 Before proceeding further, let us briefly review the concepts we have considered so far. We ask the question that what determines the properties of materials and the answer we gave was it was a combination of the composition of the material. The phases present in the material and their distribution we have to consider the defect structure, the definition a formal definition of the defect structure which we will consider soon. And last but not the least we have to consider the presence of residual stress in a material which is present even in the absence of any external loading or constraints. We said that this becomes especially important when we are talking about structure sensitive properties like yield stress and fracture toughness. And as an example we had considered the micro graph shown on the right hand side wherein there is a steel with a cementite network all along the prior austenite grain boundaries. We had also asked the question that if you are talking about phases in the distribution what kind of phases exist and we had classified phases based on the geometrical entity or the physical property. We had also considered various ways of looking at atomic form of matter. And we had come across important concepts like the atomic base structure which is can be classified into crystals, quasi crystals and amorphous phases. We also said that based on band structure we can have metals, semiconductors and insulators. And from this course perspective we had talked about a size based classification which gives us nano crystals, nano quasi crystals, nano liquid crystals etcetera. We had also gone ahead and defined water crystals in a very simplistic way. And we had said that crystals are ordered and periodic and amorphous phases on the other extreme are neither ordered nor periodic. Today, let us consider classification of crystals based on the bonding characteristics. Now, based on bonding a substance could be for instance belonging into a certain type like an ionic crystal. But based on the atomic order the same thing could be glassy in other words could be amorphous like before we had considered that one way of classification will not clash with another way of classification. The bonding characteristics of the material play a very very important role in all the properties which we think of. So, based on bonding we can classify crystals into two types, the molecular crystals and the non-molecular crystals. In molecular crystals there are covalently bonded molecules like for example, in fullerine we have the C 60 molecule, in water molecule we have the H 2 O molecule. Another examples of molecular crystals are crystals based on carbon dioxide molecule sucrose molecule etcetera. The bonding within the molecule is of one of the is typically of the covalent type. But the intramolecular bonding which actually gives rise to the crystal is usually of a weak type. It is a non-covalent interaction typically they could be of hydrogen bonding type or dipole-dipole bonding a detail list of which which we will soon consider. As we have seen that molecules can not only form crystals, but these molecules can also get ordered in amorphous form or you can even think of a quasi crystalline order for these molecules. So, but the important thing in the molecular crystal is that the bonding within the molecule is covalent type and the bonding between the molecules which gives rise to the order or the lack of it is typically of a weaker type which we can which can be for instance and hydrogen bonding type or a dipole-dipole kind of an interaction. On the other hand there are these familiar types of crystals which we are which you might have been exposed to before which are the non-molecular crystals. An examples of non-molecular crystals are the covalent crystals an example of which could be our diamond carbon base diamond. The ionic crystals the common salt of the sodium chloride is a nice example of an ionic crystal or the metallic crystals like gold, iron, aluminum, copper etcetera. The kind of bonding characteristics will reflect in all properties which we can think of for example, if I am talking about the melting point of a material a molecular crystal will typically melt at a low temperature because the kind of interactions holding together the molecule which gives rise to this atomic order in the form of a crystal is of a weak type and therefore, such a crystal will typically melt at a low temperature. On the other hand a non-molecular crystal like for instance diamond which is covalently bonded you would have a very high melting point for such a material. Not only that if I am talking about the what you might call the plastic behavior of a material typically the lattice parameter of example and covalently bonded crystal or a metallic crystal would be small. And therefore, what I am considering here is the usual kind of covalently or metallicly bonded crystal and I am not taking into account for now those kind of crystals which are which have which can have large lattice parameters the usual ones like gold, silver or diamond have reasonably small lattice parameter. And therefore, we will be having a small burgers vector which means that my inherent lattice resistance to the motion of dislocations would be small which would translate into easy plastic deformation of especially these metallic crystals. But on the other hand molecular crystals typically suppose I am talking about fullerene is made of large molecules and the burgers vector will be very large. Now, the bonding characteristics with respect to for instance the pearl stress which otherwise called the inherent lattice resistance can be compared between the covalent and the metallic crystals also. In the case of a metallic crystal the pearl stress is typically small while in the covalent case of the covalent crystals the pearl stress is very large. And typically therefore, covalent crystals are not that plastic especially at room temperature or low temperatures which means below the 0.5 of the melting point of the material. So, this all these properties are naturally coming out of the bonding characteristics. In ionic crystals for instance if I am talking about plastically deforming an ionic crystal like sodium chloride typically it will fail a fracture rather than plastically deforming that is plastically deforming by slip. And reason being that a ductile material is one for which the yield stress is lower than the fracture stress. So, if I am considering a ductile material a brittle material on the other hand is one whose yield stress is larger than the fracture stress. So, a ductile material will yield first before fracturing. In other words the yielding we are talking here is specially by a mechanism known as slip. And fracture is caused by propagation of cracks. So, when I have two competing mechanisms which can take up my external loading one being slip which is listed here. And the other being propagation of cracks and if my yield stress is smaller than my fracture stress then the material is called ductile yield stress is a macroscopic manifestation of the inherent lattice friction which is otherwise called the pearl stress or the pearls in a barrow stress. So, other factors would come into picture when I am taking my inherent lattice friction which is otherwise I called the pearl stress I take my pearl stress and go to a macroscopic gross property like yield stress. So, this pearl stress is a strong function of the bonding characteristics of the material. A covalent material typically has a high pearl stress and therefore, has an high yield strength. And therefore, if I am trying to plastically deform a covalent material like diamond then it turns out it is difficult. And typically anionic material which again has the scenario of a high pearl stress would fail by brittle fracture rather than plastically deform. Therefore, if I am looking at any property then the bonding characteristics become very very important in determining the properties. On the left hand side there is an example of an hex hexagonalize which is a molecular crystal. In other words in the ice crystal there are covalently bonded water molecules H 2 O molecules which form a crystal via the van der Waals bonds. If you want to talk about bonding characteristic based on the type of bond like in for the non covalent non molecular crystals like covalent ionic or metallic these what we might call are the end pictures. And the real bonding characteristics could be somewhere between all these extremes possible. So, these three extremes the metallic the covalent and the ionic represents three extreme bonding characteristics. And a given material for instance could actually fall somewhere between the triangle it could have some covalent characteristics, but a little bit of ionic characteristic. And therefore, in this triangle it could lie here certain metallic crystals could also have a certain amount of covalent character. And therefore, they would not be on the extremes which are the metallic covalent or ionic extremes, but would lie somewhere in this what you might call a ternary looking plot. Therefore, real crystals have characteristics which have a bonding which is a combination of covalent ionic and metallic characteristics. We will consider the next slide that there are other weak interactions which can mediate the formation of crystal and molecular crystal apart from the hydrogen bonding, which is responsible for the formation of the ice crystal. And therefore, the kind of bonding which we are considering here forms a important basis for the properties that the crystal exhibits. And therefore, it is important to note if the crystal is a molecular crystal or a nonmolecular crystal. And given it is a nonmolecular crystal which will form much of the considerations in this course for instance, we have to consider if it is a covalent crystal, an ionic crystal or a metallic crystal. Now, we will briefly consider here various kind of interactions in molecular crystals the weak interactions though we will not going to detail. And an interested reader may actually want to refer to details for various individual molecules or various individual crystals as to which bonding is responsible for the formation of the molecular crystal. Typically in this molecular crystal as I told you it is covalent interactions which gives rise to the molecule. And these are typically given symbols like Simba pi delta the intermolecular interactions which is responsible for the crystallization could be the hydrogen bond or what is called the van der Waals bond which includes dipole-dipole interactions. Like here we are talking about permanent dipole-permanent dipole interactions or it could be a permanent dipole which actually induces any dipole in the neighboring molecule. Therefore, you have a permanent dipole induced dipole interaction which can also give rise to some bonding or there could be an instantaneous dipole induced dipole interaction which is typically called the London dispersion force. And there are other forces like the ion dipole the cation pi and pi pi interactions and all these various interactions listed here like the hydrogen bond the van der Waals bond etcetera are actually weak interactions. The typical relative strengths of some of these bonds are the dispersion forces are the weakest the dipole-dipole interactions that is the permanent dipole permanent dipole interactions are usually stronger. And the hydrogen bonding is usually stronger than the permanent dipole permanent dipole interactions. The book on non-covalent interactions is a interesting it is an exhaustive study of these interactions and an interested on the paper on in chemical review would be a good reading place for other students to learn further about these non-covalent interactions. Now, we have to ask ourselves that we have talked about phases, but there is a larger picture beyond the phases when a material is given to you typically for instance I am holding a pen here. You can see that this pen is not made of a single kind of a material there is plastic there is there are some metallic parts and other parts which are hidden away inside. So, such a material or for instance your cell phone your typical cell phone is what might call of course it is an entire device a device has many components and each some of these components may actually be what is called an hybrid. It is not a single material which goes on to make your entire cell phone or some of its components. Now, why is that this consideration is very important or the question that why what kind of bulk materials exist is an important question is because later on we will see when we talk about nano materials that not all components of the nano material may be nano in size only a few of these components and some of these may be even property related may be actually nano sized and remaining of the components may actually be bulk like and those bulk like components will continue to have the properties which you normally expect for bulk materials. Therefore, it is a very important consideration that what kind of bulk materials exist and therefore, which of these components of these bulk materials can actually get into the nano scale which is going to give us the interesting properties which we are interested in the study of nano science and nano technology. Now, when you are talking about bulk materials on one hand as I told you there is a scale of the component for instance it could be a the scale of the component could be of the order of centimeters or even meters and then there is a scale of the phases which could be of the order of microns or tensor of microns and when we want to classify materials we have to classify them as monolithic materials and hybrids. Monolithic materials are simple materials like for instance the word of course, has the root that monolithic means single stone. Lithic has the word origination origin the word lithos which means stone which essentially in this context translates into a single kind of a material. For instance you could have a copper wire which is just pure copper of course, it is polycrystalline copper nevertheless it is a monolithic material. For instance a ceramic for instance your brick is also another kind of a material in one view in a more macroscopic view it can also be considered as a monolithic ceramic. But of course, if you go a little deeper you would notice that the brick actually consists of lot of pores and also lot of material and therefore, truly speaking it will come into a structure which is known as the lattice structure which is a subset of the hybrid. Therefore, if I want to understand what bulk materials are I classify them into monolithic materials which includes metals and alloys, ceramics and glasses and polymers and elastomers. And this classification is what is called the usual engineering classification or the usually common practice usual kind of classification wherein you have monolithic metals, monolithic ceramics and glasses and monolithic elastomers. But we know that instead of actually working with monolithic materials we can actually tap into the potential of a multiple materials in a single component or a single material actually having multiple components which can therefore, give us the benefits of both kind of presence of both kind of components and these are called the hybrids. Now for instance suppose I am talking about the blade of a helicopter aircraft the maximum bending stresses come on the surface of the blade. And therefore, I may want to have a hard material on the surface the interior of the material can be relatively softer as compared to the surface. Also we know that the surface is what is usually exposed to the atmosphere usually exposed to erosion and therefore, I would like to choose a material which is most appropriate for this purpose. And therefore, I can make a sandwich structure in which the outer layers the colored grey is the load bearing or the more stronger one or the stiffer one and the inner one can be less stiff. Therefore, the philosophy in forming a hybrid is to tap into the potential of all the components to make a material which is actually having the benefits of both of those. Now what kind of hybrids exist hybrids can be classified into composites they can be classified into sandwich structures they can be classified into lattice structures and they can be classified into segments. We should be noted here that the word use of the word lattice is different from the use of the word lattice in the context of crystallography. Here the word lattice implies a presence of a composite or a hybrid between air or vacuum and a material. For instance in this example there are rods of a material and there are regions which are voids basically. We will also consider soon an example where in these voids are themselves in nano size and therefore, that can be a nano sized material or a nano structured material. In composites for instance if I want a material which has good toughness at the same time has good strength. Then I can use a load bearing reinforcement which has been shown in black and gray color here rod like structures here which is very stiff, but is brittle. On the other hand I can use a matrix which is not that stiff, but is ductile and can take all the damage which may accumulate during the in service operation of the material. So, these reinforcements can be form in the form of long rods they can be in the form of particles they can be also in the form of plates etcetera. In sandwich structures typically you have the top and bottom constituting two different materials while the inside is of a different kind of a material. We had seen that the lattice structure is one which is a combination of material and void. So, this hybrid of a material and a void is called a lattice structure and lattice structures have very important uses like for instance suppose I want to impregnate certain lubricant into a material which is part of the material itself and plays a role in lubrication of the component. Then I can use a lattice structure suppose I want weight savings wherein I do not want too much of I want a lot of volume of material, but actually of much less weight. Then what you may call volume in this case is actually an effective volume then I can use a lattice structure and these lattice structures sometime are also referred to as forms and you can have forms typically of metallic forms or ceramic forms which have important roles to play in various kind of engineering applications. Segmented structures again are in some sense an expansion or a of these sandwich and lattice structures where you can see clearly see that there are multiple materials which are put together to form a segmented structure and this is of course, a one dimensional segmented structure. There is a two dimensional segmented structure where there are multiple layers which form go on to form the hybrid. Now, the important thing of considering this form of material in a monolithic material of course, you have a single face like a metal and therefore, if I am talking about a nano structured monolithic material then I have to pick up certain length scale in the material which can become nano structured for instance in a metal it could be the grain size which is becoming nano scale. On the other hand in the case of a composite just one of these components could be nano scale and of course, there is no stopping has been putting for instance two or three types of reinforcements and therefore, one of these reinforcements could be nano scale or two of these reinforcements could be nano scale or for instance suppose, I am talking about reinforcements which are particles and rods then the particle size could be nanometers. The rod diameter could be nanometers, but not the rod length which could be much larger and therefore, the important thing being here one of only one of the components could or one or more of the components could be in the nano scale and not the entire composite or the entire sandwich structure. Therefore, this classification tells us that once I have a broad overview of what kind of materials exist then I know which of these can become nano sized. Further to these kind of a classification we have additionally another important kind of class of materials which we need to look into which are called the functionally graded materials. In a functionally graded materials the concept is that for instance in a component this could be the inside of the component where the fluid flows and this could be the outside of the component where in for instance which could be exposed to erosion or corrosion. Therefore, even though I have a single material here I want to make it graded and I can make it graded in terms of the composition I can make it graded in terms of for instance the precipitate density etcetera. So, that there is a gradation in the properties for instance this surface could be harder and this surface could be softer and I am plotting my hardness with respect to surface. So, this is my outer and this is my inner and I can see the hardness could be varying of course, it need not be a linear variation nevertheless such a functionally graded material can perform a very important role that in a single component actually I do not have two or more distinguishable component which can I can say this is A and that is B, but there is a continuous gradation of the properties and I said that this gradation of the properties could actually come from change in variation in composition or if I am talking about a composite then I can talk about a reinforcement density which is higher here for instance here I could have more particulate reinforcement while on this surface the density could be little smaller or I could think of the composition here being rich in phase A and poorer in phase A as I go out from here and this side could be pure B and this is almost pure A. So, there are various ways of making compositionally graded materials and the purpose here is to build in a single material a change in properties as you go from one special region to another and this could be a continuously varying property a classic example of this could be considered as the case carburized steel. In case carburized steel for instance suppose I am talking about a gear wheel and say this is my gear wheel tooth I can think of a decreasing carbon composition from the outside to the inside suppose I am talking about this plane as P 1 and this is going inward as I go from P 1 I can actually have a carbon concentration which drops off. So, this is concentration of carbon now the important point is that I take a material with a certain amount of carbon in it for instance I would take 0.2 percent carbon steel then I would impose a carbonaceous atmosphere on the surface which will now allow carbon to slowly diffuse into the material and after some time I will stop the carburization process cool the material later on take the material to high temperature and quench it in this process what would happen is that the surface would have a high carbon martensite where the interior would have a microstructure which is like a pearlite. So, I have a surface microstructure an outer microstructure which is an interior microstructure which is more like a pearlite. The reason for this variation in microstructure is related to the cooling rate the surface feels a very high cooling rate or a high quenching rate which implies that the high carbon which is in the solid solution the interstitial solid solution form forms a martensite while the interior is facing which is facing a low cooling rate gives rise to pearlite and this pearlite which on the interior side is also having lower amount of carbon which is also similar to the original carbon which was there in the material which I could call something like a 0.2 percent carbon. And therefore, I will have a metal in which the surface is extremely hard and interior is tough. So, this structure which is now can be thought of as an classic example of a functionally graded material is having a gradation in the properties as you go from this surface to interior. And as you know the gear wheel actually measures with the remaining gears in the system and therefore, it needs to be hard the interior of the mill actually needs to be tough because the material has to be resistance again fracture. Suppose the material was like we know that martensite is very hard, but very brittle. So, we do not want to have a material with which is throughout martensite because such a material will be very brittle and would have a very poor impact and toughness in other words very poor tolerance to presence of cracks in it which are unavoidable during actually the fabrication of a component. And the cracks you are talking about here typically are micro cracks and not large size cracks. Therefore, in this example you can clearly see that I have under my control the variable which is composition I have under my control a gradation in composition I have under my control the formation of the kind of phases like the surface on the surface is martensite the phase on the interior is more like pearlite which is actually not a phase, but a micro constituent. So, I can have a gradation in the what you might call the formation of the phases in the micro constituents and therefore, I have a handle on the properties. We shall soon see that how this concept of controlling composition or going from composition to phases to micro constituents can be thought of in a in the what you might call a functional definition of what we call a micro structure which we will make an all encompassing kind of a definition which can actually give us a handle on the what we had defined before the micro structure sensitive properties. Another simple way of creating for instance gradation based on precipitation which is what we consider here is to have actually what you might call a precipitation hardened system. In the case of a prestation hardening system essentially what we do is the classic example of the aluminum 4 percent copper alloy system in which we take the system we take the system to high temperature where you have uniform solid solution we quench the system to room temperature typically from a temperature like 550 degree Celsius which according to the phase diagram tells you is gives you a uniform solid solution of a copper in aluminum. When we quench it we actually at room temperature we have a super saturated solid solution of copper in aluminum additionally the system will also be super saturated with respect to vacancies. Now, I can age this system to act at a temperature like 180 degrees or lower, but around not as high as close to the equilibrium solvus line and in aging so I will produce a fine distribution of precipitates. Later on we will see an example of how this fine distribution of precipitates helps us in increasing the strength of a material. But the important point to be noted here suppose I use an aging temperature which is T 1 on one side and an aging temperature T 2 on other side then the kind of precipitate which is produced would actually vary from left to right. If T happens to be the higher temperature then you would tend to produce more of the equilibrium large size precipitates theta. So, I am schematically showing this large size precipitate as bigger circles on the other hand the lower aging temperature might produce fine g p zones or theta double prime precipitate. So, I can now engineer a gradation in the kind of precipitate or the kind of phases which are produced during the heat treatment and in this process I can have a gradation in the properties. Therefore, I can have monolithic materials which of course could have a variation in composition from one side to another. We can have hybrids and added to that more importantly we can have hybrids and monolithic materials which can later on be what we might call made into a more sophisticated version of these which is called the functionally graded materials which would actually help in the actual engineering component where in I have a site specific property which will help me in better performance of my component. Now, when we had considered nanoscale materials an important concept was that there are entities in the system which are nanoscale, but the more important thing to note is that whenever we have a system we cannot understand its properties or we cannot understand entirety of the system without actually traversing across lens scales. Now, what is the lens scales we need to consider is what this diagram shows you and this also tells you a bottom up approach towards what you might call assembling a component. Of course, this is more like a conceptual understanding of assembling a component and in reality a component may actually be formed by certain method like casting or a welding or could be another other processing methods which would in turn actually engineer the kind of micro structures which are produced or kind of phases which are produced. But let us consider this traversing across lens scales and see how at one end of the spectrum we have atoms and molecules which are typically of the order of angstroms. And the next scale is the scale of the phases which could be of the order nanometers or could be of the order of microns. Then we have the scale of the micro structure where in multiple phases come together to form a micro constituents and multiple micro constituents may come together to form a micro structure. So, let us briefly explore this pathway which will actually form the basis for this large broad spectrum understanding of materials and their sub components. So, we have atoms or ions as the case may be and they could combine to form molecules. Many of these molecules or if directly I can go from atoms can give rise to phases and we already considered what kind of phases we are talking about possibility of many kinds of phases. These phases may come together to form micro constituents and further the micro structures and I am using micro structure. So, far in a what we might say in a simplified engineering usual use of the word sooner we will define micro structure in a more specific functional way, but for now we will accept the usually understood meaning of the word micro structure. We could have multiple micro structures coming together to form material. We could have multiple materials coming together to form a hybrid and further multiple hybrids could come together to form a component. And of course, this component could be in the scale of few hundreds of microns or it could be much larger or it could be even talking about a much larger component which could be of the order of centimeters. And we all know from our everyday experience that actually most of the components here we actually see in application are actually hybrids. For instance a pen cap could actually be having a metallic part and a plastic part. Further the metal metallic part also could have some layer coated on top of the metal to give it a certain shine. Therefore, we have already talking about a multi layered material or what you might call hybrid material. And that hybrid material going in association with another kind of monolithic material like plastic which finally gives rise to a simple pen cap. But we go to larger and larger components we will see that there could actually many hybrids which come together to form a component or many materials directly forming a component as the case may be. And therefore, I need to understand the properties of the component which I am really interested in comes from many many things which sit below in the hierarchy of the length scales which I have to consider. For instance suppose I start with atoms which are heavier obviously, the component is going to be heavier. Suppose I start with magnesium which is a lighter metal then my component is going to be lighter. But the story does not end there right. For instance suppose I am interested in a property like as we just know so wear resistance. Then if I can make a hybrid in which I can coat my magnesium with certain harder phase or have a selectively a harder phase which is impregnated on the surface. Then actually I can get a harder component and therefore, I need to worry about all these length scales which are there between the length scale of the atom and that of the component. The design of the component itself is very very important as far as the performance goes. For example, if I have a component which has sharp bends then those sharp bends can actually give rise to stress concentration which could be regions of failure. And I may want to design the component with high radius of curvature or wherever possible. Now we are in a position to actually define the term microstructure and define it in a functional way. As we have covered sufficient background to actually now go ahead and understand the term microstructure we will define it based on two important considerations which are listed there. It is going to be a functional definition and it is going to be a definition which includes multiple length scales. First I will give a justification why you need to define a microstructure this way. Now suppose I am looking the classic definition of microstructure would be that the structure I would see under an optical microscope which would typically go up to 1000 x magnification. Now suppose I am looking under a transmission electron microscope then I could be having a magnification going up to 1000 k x or 50 k x. And in this case I may have to define a new term as nano structure or some additional term will have to be defined for those length scale which are even smaller than that. Therefore, I will have to be introducing multiple new terminologies whenever I am changing the scale of my viewing. This scale of the definition of microstructure as viewed under high magnification typically 1000 x is a satisfactory or what you may call the usual general accepted terminology. And the way we are going to define microstructure could actually be called could have been given a new name. But since the most important thing we are interested is what is called the microstructure property correlation. Therefore, we do not want to introduce new terms, but instead use a term of microstructure, but built into it these two aspects the functional aspect and also the aspect which covers all length scales. And as we shall see by this very definition of this microstructure as defined here we will be including all length scales of the problem. We have already seen that at one end of the spectrum of the building block of atom sits and the other end of the spectrum is the spectrum of the component. The component typically as you know is formed by various could be formed by various kind of forming material manufacturing process like casting metal forming welding powder processing machining etcetera. These are typical some of the typical ones for metals, but there are other ones which can be used for ceramics there are still more which are used for polymers. And in the component forming methodology obviously could have a material synthesis aspect followed by actually aspect which actually shapes it into the form of a component. So, there are multiple steps which could be involved in the formation of a component. The next scale after the atom is the scale of the crystal structure or the structure as you might call. And we have already seen that for instance how atomic structure can be classified. Now, when you are talking about structure we could be talking about the atomic order base structure or what you might call the crystal structure or more importantly the electromagnetic structure of the material. In other words I could be talking about electron densities I could be talking about the orientation of spins or the magnetization vectors of individual atoms ions etcetera. The next scale after this structure or what you may call the the structure scale where in the crystal structure and the electromagnetic structure aside is the scale of the microstructure. The important thing is that this microstructure can form by those processes which actually are used to form the component for instance. In other words what are the processes key features of those processes which give rise to the microstructure or for instance the component are the thermo mechanical treatments. In other words I could be talking about a material heating the material or I could be talking about forming the material like for instance I could use extrusion I could use rolling or I could use a combination of both. I could use a high temperature what we might call a thermo mechanical process where I could actually do the rolling at a higher temperature. Therefore, the basis for formation of the microstructure is very similar to the basis of formation of the component. Of course, I may decide to form the microstructure first for the material and they later on do additional processing to form the component. So, that is a possibility, but essentially the thermo mechanical treatments which undertake to actually make the component or make the material itself would give rise to a microstructure. Further of course, I could use a series of these thermo mechanical treatments to engineer my microstructure even further like the example we had considered is just now wherein we took an aluminum copper alloy which could have been formed by melting and further we did a certain set of heat treatments which can give us which might call a thermal treatment which can give us a desired microstructure. And more importantly we even considered a gradation in the microstructure which can give rise to a gradation in the properties and therefore, the gradation in the performance of the material. At the component scale we already saw that we need to avoid stress concentrators which would in fact we very could prove deleterious for the operation of the component. Now, what is this word microstructure mean? What are its components and how each one of these components give rise to a handle on the properties is the important question we are going to answer next. We can think of a microstructure as phases and their distributions defects and we will soon introduce a term called defect structure. So, defects and their distribution and last but not the least residual stress and their distributions. So, we have three important components to a microstructure the phases the defects and the residual stress and not only these three components we have to consider, but we have to consider their distributions. So, we need to understand the terms used in this definition and also what do we mean by the term distributions. We have to note that residual stress can be an integral part of the microstructure itself or can be on coming from a larger scale like when we form the component. So, there could be multiple origins of residual stress, but more importantly once the residual stress is present in a material it might actually play a profound role in the properties of the material. Now, we have already seen what kind of phases can exist for instance we had already seen structure based definition of phases like the crystalline amorphous etcetera. We had also talked about a property based definition of phases like the ferroelectric ferromagnetic etcetera. Therefore, we are have a clear understanding of what these term phases mean, but we need to be introduced to the concept of a defect and more importantly the concept of a defect structure. And as I said it is not essential I only talk about defects I need to talk about certain further considerations about defects like the distribution of defects the association of defects etcetera. To have a first glance of what we mean by these defects these defects could imply zero dimensional defects like vacancies, one dimensional defects like dislocations, twins, stacking faults, grain boundaries, voids cracks etcetera. In other words anything which sort of interrupts my perfect crystalline order and of course, I am now considering a crystalline material whichever interrupts my perfect crystalline order can be thought of as a defect in the crystal. And suppose I am having amorphous material then in that case voids in amorphous material or crystalline regions in amorphous material could also be thought of as defects in the perfect or the existing amorphous kind of a structure. So, once I have an understanding of these three components of the microstructure the phases the defects in the residual stress then we can go ahead and try to understand how this microstructure is going to influence microstructure dependent properties. And last once again to reiterate the processing determines the shape and the microstructure of the component. In other words the scale of the microstructure is intimately related to the scale of the component. And of course, when we are doing certain processing that also tells us the kind of structure which is going to evolve. For instance suppose I am going to slowly cool a material I may get a crystalline material. If I cool it very fast then I may get an amorphous material. And after cooling it very fast suppose I heat it again I may start to produce crystallize in the amorphous material. Therefore, I need to know the thermo mechanical history of the material if I want to know what kind of a microstructure has been obtained by this kind of a processing. Therefore, this is perhaps one of the important slides in this whole lecture or this whole course because now we have now not said anything about the scale of the microstructure. We not said that it is only at the micron scale. For instance in the case of the GP zones which we talked about which are essentially copper rich regions in an aluminum copper alloy matrix they would have a length scale of the order of nanometers. Not only that these GP zones are coherent in nature that means GP zones have a residual stress field associated with it. So, this is an important concept now that we have GP zones. And these GP zones are basically both the stress associated with the GP zone. And the copper rich regions the physical dimensions of that both of these are in the nano scale. And both of these presence of both of these is going to affect the properties of the material the aluminum copper alloy which has these GP zones. Had mentioned that I have to worry about the phases present in the material, but along with it the distribution of the phases. We have already seen one clear cut example and the example was the presence of cementite in steel along the prior austenite grain boundaries that how the distribution can actually drastically alter my properties. So, for a schematic let me consider four distributions of phase B in a phase A. And in this case let me think of the phase B to be a hard, but brittle phase and phase A to be more ductile kind of a phase, but not that hard. Therefore, the black phase the region which is shown by black which is right here is my hard and brittle phase which as you can see has multiple morphologies as in the four schematic shown. Therefore, when I am talking about distribution of phases I need to know the shape of this phase B the way it is present. I when I am talking about shape it could be needle like as in this case which is typically the morphology observed in many cases. It could be spherical, it could be cylindrical, it could be irregular, it could be feather like etcetera. I need to worry about the connectivity of these phases. For instance as you can clearly see in this example which is on the top which you can see here top example. You can see that the phase A is not connected to phase A, but phase B forms a continuous network. So, I need to worry about the connectivity of these phases. Suppose I am talking about a lattice structure in this case I am talking about a lattice which is a hybrid and suppose I want to use it for filtration purposes. And therefore, in such a case I would want interconnected porosity in the material. So, that a fluid can actually be passed through this interconnected porosity or I want to store some lubricant in the system throughout the volume or I want to store some material throughout the volume. Then I need interconnected pores and if the pores are isolated then that would not help in the filtration process. Therefore, I need to worry about the connectivity of the phases. Then I need to know the spatial distribution of these phases. And suppose if this microstructure is evolving in time then I need to know the spatiotemporal evolution of this microstructure. For instance in the example we just now took of GP zones if suppose this component which has GP zones is employed in service at high temperatures. Then what would happen is that these GP zones will slowly transform into theta double prime precipitates which will later on transform into theta prime precipitates. Then finally, you will get the equilibrium theta precipitates these two are metastable phases and GP zones are metastable as well. And therefore, they will transform finally, to the equilibrium phase theta, but it would not stop there will be coarsening of theta. In coarsening of theta what will happen is that the larger precipitates of larger sized precipitates of theta would actually grow at the expense of small size theta. And in the end actually the average particle size would increase, but the inter particle or the inter precipitate distance would decrease. And we are talking about the average precipitate says. So, during the coarsening process two things would happen the average precipitate size will increase and the inter precipitate distance would decrease. And in a later work numerical example later on we will see that this is actually going to be deleterious for the hardness of the material or the strength of the material. Now, and as you have seen now that actually when you are doing the precipitation process some of the nucleation events would occur earlier and some of the nucleation events would occur later. And therefore, at any point of time suppose I freeze my microstructure and have a look then you would have a distribution of sizes. And if you look at the distribution of sizes there could be extremely small size precipitate particles as you may want to call them which are in the nano scale two precipitates which are in the micron scale. Therefore, there could be a range of sizes. So, when I am talking about distribution of phases I am talking about the spatial distribution of sizes and the frequency of occurrence of various sizes. Therefore, you can actually plot at some point of time the size which could be measured in nanometers for instance and the frequency. And you can see that there could be actually a variation which could also be thought of as a distribution of sizes. So, I need to worry about the spatial distribution of these second phase I need to worry about the connectivity of the second phase. I need to worry about the frequency of occurrence of various sizes. I need to also worry about how the what is the shape of these second phase particles. Again, if I am talking about a temporal revolution of the system with the temporal revolution the shape of these particles may also change. In for instance suppose I am talking about in some systems the precipitation of gamma and particles precipitates. This gamma and initially precipitates spherically, but later on when the precipitate becomes semi coherent or later on incoherent then it assumes a certain shape which could be cuboidal or a cube. Therefore, this spherical precipitate with time changes into a cuboidal shape and this is coming out because of the temporal evolution of the precipitate. And this is intimately related to the characteristics of the interface which could be which changes from coherent to a incoherent one. Therefore, when I am using the term distribution of phases there are multiple parameters which I need to keep in view and all these as is towards understanding properties of the material. Now, another example for instance this is the right hand example there is a this is the example of inter granular glassy field in a silicon nitride sample. This happens to be a luteatium magnesium dode silicon nitride sample and you are noting that there are these crystalline regions on the top and bottom which is labeled as green one and green two, but there is an amorphous region along the green boundary which is very similar to the continuous network of the brittle cementite along the prior austenite green boundaries. Now, suppose the silicon nitride sample is loaded sometimes in impact then it could so happen that the cracks may propagate along this glassy phase rather than actually propagating through the green. And therefore, this material may have a characteristics which is brittle as compared to if the crack was propagating in an inter trans granular mode. Now, we had considered four schematic examples and in some sense it was this example A which was exemplified in this example of steel and the case of the silicon nitride sample. One case of course, there was a crystalline phase like cementite along the prior austenite green boundaries and the second case it was actually an amorphous field. And if you look carefully the scale bar here actually this field actually happens to be in the nano scale. While the silicon nitride grains are actually large grains and they are not nano scale only this inter granular glassy film which is in the nano scale and that too in the dimension which is which has been marked in the figure. Therefore, I need to worry about the connectivity of the phase B its distribution etcetera. If you look at the figure B here exactly the two phases are present which were present in the figure A which is phase A and phase B. And for now we will consider that the volume fraction of phase B is also constant and the thing which has been altered is the shape and connectivity of phase B. And of course, you could further go ahead and even make the microstructure more complicated by changing the sizes of the phase B as well. But you can clearly see in the example B that the phase B is in this form of a needle or a lens or what you might call an highly oblate sphere spheroid in three dimensions. This kind of a morphology would mean that at the tip of these precipitate which I am marking here in a low there will be actually high stress concentration. So, let me draw that here. So, I have a precipitate which is like this and ahead of the precipitate this region acts like. So, if this acts like stress concentrator then actually cracks may propagate cracks may initiate at these regions which have been marked in this case by this circle. So, this cracks could nucleate here and therefore, propagate and lead to the failure of the material. On the other hand suppose I consider the same distribution of B in A like in the case of C or in the case of D then you notice that the same phase is in the present form of a sphere course depicted as a circle in two dimensions and in that case there is the stress concentration effect is much reduced. And therefore, you would notice that such a material the propensity for crack nucleation at the second phase particle would be reduced. But now I have two further examples or two distinguishable cases for even for the spherical case one the case D which has been shown here and one the case C. In case C and case D the volume phase volume fraction of phase B is same which as I told you is a brittle phase. But the size of the precipitate in the case of C is larger what does this mean in terms of the properties what are the now what is meant by size here. Of course, we have to compare it with certain natural length scale in the material or a natural length scale in the component. So, for now we will restrict ourselves to the natural length scale in the material. So, automatically one of the natural length scales could be the lattice parameter of phase B or it could be the lattice parameter of phase A. And typically the lattice parameter as we have seen before could be much smaller than the length scale of the phase. But there is another and but there is an important another length scale which comes into picture which is the length scale at which some of the defects in the material reside. Though we are not exposed to it at this point of time, but we will take a small peak ahead and we will see that the distribution like in the case of a D actually would give rise to a better hardening in the material as compared to a C. And we will also consider what is the origin of this kind of a hardening effect coming in the case of a distribution like D. And more importantly from this point of view of the course that suppose I keep on making the second phase or the prestate size smaller and smaller. Then at some point of time it will become in a nano scale and therein lies lot of interesting effects which we will observe as we go along. Now, when considering these phases one important thing we have ignored is the interface. The important thing is that why is interface important is because we have talked about phase A its characteristics, we have talked about phase B and its characteristics. And we have been talking about characteristics we have talked about things like connectivity shape etcetera. And we are inherently assuming that we also know everything about the bonding characteristics of the material. For instance when we talk about a brittle material it is essentially we already seen that that is coming from a comparison of the pulse stress or the inherent lattice friction with the fracture stress of the material. Therefore, we assume that I have an understanding of the bonding characteristics and I also have an understanding of the way the phases are distributed. But there is one important thing still left out before I can claim that I understand this distribution of phases which is the interface between the two materials. Suppose I am talking about loading such a material which has the distribution of phases it could so happen that there are no cracks forming in material B there is no cracks forming in phase A. But the interfacial bonding is so bad that suppose let me zoom this part out that actually an interfacial crack forms. In other words there is an interfacial debonding because of this loading. So, this debonded region has been shown in red. And therefore, in spite of a microstructure which might I am which is very desirable like for instance D which might I may use for some purpose. If the interface is not good then the properties may not be up to my expectations. Therefore, I need to understand the distribution of phases and also the characteristics of the interface. If I want to understand the complete picture for how this microstructure or actually to put it rightly the first step of understanding of how microstructures will lead to properties naturally.