with a micron grain size sample. Here we are comparing two nanometer grain size samples and we see that there is actually an increase in creep rate as we decrease the grain size. In cases where high creep rate expected for nano crystalline materials like we see for palladium and copper which are nice metallic materials where the diffusion rate is high was not observed. The reasons are typically attributed to the presence of low angle green boundaries and twin boundaries. These low angle green boundaries are as you know low energy configurations and typically low angle green boundaries by the Reed Shockley model are decorated by these structural dislocations which actually accommodate the misorientation. These are not prone to sliding and have a low density for vacancies. Therefore, because there is a predominance of these low angle green boundaries which is what is theoretical basis for understanding that why such a material in spite of being in the nano scale does not show high creep rate. In additionally low dislocation activity is also being attributed to this low creep rate. We had seen that even when there is a green boundary sliding two other factors often come into the picture. One is dislocation activity another is diffusion. So, because you have just green boundary sliding you will have triple junction cracks and these triple junction cracks have to be healed by diffusion and often have to be otherwise what you called healed out by plastic deformation which involves dislocation activity. Therefore, to summarize these two slides on creep of nano materials we have cases where there is an increase in creep rate on decreasing size. There are cases where there is no not much difference to be talked about, but there are also cases where there is an increase creep rate on decreasing the grain size. And one nice example where actually an increase creep rate with decreasing grain size was seen is in nano crystalline nickel and these are room temperature studies. So, this is very very interesting because now we are know this is something very close to the kind of expectation we had earlier raised that we would have higher creep rate under two conditions perhaps under higher strain rate and at lower temperatures. So, here the temperature is at room temperature and of course, we are now making comparisons of grain sizes in extremely smaller g in the grain size of the road of 6 nano meter 20 nano meter and 40 nano meter. Now, if you see the plot of these three grain sizes. So, you have the highest grain size the 40 nano meter grain size here and you have a decreasing grain size as you go from here to here. Now, what you note that this is a stress strain rate plot and for a given stress and for a given testing time you notice that actually the strain rate increased with decreasing grain size. The smaller grain size sample the 6 nano meter sample show a faster creep rate and this behavior was attributed to grain boundary sliding and which is of course, accommodated by certain diffusion mechanism, but the high stresses and larger grain sizes that means that if I go to the higher stress regime and if I am talking about the larger grain sizes like the 20 nano meter or 40 nano meter samples then dislocation creep seems to be the important mechanism. So, we can replace this for 50 by 40 because this was the one which is originally involved in the study. So, this is a very nice example the creep of nano crystalline nickel at room temperature wherein some of the initial expectations are actually full fit and within the small grain size regime of about 60 to 40 nano meter we are actually seeing a switch in the mechanism. The small grain size seems to be actually seem to some sort of undergo grain boundary sliding accommodated by diffusion while the larger grain sizes under higher stresses seem to undergo dislocation creep and we had noted some of these regions in the creep mechanism map which we had seen earlier. So, the creep mechanism map we had noted that it is usually in the higher stress region which is in this axis that you tend to observe a dislocation creep and in the low stress region you tend to observe diffusional creep. So, you see that this is the region of the diffusional creep and in higher stress region you actually obtain dislocation creep. So, this is a very interesting study again we have to keep a few things in mind that when you talking about 6 nano meter grain size we have to worry that obviously the grain size is not just one number like 6 nano meter there is going to be a spread in the grain sizes. But, nevertheless keeping all the other artifacts away we notice that this is a very interesting example where creep rate creep increase creep rate has been observed at room temperature and the creep mechanism is consistent with our expectation that it is going to be grain boundary sliding at low grain sizes. But, nevertheless in spite of 40 and 20 nano meters being a small grain size we use a switch in mechanism especially when you apply higher stress. So, we have all kinds of material here we have pure palladium pure copper we have alloys like nickel phosphorous nano crystalline material and we also have nickel and you see that each one of these though some of them are very similar like nickel and copper are FCC materials we do see a very wide variety of behavior in the nano scale materials. So, as far as the understanding goes today that there is no what they may call generalized principle which you can apply to understand creep of nano materials though we do understand some of the mechanisms which would be operated a larger grain sizes and the mechanisms would be which would be operative at smaller grain sizes. We had made lot of observations regarding super plasticity in nano materials and we had also noted previously that super plasticity in some sense is a very closely related phenomena to creep except that in super plasticity damage accumulation does not lead to failure and therefore, you able to get long a very long tensile elongations of the order of 350 percent to 2000 percent. And therefore, this gives us a beautiful mechanism also by super plastic deformation we can obtain nice shapes and we can use it as a nice production method, but in most cases it is observed that initial expectations are again not fulfilled as far super plasticity nano materials is concerned. In many cases super plasticity is only observed in nano crystalline samples where it is already observed in micro crystalline counterparts that means, there is nothing very surprising and we have already seen that many cases we see a completely contradictory behavior in nano crystalline materials as compared to bulk materials. And later on also we will see examples for instance there are materials which are anti ferromagnetic in the bulk, but which will tend to become ferromagnetic in the nano scale. So, these are very surprising effects, but in case of super plasticity most of the cases it is seen that super plasticity is only observed in cases where already in the microns case grain size sample you observe super plasticity. Super plasticity observed in micro nano crystalline nickel with a grain size of about 20 nanometer at 0.360 m that means, it is more than about 450 degrees lower than the bulk material. So, having said that the initial expectations are not fulfilled we will take up a few examples to see that where there is some interesting results that means, there are some examples where you did not observe super plasticity in the micro crystalline counterparts, but you did observe it in the nano crystalline version or you observed it at a higher strain rate which is also very good or you observed it at lower temperature. So, all three cases would be very very interesting. So, maybe I should write this down. So, we will take up a few examples to see some of these what you might call interesting cases do exist when you are talking about super plasticity nano materials. And the first one is a case of nickel where in the 20 nanometer grain size sample super plasticity was more than 450 degrees lower than that for the micron grain size or larger grain size bulk counterpart. So, this is very very interesting in nano crystalline Ni 3 Al and you know Ni 3 Al is an inter metallic which and which has got a structure of CP 4 and the unit cell of a typical Ni 3 Al unit cell is shown here at the bottom of the graph. And when compared to the disorder the law you would notice that the burgers vector is larger in this structure. Now, the fundamental lattice translation vector because it is a primitive structure is this and if you had a disorder Ni 3 Al it would have been this vector which is as a length of root 2 by 2 while in this case it a root 2 by 2 a, but in this case the burgers vector has a magnitude of 1 0 0 and therefore, the mod of the burgers vector is equal to a. That means that the pulse stress in such a law is this ordered structure is going to be large and typically they would behave in a very brittle fashion and with very low tensile ductility at room temperature. So, if you observe super plasticity in these cases it is actually very surprising and the 15 nanometer grain size nano crystalline Ni 3 Al became super plastic 450 degrees below its micro crystalline counterparts. So, this is again very beneficial that means that Ni 3 Al is a technologically important inter metallic. And therefore, if I am able to super plasticly form Ni 3 Al 450 degrees below its micro crystalline counterparts then I have very important industrial applications for the nano crystalline sample. Ni 3 Al had a ductility of 350 percent at 650 degrees at a strain rate of about 10 power minus 3 per second. So, here on again we are not talking about very high strain rates of deformation reasonably what you might call slow strain rates of deformation, but nevertheless we have a good ductility of 350 percent. And given the fact that this inter metallic normally tension and tested in tension would have very negligible ductility this is very good and you can see the temperature is also very reasonable for an industrial application. So, therefore, we are able to see super plasticity at reduced temperature in a pure material like nickel, but also in inter metallic like Ni 3 Al. In the case of 1 4 2 0 aluminum alloy showed super plasticity at high strain rate of about 10 power minus 1 per second. High amount of work hardening and higher flow stress for super plastic deformation as compared to the micro size sample is also observed in these cases. This implies that one of the at least the important expectations is fulfilled in the case of the 1 4 2 aluminum alloy where in very high strain rates 10 power minus 1 is typically the almost like a normal tensile type kind of a test strain rate which you in a slow test you might want to perform. And therefore, this is not typically the regime of super plastic forming like for instance 10 power minus 3 or 10 power minus 4. So, these are couple of orders of magnitude higher than what you would usually employ in a super plastic deformation and still you are able to obtain a good deformation in the case of this aluminum alloy. The high amount of work hardening also implies that there is an accumulation of what you might call dislocation density which is actually hardening the material. And here also you observe that the stress for super plastic forming is higher than it is micron sized counterparts. Another interesting example is in the case of super plasticity in the 40 nanometer grain size zinc aluminum alloy. And this example is interesting because this alloy showed super plasticity about 373 Kelvin which is a very low temperature. And strain data is of course, small, but the important thing here the micro crystalline samples that means the bulk counterparts of this showed no super plasticity. So, this is another very interesting example and now therefore, we have covered a gamete of all the possibilities we have covered pure materials like nickel, we have covered inter metallics like N I 3 L, we have talked about alloys like zinc aluminum alloy and 1 4 2 0 aluminum alloy. We have seen that super plasticity does take place in one of these cases in high strain rates. In couple of these cases you observe super plasticity at what you might call much lower temperatures. And additionally you also observe super plasticity in cases where there is no super plasticity in the bulk counterpart. So, this is a very interesting gamete of possibilities when it comes to super plasticity of nano materials. So, we need to now worry about what are the mechanisms underlying the super plasticity and what are the issues which we need to address if you want to understand the results correctly. Super plasticity at low temperature or equivalently of course, super plasticity at high strain rates at a given temperature in the super plastic regime is caused by increased diffusion grain boundary sliding and dislocation activity. So, we already seen that when you go down to nano crystalline sizes it is usually the grain boundary sliding mechanism which becomes prominent. And this grain boundary sliding it has to be accompanied by some diffusion and dislocation activity. So, this seems to be the overall picture regarding how the super plasticity is obtained in such kind of materials nano crystalline materials at either high strain rates or at lower temperatures than what you expect for the micro crystalline counterparts. Like in the case of creep grain growth seems a very serious issue during super plasticity experiments. And if grain growth is going to take place and if you are expected super plasticity mechanism is grain boundary sliding then obviously, the elongations you are going to get is going to be limited purely because of grain growth issues. In the case of nano crystalline nickel it was seen that the grain size could increase to micron sizes starting from grain size order 20 nanometer. So, this is happening during the testing that means during super plastic forming the grain size is increasing from about 20 nanometer to about something of the micron size which is a very serious issue in super plastic testing. That means that even though my initial material had this ability to deform to large extent, but during the test itself the grain growth would rather reduce my overall available ductility. In other materials the grain growth could be less. I mean this was a very drastic example in the case of nano crystalline nickel, but in other experiments it was not necessary that the same kind of grain growth was the issue, but nevertheless grain growth could have taken place. And you always expect that grain growth is going to be less in a two phase mixtures if the second phase especially is a precipitate. And or if they are inter metallic compounds because in inter metallic compounds as you know they are very hard then and the grain boundaries less glycite. In two phase mixtures the second phase as a pinning effect on the grain boundaries while in inter metallic like N a r 3 a l the order has to be maintained as the grain growth has to take place. Which means now that suppose I really want super plasticity retaining my grain growth and in my final product has to have the same grain size as my initial starting testing sample that implies that I have to either work with a two phase mixtures where the second phase could be a precipitate or a kind of a dispersion which will sort of impede my grain growth which will have a pinning effect on the grain boundaries migration. And therefore, leading to grain growth or I need to work with the inter metallic where in the grain boundary migration involves transfer also is impede by the fact that now you have two sub lattices or more. And for instance in the case of the N a r 3 a l one sub lattices occupied by aluminum and the remaining three sub lattices are occupied by nickel. And therefore, this sub lattice structure has to be maintained and this means that grain boundary motion is going to be more difficult. In cases where grain boundary sliding is the predominant mechanism for super plasticity. And one example for that is typically magnesium based alloys it is seen that non equilibrium grain boundaries give a lower elongation as compared to equilibrium grain boundaries. And this is expected due to the long grain stress fields associated with non equilibrium grain boundaries which are which is expected to hamper grain boundaries sliding. So, this is an important effect where in we are talking about two kinds of grain boundaries that grain boundary which is called an equilibrium grain boundary. But, when we use the terminology equilibrium we have to remember that we are not talking about a global equilibrium because in the global equilibrium case the system would not want to have a grain boundary. And it would rather prefer to be a single crystal. What we mean by a equilibrium in this case is a local kind of an equilibrium. And what is implied by non equilibrium grain boundary is a fact that there are additional dislocations which are not the structural dislocations which reside close to the grain boundary. So, you have a grain boundary and this grain boundary itself may be by the Ried Schochlin model may have certain dislocations which are now the interfacial dislocations but are the or the grain boundary dislocation. But, in addition to it this grain boundary may be associated with additional dislocations. And these additional dislocations which I am drawing in red give rise to a long grain stress field for this grain boundary. Because, this array of dislocation do not does not have a long grain stress field while these red dislocations with give rise to a long grain stress field. And due to these long grain stress fields the associated as a non equilibrium grain boundaries is expected to hamper grain boundaries sliding. So, this is a issue which is wherein they have people have gone into details of the mechanisms of how the grain boundary sliding take place. And what kind of a grain boundary would give you what you call an easy grain sliding versus a difficult sliding. And it is seen that equilibrium grain boundary should slide easier as compared to the non equilibrium grain boundaries which are associated with a long grain stress field. In the case of Ni 3 Al the high flow stress and extensive strain hardening during super plastic deformation has been attributed to depletion of dislocations and high stresses required for nucleation of new ones. So, we notice when we talked about the Ni 3 Al structure and it is super plastic forming here. And we notice that you have super plastic deformation of 50 nanometer grain size sample it is observed here that the high flow stress and is observed. And additionally there is extensive strain hardening during super plastic deformation that means with progress in super plastic deformation the stress has to be increased. That means the forming cannot take place at constant stress and this is attributed to depletion of dislocations and high stresses required for nucleation of new ones. So, this is been the reason why Ni 3 Al is difficult to form, but we have to also note the additional fact that Ni 3 Al being an ordered structure the dislocation structures the kind of partial we are talking the kind of stacking faults we are talking is going to be very different from that of a normal material like aluminum. For instance Ni 3 Al would have something known as super lattice intrinsic stacking faults and super lattice extrinsic stacking faults which are not observed in the normal metallic counterparts. Next we take up the important issue we had lot to say about a quantity known as the strain rate sensitivity. So, let us go back and review our size wherein we had talked about this quantity called the strain rate sensitivity. We had said that we can do deformation at low temperatures or high temperatures and when I mean low temperatures we had said that temperature below the recrystallization temperature is about 0.5 T m less than the 0.5 T m or less. And we noted at low temperatures the important variable the relevant variable amongst the four important variables stress strain, strain rate and temperature is strain at high temperature another system at low temperature system sort of becomes a build for energy more and more dislocation densities tend to increase and the system is a battery and if you are spending x amount of energy part of this energy is stored in the microstructure in the form of increase point defect density and dislocation density. So, it becomes a battery at high temperatures the microstructure continuously renews itself that means you have recrystallization recovery process taking place as the deformation is progressing and this is typically called dynamic recrystallization. And therefore the microstructure is constantly renewing itself and therefore the flow stress is not increasing with progressive deformation. So, here there is strain hardening and therefore you have an exponent known as the strain hardening exponent at high temperatures the relevant variable is strain rate and not strain and of course you would do all these test to a constant strain at a constant temperature. And the important para exponent here is a strain rate sensitivity and of course these two equations the first one above and the second one which is relating the first one relates stress strain and the second one relates stress strain rate both are phenomenological equations typically found through for a certain broad class of materials and approximately true for the other kind of materials. Therefore, at high temperatures the strain rate sensitivity becomes an important parameter and we had noted that when you have a high strain rate sensitivity we typically expect super plastic behavior. And we had seen examples of this high strain rate sensitivity in super plastic deformation and we had noted that in the case of super plasticity the region with high strain rate sensitivity like between 0.4 and 0.67 is referred to as a super plastic regime in a log stress strain rate log strain rate log. So, this is where you get extensive super plastic deformation and this is the region of high strain rate sensitivity. Now we will few more things about this strain rate sensitivity especially the difference in the behavior of strain rate sensitivity between FCC and BCC materials. So, what is how is that the strain rate sensitivity is going to change in nano crystalline materials especially as you change the grain size as shown in the plots below. First I will go to the plots and we will come back to the text very soon if a plots strain rate sensitivity as a function of grain size and now in I mean the nano scale regime and of course, I am plotting log of the grain size. You notice that for FCC nano crystalline materials the strain rate sensitivity decreases with an increasing grain size. While on the other hand suppose I talk about nano crystalline BCC material like iron then I notice that the strain rate sensitivity actually increases with an increase in the grain size. So, the effects are exactly opposite when you talking about nano crystalline materials and the important parameter of strain rate sensitivity and this that implies that the behavior of strain rate sensitivity is drastically different between FCC and BCC materials. There is some understanding which we will see very soon, but the complete picture is not yet out. In FCC material M decreases with grain size and this grain size variation is over a few orders of magnitude and in BCC material M increases with grain size unlike in the FCC materials. And you should be noted that the trend lines which we have seen below. So, these are trend lines and these are not exactly followed for one material or one testing condition are arrived putting together results obtained many materials and these are obtained through many processing routes. And we have already seen the important differences and important property differences which can come from processing route itself. We had noticed that in the case of for instance electro deposit nickel how different in properties it can be from for instance a powder consolidated nickel. So, we have seen that processing route can play a very profound route profound in have a profound influence on the properties. And therefore, when we see such trend lines we have to keep that at the back of the mind. In FCC materials so far our understanding goes that forest dislocations that means a single dislocation cutting through a forest of other dislocations and grain boundary impediment seems to play an important role. And exact reasons for the strain rate sensitivity are not a clear. So, we will not discuss that aspect more, but this forest dislocation hardening mechanism. And also the grain boundary impediment mechanism seems to play an important role in FCC materials. In BCC materials on their hand mobility of screw dislocation seem to control the whole plasticity. This is true for any kind of BCC material and this strain rate sensitivity dependence also seems to have a very profound connection with this mobility of screw dislocations in BCC materials. The reason being that in BCC materials the edge component actually has a lower pearl stress as compared to the screw component in any material. And in BCC materials the screw dislocation actually has a core splitting along the 1 1 1 plane in the 3 equivalent 1 1 kind of a direction 3 perpendicular 3 1 direction which are 120 degree upon. As you know in screw dislocation in BCC materials or in the burgers vector is along the 1 1 1 direction. And the screw dislocation actually splits the core of the dislocation splits along 3 directions which are 120 degree upon. Now of course the this kind of a splitting implies that if the screw dislocation has to move then the core has to collapse and move to a new plane. And this implies that the pearl stress for motion of screw dislocations is very large. And therefore if I am doing a plastic deformation of a sample having edge and screw dislocations or more precisely having edge and screw components the edge components would actually leave the crystal which implies that I will be left with more of screw kind of components in the material. And this high pearl stress implies that instead of the entire dislocation line moving there is a mechanism which is if you refer to the slide now known as the kink pair formation mechanism its propagation seems to play a very important role. So, I will briefly draw what is meant by this kink pair formation mechanism and its propagation to understand plastic deformation in BCC materials. And also the case of which is directly connected or which is given as one of the important reasons for this strain rate sensitivity. So, if I have a dislocation line the entire dislocation line can move by a burgers vector and come here. An alternate possibility is that this dislocation line may actually develop a kink pair that means it can form a double kink like this. And then this double kink can actually propagate that means now the stress I need to apply is much smaller because I am only propagating a small segment I am not propagating the entire dislocation by one by one burgers vector. So, this can actually propagate and finally of course when the entire this segment would have left to the top this segment comes down to the bottom I would have the motion of a dislocation stepped up by one B. Therefore, I can see that dislocation itself is a medium by which actually you can actually avoid the shearing of the entire crystal you reduce that problem of shearing of the entire crystal to small regions in the crystal. And typically the analogy given is a fold in a carpet that you actually make a fold in a carpet and roll it. So, moving they pulling the entire carpet I make a fold and roll down this fold down to actually get a little elongation and I can make repeated folds to move the carpet. So, this is the analogy given to understand how a dislocation we can say crystal, but this is a second order effect where in even this whole dislocation need not go by one single burgers vector, but you can nucleate a kink pair and this kink pair can propagate orthogonal to the direction of the motion of the dislocation finally moving the dislocation. So, I can actually have a second order of mechanism operating which is going to be in my crystal, but nevertheless it is these trend lines we need to keep in mind that we have exactly opposite trend lines when it comes to strain depth sensitivity of nano crystalline materials. And this is for instance could be a material like BCC FCC copper while this could be a material like FCC ion BCC ion. Additionally a few more points to be noted are the deformation in nano structured materials seem to occur predominantly by dislocation at interfaces and not bulk deformation. You notice that and this of course we are talking about very small grain sizes of the order of about 30 nanometers. We are not talking about the really large grain sizes where 100 nanometers and more where actually you can have bulk dislocations. You can continue to have pile ups you can continue to have what you call Orvan and Orvan boving and Frank Green mechanisms, but you are going to really small grain sizes then dislocations at interfaces seem to play a very very important goal. And you have noted that an example here that these are some of the interfacial dislocations, grain boundary dislocations and additionally some of these which get closely associated which are which creates my non equilibrium grain boundaries. And if these dislocations sit exactly at the grain boundary then they seem to have a they have a burgers vector smaller than the lattice dislocations. And in some institute EM experiments mobile dislocation observed where observed were not observed when the grain sizes below 30 nanometer. That means really EM experiments have confirmed the fact that when you go to really small grain sizes like 20 nanometer and 30 nanometer. There seems to be a positive of lattice dislocations and it is a grain boundary region which becomes important from including from sliding perspective and also from the perspective of dislocation activity. And in brittle materials like ceramics at small grain sizes grain boundary sliding may be the predominant mechanism for plastic deformation. So, this is already we have stated it before which is restating it that grain boundary is the region of activity and in brittle materials like ceramics typically there is not much of dislocation activity at low temperatures. And therefore, you expect that grain boundary sliding is going to be an important phenomenon. However, we have been repeatedly saying some of the aspects and we just summarize this here that much more work has to be done to understand creep super plasticity and also plastic deformation in general in nano crystalline materials. We have already noted that in some cases the grain boundary structure is found to be similar to the bulk counterpart. Some cases there is a difference between the grain boundary structure in a bulk versus the nano. So, what is the work which we need to be done. So, that we can now put creep and super plasticity in a sound footing wherein we can talk about a broader class of materials under one umbrella of or one or fewer parameters of understanding. In the case of creep understanding rate control mechanism as various temperature and strain rate needs to be understood creep test need to be conducted over wide range of temperature and stress and stress exponent and activation energy needs to be determined. Grain size sensitivity needs to be determined by synthesizing materials with a wide range of grain sizes. It is a very challenging problem and not only when we are talking about wide range of grain sizes we are talking about a close to mono disperse grain size. Large strain steady state creep experiment need to be performed which is another area where lot of work needs to be done. Pure materials should be used because in typically in multi phase materials we have seen a few examples though there is an advantage of using them because grain growth is small, but then understanding the underlying mechanisms become difficult in multi phase materials. The role of triple junctions in creep also needs to be ascertain that means that we already seen that triple lines and quadruple junctions are all very important in the case of nano materials, but their role is poorly understood when it comes to creep. In case of super plasticity we need to obtain porosity free samples and surface scratch free samples. The surface scratches can severely limit the overall super plasticity which I am going to get. The role of grain boundary sliding in deformation needs to be determined that how much part of it is actually grain boundary sliding, how much of it is actually plasticity or dislocation related mechanisms. Role of grain size on flow stress and mechanisms operative also need to be determined. So, though we have briefly listed some of the factors it is also clear along with these we have to talk about additional effects like for instance artifacts which can come from the samples, processing routes and etcetera which also always underlie when we are talking about some of these important effects which need to be deconvoluted that means important effects which we need to understand. So, that I can understand creep and super plasticity and also general plastic deformation of nano crystalline materials. So, we will take up two case studies two interesting examples of deformation of nano structured materials or nano crystals. In one example the first example I talk about what was done is that a carbon onion if you look at the figure below there is a carbon onion that means there are multiple layers or graphitic like shells inside which there is gold nano crystal or in an experiment conducted this could be gold or platinum nano crystal which is enclosed within this cage. So, during the experiment what is done is that so you have a gold which is a metal which is inside these graphitic or carbon onion shells. This is punctured by a focused electron beam the shells are punctured then this is extruded using this nano cage. Now, this is like a nano extrusion cell. So, you have a carbon onion which is punctured and this gold actually is extruded like you would do a bulk extrusion from this nano carbon onion cage and this extrusion has been studied. Now, if you go back to an very early experiment going back to Ajay and he what he did was he took such an carbon onion shell and without of course, the gold inside he put it under the electron beam of a 1.25 million volt electron microscope and to his surprise he found that the core region of this carbon onion. So, you have these nice carbon onion shells what is the schematic he found that the core region purely under the electron irradiation. So, he was using an electron microscope with 1.25 volt million volt electron microscope. So, inside this these are the carbon onion and this is this carbon onion here and this became diamond. In other words under the electron irradiation and the intense pressure coming from these carbon shells this interior of this carbon onion became diamond. So, this is a very interesting experiment which was published in nature. So, you see that these carbon shells actually imposed very high kind of compressive stress on the material inside. So, this is a later version of this experiment where in this high pressures has been used for the extrusion of gold. So, in this experiment what they do is that they take a carbon onion and then using this graphic cages they extrude gold or platinum. The size of this nano crystal is about 10 nanometer which is present inside this the blue color thing is about 10 nanometer and this is a confined kind of a nano crystal. The pressure experienced at about 300 degree Celsius is all the order of 20 GPA. So, this extremely high pressure which is what this small carbon onion cage is able to impose on this gold or platinum nano crystal. Given that the ideal shear strength of gold is only about 1 GPA you see that this regime can be actually called the ultra strong regime. Therefore, you are actually extruding or keeping the material in the ultra strong condition under these kind of a carbon onion shell. The crystal had a perfect atomic structure with grain boundaries and stacking faults occasionally present. So, the gold crystal when you observe it under electron microscope occasionally you do see grain boundaries and stacking faults, but apart from that it is a perfect crystal. And because of this high pressure the lattice parameter is actually a smaller than the bulk lattice parameter. When holes are punctured by an electron beam the nano crystal was extruded due to the high pressures inside the shell. And of course, the important question to ask if there are no dislocations in the material, because you can see that there are grain boundaries and stacking faults, but there are no dislocations then how is deformation proceeding in the absence of dislocations. Is it going to be dislocation diffusional mechanism like a creep which is operative diffusional creep or is it some other mechanisms. The mechanisms which the authors of this paper which is Sun et al. They are proposed is that the mechanism is supposed to be because of nucleation and propagation of dislocations. Though in their transmission electron microscope observation they did not observe any dislocation, but they did molecular dynamic study. And for parallel they perform diffusion calculation to show that diffusional effects could be actually smaller, but you do see that there is a fisting of the crystal when it comes out of the carbon nanotube. But this fisting cannot obviously take place without diffusion. So, that means diffusion is playing a role in the overall process, but they ruled out diffusion as a possible mechanism for this plastic deformation or the deformation of this gold nano crystal through this graphitic punctured graphitic cage. And they proposed that it is actually nucleation and propagation of partial or dislocation which is responsible for this kind of a plastic deformation in the ultra strong regime of crystals where in this material is kept under pressure of about 20 giga pascals. So, this is a one nice example where in a nano crystal is placed inside a nano cage which is extruded by a nano hole. So, this is a very nice kind of an experiment and you can clearly see that the kind of pressures we are talking about the kind of mechanisms we are talking about the kind of experimental issues in actually observing some of the effects is very difficult. And we have to do secondary computations like molecular dynamics to actually sort of propose come up with the mechanism like this partial or full dislocation moving through the crystal and causing leading to this extrusion. In the second case is a case of deformation of silicon single crystals and there are two examples we will take one is the bulk silicon wherein there is an actually an indentation experiment and there is also a compression experiment of silicon nanospheres. And we will try to see the difference in deformation behavior between bulk silicon and which is an of course an indentation experiment. And the second experiment is compression of silicon nanospheres in bulk silicon which is typically called silicon one which has a diamond cubic structure and we know it is a brittle material at room temperature. It actually transform to a tetragonal structure under high pressure which is what is experienced under a diamond indenter. And this structure which is tetragonal and which is a metallic form is called silicon two. And this structure the metallic form of silicon is similar to the beta tin structure and we know that tin also is found in alpha tin and beta tin form. And not only there is a crystal structure transformation when it goes to alpha to beta, but there is also a change in the character of the metallic character when alpha tin goes to beta tin. And this transformation in the case of silicon actually occurs at a very high pressure of about 12 gPa. And suppose I plot the load displacement curve for bulk silicon and now this is load in indentation. This shows a very interesting feature and if you look at the load displacement curve here below for bulk silicon. You see that during loading there is a nice smooth curve, but while unloading there are two important effects that the curve comes and there is an additional effect which is called the elbow. That means there is actually a sort of a curvature change and additionally there is an effect which is known as the push out or the PO effect. And this is observed only during unloading. Now what is the reason for this is that this PO or kink back effect as sometime called occurs during unloading and is a signature of the phase transformation of silicon two to other allotropic forms of silicon. So, you have silicon one which transforms to silicon two under high pressures which is under the indenter, but when you actually unload that means now you are relaxing the structure. This silicon two actually transforms to other allotropic forms like silicon three and which is BCC or rhombohedral silicon 12 structure which are meta stable forms of the silicon. And additionally this elbow part which I mention is actually a signature of the amorphization of silicon. So, some part of the silicon is also getting amorphized. Now if you compare this bulk silicon indentation experiment which is a deformation experiment with the deformation of silicon nanospheres. So, what I am doing here the second case is actually I am taking silicon nanospheres and putting them under two and actually doing a compression experiment on silicon nanospheres. In that case you observe that the loading part of the curve and also the unloading part actually shows a slight difference. In the loading part you observe something known as a pop in phenomena. And these nanospheres had a size of about 57 nanometer or smaller. So, but there was no pop out effect which we or push out effect which he had seen during in the bulk silicon. So, that part is of the curve is smooth there is no p o effect when I am unloading the silicon. So, the difference comes in the nanosphere case is while loading. And this has been termed this pop in effect as a deconfinement effect and this can be attributed to the onset of plasticity in a dislocation free crystal. So, clearly there is a very significant difference when you are trying to load bulk silicon indentation vis-a-vis the compression of a nanosphere. And there are important effects which is technically called a deconfinement effect wherein you are actually seeing the onset of plasticity in a dislocation free crystal. It should be noted in such experiments that the load is typically in the million Newton range and the dislocation is in the nanometer scale. So, these are all very sensitive experiments done on silicon nanospheres with lot of care. And you do then actually try to see how a deformation of a nanosphere is different from that of bulk silicon. And you do see a difference when you actually do such an experiment and significant difference is in the loading stage of the curve.