 In this lecture, we will learn about atomic bonding. Before we learn about a structure of a material, it is very important that we learn what is happening at the atomistic scale, because atomic structure will affect the property and the behavior in which engineering material can be applied for any particular application. So, it is nothing but the bonding which holds the materials together and interaction of this electronic charges can occur by either via primary bonding or secondary bonding. In primary bonding, we have very strong interaction of either ions or atoms and secondary bonding we have very lighter or very feeble interaction between all those electronic charges. So, once we learn about atomic bonding to define the structure of a material, the structure of a material it becomes essential to know the length scale at which we are talking about the structure of a material. If you are talking about atomic scale, then atomic interactions become highly critical. So, we are looking something more at the angstrom scale. If we are more worried about molecular structure, then it becomes very essential to see what is happening at the molecular scale. And in this case, we are talking about regime of around couple of nanometers, then if you are seeing what is happening at much more bulk level say at microstructure of a material. So, in this case we are looking at around micrometers and then obviously, the bulk scale it can go from couple of centimeters. So, in that case we can see the overall bulk properties, they are dictated by what is happening at the microstructure. The microstructure will be dictated by what is happening at the molecular level and then obviously, at the atomic level. So, the structure the context of structure is very important in terms of at what length scale we are talking about this structure. And obviously, for nanostructure we are more worried about how this atomic entities come together in terms of forming nano grains, nano entities or even molecules at this particular level. So, that becomes very essential that we learn what is happening at the atomistic scale and that is eventually leading to the generation of certain properties for its particular application. Again the type the types of chemical bonding they can come under primary or these are also called chemical bonds. They can be ionic, covalent or metallic in nature we learn about all these three entities as we go along. And that involves the valence electrons to participate and that is either by sharing of electrons or by transfer of electrons or by forming a cloud of electrons. And that involves valence electrons and the core electrons or the field electrons they become part of the ion core. And then there can be secondary bonding in which we have only very weak interaction and by this somehow influence the physical properties such as surface energy that generate out of this particular bonding or even the brittle less of a particular material. And one thing to understand in the atomic bonding is that the atomic structure once we have atomic structure it forms a building block. So, that goes on constructing itself at much higher level. So, that is the reason in which that brings the criticality of understanding the atomic bonding. Because, how this building blocks are arranged it can eventually give rise to either crystalline materials. And if there is no order it can also form amorphous materials and this class of semi crystalline or quasi crystalline material as well. But, I have mainly it the way in which the bonding the atoms are come somehow arranged to form a structure it can either form a crystalline or it can form an amorphous material. So, in this case we have long range on right in this case we only have short range ordering. And the importance of this goes to may be forming certain application engineering application such as in nanotechnology of how to arrange or to how to sense properties around and make use of these structures in terms of sensing and reverting back as a switch or as a response to the input stimuli it can also it as a sensor. It can also influence mechanical properties physical properties chemical properties also it can give rise to a different combination of how the metals are formed how the ceramics are formed and how polymers eventually lead to it is own properties. So, that is how we will see in terms of how that what are the types of chemical bonding what is primary bonding and what is secondary bonding. In primary bonding we have mainly the three categories one is metallic bonding second one is ion ionic bonding and third one is a covalent bonding. So, in metallic bonding what is happening generally the metals which are electro generally they have tendency to give out electrons. So, metals will have the all the metals in the first column of the periodic table and second and third column of periodic table they have tendency to give out electrons too. So, that they can stabilize their outer most electronic shell configuration. So, like for lithium we have 1 S 2 2 S 1. So, it will try to give out its outer most shell to become lithium positive and similarly with say sodium magnesium aluminum and so on. So, there are couple of metals which will tend to give out electrons. So, these are nothing but valence electrons and these electrons now come out and they can form a kind of cloud of electrons. So, they can form a something called C of electrons around that particular atom and then. So, sodium gives become sodium plus and it gives out gives out an electron and so around all these ions we have cloud of electrons which have which are not limited to only this particular sodium atom, but to other sodium ions as well and now they are free to move throughout the entire material. So, we can see we have charges of plus this which can be sodium and then we have cloud of electrons which is roaming here without any restriction. So, we can see this is a cloud of electrons which is basically the electrons are free to move along any of these region and they are not limited. So, all the electrons can go along everywhere. Apparently, this also has to be observed that these positive ions are held because of the electrostatic interaction between this negative charges. So, it is more like a negative cloud in which you have all the positive ions which are staying there because of the electrostatic interaction between these negative ions. So, that gives rise to a stable structure. So, this negative ion is being held because of the all the positive ions which are nearby. So, in this case we are forming an electron cloud and these non-valence electrons which are still with the sodium ion they will form ion core. So, only the valence electron is free to move and other electrons they become part of the atomic nuclei surrounding it and it forms something called ion core. So, in this case what we can see there is a balance of positive and negative charges. All these negative charges are roaming around and this positive ion it is staying stationary and the interaction between this positive and negative ions causes a balance between the charges. So, this is the interaction between ions and electrons. So, it is more like electrons which act as a glue and hold the positive ions. So, interaction between this positive ion, negative ion and again positive ion and negative ion it creates a balance that holds both ions and electrons in place. That is nothing but metallic morning. So, we can see metallic morning we inherently have a metal which is a tendency to give out electrons and become an ion and all these extra or valence electrons they are now free to move around anywhere and that negative charge and the positive charge of the ion it creates an interaction and that holds everything together. Apparently the ion it has certain non valence electrons as well those and the nucleus they form the ion core and the balance between this particular ion core which is again some positive charge because electron has gone out of it and the negative charge of the electron together they interact and they render a stable structure and that interaction holds ions and electrons as single entity and that is the metallic bonding which we call. Now, on the coming to certain characteristics or properties of this metallic morning first of all these valence electrons they are free to move because they form something called electron cloud or sea of electrons and apparently these valence electrons which are free to move they get associated with multiple number of this atom or ion cores. So, first of all these valence electrons they are free to move. So, they are not limited by only one ion they are not limited by one ion they are free to move throughout and they get associated with multiple number of ion cores and these positive charge of ion core and the negative charge of the of electron it now holds everything together provides a mutual interaction and this mutual interaction is very very strong and that results a strong metallic bond. Apparently since electrons are free to move anywhere else they show very good electrical conductivity even at lower temperatures say around 300 Kelvin because the valence electrons are not fixed at certain location and they are free to move because electrons are free to move. Apparently this negative and positive charge they are they are very very strong metallic bond. So, our Young's modulus or E is very high also since the bonds are not directional because electrons are free to move anywhere else there is no directionality. So, there is no directionality and that is very good ductility, but owing to the fact that there are so many electrons which are roaming around and the nature of particular metal is electro positive it can easily donate electrons. So, once it comes in contact with oxygen or something or some oxidizing entity it becomes easily corrodeable. So, it can easily undergo oxidation or corrosion and also this serve as very good conductors of. So, we can see that valence electrons are free to move because it forms a cloud of electrons and because of that they can conduct electricity even at very low temperatures and since they are not the bonds are not directional it means the one electron is not associated with only one ion they are now free to move and that can render much more ductility to the material. Also the bonding is very very strong that gives rise to very high Young's modulus and since all these ions or metals they are the metals are electro positive in nature it means that they can easily donate an electron that creates them poor oxidation resistance. So, they can easily get corroded or oxidized by the environment at the same time they are very good conductors of heat. So, those are the characteristics of properties of metallic bonding. Now, coming to the next category of covalent bonding here we can see that in this covalent bonding we have nothing but shearing of electrons and those shearing of electrons it means now that electron is now bound to two atoms and this covalent bonding is shown when both the materials both the atoms they show similar electro negativity it means there is no tendency for any one atom to donate an electron to the other and to satisfy their outermost shell they want to shear the electron because no one wants to donate the electron they want to shear the electron. So, that they can fill out they can complete the outermost shell and then that makes it much bond much more covalent covalent in nature and that also gives rise to directionality it means that specific atoms they are limited by direction from one to another because in order to shear the electron the two atoms have to be in a certain location. So, that they can shear the electron let us take an example of silicon. So, we know the silicon has four electrons in the outermost shell and to complete the electronic structure it needs to shear electrons with the other silicon at the four ends it needs to shear four electron with the other silicon atoms. We can see there are two electrons here one electron here one electron here one electron here. So, I have silicon here silicon here. So, now the outermost shell of this particular atom is now satisfied because it is shearing electrons with the four nearby silicon and similarly this also has to go on like this in order to satisfy their outermost shell. So, for this particular silicon we can see their total number of eight electrons and now for it to form the bond say with silicon one silicon one has to be at a certain location so that it can shear the outermost electron. So, that provides a directionality to the bond. So, in this case we can see there is a directionality associated and it can form a tetrahedron with the angle of around 109.5. Otherwise this bonding may not be possible and electrons have to be at certain along certain direction. So, that it can go uninterruptedly from this one silicon center silicon to the number one silicon or from number two to main silicon and silicon to number three and silicon to number four. So, this some sort of a directionality and each atom has now four neighboring atoms and now these each electron is now restricted to only two of the silicon atoms because it has to be sheared between those two atoms. So, it creates a certain fixed directionality or a relationship. So, in this case it is resulting a tetrahedron with an angle of 109.5 and certain other examples can be silicon carbide boron nitride silicon nitride many other. We can see in this case in the covalent bonding we have shearing of electrons and because of the electrons are being sheared. So, because of the directionality of the electrons because the electrons are being sheared the two atoms have to be positioned in a particular manner that they are conducive to each other and they can shear the electrons and then because of that electrons now have a certain relationship in which only they can be unrestricted and then they have certain direction associated along these two particular atoms. So, in this particular case it is forming a tetrahedron and now owing to that since the shearing is occurring and it creates a very strong bond and there is a certain directionality and that restricts the movement of all these atoms or ions all these atoms which are shearing the electron. So, it also makes the material very very hard and since the bonding is also very very good it has a very high melting point high melting point it should be mentioned that the covalent bond is strong and extends to long range, but in case of small molecules like methane the bond may be strong, but the secondary bonds that are mind whether the material is solid or liquid at a given temperature. So, it should be clear that covalent solids are hard and not the covalent molecules. So, again the pros and cons of these materials go hand in hand that these are very good for high temperature applications. So, then this creates a need of developing new processing techniques of utilizing their melting in air and then forming some useful shapes out of it. So, it has both challenges as well as advantages opportunities because of their high temperature application, but also opportunities in processing them and generally the since because of the directionality they are also very hard at the same time they have very low ductility, because of the directionality which is associated with these particular materials. And apparently they also have very poor electrical conductivity since the electrons are somehow locked. So, we find very very very poor electrical conductivity since electrons are locked into certain positions in bonding. So, we can see the covalent bonding they are very very strong very very hard, but they have very poor ductility and because of their very stiff nature and very strong bonding they have very high melting point. And since electrons are also locked they also show very poor electrical conductivity, but one thing has to be noted that the strength of material depends on the structure of material at atomic or micro or macro scale. So, these bonding they cannot really predict whether material will be brittle or ductile or will have high strength or low strength that totally depends on how the structure of material the structure of material is developed both at nanometer scale and micro scale and as well as bulk scale. So, it is a design or the structure in which material is developing finally. So, though we say the ionic bonding or the metallic bonding or the covalent bonding is predominant in a particular material that will just tell how the bond will behave once a force is applied or how when the temperature is applied what will be their nature, but the overall properties or mechanical properties such as brittleness or ductility or even the strength of a material is highly dependent on how the structure has evolved in a particular material not really the bonding. Bonding just forms the short range order of a material and then how that short range extends to long range that is much more critical in designing a particular material. That basically tells how the properties will evolve in a particular material. So, in this case you can see for the covalent bonding that all these properties are predominant they have poor electrical conductivity, low ductility very very hard high melting point and very strong bonding, but this bonding generally is does not currently predict what will be the nature of a material in terms of its mechanical properties, whether material is brittle ductile it has low strength or high strength that is more dictated by the structure of material that will basically develop. Now, coming to the third part after metallic bonding covalent bonding now this is again one more type of primary bonding it is called ionic bonding and in this case we can see in this case we have more than one type of atom and they have difference in their electro negativity. Generally the way we can see is one atom will be from the left most side of the product table other element will be from the right side of the product table. So, because of that they will have very high difference in electro negativity. So, those metals which have a tendency to donate electrons such as metals they become cations or positively charge they donate the electrons and non metals which are on the right hand side of the product table they have a tendency to accept the electrons and they become anions. So, in one case if I have Na NaCl Na has tendency to give out electrons. So, it becomes positive plus electron and then this chlorine it accepts the electrons it becomes negatively charge it takes away it takes that particular electron. So, we have electron plus chlorine it becomes chloride ion and in turn what we get is Na plus Cl minus gives NaCl that is what we can see here and in this case we can see that our sodium sodium atom it has one extra electron in the shell whereas chlorine has 7 electrons in the shell. So, to satisfy itself this electron will be transferred here and then we get Na plus which is now 8 electrons in the outer most shell and then we have chloride which is around now 8 electrons in the outer most shell we can. So, we can see that Na has become plus and chlorine has become chloride ion. So, we have sodium ion and chloride ion to give right to NaCl. This is arising because now this has a positive charge and this chloride ion has a negative charge. So, these positive and negative charges because of electrostatic interaction they tend to attract each other. So, this has become now cation. So, sodium ion is nothing but a cation and chloride ion it has become anion and this positive and negative charges they interact with each other and they acquire stable configurations. So, we have sodium chloride sodium. So, we have NaCl Na NaCl is positively charged negative positive is negative positive negative positive negative positive. So, we can see there is a cloud of positive and negative ions. So, this cations and anions they somehow hold themselves to each other they hold on to each other because of the difference in the charges and that is again non-directional in nature because now sodium also is satisfied chloride ion is also satisfied. So, it creates a overall neutral electrical charge and there is no directionality involved in out here and that is nothing but a ionic bond. So, we can see there is a wide difference in the electronegativity sodium has a tendency to give out electrons chlorine has a tendency to accept electrons. So, sodium becomes cation chlorine chlorine becomes anion and then because of the electrostatic interaction between them they acquire stability and these charges finally give out stability by and they are again non-directional in nature. Coming to the characteristics of properties first of all they are non-directional in nature. One more thing to note is that all the positive ions they have nearest neighbors of negatively charged ions and vice versa. It means all the positively charged ions have neighbors nearest neighbors which are negatively charged and all the negatively charged ions they have neighbors which are positively charged and that creates the overall electrostatic interaction and because of that the bonding energy is generally very very high and because of that again they have high melting points and again they are pretty hard and brittle in nature and again since everything is not satisfied and there is no directionality involved and again the electrons are not really free to move along they are generally electrically and thermally insulator because there are no free electrons which are available. So, and there are no electrons which can move around the entire space freely they make very poor electrical or thermal conductors. So, that part we can see from here that there are the bonds are non-directional the binding energy is pretty high very very high because of the interaction between them and all the positive charges they have nearest neighbors of which are negatively charged and all the negatively charged ions will have positively charged neighbors and these particular materials are very hard and brittle they have high melting point and they form electrically or thermal insulators. So, we do see the contrast between the properties of the ionic bond the covalent bond and the metallic bond. So, that that part we can see in this particular case and these all are primary bonds it means the bonding between the atoms or the ions is very very strong. Now, let us come to the second part which is nothing but the secondary bonding. So, in the secondary bonding there is attraction between true charges there is no bonding there is no shearing of electrons or interaction of no shearing of electrons or donation of electrons, but in this case there is attraction between two charges which are which are separated by a distance by a distance. So, we charge of plus q and minus q that forms a dipole which is being separated by a distance d that forms a dipole of q into d and again we can see that neutral atom will not have any dipole moment and because what is happening here is we have an atom it has some positive charge and again it has some negative charge around it and the center of each and everything is the same and again the overall charges are also the same. So, what is happening there is the distance of the centers is 0. So, apparently q into d also becomes 0. So, there is no charge or dipole which is happening in the particular neutral atom, but when some external field is applied then if I apply external field the negative charges will tend to go towards this side and positive charges will try to come to this side. So, in this case we can create a dipole by externally applying a field. Apparently some atoms or molecules they have a permanent dipole like in case of carbon dioxide it is a neutral atom it does not have any dipole, but in case of H 2 O we have oxygen. So, in this case we have a permanent dipole which is in this particular direction. So, we do have dipole moment which is because of two lone pairs of electrons in oxygen atom. So, how this charges which either through when we are applying an external field or once they have permanent dipole. So, these charges somehow can interact with each other and that interaction is very very feeble it is not as strong as the primary bonding it is very very feeble interaction between those two because of the opposite charges which are separated by a distance and that forms a secondary bonding. So, that part we can see and these interactions can be defined into three categories. First one is the London charges second one is the Debye third one is the Casems also known as hydrogen bonding. So, in London forces what is happening is we have interaction between two dipoles these are not permanent dipoles, but induced dipoles. So, we have plus minus plus minus. So, interaction between these two and similarly it will go on. So, there will be some interaction at these locations. So, we have we can see interaction between two dipoles and that is called London interaction. This interaction can also happen between the induced dipole. So, we have plus and minus and between a permanent dipole. So, we can have a permanent dipole which anyway has plus and minus along certain region. So, now we have a permanent dipole and this is induced and now these two entities can interact and that is called a Debye interaction. Example can be H 2 O and carbon this carbon tetrachloride. So, we can see the interaction this is a permanent dipole and that can interact with the once we can induce a dipole in C C L 4 and that can interact and that that that will result something called Debye interaction. Then there is third type of interaction which is called K Sums interaction K Sum interaction also called hydrogen bonding. In this case we already have two permanent dipoles such as H 2 O and H 2 O. So, we can see we have oxygen and then hydrogen H again will have positive charge this will have negative charge it can again interact with oxygen which is a negative and again which is a positive charge. So, this interaction is called hydrogen bond apparently what can happen these secondary bondings are very very feeble like if we heat this particular material to 100 degree centigrade the water will convert to steam. So, we have liquid to gas transition at 100 degree centigrade. So, we have water which was liquid it has now gone to gaseous state it is just breaking the bond. So, that there is a phase transition, but at this temperature the bonding between hydrogen and oxygen is not breaking off and that is the primary bond the bond between oxygen and hydrogen is the primary bond and the secondary bonding or the hydrogen bonding is much more feeble in nature because at 100 degree centigrade that bond is particularly breaking. So, the water is converting to steam, but much higher temperature might be required to break the bond between oxygen and hydrogen which is forming the entity H 2 O. So, that part we have to keep in mind. So, apparently this secondary forces that determine the surface tension or surface energy of a material they also dictate the boiling point of liquid and again this also must be kept in mind that once we have those secondary interactions. So, in polymers what can happen it can create some secondary linking of wind of all bonding and that will limit the manner in which a polymer can deform. So, once we have those secondary linking available then that makes the polymer very hard to slip along certain directions and that makes the polymer very very brittle. So, what we can see the secondary bonding are very they may not be good once we want to deform a polymeric material and also they are also helpful in once we want to disperse an entity. So, we can take a material and it has a tendency to acclomerate then we can release those release them we can disperse them and we can reduce the surface energy by dispersing them into certain liquid media or some organic media. So, those are also required for dispersing a particular material. We can see that how those secondary bonds are very necessary in terms of using them for certain applications such as changing the surface tension or evaluating the evaluating point of a material or defining the brittleness of a particular polymer or even dispersing a particular material. That brings to now the concept of whether we can have mixed type of bonding that can occur in a particular material like in one case we can have mixture of metallic and ionic bonding. So, once we have mixture of metallic and ionic bonding. So, like in this case we need to see that we have aluminum and lithium and both both have tendency to give out electrons. So, they will give rise to metallic bond at the same time our aluminum has 3 plus whereas, our lithium has 1 plus. So, again there will be some sort of a ionic interaction between them because there are difference in the electronegativity which is 1.5 for aluminum and 1 for lithium. So, in this case they are primarily metallic as well as ionic in nature. When we once we go go with only metallic bonding like we have case of aluminum air 3 v they both have electronegativity of 1.5 and they both are now bonded by metallic bond and mixture of metallic and covalent can be a case of iron because iron it has again metallic nature. At the same time it is bonded covalently with other iron atoms and that is one more reason that it is metallic at the same time it is covalent. And because of covalent nature it has to be placed at certain location only it can be free to move around any other place or. So, the direction it between the between the iron ions or atoms has to be specific and that gives rise to very inefficient packing which is nothing but b c c for iron at the room temperature that body centered cubic at room temperature and that is very inefficient packing because of the covalent nature of the ion. So, we can see that all we can also have mixed sort of bonding it is metallic plus ionic. So, we in this case we have aluminum lithium. So, they will have both characters of metallic as well as ionic and that that part we can see with similar electronegativity we can have mostly metallic bonding and once you difference in the electronegativity it can be both ionic and metallic. And once you have a nature of metallic plus covalent like in case of iron it generally yields to a leads to a inefficient packing apparently the fraction of covalent can also be calculated. So, we can see the fraction of covalent bond that can be calculated by exponential of multiplied by delta e square delta e is the difference in the electronegativity of a particular material. And like for silicon oxide if we can take an example silicon as a electronegativity of 1.8 for oxygen it is 3.5. So, in this particular case the fraction covalent. So, once we have fraction of in case because generally the bonding will have both the characteristics ionic as well as covalent or even metallic the fraction covalent bonding can be calculated by the difference in the electronegativity. So, we can find the fraction covalent is equal to exponential of minus 0.25 multiplied by delta e square delta e is the difference in the electronegativity. So, we can see that if we have silicon Si O 2 then our silicon has a electronegativity of 1.8 whereas, for oxygen it is around 3.5. So, we can see the fraction covalent can be exponential of minus 0.25 multiplied by 3.5 minus 1.8 square and that becomes exponential of minus 0.25 multiplied by 1.7 square and that comes out to be around 0.486. So, for silicon oxide the fraction covalent is around 48.6 percent. So, we can easily see the fraction covalent bonding how much it is arising in a particular material. And now it becomes essential to learn what is the binding energy? Binding energy is nothing but energy required to make or break a bond and apparently that dictates what is the spacing that is that will arise as a equilibrium distance and which is being balanced by your repulsive and the attractive forces. So, let us see what is the overall interaction once we increase or decrease the distance and how are the forces act on a particular material. So, distance curve can be given like this that we have as we go near the near the nuclei what can happen we can express very strong repulsive forces. So, we can have we have very strong repulsive forces as we go and then we also will have some attractive forces which will predominate at higher. So, in overall we can see the overall curve will generate like this. This is a repulsive force, this is attractive force, this is our force, this is distance. These repulsive forces arise because of the interaction of two ions or nuclei. So, the the core ion core will have generate the they have the ions positive charge ions are there because of that we experience very strong repulsive force. When we reach the very nearby of the atom these attractive forces arise because of the interaction between or positive or the core and the electron cloud. So, we can see the attractive forces they vary along very long long long distances whereas the repulsive forces are predominant mostly in the nearby region of the of the of the atom. And apparently we can see the net charge which is arising in the net force it is dominated by repulsive forces in the near in the near region in the near atomic nuclei whereas it confirms to the attractive forces at certain distance later on. So, at a certain point when we have a zero force acting on a on the two nearby entities or the two nearby atoms isolated atoms. And that is becomes a stability point because below this distance we have mainly repulsive and above this one we have mainly attractive forces apparently that converts to energy. So, in this particular case when we have the minimum or zero force that gives rise to minimum energy. So, we can see our energy cause looks more like this. So, here when we see apparently when we draw it will see that the force here will be zero and that is the minimum energy that is nothing but the binding energy of a material and up and this distance energy. So, we can see that this is nothing but your energy minimum energy is nothing but the binding energy and this distance is nothing but your inter atomic spacing and in this case you will feel attraction. So, we can see at this particular level when we have exactly the lowest energy in that case we have zero force acting on the material. So, if you increase the distance or if you decrease the distance of your decrease in the distance or increase in the distance we can see an increase in the energy value that may not be very stable. So, at this exact point we have inter atomic spacing which equals to our a naught this is the minimum energy that is nothing but your binding energy or we also call net energy which is nothing but your a naught. So, we can see the combination of forces we had repulsive force and we had attractive forces that gives rise to the overall energy. So, net energy is a sum of repulsive forces and the attractive forces along the distance and that gives rise to energy of which is repulsive energy plus the attractive energy and apparently the steepness of this curve is also very critical of how deep this particular curve goes what is the ratio of this particular force to the slope of this particular force by distance curve. So, we can see if our slope is pretty high and our slope is pretty low. So, we have force and distance and then we have energy very steep. So, in this case we can see over d f by d r it is very very steep. It means we require very high force if we want to bring a change in the distance or in other words the bond is very very strong in this case and we require very high energy if we want to separate the materials or we want to bring them much closer. So, we have to spend very high energy and in this case we have very weak bond and if we see out here in this case we have very steeper or very very deeper trough. So, in this case our binding energy will be very very high had we had a shallow it means our binding energy is very very low. So, generally when the binding energy is very very high it means we generally have very high melting points and apparently the overall stiffness of the material is also very very high when we have a steeper and since we have to spend very high energy in order to make them go apart in order to in order for atoms to go apart or come closer they also have very low coefficient of thermal expansion. So, when we have very steeper steeper curves like in this case we have this one is like that. So, they will have very high force is required to change the distance they will have very high stiffness they will low coefficient of thermal expansion and generally they have very high melting points. So, we can see that that is how is basically occurring in the material. So, we can see the comparison of properties between them the coefficient of thermal expansion it is dependent on how much force or how much energy is required in order in order that atoms can go further and further. So, that is dictated by the overall steepness of the slope of the curve in the force distance. So, as the force distance curve is very very steep we will have lower and lower coefficient of thermal expansion and that will again will have very high stiffness very high modulus of elasticity similar to the rate of stiffness and again melting point is dictated by the kind of binding energy and that is that has to be much more steeper in order to have a very high melting point. So, the typical bonding energies of metallic materials it range ranges between around 150 to 370 if we take kilo calories per mole it can again be kilo joules per mole. So, for metallic it is around 600 to 1000 kilo joules per mole for ionic it is for the ionic. So, we can see the energies of the binding energies or the bonding energies of metallic materials it ranges between 25 to 200 kilo calories per mole or from 300 to 850 kilo joules per mole for ions ionic it might range from 150 to 370 kilo calories per mole that converts to around 600 to 1000 kilo joules per mole for covalent it can be 125 to 300 again that is approximately 450 to 700 kilo joules per mole and secondary bonding it is very very feeble in nature. So, it can range up from 10 to around 45 kilo joules per mole. So, that part we can see the how the bonding energies are very very high for the primary bonds whereas, for secondary bonding it is very very feeble around 10 times less than that of a other type of a primary bond. So, in summary we can we have learnt how the primary bonds are generated in terms of metallic covalent or ionic and how each and everyone has a different characteristic in itself. And again coming to secondary bonding we have Debye interaction London interaction and Kassum interactions and how these values are much more feeble there were 10 times lesser than that of a primary bond. And again the characteristic of metallic bond is very very different in this case we see a C of C of electrons and ionic bonding we see a donation of electron and acceptance of an electron in covalent there is a shearing of an electron. Apparently then the force distance of force energy energy distance curve also play a very strong part in terms of defining what will the stiffness of the stiffness of the material what will the coefficient of thermal expansion and again what is the what is the modulus of elasticity what is the melting point. So, all these things are very very important in very very important in dictating them design of a material and those are being defined by the force distance or energy distance curves. So, we can see those dependences out here. So, the depending on how the force distance curve and energy distance curve behave at more fundamental level and they dictate the overall performance of the material. So, with this particular summary I will end my lecture here.