 Now, the next important term is the class of nano phase materials and the phase which is being referred could be based on atomic order in which case I would have terms like crystalline, quasi crystalline or amorphous nano phases or it could be based on a property rather than a structural entity. And when I am talking about a property I would be referring for instance to a magnetic phase, a ferroelectric phase or a conducting phase which could be in the nano scale. One example of such a nano phase material is shown here which is a very interesting example in which you see a sample of silicon nitride which is actually a lutetium magnesium dot silicon nitride ceramic. And in this ceramic there are two parts which are which have lattice fringes which are the what you might call the crystalline grain. So, this is a crystalline grain it is another crystalline grain here between the two crystalline grains is a different kind of contrast which is seen in a high resolution lattice fringe image in a transmission electron micro graph. And you can see that this kind of a contrast actually comes from a glassy material. The word glassy has been used in so the word glass because the structure of this what you might call the inter granular glassy film is slightly different from that of the bulk glass which is typically formed. And this differences is precisely coming because of the nano scale confinement between the two grains which is the grain one which is a crystalline grain of silicon nitride and a grain two which is another crystalline grain of silicon nitride. So, therefore, it is the phase which is in between which is of course, as we shall see later will be called a one dimensional nano material or which has been constrained in one dimension. Therefore, there are two dimensions are bulk and in an alternate classification you could call it a two dimensional nano material is about 1.4 nanometers thick. And the other two dimensions of course, it behaves it is pretty long. That means, if I am talking about this is the x axis it is pretty large that axis going inside which is the z axis also pretty large only in the y dimension this is nano scale is about 1.4 nanometer. Now, there are other examples like for instance the theta double prime precipitate in an aluminum copper four percent copper alloy which has been aged. That means, you do as we have seen before you take a aluminum copper four percent copper alloy. Solutionize it at high temperature quench it to retain a super saturated solid solution. And then when you age this alloy you actually get a initially a GP zone which is itself a nano structure or a nano phase which is a copper rich zone in an aluminum copper matrix. Then you get the theta double prime and theta prime states and in the initial stages of their growth these are actually in the nano scale. You could also have as I pointed out a classification based on a property and you could have super paramagnetic clusters in an 90 percent zinc 10 percent nickel ferrite. Therefore, when I am talking to summarize this slide when I am talking about a nano phase this phase could be a phase defined based on a structural entity like a quasi crystalline and amorphous. It could be based on a property like in the case of a ferroelectric material or a ferromagnetic material. And as we shall see later that this phase can be nano in one dimension, two dimension or three dimension. The example of three dimensionally confined clusters are the super paramagnetic clusters in nickel 10 percent nickel ferrite. Now, some of the details of some of these phases like super paramagnetic phases and the amorphous grain boundary which we have seen here we will consider in detail later. But for now it is important to note that the definition of nano crystallinity or nano oneness is based on a phase. And therefore, here we are not actually considering the geometry like I would consider in the case of a nano structure. So, there is the importance to geometry given here is less its importance is given to the formation of a particular kind of a phase. Now, we can proceed to other examples or other classifications and other terms. One of the important ones is a nano composite. Now, we have seen that there is a class of monolithic materials and the class of hybrids. Sometimes the word hybrids is used synonymously with composites, but we have to be careful that composites is actually speaking a subclass of the hybrids. And we have seen some examples of hybrids like before like for instance the example on the left hand side where we have a fiber reinforced composite or a kind of a lattice structure which is a composite or a combination of a pore and that is material and wear or we could have certain laminates. So, these are examples of what we may call hybrids. And when I am talking about a nano composite I am actually referring to one of these or at least one of these components being in the nano scale. Of course, all the components could be in nano scale, but typically at least one of them has to be nano sized for us to call this composite and nano composite. The reason of course, we have we form these composites or hybrids is because we get a synergistic effect on in terms of the properties. And therefore, I have enhanced properties because the property being talked about is a specific property in a given context, but in general we have an enhancement in a specific property. And therefore, we have these hybrids which we engineer. In the case of nano composites of course, I could have for instance suppose I am talking about a reinforcement phase which is in the nano scale. So, now in this whole composite the matrix could be a bulk phase which is the matrix here. The reinforcement could be in the nano scale. So, we have an example of such a real scale real example of that on the right hand side you see here you see that this is actually an hot isostatically pressed sample. And in this sample you have a carbon nano tube reinforcement. So, this is a ceramic alumina which has been reinforced with carbon nano tubes. Of course, the reason for doing such a reinforcement is because typically ceramics are brittle they have a low fracture toughness. And when you reinforce it with carbon nano tubes the toughness of the material increases. So, in this sample you can see that the carbon nano tube which is here you can see certain regions where there are carbon nano tubes you can see here. This are typically multivolt carbon nano tubes which is now reinforcing my matrix which is now poly crystalline alumina. So, you can see the different grains of this is for instance one grain of alumina this is another grain of alumina we can see here. And therefore, the carbon nano tube is which is the nano scale in this nano scale structure in this whole composite is actually reinforcing alumina. The alumina grain size if you look at it is typically of the order of microns. So, therefore, the alumina is not nano structured it is only the carbon in the or the carbon nano tube in the reinforcement which is nano structure. And of course, this satisfies our condition for us to call it a nano composite because one of the faces at least is in the nano scale. In any of the other examples for instance a composite like these we will specifically take up a lattice structure in the coming slide. In which you have a what you might call a composite or a hybrid of air and material and in this case again at least one of the two has to be either the air face which is the pore face or the material has to be in the nano scale. And we will take up an example. So, in a laminate like this for instance you can see that there are two components for instance let me call the bright component A and the dark component B. It could so happen that A and B both are nano scale or at least one of A and B have to be nano scale for us to call it a nano composite. We could also have reinforcements like nano particles of alumina in a nickel matrix. We could have nano protein layer sandwich between calcite layers in an abalone shell. So, these are all examples of what you may call nano hybrids or nano composites. And of course, we already know the clear difference between what is a hybrid and which subclass of these hybrids should be called composites. So, let me summarize this slide that when we work with hybrids we get certain important benefits. In the case of nano materials if one of the phases happens to be nano scale not only we get the usual benefit we expect to get from a composite, but this benefit could be highly enhanced. And in the case of a composite at least one of the entities has to be nano scale. It could so be possible that all the entities are more than one entities in the nano scale and nano composites are a very important from the point of view of applications and enhancement in the properties. So, one such example was considered here which is now an alumina 4 weight percent carbon nano tube composite which has gives us good fracture toughness. We had talked about a composite of air and material which we called a lattice structure. And of course, we have already differentiated this kind of a lattice structure from the lattice structure in the context of crystallography. And these hybrids or these hybrids which are lattice structure are a composite of matter and voids. And in the example as you can see below here this is now porous alumina where in the pore size of the order of 75 nano meter. But if you look at the interconnects between the pores that is also of the nano scale because now my pore size which is here these are my pores here the black things are my pores. This is in the nano scale, but additionally the interconnects for instance there is material between the two pores that is also in the nano scale. So, let me draw this in a little expanded fashion in the board. So, I have approximately hexagonal pores and this pore diameter the nano scale. But actually these interconnects between the two like this regime. So, these kind of materials where in you have a pore and material it can also be used for certain very special purposes like for nano filtration membrane to actually filter out bacteria from water. They may have other interesting uses where in the pore can actually be filled with other kind of metals and other kind of things. And of course, when you fill it with the metal that would now be a composite with a metal with alumina and can no longer be called a lattice structure. Typically one class of materials we exclude from this definition and that class of materials typically of course, we may want to if intentionally done it can also be included in the definition is the fact that when you do a thermo mechanical treatment sometimes a few isolated pores may occur. So, this is actually a defect in a larger material it is not been engineered to put these small pores in the material. And typically we do not include these pores into a nano porous material. If you take an irradiated material and then anneal it often the vacancies present in the irradiated material may come together to give a small void which could be a nano void. This presence of these nano voids can alter the properties of the bulk material especially if you are talking about a nuclear component where in actually the component is actually being irradiated continuously. But this class of materials may not be called nano porous materials because it has not been engineered to put those pores in place. It has been coincidentally coming because of the what we call irradiation treatment or certain kind of thermo mechanical treatment. And but most of the structures like suppose I am talking about zinc oxide layer having nano pores on membranes or I am talking about the example which we considered below here which is anodized aluminum oxide templates with hexagonal arrayed nano pores. These are all definitely nano porous materials and as we shall see later that of course there could be some pores which are in the nano scale some pores could be larger in size. But and therefore such a material can be thought of as an hierarchical arrangement of pores. When you are talking about nano materials and nano structures and the nano signs there are very many additional terms which have pervaded into literature. We are not going to each one of those in detail at present. But we have to remember that these additional terms can be understood in the background of all the terms we have described so far. Some of these terms I am listing here for example nano chemistry, nano mechanics, nano tribology. We will also talk a little bit more later about this which is the field of nano ethics, nano fluidics etcetera. The reason for emergence of these four fields and therefore dedicated books handbooks and journals to these fields is the kind of interesting effects and phenomena which come about when we study material and processes and various kind of scientific disciplines at the nano scale. And this is been some of the thrust reason why nano science and nano technology has grown over the years. We have considered of course a small set of some of these things which can be nano. But often we may not explicitly be stating them in a material but in terms of their actual effect. Some of the other things also could be nano but we may or may not want to classify them as nano materials. For instance cracks in a material could be nano sized which we can call nano cracks. We could have actually surface steps in materials which could be nano sized. Some of these surface steps you see here and this is it could be nano sized. For instance this is in hot isostatically pressed alumina and in this hot isostatically pressed alumina you can see there are lot of surface roughness in surface steps and the step size could be of the order of nanometers. In modern tool which is of very important from the determination of mechanical behavior of nano materials is a tool of nano indentation. And the tool is very important because suppose I have a nano material. For instance I could be having a nano film on a substrate. Now, suppose I want to determine the properties of the nano film selectively without actually taking into account the substrate effects. In such a case the indentation obviously cannot pervade too much into the depth. So, typically I would like to keep my indentation less than half the distance of the thickness of the film. Therefore, I cannot use my bulk indenter suppose I put a bulk indenter it may actually penetrate my sample into lot of depth which could be of the order of microns. And therefore, I will actually not be sampling only the nano film. Additionally I cannot make a tensile specimen that easily from my nano film or use one of the standard tests like a fracture toughness testing only by studying making actually a large specimen. Therefore, now I am restricted because of the volume of material and the geometrical configuration of the material to do a test which is now my nano indentation. And here the depth of the indentation is typically of the order of nanometer. Hence often in nano materials the testing technique is very much altered with respect to the bulk testing techniques. And often we have to come up with new standards for testing these materials. And in this example which we have considered here we have talking about nano indentation. And in a nano indentation which has been shown here we can clearly see that the of course, the diameter of the indentation or the dimension of the indentation on the surface is large. But the depth which is shown in the scale here is of the order of nanometer. Therefore, you have a indentation depth which is of the order of nanometer. And this is as I pointed out very important powerful tool in the study of nano structures, nano films, nano phase materials etcetera. Another interesting example is shown here which is now a zigzag spiral structure made of MGF 2 on glass slide by a technique known as electron beam procession. In this technique you can see that these are now MGF 2 spiral like structures or zigzag structures which are growing. Each individual entity can actually be referred to a nano structure. So, now if I am isolating this individual entity here this itself is a nano structure because it has a very specific geometry and its geometry happens to be in the nano scale. Of course, as a whole now this combination can be called a nano material now. And I may use some of the techniques like for instance I could if this were not MGF 2, but carbon nano tubes aligned grown then I could actually do a compression test on the cylinder which is grown from such an aligned growth. And therefore, this is a very nice example of a totally different kind of a nano structure as from what we have seen before. And also an aligned kind of a structure wherein there is a what you might call a correlation in the way the various what they call structures are grown. By changing the deposition condition and the way the angle to which the deposition is done and the angle at which the substrate is rotated we can get very many interesting structures using this technique. And this is just one of the examples which we have shown here. So, when you entering the nano world there are very many more things which can be nano. We will deal with some of them as we go along, but it is important note that some of these are by choice like for instance when you are doing a nano indentation or we are growing a layer like this zigzag spiral layer, but sometimes it is just coincidental that you may have a crack in a material which is nano sized. And you may want to call it a nano crack, because now it is confined within for instance a certain phase which is of the nano scale dimension or you could have a coincidental nano surface steps which is which one may think that actually has not been engineered to be so. Therefore, we have exposed ourselves to quite a few nano terms now and we have to be a little careful in understanding what is nano in nano. We have seen for instance in a previous example that in this sample everything is not nano for instance if I am talking about this nano composite everything is not nano. It is only a specific entity in the structure which is nano and do the properties of this material deviate from that of the bulk material is another question which may want to ask. Therefore, we have to specifically ask ourselves what is nano in nano because a nano prefix may often be attached to the entire material we may call it a nano material, but everything within the nano material may not be nano and it requires a little bit of attention to see what is nano and what kind of properties behaves specially which is warrants it a specific classification. So, let us take up a few of those and some examples we are considering here to see clarify the point that what can be nano in nano a collection of free standing fuller in molecules is of course, each one of those molecules is a nano structure and in this case each one of those entities in the collection is also a nano structure. Therefore, this is a very simple thing to identify what is nano there we could have a collection of free standing diamond crystals. These are all just nano crystals and in this crystal we can visualize a collection in which some crystals are nano size and remaining are larger. Therefore, now you might have a bimodal distribution of sizes where in some are in the nano scale some are in the micron size some could even be larger and for instance we could have a collection of two different types of crystals say diamond crystals and sodium chloride crystals where in the diamond crystals are the nano size and the sodium chloride crystals are larger in size. And we should be clearly we should be very clear that which is the crystal which is nano size because often in such a mixture or such a aggregate the specific property may be arising only from one of the two entities in the collection. We can also visualize micron size particles which are an assemblage of nano crystals. That means now my particle is not nano sized, but the particle itself consists of subunits which are nano crystals or of course, they could also be other kind of we have seen the nano crystals separated by a nano amorphous kind of a phase. So, that is another possibility and the bonding of course, between the nano crystals could be weak or strong like in the example we had considered here. Suppose I were to test the fracture toughness of such a material or try to do an impact test typically one finds that the crack would tend to propagate through the glassy layer. Or suppose I were subjecting this silicon nitrate to creep test then I would notice that the creep typically occurs by grain boundary sliding where in the glassy phase softens and actually you have a sliding. Therefore, when it comes to deformation of this material it is not just the large volume fraction of material which is the crystalline grains which is determining the behavior of the material, but it is a small volume fraction of this nano size regime between the grains which is actually going to dominate the response of the material. Therefore, we have to be absolutely clear even though the volume fraction of a nano phase or the volume fraction of the nano crystal may be very small its effect on properties could be extremely large. An extension of these kind of the concept of collection nano particles is the case of a poly crystal with nano size grains. Here of course the whole crystal could be of the order of millimeters you could have a large poly crystal like our macroscopic copper wire, but the grain size could be of the order of nanometers. And typically you will be talking about 10 nanometers to 15 nanometers to even up to 100 nanometers. And we shall see later that what are the techniques by which such kind of what they call a nano structured poly crystal may be produced. I can name a few for instance for now for instance high pressure torsion or severe plastic deformation techniques like EQ channel angular pressing, but we could also end up producing a nano poly crystal in which not all the grains are in the nano size. There could be a again a bimodal distribution of grain sizes or a larger distribution of grain sizes in which you could have an extending. So, if I am plotting my frequency versus grain size I may have some distribution like this where in this could be of course for instance 100 nanometers and it could extend all the way up to say for instance a micron. So, only these crystals are typically in the nano scale regime which are lying here, but if the processing condition is very drastically different from the one I am describing here you may end up even producing a bimodal distribution where in the crystals belonging to this could be in the nanometer regime while this could be in the micron scale. Therefore again when I am talking about a nano poly crystal I have to be clear that what is the component which is in the nano scale and here it is the grain size and not that all the grains need to be in the nano crystalline regime. It could be only a small fraction of the grains which are actually in the nano crystalline regime or it could be that we end up because of the processing condition into a bimodal distribution where in one set of grains could be in the nano crystalline regime. And it could so happen if I am talking about a multi phase material then one of the phases which is now in this distribution regime which is now my distribution regime in the left. So, this could typically be one of the phases and this could be the distribution which is coming from phase b. So, all these are possibilities and as long as I understand that which entity in this collection is in the nano scale I am pretty much safe because I know now that if I am talking about certain enhancement in properties or a change in properties where is that coming from. We can also we have already considered this we talked about the case of nano structures or nano crystals embedded in a matrix the matrix itself may be amorphous or could be poly crystalline or could even be a single crystal. So, these are possibilities for the matrix and the second embedded phase could be the nano phase for instance only the second entity is nano sized and not all the components. We can also think of a construct of a material which is nano structured embedded in a nano poly crystal as we had visualized earlier. So, we have three possibilities when you are talking about a composite for instance we could have a nano poly crystal in which there is a nano scale for instance a nano tube reinforcement. We could think of a multi phase poly crystal in which one of the phases in the nano scale and additionally the reinforcement in the nano scale and many other such possibilities which exist and we have to absolutely clear here again that which of that which is being nano scale though we may end up using a common nice terminology for this whole kind all these class of materials and call it all nano materials. So, we should not get confused that even though we are calling all of the nano materials not all this nano in such a material. Another example would be some domains in a ferromagnetic material could be nanometer size range. There could be other domains which are extremely large in the micron scale, but typically we have noted that even in a large domain sized material we could have domain walls which are typically called the block walls which are which have our diameter about 100 atomic diameters wide and therefore, they are in the nano scale. So, even if you had a ferromagnetic material whose grain size was in the microns whose domain size is also in the microns, but we could have these block walls which is the nanometer landscape. Additionally of course, we could have for instance surface domains in an ferromagnetic material which are small in size, but other domains within the bulk of the material could actually be large in size. Therefore, again in this ferromagnetic material not everything is in the nano scale. We already seen the example of a pore size in a lattice structure which is in the nano scale which was the specific example we saw the micro graph was the anodic aluminum oxide template which as I told you can be used to actually do further processing and embed lot of and use them for making metallic nano wires. So, that is a very nice starting point further processing, but it itself actually said is a nano porous material. We could think of micelles a collection of with a collection of hydrophobic heads and hydrophilic tails and this each one of this itself is a molecular chain and this is aligned as a sphere with the hydrophobic ends merging in a central cluster with the tails dangling out. Because, now suppose I were to disperse these micelles into water then the hydrophobic ends would tend to cluster together and this cluster could be in the nano scale. And of course, the components there are these molecular chains and this molecular chains themselves are of course, could be of the nanometer landscape. There are many very many entities we already seen of biological origin like the DNA and the nucleus of a cell which could of could be of the order of 2 to 3 nanometers. The virus for instance many of the viruses are also in the nano scale and people are actually crystallize these viruses and they could be in the nano scale cell walls could be in the nano scale. But, cell itself is not a nano scale entity typically cells in the what you may call the human beings are pretty large most of the cells. But, some entities of cells themselves as we have seen in the cell walls the DNA etcetera are could be in the nano scale. And of course, biology is about which many many more examples wherein you have the nano scale present and nature has been always been benefiting from the use of nano scale materials, the nano scale structures and various phenomena which are very much altered at the nano scale. Typically, if you look at a cell wall of an animal cell it is actually made of a kind of an protein which would actually be like an having a consistency of that of oil or a thick oil. But, in the nano scale this become very fiscous and actually can perform the role of a cell wall which now of course, regulates the entire functioning of the cell. There could be also structures like the core shell nano structures and I will draw you one of those. We could have other geometrical entities like nano flowers, nano springs, nano rods, quantum dots etcetera which are also nano structures. And in these things of course, all the entities we are talking about could be in the nano scale in a core shell structure. For instance, the entire core shell this is what I call the core and this is my shell and this entire length scale could be of the order of nanometers. Now, of course the reason for engineering core shells we will see later, but sometimes it is unavoidable because you have a core of a metal then this metal may get oxidized. Therefore, you have a shell around it and of course, this oxidized core shell structure may itself provide you lot of interesting properties and we want to study them. An interesting point to be noted here we talk about in also in the coming slides is the fact that the structure will be nano important class and it is very different and because now we are not talking about a nano structure in the classical sense of the word that the scale of the structure is not in the nano scale, but the response of the material to a certain kind of a stimulus could actually be occurring in the nano scale. So, this is very different from what we have been talking so far. An example could be when and we will reconsider this example very soon that when current is driven through micron size rods it may behave like a nano sized conductor. And of course, this is observed for very specific systems and at a very specific conditions when many of the conductors we are talking about actually are conductors draw a schematic of this process. So, I actually have a micron sized conductor, but when I am trying to drive once suppose let me draw a picture of this in this now I have a rod and rod which is now micron sized in which I am trying to drive current. It so happens now I am looking at this cross section here and I am trying to drive current through this cross section it ends up sometime that the region through which the current actually passes could be nanometer sized. And in specific structures the current I am talking about could actually be here ionic current and not an electronic current. And more easily tangible example is a one which we might consider next like for instance suppose I am driving through a normal conductor alternating current. And if I suppose keep on increasing the frequency then we know that even when alternating current is not carried throughout the conductor most of the current density is on the outer region of the conductor which is called the skin of the conductor. As you increase the frequency the skin depth keeps on coming down. And when you reach very high frequencies of the order of gigahertz of course, maintaining this kind of high frequency current without the current the conductor becoming a very effective radiator is a challenge in itself, but we are not concerned about that now. So, the point is that suppose we have a very high current being driven this normal conductor. Then you would notice that when this frequency reaches about gigahertz the skin depth can come down to about a few hundred nanometers. Therefore, you can see here the conductor itself is not nanoscale the frequency of course, is of the order of gigahertz, but the effective region through which the electricity is being conducted is of the order of nanoscale. And this is actually the inverse of this kind of a conduction where the core is conducting. Here the shell is actually conducting because now I am talking about alternating current through a conductor and it could so happen. So, effectively of course, this is not to scale you may notice that this conductor could even be of the order of millimeters, but the region which is now my skin depth could be of the order of hundreds of nanometers. So, clearly here there is no nano structure in the problem there is the conductor itself we consider is uniform in composition we consider the grain size to be of the order of microns. Therefore, there is no nano scale entity involved in the conductor, but the response of the conductor is as if this material was a small shell which is now of the order of nanometers or a few hundred nanometers. Therefore, these we will take up little more of we will talk a little more about these kind of aspects in the coming slides, but it is very interesting to know that as we are ultimately interested in the properties of the material which is coming out even if the structure or the material or any of the sub components may not be of the nano scale, but the response of the material could often turn out to be in the nano scale in such kind of materials we should of course, classify them separately and also deal with them separately, but also, but keep an eye towards these because now I do not have to engineer my nano structure, but my response comes out in the nano scale. One other class which we may want to mention here which we have briefly considered here suppose we go back to a few slides and we see the surface this can be thought of as roughness at the nano scale. Here of course, this surface roughness has not been engineered to be in the nano scale, this turn out to be in the nano scale, but it may so happen that we may we will take up one important example of this kind of a surface roughness in a very specific context, but this surface roughness it can be. So, this is not the bulk of the material in the nano scale, this is not any structure within the material which is in the nano scale it is just the surface roughness which is nano and this nano scale surface roughness may actually influence the properties of the material in a very profound way. And one such example would actually be for instance the lotus leaf where we get a property known as super hydrophobicity which will take up in a little more detail now and much more detail later. We have already integrated residual stress into the definition of what you may call the microstructure and microstructure is what is going to determine my microstructure sensitive properties therefore, I want to engineer my microstructure. If you talk about residual stress, then residual stress itself could be present in a nano scale for instance when I am solidification of a liquid glass could be carried out in such a fashion that the compressive region of the surface of glass could be of the order of few hundreds of nanometers. Here of course, the glass itself is a macroscopic glass of course, the glass could have small clusters or regions which are slightly crystalline which is called the short range order, but we are not concerned about that, but we are concerned about the fact that the residual stress on the surface is nano scale. A bit axial films and we have seen example of such an thing such an example before could be have a thickness of few hundred nanometers and the compressive and tensile regions again therefore, are of the order of nanometers. So, therefore, this is now for instance a material in which the residual stress is in the nano scale. The part of the residual stress which is in the film which is now my film is here is expected to be in the nano scale because the structural entity itself is in the nano scale, but suppose I look at my substrate my substrate is a bulk substrate it could have a thickness of the order of millimeters, but you notice that the effective region of residual stress in the substrate is very limited and is the order of nanometers. The region as you can see will much below the substrate we go down in depth more than say for instance 5 nanometer or 10 nanometer or 20 nanometer then the residual stress becomes very small in magnitude and therefore, my effective region of residual stress in the substrate is of the order of nanometers. The film is uniformly strained that means it is now the residual stress is basically nano in this dimension. In the other dimension it is not nano, but if you look at the substrate, substrate is bulk in both structurally bulk in say for instance could be bulk in all the three dimensions. So, suppose I am talking about the z direction the x direction in the or the x direction in the y direction all three are bulk, but the effective region of residual stresses is nano scale in all three dimensions because now it does not extend too much from the free surface here. So, this is my free surface it is does not extend too much from the free surface it does not extend too much in the depth of course, the third dimension it can be a little extended. So, now we are talking about regions in a material having a residual stress in the nano scale. So, and this is clearly not a structural entity it is as you can see residual stress. It is not one of those classical things we have been which has talked in text books to be of the nano scale, but residual stress in the nano scale can have very profound influence on the properties. For instance the stress in the film can be engineered to as well as the band gap in a material. Therefore, this residual stress is very important in terms of the application point of view because now we are using the residual stress and the resulting strain to actually engineer the band gap. So, this kind of a definition of a nano is very different from the definition of nano based on a structural entity. So, far we have talked a lot about nano and we have been using the phrase called bulk very frequently. And often you would come across terms like bulk nano structured materials. This seems what you might call an oxymoron where in we are also talking about bulk we are also also talking about nano in the very same phrase. So, what does such a term mean and more importantly what is meant by bulk? What is bulk in bulk? Like we ask the question ourselves what is nano in nano? We have to also question what is bulk in bulk? What how do we go into define bulk? And how do we address such kind of contrary terms like there are apparent contradiction in the definition like a bulk nano structured material. So, and the second question we would like to ask ourselves is that what are bulk properties? And this is a very important because if you do not understand what are bulk properties then we are not going to understand how the properties are going to change when there is a nano scale confinement. So, these two are very very interrelated questions. So, let us start with the question what are nano structured materials? What is actually implied by this phrase is that ideal under consideration is bulk. That means it has got a tangible size typically say greater than 1 millimeter. Of course, a human eye can has a resolution of about 0.1 millimeter. Therefore, anything more than say 0.1 millimeter we can see and therefore, we can call it a tangible material. But there is some unit within the material which is in the nano scale that is what is implied by calling it a bulk nano structured material. For instance, we could be consider a copper wire which is 2 millimeter in diameter whose grain size is of the order of 100 nanometer. So, this would qualify to be a bulk nano structured material. And often there are other additional terms by which these bulk nano structured materials are described. A few of those are nano structured materials, nano phase materials, nano crystalline materials and all of these when we are using these kind of word materials along with it. What we are referring to is a fact that actually the end product of all this is a tangible material usually that is the implication. And there is some component within the material which is what you might call nano structure. A more important question in this context of bulk is what are bulk properties. And we will also take up later on that what is a bulk dimension. So, that another question we will ask ourselves later, but for now we will ask the question what are bulk properties. As we have noted some properties can change drastically when a relevant dimension in the material is reduced to the nano scale. On the contrary bulk materials of different sizes for instance centimeter cubical copper block or a 1 meter copper sphere the properties are not size dependent. So, what we are talking about is as a bulk material now is a material whose properties are not going to change with size. Suppose I am measuring the hardness or the tensile strength of a 1 centimeter copper block I make a specimen out of 1 centimeter copper block and measure its tensile strength or the yield strength. I would find that it has a certain value now I take a large much larger material for instance 1 meter copper rod. And then make a tensile specimen and test its yield stress it is expected to be very close to what I observed in the case of a 1 centimeter copper specimen. So, these are all called bulk materials and therefore, the properties do not change as you go even for instance 1 or 2 orders of magnitude in size, but this is not the case when we go to nano scale. This is why this is what makes study of nano materials interesting. However, we should note that many of the properties may show bulk like behavior even when the relevant dimension is reduced to the nano scale. That means I have gone down structurally to the nano dimension I am now completely within the logical definition of what we may call a nano material, but I am not getting any drastic change in properties. Of course, there might be some change in properties, but there is no drastic change in properties which warrants its study in detail. For instance if I am talking about fractive index or electric permittivity and many classes show that when even when you reduce the size of the sample to a few hundred nanometers you would notice that the property has not changed much. And therefore, we could be in the nano scale, but we may not get a property which is of the nano scale or any special property and therefore, we may want to call this a bulk property. So, even though the material is not bulk material we may want to call it a property as a bulk property and we may want to feed in the for instance the refractive index that corresponding to a bulk material. And often we will notice that the physics describing the bulk system which includes of course, the equations which arise from the physics may be applicable to the small scale system as well. So, we may be talking about a very small scale system like an a 5 nanometer by 5 nanometer by or maybe let us take a little larger size may be 100 nanometer by 100 nanometer 100 nanometer plate or a block or 100 nanometer by 100 nanometer by 50 nanometer plate. And I may well find that the equations and the physics may very very similar to that in the bulk material. One such example could be for instance the stress field of an edge dislocation. So, I know that my stress field of an edge dislocation in a bulk material of course, this is now my dislocation infinite material. There are similar equations describing the stress field for a finite material I can take for instance for a finite cylinder. And I take my equation from linear theory of elasticity of bulk materials and try to apply it for instance to some of the materials which is of the order of 100s of nanometers. Then I would notice the stress field is very accurately describing the equation is very accurately describing or very closely describing these stress field present in the nano scale material as well. Therefore, I do not need equations to describe my stress field in a plate which is or in a block of material which is about a sphere for instance of about 200 nanometer. And I have to keep make sure that I do not put my dislocation very close to the surface of this sphere and as long as I am say reasonably safely away from the surface of the sphere. I would notice that my equations which are applicable actually to only to bulk materials can reasonably give me a good approximation or a good estimate of the stress field in the case of a nanometer. And of course, we have already describe an effect which is exactly opposite of this one. And what is this effect we are describing here we describing a structure which is in the nano scale, but the property as if it is bulk. The opposite of this would be a macro scale material, but property in the nano scale and that we have already done for instance in the case of a skin effect when very high frequency alternating current is passed through this bulk wire. So, if I were to summarize this slide that what are bulk properties the important take home message from this slide is that I am actually in many cases be doing or trying to study nano materials. Of course, there are important new effects which may come important new effects may come purely from the geometry of the nano material etcetera, but many a times I may notice that I can actually get away by using the equations the physics and the properties which are used in bulk materials. So, and this may be a very good approximation and this in some sense is as my calculations done on these nano structured materials or the nano scale materials. And so, both are possible we have a bulk material with a nano scale response and nano material with bulk like response. So, these both are these possible and we should of course, be careful with respect to each one of the properties that which property I mean having in mind which property gets drastically change when I go to the nano scale which other property remains bulk like that is of course, I have to keep in mind. The standard way of classifying nano materials and nano structures is based on the dimension. So, this is the formal standard way of classifying nano structures and nano materials and let us take up that next nano materials that can be classified based on the dimension of the entity which is nano sized. To import special properties to a component or material all parts of the material need not be nano sized additionally the parts need not be nano sized in all three dimensions. Of course, at least one of the parts has to be nano sized in one dimension. So, suppose I have a material I have to have at least one part of the whole system and it has to at least be nano sized in one dimension in order to impart typically a special property or at least classified into the class which is called nano structured materials and nano materials. Otherwise we would not be wanting to include it in a topic like nano structured materials. The next we will consider the classification based on the dimension of a nano entity. There are two ways of looking at dimensionality of a nano entity. One is either I look at the dimension which is micro sized or the large sized or I look at the number of dimensions which are nano sized. So, let me take up the next slide. So, for instance suppose I have a sphere which is now the number of bulk dimensions is 0, but it is nano scale in all three dimensions. In a typical classification this would be called a zero dimensional nano structure. Though I am calling it a zero dimensional nano structure what is meant is that the number of bulk dimensions is 0 and it is not meant that all the nano dimensions is 0. So, this is a typical classification, but of course if somebody specially wants to say that he can say it has got three nano dimensions. If to be very specific that actually he is talking about the number of nano dimensions and not about the number of bulk dimensions. And examples of this we already seen like for instance nano crystals of gold. If I am and very very small versions of these for instance sometime are called quantum dots. Where in you can think of not only that all the three dimensions are nano scale, but this is typically less than about 10 nanometers such a thing could also be called a quantum dot. If I am talking about only one dimension which is bulk which can happen in the case of for instance a nano cylinder. Of course the geometry could be different from that of a cylinder it could be a hollow cylinder. It could be a square cross section tube it could be a square cross section prism, but at least one of the dimension or one dimension is bulk the remaining two dimensions are in the nano scales. And based on geometry I could call it nano wire nano rods nano tubes etcetera. And a nice example of this would be the carbon nano tube. So, here in this case we are talking about. So, the only nano dimension the only bulk dimension is this dimension a little word of caution is required here. Sometimes we may be calling for instance a carbon nano tube as a one dimensional nano crystal or a one dimensional nano structure. It may so be that the other the dimension we are talking about could be a few nanometers and therefore we need to call it a one dimensional nano structure, but the larger dimension which is the dimension of the length could also be in the nano scale. For instance it could be the length of the carbon nano tube could be a few nanometers. It may not be much larger than this it could be 15 nanometers if it is a short length carbon nano tube. Even though now in some sense all the three dimensions are in the nano scale we typically classify it under the what you might call the one dimensional nano structures. We could have further two of the dimensions being bulk like this example of the plate shown here. So, this dimension is bulk and additionally this dimension is bulk and it is nano in the third dimension. We already seen examples of this for instance the epitaxial films we considered in respect to stresses. They are typically having this geometry where in only one of the dimensions in the nano scale and two of the dimensions are bulk and such a thing would either be called a nano layer or a nano film. Instead of having silicon germanium on silicon we could other think of other kind of epitaxial systems like indium gallium arsenide on gallium arsenide or thin layers of coatings which are not coherent with the matrix, but all in all these cases if one of the dimensions is in the nano scale we call it a two dimensional nano structure. Of course, the other extreme of a zero dimensional nano material or a nano structure would be actually a bulk material which in some sense we can call it a three dimensional material which is actually has no bulk no nano scale dimension and this is the other extreme. Therefore, this is what we call the bulk material and for now simplicity we take an example like a single crystal of silicon which is in the bulk. So, let us summarize what we mean this because this is the most standard way of classifying nano structures is based on the dimension of the nano structure and therefore, we could have nano structures which is bulk in zero dimensions, bulk in one dimension or bulk in two dimensions and correspondingly you will have three nano dimensions, two nano dimensions or one nano dimension. And therefore, if I at least have one nano dimension in the whole system then I would be logical in calling it a nano structure or nano structured material. When you talk about the dimensionality a further question needs to be ask that what is the dimensionality of a system or in other words how many dimensions it is an object have. So, again we go back to what we might call a real physical perspective on this problem and this is very important to consider because often we may have a three dimensional object, but the relevant dimensions just may be two. So, this is an important question we will ask.