 We have already traversed across multiple length scales and you have seen that one has to perhaps go many a time multiple order of length scales before we understand how a certain property arises or how a certain order has been defined with respect to the structure or even a property. Now, we will take up a particular type of ordering or what we have been call a hierarchical construction which is found in many materials and this hierarchical construction actually gives rise to certain important properties. In the context of nano materials, this hierarchical construction typically starts with some building block which is actually in the nano scale and therefore, we have to start with a certain building block and we will take up a couple of schematics to understand how this hierarchical development takes place before we go to specific examples, wherein such an architecture gives rise to some very important and very specific kind of properties which otherwise cannot be obtained by using a monolithic material or even a certain kind of an hybrid. In hierarchical construction, a basic building block is used as a subunit of a larger block. This method is actually iterated a few times to obtain larger and larger units. The important thing to note here is that the fundamental building block does not lose its identity during the hierarchical construction. Therefore, if I have to get that specific property, each one of these fundamental units is important and they should not lose its identity while I make this hierarchical construction. So, let us take a schematic example explaining the meaning of what is meant by this hierarchical construction. So, I have a for instance a large macroscopic or a micron size block which I can which I have see which can be considered here. This can be constructed starting with a single unit for instance, this is a brick a rectangular brick and I can use this rectangular brick as a subunit in a larger unit. So, you can see that when I make this larger construction, this rectangular brick with similar rectangular bricks gives rise to a larger unit which itself is a rectangular brick of a similar aspect ratio. In doing going from step a to step b, of course, I may have some kind of an interlayer that means some kind of a cement or some kind of an layer which separates actually one of these building blocks like the one marked in gray with a different part of the system like the one marked by this single dot or one marked by this double dot. Therefore, I may use some interlayer glues or I may use some kind of an interlayer which as we shall see can actually be and play an important role in this hierarchical development. Therefore, if the block itself is of nano size dimensions, then the interlayer also which now for instance I can draw schematically as a layer in between will also be of the nano scale dimension. Now, in stage C I take this block which I have used which I have constructed using blocks like a and use it itself as a fundamental building block. So, therefore, now if I look at stage C there is one unit like b here, there is another unit like b here, there is another unit like b here and finally, there is a unit like b here. At each stage you can see that I am using four of these blocks to construct a larger unit and finally, you can see that the stage D also involves putting many of these C blocks together. And therefore, I am obtaining larger and larger units, but at each stage there is a building block somewhere which is hidden which is like the a block with which I started and of course, as I pointed out there could be interlayers which separate this individual building block with the other parts of the system. Another nice example would be for instance I will explain on the board what you might call the evolution of hierarchical surface roughness. For instance suppose I talk about my surface and I am talking about for instance a material like this and I am focusing on the surface now. For instance surface could have a certain wavelength like this it is roughness. On this surface roughness for instance I could have another wavelength of surface roughness for instance I could think of a wavelength superimposed on top of this. In other words in the presence of this blue surface line blue waviness the actual surface will be this, but I need not end my story here I can go one more level for instance and talk about even finer surface roughness having a even smaller wavelength. And of course, I can go to finer and finer kind of roughness the surface as it is getting rougher and rougher the important point to notice that say suppose I take my block like this the apparent surface area would be the surface area A, but I as I make my surface rougher and rougher and rougher the actual surface area tends to increase. Therefore, for a given unit surface area suppose I am looking in three dimensions this kind of a surface the apparent surface area which is this. This apparent surface area is constant, but as you can see the actual surface area keeps on increasing as I increase my surface by making it more and more corrugated or more and more rough. In the per context of nanostructures at some point of time I would like to put a wavelength for instance this rate could be a wavelength which is of this scale nanometer. So, I could talk about a wavelength like this which is having a nanometer lies. So, this is a very nice way of actually increasing the surface area of the material without actually breaking the particle into finer and finer stages. And in some sense you can see that the structure is self similar that means I look at go to deeper and deeper scale and I find that surface looks exactly identical at various length scales. If of course it were a self similar across all length scales and I would call it a fractal and but in typical systems you would notice that at least there are a few wavelengths which are present when I am talking about a surface roughness. So, similarly we have taken up at least two examples to understand that how we can have a hierarchical development one of course of a bulk material one of the surface and in each one of these cases as we shall see there is certain enhancement in the property which we can obtain. And if my fundamental building block or the lowest wavelength in the case of the surface happens to be of the nanoscale then I can clearly see that this comes under the class of hierarchical development of nanomaterials. Now, let us see some examples of hierarchical structures and how these hierarchical structures give us some kind of an what you might call extremely beautiful properties. Three examples are live in here all three are from nature because nature has somehow mastered this art of doing a hierarchical construction to obtain a given set of properties which otherwise can be thought of as contradictory to each other. Gecko is a lizard kind of an creature which is known for its super sticky feet. You can even stick on glass surface in other words it can hang upside down from a glass surface and its beauty is that its sticking property works on any surface. In spite of the strong addition provided gecko's feet the animal can move around with ease that means that the addition is carried out with considerable ease. Now, if there are known substances made by man which are extremely sticky, but in such materials the problem is that if addition is very easy then de addition becomes extremely tough. That means it is it is usually a one way process and if de addition is easy then addition is not that good, but here is a beautiful example where nature has engineered the feet of gecko. So, that it can walk around on any surface and while walking around it requires repeated addition and de addition of its surface and this is achieved with considerable ease. And the body weight of the entire animal has to be carried and even when it is upside down and this is done with considerable efficiency. Now, this is done by actually having that gecko's feet which consists of ctae about 106 ctae on each foot and each one of these is 5 micrometer and diameter. These ctae are tipped with a few 100 fine hair like structures called spatulae. So, here we have an hierarchy construction of the feet consisting of ctae, ctae consisting of spatulae and the spatulae actually increase the surface area of contact. In other words even though my apparent surface area remains constant, but the effective surface area is increased considerably by the presence of these fine hair like spatulae. The addition is through van der Waals forces and as we know that van der Waals forces are weak forces. They are not like covalent bonding, they are not like ionic bonding, but in spite of the fact that now we are dealing with van der Waals bond as the surface area has been increased considerably the overall bond strength is very good. The ctae can be detached with by increasing the angle it makes the surface and low forces are required in this process. This is what is actually giving it this considerable ease of de addition the fact that it is like the ctae sits here. Now, suppose I increase my angle of contact it can come off. So, let me show you this on the board. Suppose I have a hair feet sitting here then it can detach by increasing the angle. So, at any point of time the entire feet is not being detached, but only a row of these spatulae and ctae ctae are being detached from the surface. One other great beauty of this kind of what you might call gecko feet is the fact that when you expect something to be very sticky you expect it to pick up lot of dirt. Because it is not only sticking to as we said it sticks to any surface. So, correspondingly of course dirt will also stick to the surface with considerable ease, but this is not the case and in spite of being a very sticky material gecko feet have a property of self cleaning. Actually the very walking process itself acts like a cleaning process and it can clean itself within a few step. Another interesting property is that if the ctae sticks to any surface it should stick to each other as well, but this does not happen and the geometry and the configuration of ctae are such that they do not stick to each other and if the ctae were to actually stick to each other then this would imply that the overall surface area available for the ctae to or the and the spatulae to stick with the given surface would become reduced, but this does not happen and you actually have a marvelous kind of a device which has multiple roles. So, it is a and there are of course now efforts in what you may call mimic this structure or what you may call biognostic structures which can do the job of a gecko and perhaps with time we get closer and closer to what nature has been engineering for quite a some quite some time already. So, to summarize what gecko feet does it gives good force of addition using water walls forces by an increased area which consists of an hierarchical construction involving ctae and spatulae. In spite of having this extreme ability to stick it does not stick dirt on itself too much and it while walking the cleaning takes place this feet do not stick to each other and de addition is also achieved with considerable ease in spite of the fact that you actually have a strong bonding between the surface and the feet of the gecko. So, here is one marvelous example of an hierarchical construction in nature which is giving us an unique set of properties which cannot be achieved by using for instance a monolithic kind of a material like a glue which we typically use in industry for sticking. Another beauty of nature is the example of the knaker the seashell or knaker has tablets or piles of calcium carbonate sandwiched by a very fine protein layer. This protein layer acts like a glue to hold the layers similar to cement in a brick cement structure. This structure has a beauty that it has a high fracture toughness and it exceeds 1000 times the structure of calcium carbonate from which actually this structure this knaker is made. Hence rearrangement and gluing of protein nano layer can drastically enhance the fracture toughness while retaining its hardness. So, this seashell has a beautiful property because it is essential to its survival that it has got very good impact resistance and fracture toughness because often in the sea these seashells would be smashed against rocks and if the seashell would break then it would be not good for the organisms life. Therefore, the seashell has engineered itself or nature has engineered the seashell in such a way that it has extremely good fracture toughness, but if you look at the constituent layer it is actually made of calcium carbonate which as you know is extremely brittle material. Then how is this calcium carbonate giving rise to this good fracture toughness this is done in a manner though not identical to this kind of construction, but very similar to this construction wherein you have these calcium carbonate layers and in addition you have these knaker layers which is intertwining these calcium carbonate layers. There and we have a hierarchical construction of this and the overall geometry and arrangement of these two layers this nano protein layers along with the calcium carbonate layers gives this knaker very good impact toughness. So, the protein layer performs two functions one it acts like a glue between the two bricks of calcium carbonate, but in addition it also provides it what you might call the energy absorption ability which gives it its beautiful impact resistance and fracture toughness. The third example we are considering again for a hierarchical construction giving rise to a specific property is the case of the lotus leaf which we have already encountered before and we have already seen that it has got the property of super hydrophobicity and super hydrophobicity as we pointed out implies that we are talking about very high contact angles greater than 165 degree. Now, this 165 degree is what we might call the apparent macroscopic contact angle and microscopically if you look at this system things are very interesting and this is happening because of a hierarchical construction as shown here. So, if you look at the lotus leaf now this is at a scale of about 100 microns in a scanning electron microscope you can see that there are these protrusions. So, you can see there are these protrusions which are the wide kind of structures here. Now, these protrusions are of course, they have a certain and we would like to call them about micro protrusions they are about 10 micro meter long 10 about 10 micro meter high and about 15 micro meter apart as you can see in this kind of a picture. So, these are about 10 micro meter in dimension and they are about 10 to 15 micro meter far away from each other. So, they have a very specific kind of a geometry. So, they are these micro protrusions here. Now, it is obvious that the kind of property of super hydrophobicity we are talking about here is with respect to some kind of a dirty kind of water. And obviously, this kind of a contact angle cannot be achieved for any kind of solution we would like to throw on the material because a lotus leaf is typically has optimized the structure. So, as to only what you might call get rid of dirty water and not other kind of solvents which we might want to try on this. So, microscopically if you look at this lotus leaf it consists of a fine distribution of micro protrusions which enhance the surface roughness and increase the contact area by a few orders of magnitude. But, the structure does not stop there further these micro protrusions and the base of the leaf itself have nano hairs and these nano hairs of 80 to 150 nanometer in dimension. So, the heart of this whole hydro super hydrophobicity is a nano structure and this nano structure has a dimension of the order of 80 to 150 nanometers. And this is spread over the entire lotus leaf that means it is present on the micro protrusions and also on the base of the leaf making the surface super hydrophobic. Now, as I pointed out let me first show you where is this micro protrusions. So, these hair like structures you can see here. So, these are the micro protrusions and then you can see that there are hairs on the base here and also hairs on the micro protrusions. And if you look at the water droplet it is actually being not supported by on directly on the leaf lotus leaf surface. But, it is being supported by these nano hairs and this is what is actually leading to finally, to the fact that macroscopically we can achieve a contact angle which is in excess of even about 150 degrees. So, this kind of a construction you can visualize as some kind of an analog of the what you might call the surface roughness which we had considered. Of course, this is not a very simplistic kind of a surface roughness which was a schematic analog which I showed you here. This consists of a very specific kind of a structure and this structure as you might imagine has to perform other roles apart from of course, being super hydrophobic was a leaf is a living entity and the leaf surface has to perform other roles like photosynthesis extra. And this structure which is making it super hydrophobic cannot interfere with other roles of the leaf. And this is what this beautiful kind of a hierarchical structure consisting of micro protrusions and nano hairs does. So, we have considered a few examples and we have seen that hierarchical construction is found in many places in nature. And the beauty of this hierarchical construction is that it gives rise to a combination of properties which otherwise cannot be obtained by what you might call monolithic construction or a single length scale construction. Now, we have asked this question implicitly a few times before, but let us now explicitly list out that why we need to go to the nano scale. And this listing is important because often our research and our effort should be directed in such a way. So, as to get the maximum benefit out in terms of properties and performance. We should note that only certain structures like folory in carbon onions etcetera and carbon nanotubes exist only in the nano scale. There is no bulk counterpart to that and therefore, we have to go to the nano scale if we have to study these structures and utilize them. So, clearly there is a very strong impetus to go to the nano scale. Certain properties arise only in the nano scale again it that implies that there are no bulk counterparts to these properties. We have already talked about a few of these for instance super hydrophobicity, super catalytic activity, super paramagnetism, giant magneto resistance etcetera. And we have noticed that actually there is no bulk counterpart to these properties and this implies that we have to go to the nano scale to exploit and bring out these properties. An additional factor could be that certain combination of properties can be only obtained when we go to the nano scale. And we have already seen for instance in the up loan shell it has got good fracture toughness reaching more than 100 times that of the calcium carbonate while still retaining its hardness. Typically, we note that if a material is very tough that means it is very ductile and usually less hard, but here you have an extremely hard material which has been engineered which is also retaining the usual hardness. So, and we have already seen some more combinations like this and we will encounter more of such combinations as you go into various topics in this course, but we have to note that it may not be the individual property which is unique, but the combination could be unique as you go down to the nano scale. And this combination is what gives for instance the component its application and its performance in an actual service. There could be drastic change in properties as you approach the nano scale. We know that for instance we already seen that when you go down in grain size in a nano structured or nano crystalline poly crystal you actually increase the hardness of the material, but this increase in hardness is a more what you might call at the macro scale or the micron scale is actually a gradual increase. But if you want to really see drastic increase that means increase of a few orders of magnitude or at least a factor which is making it worthwhile to study these materials such may start happening only in the nano scale. For instance fracture stiffness strength of nickel has been shown to increase from 100 MPa to 900 MPa once nanometer size grains have been achieved. So, the fracture strength can be increased and now it is happening only when you go down to the nano scale. Similarly, there are other properties we will see for instance adsorption of gases and we will actually make a calculation to show that how the surface area increase is going to give us a drastic increase in the amount of gases which can be absorbed on the surface. So, this implies that we have to here there is the property is varying, but we want to wait we want to go down to the nano scale to see an considerable enhancement in the properties nothing new properties are arising. Not that new structures are forming here, but does that the amplification factor is large and this warrants us to go down to the nano scale. The other thing which could happen is that the performance of some system depends on a functional entity at the nano scale. Now, this is again new that if I start with macro scale entities then I will not be able to get the performance which I can get by going down to a nano scale entity which is performing a very specific role. And we have seen that a device sensing signal from a single DNA can be extracted if you have a nano structure like a carbon nano tube and whose electrical output is what we are studying. So, that means that if my if I have to extract a signal from a single DNA then obviously my sensor or my probe has to be of the same length scale. I cannot use a macro probe then which will actually average out my signal across many cellular structures which is what not my goal. And if I have to do this then obviously my probe also has to have a wavelength or have to have has to have the length scale which corresponds to length scale of the problem which I am trying to study. So, it is clear that I have to go to nano scale if I have to for instance go to a single cell and deliver a drug or I have to extract a single signal from a single DNA or I have to affect only a few cells in the tissue. Then we already seen one beautiful example that in a multi length scale structure and we have seen that they have the very special properties the fundamental unit has to be of a nano scale. If I do not start at the fundamental unit of the nano scale then I may have some enhancement in the properties, but the overall structure will not have this kind of a beautiful property which we see so for the case of the lotus leaf or the case of the gecko feet. And at the heart of this we saw in the case of the lotus leaf there are non buckling nano hard nano has which is of course hierarchically built into the surface of a leaf which gives us super hydrophobicity. So, there are clear cut reasons why we want to go down to the nano scale because, but we have to differentiate all these cases because only then can we get the best out of our design to see how actually this new things which are coming at the nano scale and how we can achieve those new things with minimum effort. So, just to summarize this slide certain structures exist only in the nano scale certain properties arise only in the nano scale, but there are certain other cases where the property exist in the macro scale, but there is a drastic enhancement in the properties. You may want to have a certain specific combination of properties which is may not be possible by using macro scale entities. In a hierarchical construction for instance you may want to keep the nano in the fundamental unit may be of the nano scale to get that important benefit in terms of properties or a combination of properties. And of course, as we saw based on the kind of system you are trying to study and if that system itself happens to be in the nano scale or below you need to have your sensor or your drug delivery system corresponding to that very fine scale or the nano scale. Now, let us ask a question that we have noticed that there are some specific properties coming about we have to ask ourselves that how do these properties come at the nano scale. The broader answer of this question will be obtained when we see many more examples as we go across various topics in this course but we should understand that the and differentiate the various classes of properties which come about in the nano scale. And here we are especially talking about those structures which also exist in the macro scale. So, it must be clear from the outset that certain benefits can be up derived working with materials and structures in the nano scale. And of course, that makes it you know worthwhile to study this otherwise this would be in pointless exercise. Assuming there is a radical change in the properties which can of course, we utilize for making device in components. And the question is that how does this change in properties come about. And this is a of course, a very very important question because once we have our classification and the approach path in our mind the mechanism in our mind then of course, we can engineer our components better. Four methods can what you meant we can delineate four methods. And these four methods specifically refer to those cases wherein there is a bulk counterpart. That means, I have a case where there is a grain size in the micro on scale. And I keep on reducing my grain scale and go to the nano scale. I could be talking about a crystallite which is even millimetre in size and slowly reduce my crystallite size to the nano scale. So, in other words I if I am going from the bulk state to the nano state then how is it that the property is changing. And here we are not considering the cases like for instance the exist the properties of a carbon nano tube which have no bulk counterparts. That means that they exist only the nano scale. And therefore, we are not talking about properties which arise in the very specific case where there is no bulk counterpart. And in this particular classification we are also dealing with property in the language that it is a specific property. That means it is surface energy or grain boundary energy and not that of the whole material. So, we are talking about a property which is for instance the surface energy per unit area or grain boundary energy per unit area. And we are not talking about the overall energy of the whole system. So, in this classification we will see that there are four possible methodologies crudely speaking that you have a change in size. That means you are reducing the size and simply this may lead to a change in performance. This is what we might call this trivialist way of understanding or trivialist case by which a new or an enhancement in performance comes about. Of course, this simple way to understand is that suppose I have a material and I keep dividing the material into smaller and smaller pieces as we had considered. We see that the surface area is going to increase and for now assuming that the surface energy per unit area is not changing much. Then in spite of the fact that there is no change in the specific property we see that the overall amount of gases that such a surface can adsorb we are going to increase and therefore, you will have a change in performance. Here there is no great change in mechanism or any one of those very interesting scenarios which take place and this is at least what you expect from what you might call reducing the bulk crystal to a nano crystal or a bulk system to a nano size system. That means this is guaranteed to take place for you because now you have reduced the 11th length scale and in spite of fact that there is nothing interesting happening you are still getting a change in performance. The other end of the spectrum is a case a where in the change in size leads to a change in structure and we will have a comment to say about what the structure we are referring to here. This can lead to a change in mechanism which is operative in the system. This can further lead to a change in property and of course, whenever there is a change in property this will lead to a change in performance of the component or the specific device or the specific material we are considering. In between the case a which is shown here and the case d there can be other scenarios like a change in size may not lead to a change in structure, but can directly lead to a change in mechanism. This change in mechanism will most probably lead to a change in property and finally, of course this will lead to a change in performance. So, this is another pathway which can lead to a change in performance. Case c is a change in size leads to a change in property directly that means there is no change in mechanism and this can lead to a change in performance. So, to summarize this rather complicated looking table or a complicated looking flow chart there are 4 possible scenarios with a sub scenario which is also been marked as a prime. So, in case a the change in size leads to a change in structure which leads to a change in mechanism which can lead to a change in property and finally, a change in performance. The other end of the spectrum involves a change in size directly leading to a change in performance without any change in structure mechanism or property. Intermediate between these two is a change in size leading to a change in mechanism which is leading to a change in property and finally, to a change in performance. So, but in some cases it is possible that a change in size leads to a change in structure, but still there is no change in mechanism and that means that I can directly jump from stage 2 in the classification A to a stage 4 which is now a change in structure leading to a change in property which is leading to a change in performance without actually involving a change in mechanism. So, in this case we have used a word structure, we have used a word mechanism and of course, we have already defined what we mean by a property. So, the structure being referred to is usually the crystal structure and however, if one wants to you know relax this condition and the scope of applicability of this kind of a flow chart then other kind of structures like defect structures or microstructures could also be brought into the scope of this classification. The first change in mechanism usually implies a drastic change, change in mechanism for instance of plastic deformation from slip to twinning or from slip to green boundary sliding. However, minor changes like slip change system which is truly not a change in mechanism can also be brought into this category, but while listing the change in for instance mechanism we may want to say that for instance, when you had a macro scale system it was slip dominated by or plastic deformation dominated by slip and when I went to for instance a 15 nanometer green size it could be actually be slip dominated by green boundary sliding or slip dominated by twinning. Therefore, there is a clear cut change in the mechanism by which plastic deformation is taking place, but however, it could so happen that when you go reduce the grain size additional kind of slip system slip systems may be activated, but this is not what we might call in principle a change in mechanism, but this may be listed somewhere under the category of change in mechanism. It should also be noted that when fundamental studies are carried out say on single nanoparticles primary focus is usually to look for fundamental change in mechanism or properties and attention is usually not paid to performance in these studies. This is an important point to note because sometimes you have a single particle on which the entire test is carried out. For instance, you may have a nanoparticle which is 15 nanometer in size and you may carry out compression studies on these particles and therefore, what you get out of such a study could be a property like an elastic modulus or it could be a stress at which dislocations are nucleated in this system and here we are not specifically talking about the performance of say a nanoparticle like this in the making of a say for instance a MEMS device or a MEMS device. So, this is sometime very carefully has to be carefully kept in mind that there may not be a report in literature of the kind of performance we are expecting from this kind of a property and we have to at that stage for instance put in our thinking into understanding that how if a given this that this particles have these kind of a property what kind of a performance I can gain by using these particles because often when such particles are put together to form a component there may be a synergistic effect or of course, there could also be a problem with respect to a what you may call a destructive interference in the between the particles giving rise to a loss in property which we had observed for a very single for instance single nano crystal. So, here we are to summarize this slide here we are talking about those properties which do not or those structures and those cases where and there is a bulk counter part and obviously, we are excluding those which have no bulk counter parts. And the property we are referring to is a specific property and we want to see how this specific property finally, giving rise to a change in performance is achieved and this classification helps us mentally to work out you know for instance work out and engineer the material. So, as to get the required change in properties on performance. So, let us take up a few examples to see and maybe we will revisit this topic later on that how change in crystal structure takes place when there is a reduction in size. That means, we all know that there is a certain bulk crystal structure which is stable at a given temperature and pressure and here we are talking about not change in temperature or pressure to achieve these new crystal structures, but typically we are talking about a change in reduction in size. So, purely this is a size dependent phase transformation or a change in crystal structure and that means that at small sizes certain other crystal structures may become stable purely because of size effects, but additionally we may want to subject these small scale crystals or small scale structures or reduce dimensions structures to pressure or change in variations in temperature to see how these kind of materials behave. This crystal structure of bulk system materials could be very different from that of the nano crystals two important effects may be observed on reduction of crystallite size. One of course, is a change in crystal structure itself which is of course, a drastic change. The second possibility is an anisotropic lattice distortion which is a direction dependent change in lattice parameters leading to change in symmetry of the crystal. So, there are two possibilities one is change in crystal structure second in change in lattice parameter. This change in lattice parameter additionally could be anisotropic that means the change along one direction in lattice parameter could be different than the change in the other direction. The second effect which is the change in lattice parameter or anisotropic lattice parameter is actually a subtle effect as compared to one which is a very drastic effect and can have profound effect on the properties of a nano crystal. In metallic nano particles the dominance of surface tension effects is expected to lead to a contraction of the lattice parameter. That means that in metallic materials the surface which is now the seat of the surface tension can lead to a contraction of the lattice parameter and therefore, this is the direct cause for reduction in lattice parameter. In non metallic materials the situation could be very different from metallic particles and these non metallic particles we are referring to are those which are which have a polar surface. And in unlike the metallic particles there may be an expansion of the lattice parameters and this has been observed in the case of gamma Fe 2 O 3. And for this effect we have become a prominent effect typically we have to reduce the crystallite size to the nanometric length scale. This polar surface wherein there is a repulsion in the dipoles from the surface can actually lead to an expansion in the cell volume with a decrease in size. So, this there are two distinct effects when you are talking about surface tension and its role in what you might call the lattice distortion or the lattice contraction or lattice expansion. One of course, the lattice expansion could be uniform or isotropic some other cases the lattice expansion could be an isotropic. In the case of metallic particles you could have it is metallic particles at nanometer length scale are dominated by surface tension effects wherein you actually observe a contraction of the lattice parameter. But, in specific examples like gamma Fe 2 O 3 which have a polar surface when you are talking about 50 5 to 30 nanometer crystallite size actually there could be a lattice expansion which is now cost by the polar surface wherein the dipoles tend to repel each other. So, let me show this schematically. So, suppose I have a metallic surface in which there are atoms and the surface itself wants to contract itself to reduce the surface energy because the atom sitting on the surface have a higher energy and this is the origin of the surface tension. And this surface tension effects can lead to a lattice parameter contraction. Now, we know in nanoparticles the overall surface area is or the surface to volume ratio is very large. But, suppose I am talking about a polar molecule with actually dipole electrical dipoles on the surface. Now, these dipoles will tend to repel each other and this repulsion implies that actually we are talking about a effect which is something like surface contraction. And this surface compression in as suppose to surface tension which is a extremely new effect seen which becomes dominant in the nano scale can actually lead to perhaps a lattice parameter expansion. Of course, in the case of this gamma Fe 2 O 3 more studies have to be done to carefully analyze this effect and the role of surface expansion in leading to a what you might call a lattice parameter change. Other examples interesting examples or in case of change in crystal structure is the case of the silver. Silver as you know is a cubic close pack crystal having an FCC lattice and typically what you may have it has got to a 3 C stacking structure. That means, there is a what you call stacking a 1 1 1 planes on the 1 1 1 direction. Each one of these planes has hexagonal symmetry, but the overall symmetry along the 1 1 1 direction is 3 fold. On reduction of the size of the cellular particles below about 30 nanometer we find that the 4 H hexagonal phase is stabilized. So, the bulk phase is the 3 C phase which is a cubic phase and when you are reducing the particle size to about 30 nanometer. You notice that actually a hexagonal phase which is classified as a 4 H because a repeat unit is 4 layers long is stabilized. Similarly, if you notice that we are talking about the case of the tetragonal phase in zirconia is stabilized at room temperature when particle size is less than about 10 nanometer. So, we have taking up a few examples here number 1 is of bulk silver. Number 2 is a case of zirconia wherein typically at you find that if you taking bulk zirconia tetragonal phase is meta stable at room temperature, but by reducing the particle size to about 10 or less than about 10 nanometer. We can actually stabilize the tetragonal phase while the actual bulk stable phase is the monoclinic phase and we have noticed that this partially stabilized zirconia is in the meta stable structure is in the case of bulk meta itself is responsible for the transformation toughening effect. The third example is the case of the alpha Fe 2 O 3 when the crystallite size is above 30 nanometers alpha Fe 2 O 3 with rhombohedral structure is stable, but between 5 and 30 nanometer the cubic Fe 2 O 3 with an inverse final structure is stable, but this is not the end of the story when we actually go down to even smaller sizes like less than 5 nanometer. We find that the amorphous phase has been stabilized of course, there are. So, let us summarize the points with regard to Fe 2 O 3 above 30 nanometers it is the rhombohedral structure which is stable between 5 and 30 nanometers it is the cubic phase which is stable with an inverse final structure and below 5 nanometers it is expected that the amorphous phase becomes actually the amorphous phase is observed. Is it truly stable or not it is a question which is a more profound question and we are not taking up here and further studies may be required to see if actually an amorphous structure can be stable above what you might call a crystal structure. The issues involved here of course, is the fact that how many units cell do we have to put together before we can call that long range order has to be established. So, there are some very profound issues with regard to actually classifying an amorphous structure to be more stable than a what you might call a crystal structures. There are reports in the year 2000 and before which have shown that actually an amorphous structure is and these are theoretical reports that amorphous structure could be more stable than a given crystal structure not any given crystal structure, but a given crystal structure and typically of course, the given crystal structure they are comparing with is the crystal structure which is stable in the bulk form. Therefore, from these examples we can clearly see that there is a tendency in many materials to change its crystal structure when the crystallite size is reduced and these three examples we have considered so far is a case of silver, the case of zirconia and the case of Fe 2 O 3 and we are seeing that such considerations put forth very profound questions as to can an amorphous phase be more stable than any given crystal structure. So, this is a more profound question of course, which needs to be addressed further. Now, another example is the case of the tetragonal ferroelectric phase of barium titanate. On reduction of the particle size the ferroelectric phase converts to a para electric cubic phase and this is again now when we are talking about ferroelectric and para electric we are of course, talking about a change in crystal symmetry, but more importantly we are also talking about a change in the physical property. So, a ferroelectric phase actually changes into a para electric phase when the crystal size is reduced and we will take up more such examples when we study electric behavior and magnetic behavior of particles wherein we see that reduction in crystal size can actually lead to profound changes in terms of the magnetic or electric behavior of particles. Other examples which we can take up or which have been studied in literature include materials like alumina Fe 2 O 3, P V T i O 3, yttrium barium copper oxide that they with a decrease in crystal size, the crystal structure changes to one of higher symmetry. So, this what you might call the change in crystal structure effect with reduction in particle size is not restricted to the few examples we have considered here. It is formed in many more systems and this change in crystal structure as you can see from the picture we had considered that if there is a change in crystal structure this is expected to be accompanied by a change in mechanism and or definitely if you are going bypassing the mechanism route definitely to a change in property. Therefore, it is very important to note if there is a change in crystal structure as you reduce the size and even if there is no change in crystal structure is there a change in for instance the lattice parameter because any anisotropic lattice distortion or a change in lattice parameter would itself contribute to a change in property to some extent or the other. So, we have already seen how properties can change as you go down to the nano scale and we have considered various methods by which can happen which we have classified as A B C D, but we ask a very similar and light question why do properties change at the nano scale. We are listing here a few of the important reasons and we would note that they will range from the most trivial perhaps to perhaps the most profound. So, the reasons are sometimes extremely trivial and therefore, there is what you might call in some sense a lackluster reason you might call it, but on the other hand there could be reasons which are extremely profound. So, we will start from one of the what you might call a trivial or a simple kind of a reason that there is actually lack of sufficient material and we include here quantum size effects, but there is simply lack of sufficient material and therefore, the property changes. To give an example for instance if you talk about bulk gold it is not transparent, but suppose I make my gold foil very very thin it becomes translucent. It is not that the inherent property of the gold is not to absorb because now when you throw light on gold it is going to excite plasmon resonances and therefore, it is going to absorb light, but there is not enough material to actually absorb all the light which is being thrown at it. So, therefore, in some sense this is an effect which may call lack of sufficient material. Let us take a few more examples we know that electronic energy levels in isolate atoms become nearly continuous as bands when they come together to form a bulk solid typically let me consider for instance a bulk crystalline solid. As there are huge number of atoms involved in this whole process typically a mole or more we can think of these energy levels to be so closely spaced that they are nearly continuous or we might call they are continuous band kind of a structure. This implies that electromagnetic radiation with a range of frequencies can be absorbed with a solid unlike the discrete frequencies which an isolated atom would absorb. So, this range of frequencies being absorbed is a pure effect because of the fact that there is a continuous band and a band can accommodate many kind of excitations. However, in nano crystals wherein there is insufficient number of atoms involved in the formation of the solid the energy levels could of course, be closely spaced will remain discrete. So, this is insufficient number of atoms to actually make this band continuous and therefore, the absorption similarly will tend to be discrete as compared to the case of a what you might call a bulk solid which has nearly continuous energy levels. We will take up more of these examples later on when we talk about electronic properties, but it is important note that this is of course, quantum size effects, but there is a simplistic reason behind what is happening. We already consider this example that bulk metals are opaque, but thin films of metals are semi transparent as there is not sufficient material to absorb the light. And of course, we are not talking about absorption of light we are talking about certain other kind of radiation this would equally be true if the that radiation can pass through less amount of atoms that it needs to encounter. Now, suppose a very related kind of phenomena we talk about which is x ray diffraction. In x ray diffraction we know that for instance suppose I have a polycrystalline material if I reduce my grain size to micron level and further I can use x ray diffraction to actually measure the crystallite size. This is because when you reduce the crystallite size the peaks in an x ray actually broaden. Of course, peak broadening can come from other effects like for instance strain, it can come from stacking faults, it can come from what you may call instrumental broadening etcetera. But now for now I am restricting myself to the peak broadening which is coming from x ray what you may call the crystallite size. And we typically use a sharers formula for the calculation of the crystallite size. And we know of course, that the sharers formula itself has a certain regime in which it is it efficiently what you call can give us the crystallite size. Now, this effect of broadening is happening because there is not enough amount of sufficient number of atomic planes to destructively interfere with the incoming beam. In other words outside the brag angle whatever destructive interference should take place there is not enough number of planes in the material to give us that destructive interference. And therefore, you actually observe a peak broadening. So, this peak broadening in some sense is an effect which is purely coming from lack of sufficient amount of material or as in the case of x ray diffraction lack of sufficient amount of crystallographic planes. So, when we go to nano scale you will observe the peak broadening is more as you keep on reducing the crystallite size. And this is an effect which is in some sense a very simple effect coming from lack of sufficient material. So, just to draw this schematically I know that suppose I have my atomic planes coming here I know that if I am sending a beam at the brag angle then I know that this beam will be diffracted. That means that at this angle there will be coherent reinforced scattering and at any angle which is away from this angle for instance an angle like this or an angle like this there will be destructive interference. But for this destructive interference for this beam the plane which is out of phase with the top most plane actually lies deep within the crystal. The closer you get to this brag angle the further down will be that plane which destructively interferes with this beam to get it of that beam. But suppose I truncate my crystal here that implies that not only this beam will continue to exist, but there will be a range of beams around it which will continue to exist. In the words in my 2 theta was intensity plot instead of obtaining a sharp peak or more ideally a delta peak I would actually observe a broadened peak. So, this broadening which is given by the full width half maxima comes from the fact that there is insufficient material to destructively interfere and therefore cancel all the rays which are of brag angle. Therefore, I can see that there are sufficient number of phenomena or certain kind of phenomena which can simply be explained by the fact that there is insufficient material. And therefore, you are getting certain what you might call different properties in the nano scale and this should not be confused with those more profound properties which we will come across or those more profound effects which we will take up soon. The second kind of properties which we have which is again to be expected and we have already seen some examples of these is the dominance of surface and interface effects. We know that the surface layer is a disturb layer with high energy which is a high energy region which can undergo relaxation and reconstruction. So, the surface layer because it is an high energy region to reduce its energy it may undergo relaxation because of lack of bonding in the perpendicular direction and also in some cases like silicon it may actually undergo a process known as reconstruction. That means the surface crystallography could be very different from the bulk crystallography. Impurities insoluble in the bulk will segregate to the surface and gases may also adsorb on the surface. Therefore, maintaining the surface pure in most cases is actually a difficult task. In bulk materials the surface is but a minor fraction of the material and can be ignored under most circumstances. It is not that in bulk materials the surface is very different from or may not be very different from the nano materials or nano crystals. But the point is that it can be ignored safely without you know causing much difference to the result we are calculating. However, in nano materials including nano structured materials surface and interface effects can play a very important and dominant role. The so called surface actually may be become a large fraction of the material because surface is we are when we are talking about the surface we are not restricting ourselves to just the mono layer on the surface. But sometimes what we are defining as the surface could be a few atomic dimensions into the crystal. So, when you are defining a surface of course geometrically the surface implies the outermost layer. But suppose I am talking about relaxation and reconstruction I may want to go a little deeper and actually talk about a few atomic layers. And this physical surface as we have pointed out can actually undergo things effects like reconstruction and relaxation. The surface because of its high energy is a receipt of oxidation and nano particles this may become a very serious issue. So, surface can be a region of segregation surface can be a region of adsorption of gases. But further it may also oxidize therefore, there are certain there are more than one reason why the surface actually can change its composition. And therefore, cannot be treated like the bulk in terms of its various chemical effects. And we already seen that how surface tension and an example is shown here. A nickel cluster 1 nanometer in size showed a lattice parameter can show a lattice parameter construction about 10 percent which is a huge fraction of the lattice parameter. And this is again coming from surface tension effects. We also seen the case of polar surfaces wherein we can see the surface compression effects can come into play. And in cases where there is a lot of surface surface plasmon resonance may dominate the absorption spectrum in nano structures. So, when you talking about plasmon resonances in normal materials of course, you can say that the surface plasmon do not play much of a role. But in the case of nano materials that may actually be dominating the absorption spectrum. Therefore, you can see that surface is a special region it exists in most materials. Of course, this structure of the surface itself could be altered as you go down to nano scale. But more importantly the volume fraction of the surface. And now I am talking about a physical surface is actually going to increase as you go to nano scale. And this is going to alter the properties in a drastic way. It is again to reiterate the obvious thing that is that bulk material surface effects can be very important. And examples of this is corrosion erosion fatigue crack nucleation etcetera. And in all this phenomena we can clearly see that the surface is a key factor. For instance the fatigue life of a specimen which has been machined to a smoother finish would be very different from the fatigue life of a specimen which is which is pretty rough. And if there is a way of suppressing or reducing the what you might call the steps and intrusion and protrusions which is produced during fatigue testing. Then the surface life or the life fatigue life of the component can be increased. The area of surface engineering deals with understanding and modifying surfaces for better properties and longer surface life. And surface engineering as you can clearly see is going to play a much more important role when you are talking about nano materials and nano structures. And when I am using the word surface as we shall see during the many examples we are considered. We should not restrict ourselves only to the external surface which is of course very very important because it is that region which is actually coming into contact with the outer part of the system or outer world which is now as I said pointed out could be having gases it could be having oxidizing atmosphere which could be the region from where certain impurities may actually diffuse into the system. But we should also take into account the interfaces and we shall we have already considered an example. And we will return to that example where in we will see that surface and interface effects are very dominant effect. And this effect which is present in all bulk materials can actually get accentuated in the case of nano materials. And surface assumes a very important role. But nevertheless the whole this effect of dominance of surface and interface effects is what is what we may call as expected. This is not something which is what you might call absolutely new or something which is cannot be explained in terms of a simplistic argument. So, we are so far considered two reasons as to why properties change at the nano scale. And both of them can what you might can what you might one might argue can come from simplistic arguments. One is of course from the lack of sufficient material. The second of course is by dominance or dominance of surface and interface effects. In the case of bulk nano structured materials the overall surface area does not increase. It is only the interface area which is the green boundary area which may increase as you reduce the grain size of a poly crystal to the nano matrix range. Therefore, I have to have an integrated approach where I am talking about surface and interfaces when I am dealing with nano materials and nano structures. The third is again one of those effects which we may call an obvious effect which is coming from the proximity of the surface to the bulk. So, this comes again in the class of those reasons which as one might say one can actually easily anticipate easily predict and easily perhaps even calculate when it comes to how a nano material is different in essence properties from a bulk material. This proximity of surface to the bulk implies that any stimulus applied on the surface is automatically felt by the entire material. So, this is a very special case and this is not restricted to the surface. Suppose, I am talking about photochemical reactions in transulant materials this will not obviously be restricted only to the surface, but the entire volume of the material could be affected by these photo chemical reactions. So, this is one example for instance to tell you that in nano materials the region called surface and the region called the interior may be very closely and intimately interconnected which makes a difficult for us for instance to avoid certain effects which we will take up here. And in cases where time is involved this can take place within a what for instance very short time scale. In other words if I apply a stimulus on the surface which could be a chemical species it could be for instance some kind of oxidizing atmosphere then the entire bulk of the material or the entire volume of the material will feel this stimulus within a short time scale. If a nano crystal is exposed to a chemical species like a soluble in the material the species will permeate the entire material in a short period of time. This is unlike bulk materials wherein it is easy to maintain the surface composition different from the bulk composition. And we have seen such an example before that in the case of case carburizing the surface carbon concentration can be as high as 0.8 percent while the bulk composition can be 0.1 percent. So, to summarize this aspect that in a nano material the entire material could be built within what you might call a handshake or a proximity to the surface. Therefore, now I cannot say that I will employ a certain stimulus or certain chemical species on the surface and expect only the surface to be affected. In case of bulk material typically you would call a few millimeters even as the surface, but in the case of nano material which itself is totally may be 100 nanometers in size the entire bulk could be affected when you try to impose a chemical species. And if the species soluble in the material it will completely diffuse into the material and you will have an what you might call the middle of the material feeling the excess composition which you have imposed. We are talking about photochemical reactions the entire material will be affected. And therefore, it is now difficult for me to actually isolate my bulk from the surface. And therefore, I have to read the whole system as one system in many cases and many of the effects as we have seen actually arise from this proximity of the surface to the bulk. One subset of these is also worthwhile to consider is the case of the altered defect structure. And this way as we shall see can come from the lack of sufficient material or proximity of surfaces. That means, we are talking about altered defect structure coming from some of the effects we just now seen which is proximity of surface as in the slide or the case of lack of sufficient material. So, these effects we have seen now can actually lead to an altered defect structure in the material and as you can see if the defect structure is altered then automatically you are going to have an altered set of properties which is going to reflect in terms of the performance of the material or the component which this material is used to construct. An example could be that the largest crack a particle can have has to be less than the diameter of the particle. If the crack extends throughout the particle of course, the particle will break into two and therefore, you will have two particles instead of one. Therefore, the largest crack that a material nanoparticle can sustain would also be of the nano dimension. So, therefore, nano size particles can only have nano size cracks. We will notice that nano crystals may become totally dislocation free due to proximity of free surfaces. We will take up this topic later on in a little more detail and here dislocations will be attracted to free surfaces by image forces. And when this image force exceeds what is known as the inherent lattice friction of the material which is otherwise called the pearl stress dislocations will spontaneously leave the crystal. Very small size crystals may even not support vacancies. That means vacancies will cease to be a thermodynamically stable defect in nano crystals. So, this may also happen and we will have a little more to say about this topic of altered defect structure in one of the coming lectures. But important point is that because of lack of sufficient material or because of proximity of surfaces, you actually may have a altered defect structure. And one of these for for instance, the lack of sufficient material would lead to what you might call a reduced configurational stabilization of a vacancy. And therefore, the crystal nano crystal may become completely vacancy free. And proximity of free surface could imply that the image force experienced by dislocation may actually exceed the pearl stress. And the system may become spontaneously dislocation free. So, these interesting effects are arising because of what we just now talked proximity of the bulk and lack of sufficient material. So, there are these three and effects which are finally giving rise to what you might call an altered defect structure. And when we define microstructure, we said that microstructure sensitive properties are going to be sensitive to the defect structure. Because, my defect structure is part of the definition of microstructure in our scheme of things. And therefore, you would notice that those properties would drastically change when you alter the defect structure. But there are other reasons and this is an alternate way of looking at the same problem. And in some sense, some of these can be thought of as profound effects that where in one or more of the physical length scale of the problem becomes comparable to the geometrical dimension of the system. So, suppose I have a crystallite size, then one of the important physical parameters which governs the physics of the problem may actually become the length scale of that physical entity may actually become comparable to the length scale of the physical system we are considering which could be a nano crystal for instance. There are we will talk about these various quantities in the relevant chapters, but some examples could be that the crystallite size could be comparable to the mean free path of electrons. It could become equal to the mean free path of phonons. It could be a coherence lens in the material which matches the length scale of the material. It could be a screening length in the material which is now comparable to the size of the material. And there can be many more properties which we can list which all contribute finally, to the profound effect which comes in nano materials. Because, as you can see that if my and we have already seen one such example. So, let me take the same example again is the case of the spin diffusion length becoming equal to the length scale of the material. And we before I take up that example. So, let me see that in this table there are quantities electron mean free path, the Fermi wavelength, the range of exchange interaction for instance this is now related to magnetism. And this is a very important quantity and we can also talk about the exchange length in magnetism. And there is a typical length scale associated with these physical properties. For instance the electron mean free path typically varies between 1 and 100 nanometers. The Fermi wavelength is a much smaller number numerically. In semiconductors of course, the Fermi wavelength could be larger. In the case of exchange interaction again it can range from 0.1 to 1 nanometers. In the case of exchange length in magnetism it can have a wide range from 1 to 100 nanometers. So, when my particle or crystallite size starts to approach any of these dimensions. And of course, if I am talking about magnetic material I would worry about some of these effects here. When I am talking about conductivity I would worry about the electron mean free path. Then I would see that my properties are going to drastically change when I go to the nano scale. At the heart as you can see here are more profound effects here because the fact that now I am not merely saying the material is becoming smaller. And it is not a gradual effect which is going to change. But it is going to drastically change when I hit these magical numbers or these physical quantities below which my length scale has is going to lead to a drastic change in properties. So, since we had considered this one example I will just reiterate that example is the case of the spin diffusion length. So, suppose I take a conductor on the right hand side. This is a normal conductor and this is now a ferromagnet and I pass current from left to right. So, what would happen is that the current which comes would be spin polarized into the material. So, I have a spin polarized current which is entering this material. But because now this is not a magnetic material the spin memory of this spin polarized current would die down and after a few scattering events. And therefore, after some time this would not be a spin polarized current. So, you have after a certain distance which is now my spin diffusion length I would have a. So, it is very clear that my all my spin memory dies away and after a certain stage I would have a normal current which is found in a normal conductor. And this is because of the scattering events which would take place in the normal conductor. But suppose now my length of the whole conductor which I am talking about is very small and which is what we considered as the sandwich layer in the giant magnet resistance system. Then this spin memory will not completely died on of course, there will be a certain randomization. So, I will show that the spin memory may be slightly randomized. But still there will be a spin polarization and the system the current will continue to be spin polarized even after it passes through this conducting layer. Therefore, you can see that here even though in some sense this is also lack of sufficient material you might say. But there is a fundamental physical length scale involved here which is my spin diffusion length with which I can correlate now my what you might call the physical parameter can be correlated to the length scale in the size length scale of the system. And therefore, you can see that profound effect start to appear when you actually go down below the size length scales. And we will consider some of these in the upcoming topics. So, just to summarize the set of important questions that why do properties change the nano scale. It could be because of lack of sufficient material. It could be because of dominance of surface and interface effects. It could be because of proximity of the surface to most of the bulk. It could be because of some of these effects giving rise to an altered defect structure. And finally, of course if one of the more physical length scale become comparable to the geometrical dimension of the system then I would expect that certain drastic new properties will arise in the system. We have been actually listing some important reasons why the property could change. But one other extraneous kind of reason also is worthwhile considering here though truly speaking this is not in the same class of reasons which we have now talked about. This is because when we actually for instance synthesize or manufacture some of these nanoparticles or nanocrystals or nanoface materials they may not be free standing. And they are often embedded in or supported by some other media. So, even though for instance I want to use gold nanoparticles for catalytic application I cannot have free standing gold nanoparticles because this will be carried away by the medium. And I would like to embed them on a surface or actually support it on a surface or a second medium which is substrate. And this is essential for its being continued to be part of the system and act like an effective catalyst. Now, some of the reasons why we other reason why we want to do it is to avoid coalescence of the particles. Suppose I put together gold nanoparticles they will coalesce and actually they will may grow with time and actually not lead to a the grain size may become larger than the nanocrystals with which we started. The second reason of course is that the particles may be synthesized in embedded form for instance when you are talking about nanocrystals for an amorphous matrix it may be produced by crystallization of the amorphous matrix. And therefore, it is by design or by default embedded in an amorphous matrix. So, it is not a free standing nanoparticle and therefore, I cannot avoid or cannot avoid taking into account the effect of the matrix or the effect of the supporting medium. And sometimes as we shall see as we already seen that this effect of the supporting medium actually could be positive. One good example of the support structure we have seen is the case of the gold nanocrystals supported on a substrate which could for instance be a titanium substrate for catalysis. Particles with high interface perimeter show higher catalytic efficiency it is to be noted that bulk gold is not catalytic at all. So, we have seen this example before that gold in the nano scale can become can show good catalytic activity. And in fact, it can be a very good specific catalyst for certain kind of reactions, but the role of the substrate or the supporting medium cannot be ignored here. It is seen that those particles which have a larger perimeter of support one suppose had two gold particles one like this or let me and the other one. So, this has a larger perimeter of support and this shows higher catalytic activity as compared to this which has a lower perimeter of contact which is it will show lower catalytic activity. Therefore, clearly yes gold is becoming catalytic at the nano scale, but the role of the interface or in the support structure is also playing a very profound role in the whole property. Another nice example is ferromagnetic behavior of thiol coated gold nanoparticles and we are talking about gold nanoparticles of the size of about 1.4 nanometer. The gold sulfur bond at the interface between the gold nano crystal and thiol is postulated to be responsible for this effect. So, you do not expect gold to be ferromagnetic neither is thiol ferromagnetic then how is this that this combination of gold and thiol is becoming ferromagnetic. So, it has been postulated the gold sulfur bond is actually at the interface is responsible for that and therefore, you can see that the interface itself which is of course, coming from the way the gold is dispersed in this thiol is playing a very important role in the emergence of a totally new property because gold is normally diamagnetic and this embedding is giving it is ferromagnetic behavior. So, absolutely new properties can emerge there can be enhancement in properties as in the case of the catalytic activity and one more example we would like to consider here is the curie temperature of 1 nanometer cobalt film deposited on copper 1 0 0 1 substrate can be lower than that for bulk crystals and at a certain thickness the film starts to behave like a 2 D system. So, in this case again the cobalt film is influenced by the copper substrate and if of course, I am talking about an epitaxial film then the epitaxial stresses would further influence the way this magnetism is going to be present in this material. But nevertheless in all these systems you can see that you are having a support medium because it is difficult to produce a 1 nanometer cobalt film as a free standing film it will tend to warp and it will not be a flat film even. And it may be difficult to study its properties as a free standing film typically therefore, it is on a substrate or on a support medium and this support medium could actually be influencing the properties of the system as a whole and this may have to be taken into account when you are talking about properties of a material or properties of the nanoscale system. And as you can see this is not truly a property of the nano crystal itself, but a property coming some in some sense from an extraneous reason.