 Good morning, welcome to the NPTEL video lecture on nanostructures and nanomaterials, in which we will consider characterization and properties of nanostructures and nanomaterials. My name is Anand Subramaniam and my co-instructor in the course is Prof. Kantej Balani. Both of us belong to the department of materials science and engineering at IIT Kanpur. Our email addresses are Anand at IITK.ac.in and K Balani at IITK.ac.in. You may kindly give your feedback on any aspects of the course including any possible improvement to the lectures at these email addresses. This will help us plan better for the future and also improve upon the content which is currently being recorded. Once you are aware that nanostructures and nanomaterials are age of the future, a lot of interesting research going on currently and therefore, the literature has been growing very fast in these areas. Certain beautiful references and texts are currently available. For example, the encyclopedia of nanostructure, nanoscience and nanotechnology which is edited by Dr. Hari Singh Nalwa which runs in about 10 volumes. There is also the handbook of nano phase and nanostructured materials which is edited by Wang Liu and Zan. There are other equally interesting and nice accessible texts like the nanomaterials, nanotechnologies and design which is an introduction to engineers and architects. The book by Ashby, Ferrera and Shodek. Some of these books as you can see are handbooks and therefore, they are better for consultation purposes while others are in the text book format like the first one by Professor Ashby. Nevertheless, the literature in the area of nanostructures, nanomaterials and nanotechnology has been growing so fast that often a textbook or a handbook written about 5 to 10 years back gets soon outdated and newer and newer concepts emerge. Therefore, it is very important that students also consult various journals and periodical publications in the area which include lot of new journals which have come up in the last 10 years. So, it is important from a student's perspective not only to consult textbooks and handbooks but also to consult journals because the area of nanostructures, nanomaterials, nanoscience and nanotechnology is growing at a extremely tremendously fast rate. So, with and for a simple easy accessible point of view students may consult the first text book while in no sense this book can be considered a comprehensive text on all aspects of the subject. Let us first start with some basics. In other words let us introduce ourselves to nanoscience, nanomaterials and nanotechnology in the broadest possible way and this will involve an understanding of the fundamental concepts. Right from the outset it needs to be understood that nanomaterials or nanoscience or nanotechnology is built on a foundation which is the usual science or the physics or the chemistry or the material science which we normally study. So, it is a layer up and above that which we normally study and therefore, the fundamentals in these areas need to be strong. Therefore, if I were to draw a sort of a schematic, so this will be a foundation of basic science and this foundation will include physics, chemistry, material science etcetera. And on this foundation resides the subject which we can call the nanoscience or nanotechnology. Therefore, a student should be aware that whatever the fundamental subject he is devoting his career towards nanoscience is built on that subject. For example, suppose somebody is interested in magnetism he needs to have his fundamentals in magnetism strong then on that fundamentals he can build up nanomagnetism. Suppose a person is interested in plastic deformation then a student can learn severe plastic deformation techniques which can give rise to nanomaterials. Suppose a person is interested in chemistry then he can go ahead and devise those specific chemical synthesis techniques which can produce various kinds of nanomaterials and nanostructures. Therefore, the fundamental subject is important like one might be interested in nanomechanics and then there a person may be interested in mechanics. And once the fundamentals and mechanics are strong he can go ahead and learn the subject of nanomechanics. In other words, the learning of nanomaterials is absolutely contingent upon learning the fundamentals of the various aspects of usual physics, chemistry, biology and other aspects. One of the important reasons why we want to study nanoscience and nanotechnologies is because it gives us a beautiful new array of properties which are typically not found in normal bulk materials. We will see some of these properties as we go along, but it should be remembered that the origin of these properties should be absolutely clear. So, that when we design our nanomaterial we can take into account these factors and design a nanomaterial for a given set of properties which is going to be the corner stone for the technological application of these materials. So, let us ask ourselves this question what determines the properties of materials? This is perhaps the broadest kind of question one can ask and the properties one could be talking could be mechanical properties like hardness, yield strength, fractured toughness etcetera. He could also be talking about optical properties could be talking about magnetic properties, electrical properties and many other possible properties including biological properties like biocompatibility, toxicity etcetera. But we will start with a small set here and try to understand what are the factors which determine that what how these properties come about. The first thing we see that suppose I put in about a few tens of ppm of oxygen in copper this would degrade its conductivity drastically. Therefore, I need to go in for what is called oxygen free high conductivity copper to make my copper wires which is used for electrical conduction. Therefore, just knowing the composition cannot give me my properties I need to consider further factors. For instance it is not enough I know what are the phases that are present in the material to give an example there is a micro graph on the right hand side. In which there is this pearlite which is the alternating lamellae and this is from a carbon steel and hyper eutectoid. And you can see that along the grain boundary region there is a continuous network of a second phase. This phase happens to be cementite which is extremely brittle. But if you look at the overall microstructure as you might see or the micro graph you see that the volume fraction of the second phase along the grain boundary is small. But nevertheless the presence of this second phase the cementite phase which is a hard but brittle phase along the grain boundary severely deteriorates the impact properties of the material or what you might call the impact toughness of the material. Therefore, just knowing the phases present is not enough for me to know the properties. I need to know further information about the material which will tell me how the properties of the material is going to be. In other words I need to worry about the composition number 1 I need to worry about the phases present number 2 but that is not enough. For example, if I have dislocations in a phase this can weaken a crystal severely. Suppose I take a single crystal and try to absolutely pure defect free single crystal and I try to measure its shear strength. It will turn out to be of the order of gigapascals but in the presence of dislocations which are crystallographic defects the strength of the material can fall by a few orders of magnitude and can severely weaken the crystal. This implies that I need to know the defects in the material present apart from knowing the phases and their distribution. But should I stop here definitely not and the reason being that we know that normal glass is very brittle and it fractures very easily the window pane glass. If any ball is thrown on a window pane glass it shatters so easily but we have another example of a glass which is known as toughened glass. Toughened glass consists of normal glass but in which there is certain distribution of residual stresses which is specially compressive residual stress on the surface of the glass. This helps to toughen the glass a lot that means that if I want to understand the properties of a material I need to know its composition. I need to know the phases present and their distribution it is very important not only I know the phases present but also how these phases are distributed within the material. I need to know the defect structure in the material many of these terms like defect structure and the phase and distribution we will consider little more detail as we go along. This is just an overview slide where we want to put in a broader picture of what are the factors one needs to worry about when one is interested in knowing the properties of a material. So, and when you are talking about defect structures I am talking about defects present in the phases like dislocations in the phase and between the phases like for instance interfacial dislocations also apart from the bulk dislocations. Last but not the least I need to know the residual stress and as we shall see later the residual stress can have multiple origins and to understand all these aspects I not only need to know for instance the phases present at the distribution I need to know the defect structure and the distribution I also need to know my residual stress and its distribution. And in doing so I would realize that these factors are not independent of one other they often talk to each other they talk to each other across length scales to give an example for instance suppose you had a coherent precipitate a coherent precipitate is not only a defect in the perfect single crystal in some sense, but also is associated with residual stresses. Therefore, the precipitate and the residual stress are intricately intermixed in the case of a coherent precipitate therefore, there is a lot of interdependency among these factors and this interdependency often gives rise to the properties which one observes in a material. So, let us summarize the slide because this happens to be an important overuse slide and this will tell us set the tone that when I have a bulk material vis-a-vis a nano material or a nano structure how the properties are going to arise and how the bulk material is going to be different from the nano structure or the nano material and how I can use the very same concepts which are present in the slide to engineer the nano structure or nano material to obtain a specific set of properties which are often very unique and this is what is giving the beauty to nano materials and nano structures. So, I need to understand the composition of the material and of course, the composition could be spatially varying in the material and therefore, the property could be region specific given the composition I need to understand the phases present in the material and their distribution. We will also ask a question very soon that what do we mean by these phases what kind of phases exist and what kind of distributions can these phases be present and how this distribution of phases is going to determine the properties. One example of course, we have already considered that if you have a second phase along a grain boundary which happens to a brittle phase then cracks under impact loading can propagate all along the grain boundary. And therefore, the overall fracture toughness of the material happens to be very low in spite of the fact that the second phase as in the example considered above was just present in a very small volume fraction. It is a connectivity there along the grain boundary which gave it a poor impact toughness. Additionally, we also have to consider the defect structure of the material which includes defects within the phases defects of the interfaces and of course, the unavoidable defect of the free surface along with how the defects are distributed spatially in the material. And if you are talking about a processing technique or a long hold at high temperature how this defect structure evolves in service. That means, you are initial defect structure in the material at the start of the components in service, but as the time progress it could so happen the defect structure would evolve with time. So, could the phases and the distribution evolve with time and therefore, I need to also worry about the temporal evolution of these what you might call the spatially distributed phases and defects. We said last, but not least that residual stresses play a very important role in the properties of a material. This is often underestimated. In fact, residual stresses can play a very positive role like we saw in the case of toughened glass wherein we introduced compressive residual stresses on the surface which give rise to quite a bit of toughening of the glass. But on the other hand residual stresses can also lead to warpage of the component and therefore, can be deleterious and we may want avoid residual stresses in many case. Nevertheless, the presence of this residual stresses which again has to be understood spatially and temporally. That means, how it is present how the residual stresses distributed within the material and how it is evolving time is very important for the properties of the material. Suppose, we were talking about the glass in the compressive residual stress. Suppose, we put tensile residual stress on the surface then the properties would in fact, be worse than that in a material which had compressive residual stress on the surface. But we will have some more look at these concepts as we go along. Therefore, if one wants to understand properties of a material then he or she needs to consider various factors the composition the phases and the distribution the defect structure the residual stress. And in doing so has to traverse across length scales he needs to go from as we shall see soon from the atomic length scale to the length scale of the entire component. And this journey across length scales has to be integrated into a form which we normally in a more common usage called the property of the material which could as we considered could be the ductility. It could be the fracture toughness it could be the optical transmittance it could be the magnetic electric polarization it could or polarizability or it could be the magnetic susceptibility. So, there are many very many properties which come about and many of these can be understood by travelling across length scale and considering these factors. In the previous slide when we talked about properties and especially properties which are depend upon microstructure we were making an implicit assumption regarding the type of properties. This will become clear when I classify the properties into structure sensitive properties and structure insensitive properties. We should note typically in the usual sense when we talk about structure sensitive properties it is usually meant that we are talking about microstructure sensitive properties. And we are not usually talking about crystal structure or any other kind of structure. And therefore, we should keep this in mind that properties can be structure sensitive and examples of such properties are yield stress fracture toughness etcetera. On the other hand there are properties which are structure insensitive like density elastic modulus and other kind of properties. The key word in this definition is the word sensitive here we are not using the word dependent, but we are using the word sensitive. That means that there are for instance the presence of point defects in a material would affect the density in a small way. Therefore, the density would be dependent on the presence of vacancies in a crystal, but it is not going to be the density is not going to be a sensitive function of the presence of vacancies. On the other hand the yield stress of a material could be a sensitive function of the presence of vacancies. And therefore, we have to worry about properties from the view point if they are structure sensitive or structure insensitive. And to once again reiterate when we use the word structure sensitive it is usually meant that we are talking about microstructure sensitive properties. Now, this classification is very very important because in the previous slide we had seen that the impact toughness of a material having cementite along the grain boundaries is very poor. Now, typically this is because impact toughness is a microstructure sensitive property. Now, suppose I was talking about density then if this phase is present along the grain boundary or as globules within the material which I can draw schematically on the board now. So, the case 1 is the presence of cementite as a continuous network along the grain boundaries. In the second case I can think of the same cementite in the same volume fraction present as small globules in the material. So, the figure on the left and there is a figure on the right the volume fraction of cementite it is considered to be equal in both the cases. But suppose I am talking about a structure insensitive property like density then I would notice that the density of these two phases would be equal. Suppose I am talking about a structure sensitive property a microstructure sensitive property like fracture toughness then they would be different for these two phases. Therefore, I need to clearly understand that the distribution of phases is going to change my microstructure dependent properties. But will not change a microstructure independent properties and this we shall see there are quite a few properties which are microstructure dependent. Therefore, I need to worry about my phases in the distribution and also my defect structure and also what they residual stress. Again if the residual stress state is change between two kinds of what you might call distributions the change in density would be negligible. But the property like we saw impact toughness would change drastically. Therefore, it is very very important that whenever I am talking about a structure sensitive property I worry about all the details which goes on to form what we may call a microstructure. During the course of these lectures we will also evolve a more functional definition of microstructure which can be used to directly correlate the term with properties. So, let me summarize this slide by giving this example like suppose I am talking about a microstructure sensitive property like yield stress which in the absence of dislocations can take a very high value of the order of giga pascals. But in the presence of dislocations the crystal is severely weakened and the yield stress typically turns out of the order of mega pascals. It could be of the hundreds of mega pascals, but definitely a few orders of magnitude lower than what if the crystal had no dislocations in it. Therefore, properties have to be understood in the context of structure sensitive and structure insensitive properties. In the use when we were trying to understand the properties one of the words we introduced was phases. When you understand what is meant by a phase and further of course what is meant by understand by what is meant by the distribution of phases. So, to understand material behavior one must have a thorough understanding of the phases and the distribution. So, we raise the question what kind of phases exist and how they can be classified for a easier understanding of the diverse kind of phases which present themselves. A phase can be defined based on a geometrical entity or a physical property and this is a very important classification because when I am talking about a crystal made of atoms or cluster of atoms ions etcetera. I am typically considering at the definition of a phase based on a geometrical entity like for instance a copper crystal which is a crystalline phase has copper ions sitting at the lattice point. Suppose I am talking about a sodium chloride crystal then sodium and chlorine ions are sitting in one of them in the lattice position the other in a position neighboring to a lattice point, but we may have a definition of a phase which is purely based on a physical property. For example, we could be talking about a electron spin or equivalently a magnetization vector we could be talking about the conductivity of a material and many other properties which are conceivable. And therefore, in this context often we can talk about a material being ferroelectric anti ferromagnetic we can talk about a conducting material and insulating material and insulating phase as you may want to call it. And therefore, this perspective of a ferroelectric material or anti ferromagnetic material or a conducting phase is from the point of view of a physical property and not from the point of view of a geometrical entity. And often we may come across a situation there when I am trying to generate a crystal and as we know a crystal can be defined as in other words suppose I am trying to generate a crystalline phase in which I am have a lattice and I decorate this lattice with a motif. This motif can be a geometrical entity like we considered atoms cluster of atoms ions etcetera or it can be a physical property. And in the case of a physical property like we saw we could have magnetization vector as a physical property. But there are cases wherein I need to consider both of them and the combined geometrical entity along with the physical property goes on to decorate a lattice point in a the formation of a crystal. So, let us take an example of this suppose I am talking about let me consider B C C ion that means the B C C lattice has been decorated with an ion ion and this structure I am considering at room temperature. That means it is below the curie temperature and this implies that ion would be ferromagnetic at this temperature. That implies that at each lattice point not only I have an atom like this, but I can associate each one of these atoms with a magnetization vector. And this magnetization is what makes ion ferromagnetic that means I can consider all my atomic lattice points being decorated by an ion ion which also has a net magnetization arising from the electron spin. And also from the orbital motion of the electron though the orbital motion is often quenched in the crystalline form of ion. Therefore, if I see I have to now describe this crystal in terms of the geometrical entity which happens to be the ion ion. But also along with it I have to describe it in terms of the physical property which is now my magnetization vector which is from this starting point wherein we have defined a phase based on a geometrical entity or a physical property. And a few of those methods of classifying phases is shown in the slide which is being presented to you. The important thing we note here is of course we are considering atomic form of matter in all this classification. Matter can exist in non atomic forms like plasmas and other free fundamental particles, but we are ignoring those kind of states of matter. And therefore, we are simplifying our understanding here to atomic form of matter. And from school days we know that atomic form of matter based on state or viscosity can be classified into the gaseous state, the solid state and the liquid state. And we from the our knowledge of phase temperature pressure temperature diagrams we know that there are coexistence lines and coexistence points, where a gas in a solid could coexist, where a solid and liquid could coexist. But all three of these states of matters could also coexist at certain triple points. But this is a simple and well understood concept that we can have based on state or viscosity three forms of matter which is gas, solid and liquid. But the more interesting way of looking at these states of matter is from an atomic structure perspective which is shown in the diagram on the right hand side. That is we can have classification of atomic form of matter based on the atomic structure. That means, where are these atoms positioned in the material. And as I pointed out that when I am talking about atomic structure I could also include in this picture the structure based on certain other physical properties like I could overlay as I told you magnetization associated with these atoms on top of this picture. But to start with let us consider the atomic structure of matter and the most common atomic form of matter which we usually consider which we have defined in the previous slide is the crystalline form of matter. A crystal as we shall see soon in the coming slide is defined based on two important criteria that there is it is ordered and it is periodic. It is ordered not only positionally, but it is also orientationally ordered whenever we are considering the motif to have certain orientation and it is periodic. In the case we consider here you can clearly see that the magnetization vectors are ordered orientationally. That means, they are all pointing in the same direction. In this case of course, we can think of it as the 0 0 1 direction in B C C I. Therefore, the order we are talking about here can be orientational or positional and the crystal being considered has in the strictest sense orientational order and positional order. Often in real crystals as we shall see lot of these criteria which are imposed on ideal mathematical crystals are relaxed. And therefore, we may have crystals of various degrees of relaxed definitions which we shall consider later. There are other forms of matter and the other extreme two crystals are what are called amorphous or glassy materials or glasses in which case there neither there is positional order nor there is orientational order. Therefore, it can be thought of as a material at best having short range order, but definitely not long range order. Of course, when I am defining a crystal and I am defining a crystal if based on a combination of both a geometrical entity and a physical property it might so happen that one of the two is ordered and the other is disordered. For instance suppose I take the same iron above the curie temperature. So, suppose I am talking about iron crystal above the curie temperature in spite of the atoms vibrating about the mean lattice position we consider them to be positionally ordered, but you can clearly see that the magnetization direction which was all along the same direction has will be lost and this crystal will go from a ferromagnetic state to a paramagnetic state in which case we will find that with respect to the physical property now it has become disordered. Therefore, when I am defining a crystal I have to define it either based on the physical property or the geometrical entity or both and when I am talking about disordering or amorphousness it can come from either the physical property or the geometrical entity. And therefore, we could have a material which is completely crystalline like the case of B.C. sand above curie temperature with respect to the atomic positions, but it is definitely disordered with respect to the physical property and especially the spin orientation. Further to these important states of matter like crystalline and amorphous materials there is a third class of materials though not that well studied or that well applied in terms of its engineering applications they are the quasi crystals. They are in the international tables of crystallography classified under higher dimensional crystals in other words they are sometimes considered as part of crystals themselves, but here we have given them a separate position because they represent a definitely a third state of matter. And in some sense I have to understand this picture of atomic structure as consisting of crystalline, quasi crystalline and amorphous phases added to that there is an other class of important class of materials which are between liquids and crystals which we have shown here which is liquid crystalline materials. And as all of you know that many of the displays and calculators etcetera are made from liquid crystals they are the LCD displays or what is called the and as we can see later on during the course that any one of these entities we are talking about the crystallites or the amorphous regions in a matrix etcetera could turn nano crystalline. That means that I need to know my basics regarding these atomic orderings of matter and then I go to the next level which is my understanding that some of these length scales in these could become nano. Another way of classifying atomic form of matter is using the concept of a band structure based on the band structure a material can be a metal it can be an insulator or it can exist in one of the intermediate states like what is known as a semi metal or a semi conductor. Now, when we are talking about the band structure it should be clear that one way of classification should not clash with any other way of classification of matter. For instance a material could be amorphous and still could be metallic in other words that is what we call the metallic glasses. And now we have they have produced a materials which are bulk metallic glasses in other words which have a large cross section of area or large volume of material which is fully amorphous, but is metallic a material could be an insulator, but could be also be amorphous. For example, we know our silicate glass it is typically a very good insulator, but it is amorphous on the other hand a material could be a crystal and could be a metal. For example, copper is crystalline and as we will see that it is actually not single crystalline, but typically a copper conductor wire consists of many crystals in many orientations which we call a polycrystalline material. And therefore, copper wire is polycrystalline, but it is metallic we can also consider many ceramics like silicon nitride etcetera which are also polycrystalline, but not good conductors. Therefore, one way of classification should not clash with another way of classification like for instance mercury is liquid at room temperature, but mercury is a metal that means it is a good conductor of electricity and essentially what we are talking about there. From the band structure perspective I am classifying mercury to be a metal, but from a liquid from the flow properties or the viscosity properties I classify to be a liquid. Therefore, when am I making a classification we should be clear that what is the basis of the classification and we should be able to assign materials into each one of these boxes based on the classification we are considering. Good examples of semiconductor would be silicon, germanium, solid solutions of silicon and germanium etcetera. Semi metals are those in which there is a band gap, but the band gap is across the k space. In other words if you talk considering an integration across k space then you do not have a band gap, but there is a band gap suppose you are considering a single k value. Another way of classification of matter which is very very important from this course perspective is what is we call the classification based on size. Each one of these entities we have talked about could actually end up in the nano size. For example and we will of course this set of lectures as you can see is a revision and sort of a consideration of the basics once again and some of these things would be defined would have been defined in previous fundamental lectures before for you. Therefore, based on size we can have nano crystals, we can have nano liquid crystals if you want, we can have nano quasi crystals, we can even have regions which are amorphous, but have a very small spatial extent which we can call for instance nano amorphous if you like. We could have for instance an insulating matrix in which we could embed a metallic particle in other words here based on size it is also it is nano additionally it is also nano from the perspective of being a metal which is or a conducting band structure that there are regions which are nano. Therefore, I can take each one of these entities in this diagram and make it nano for instance I could have a nano droplet which is residing on a substrate in a gaseous environment. So, let me draw a schematic of that. So, here I have considered a glass substrate on which nano droplets of water have condensed from the vapor phase and assuming that there is an equilibrium existing then I can visualize that there is water here and there is water as droplets and this size of the droplets is what is nano in this and when I am saying nano typically it I am using it in the more general sense of the definition which means that the sizes of the order of nanometers. Therefore, I can think of the these droplets if I take an individual droplet think of this dimension to be in the nanometer regime may be a few tens of nanometers or a few hundreds of nanometers. Therefore, I can take each one of these entities in this picture and I can visualize that they are in the nano scale. I can in fact invert this problem and I can take a glass substrate in which there are the vapor phases in nano scale. I can put small bubbles of water vapor. So, I am visualizing here certain gas bubbles or vapor bubbles which are entrapped in a glass matrix which are of the nano scale. Therefore, let me summarize this slide for you in the previous slide we saw that a phase which is here we are restricting ourselves to those phases which are made of atomic species and when I mean atomic species I am talking about atoms ions molecules cluster of atoms etcetera. These atomic species can form based I can define a phase based on geometrical entity or a physical property. Now, atomic matter can be classified in various ways and all these classifications are important especially when we are talking about finally, addressing the questions of important questions like what is nano in a nano structure or what is nano in a nano material or what is so important about nano. So, based on state or viscosity we have the gas solid liquid picture based on atomic structure we can have amorphous crystalline or quasi crystalline states of matter and there are intermediate states between the important phases like the crystalline and the liquid states which can be called thought of as liquid crystalline state. We also seen that based on band structure we can have metals, semi metals, semi conductors and insulators and as we know that in case of metals the valence band overlaps with the conduction band that means an infinitesimal amount of energy which is supplied can or a small amount of energy which is supplied can actually take promote an electron to an higher energy level and because there is no band gap. In the case of insulator there is actually a band gap between the valence band and the conduction band and usually if the value of this band gap is small then you call it a semiconductor. In other words in a semiconductor even at room temperature you would find that many electrons have been promoted from the valence band to the conduction band and therefore, a semiconductor at room temperature would show some conductivity. The important difference between a semiconductor and a metal being that a metals conductivity degrades with temperature while a semiconductor conductivity increases with temperature. Based on size which is very pertinent to this course we can think of some of this we are actually picking terms from the figures above. We can have nano crystals, nano quasi crystals, nano liquid crystals and as we have seen here we can have nano vapor phases etcetera. Sir size r k property. Very good question. Mr. Anil Kumar has a very important question when you are talking about nano. Is it purely a length scale problem? Is it an issue related to properties? As we shall see very soon and we will specifically address this very question using a lot of slides that it is both. Often in a more loosest sense we would define something to be a nano structure or nano material based on some length scale in the problem. As we shall see it is often not everything which is in the material which is nano. It is particularly well defined part of the system which is in the nano scale we call it a nanometer. Typically you would talk it about tens or at best hundreds of nanometers, but that does not make it interesting for us to study these materials. It is not going to give me benefit if going to this scale of say 100 nanometers would give me some special properties. Therefore, we will see that unless there is a benefit of properties it is not worth taking trouble to go down to the nano dimensions. Because as we shall see towards end of this introductory chapter that there are lot of disadvantages nano materials also. There are lot of challenges still which are open to us and therefore, we need to address the effort versus benefit issue before we go to nano scale. And therefore, in the truest sense as you I think have implicitly pointed out it is the properties which is going to tell you that it is nano or not. And we will also see cases examples where in there is nothing in the material which is in the nano scale, but the materials property behaves in the nano way. And so, we will take up those examples also where in this specific question which we have asked here would be clearly exemplified. And that would be very important for us because when there is a benefit in properties and as we shall see very soon that not only there are often benefits in properties, but there are absolutely new properties arising when you go down to the nano scale which have no counterparts in the bulk. I can mention some names for you for instance we have the phenomena of super paramagnetism or we have the phenomena of giant magnetor resistance. So, these have no bulk analogs that means, I cannot typically realize super paramagnetism in an ion particle which is of the order of millimeter size. I need to get down to the nano dimension before I even see this phenomena known as super paramagnetism or if I am talking about giant magnetor resistance the length scale in the problem has to be reduced before it becomes viable for me or it becomes the phenomena of super paramagnetism source. Therefore, whenever I am talking about nano materials or nano science even though I am talking about size in the what we may call in the usual usage sense I am always keeping properties at the heart of it. And typically I would keep one property in focus, but sometimes you may have synergistic multiple properties improving when you go down to the nano scale. We had talked about three terms in the previous slide it is worthwhile to mention that what is the basis of definition of these three terms and we should not confuse one term with the other. The three terms we had considered based on atomic order was crystalline, quasi crystalline and amorphous. And in this context we had clearly said when you are defining these terms we would worry about atomic entities or what we call the geometrical entities and also the physical property or we could even be talking about both of them put together. And crystals are based on a lattice of course, a more formal and rigorous definition of a crystal this is an asymmetric unit plus a space group. And in conjunction with what is known as vikov positions which assign these atomic entities on to the space group positions. But we will use a simpler understanding here in this course a simplified definition where in we are talking about a crystal to be a lattice plus a motive. Because it is usually more accessible to a general student a crystal is ordered and periodic. And we had already mentioned that the order we are talking about is orientational and positional. And but the heart of the definition of a crystal lies in its symmetry and the symmetry as I pointed out can be captured by the term which is known as the space group. But for now since we are sticking to the lattice plus motive definition we have to note that a crystal is typically has rotational symmetry or inversion symmetry or mirror symmetry in addition to translation. If a crystal has only translational symmetry it has no other kind of symmetry like no rotational symmetry, no inversion symmetry or a mirror symmetry or you can even think of higher order operators like screw symmetry or glide reflection symmetries. Then such a crystal having only translational symmetry is called a triclinic crystal. But typically crystals have higher symmetries than what a triclinic crystal would have like for instance a cubic crystal can be given a symmetry. Of course, this is not the only symmetry a cubic crystal can have this is the highest symmetry a cubic crystal can have. In other words this is what is called the holohedral class of cubic and a cubic lattice would have this kind of a symmetry. And whenever you see a 3 in the second place and this is what I am writing as the Herman Moghwan symbol for representation of point groups then I clearly see that it has got higher symmetry than just that of translation. And whenever I consider a crystal the kind of rotational symmetries which are allowed in a crystal are one obviously 2, 3 and 4 and 6 and no other symmetry rotational symmetry is allowed in a crystal. Of course, these symmetries can be normal rotational symmetries or they can be what we may call a roto inversion symmetries which are given a bar symbol like instead of having 1, 2, 3, 4 and 6 I could also have like in 1 bar, 2 bar, 3 bar, 4 bar or a 6 bar symmetry. Nevertheless the presence or absence of these symmetries is not going to destroy a crystal but the absence of translation symmetry is definitely going to destroy a crystal. And this translation symmetry is otherwise has been called a periodicity of a crystal. And typically crystals are periodic in 3 all the 3 dimensions but we can also think of crystals which are crystals in lower dimensions like a graphene sheet can be thought of as a crystal in 2 dimensions. Therefore, crystals are those which at least have translation symmetry but typically have higher symmetries which include rotational symmetries like the 2 fold the 3 fold the 4 fold and the 6 fold. On the other hand there are other states of matter like we have the quasi-crystalline state which are not periodic but which are ordered. The kind of order which a quasi-crystal displays would require little more thought and little more description and I am leaving out for now for that kind of a order. But this kind of an order we are talking about is typically the kind of order you would see in a pentro styling or what you might call a structural analog of a vernace sequence. But the important point note regarding quasi-crystals is that quasi-crystals can have those kind of symmetries which are allowed in crystals. Of course, they may have allowed crystallographic symmetries like the 4 fold or the 6 fold but in addition to these kind of symmetries they may have symmetries which are disallowed in the crystallographic world. For instance a quasi-crystal may have other kind of symmetries which are disallowed in the crystallographic world like a 5 fold, 8 fold, 10 fold or 12 fold. But more importantly a crystal has translational symmetry while a quasi-crystal has something known as an inflationary symmetry. Though we are not considering this inflationary symmetry in detail but it is just an important point to note and readers may want to look up some of the literature in the area of quasi-crystals to understand that how a quasi-crystal is different from a crystal. But from the perspective of the nano world we need to note that we could have a material for instance a polymer matrix in which I could disperse nano quasi-crystals and this would give me certain important benefits in terms of the properties. For example, this very experiment I am talking about of dispersing quasi-crystals and polymers not necessarily of always the nano sized but if you do this then such a material would have good the polymer would have good aberration resistance and added to that instead if you suppose you would put a hard material like silicon carbide which is a crystal into a polymer matrix. It will have also have good aberration resistance but the counter phase bar will be very high but suppose I put quasi-crystals and the counter phase bar would be small. Therefore, there are areas in which quasi-crystals can be applied interestingly. The other end of the spectrum as we saw was the amorphous phases wherein there are no symmetries present that means it is neither periodic nor is it ordered. That implies that on one end of the spectrum I have crystals which are ordered and periodic and the other end of the spectrum I have amorphous phases and often these amorphous structures are also called glasses. Though there is a subtle technical point which can be used to actually differentiate an amorphous structure from a glassy structure but for now we will not consider it from an atomic structure perspective we will treat them equivalently and therefore an amorphous structure or a glassy structure is neither ordered nor periodic. This atomic order automatically would translate into the kind of properties that each one of these phases would show up. For instance we know that a crystal can have defects like dislocations and therefore they are plastically deformable. You can easily form them at room temperature into various shapes. An amorphous phase on the other hand if it cannot be plastically deformed and would typically fracture. We know that glass silicate glass at room temperature is very brittle. Of course if you heat it up to high temperatures it can flow like a fluid. It will have a low viscosity and then it can be blown into various shapes like including a glass bottle. Therefore this atomic structure automatically translates into the properties and therefore whenever I am using any of these crystalline or quasi crystalline or amorphous phases I would worry about their atomic structure. I would worry about their band structure and I would also worry about the size before I engineer a material which can then be put to good use in an engineering application.