 previous class, we have seen the thermodynamics associated with the metal hydrides, we have also seen the different regions in the pressure composition temperature isotherm. Now the existence of this flat plateau is under ideal condition and to hold true for some of the metal hydrides. But in many of the hydrides this is not the case, so now let us see the other exceptions as well as other cases which occurs in the real metal hydride and some of the terminologies we are going to learn in this particular class. Now we have seen in the earlier class the pressure composition isotherm and the three regions that exist. Now here this this plateau region that has its own importance, this flat plateau that we have seen when we have plotted the pressure with the concentration, this is temperature dependent. So this is drawn at a particular temperature. If we change the temperature, this equilibrium pressure, this plateau pressure will also change. Now this is a temperature dependent plateau pressure is also known as equilibrium pressure. So this has a great importance when designing the metal hydride based systems or while selecting the metal hydrides for various applications. This is known as the equilibrium dissociation pressure of hydride, this is the pressure of hydrogen in the equilibrium with metal metal hydride phases or alpha plus beta phases. This also represents the dissociation pressure of metal hydride at that particular temperature. This is a very important parameter to measure the stability of hydride because we have seen that it is also related to delta H and this is the most important region in the pressure composition isotherm. So this equilibrium pressure through want of relation in the previous class we have seen that it depends upon delta H and delta S. But delta S we know that remains constant. So this equilibrium pressure it is related to delta H which in turn is related to the thermochemical stability of the metal hydride. So thus at the operating temperature of metal hydride when we are considering a metal hydride system, a system design then at an operating temperature that is that equilibrium platu is considered that is fixed by this equilibrium platu pressure and that also decides on to the end by the overall reaction kinetics and that plays an important role. So this equilibrium pressure at a particular temperature is used while designing a metal hydride based system along with the reaction kinetics needs to be considered. So this was a pressure composition temperature isotherm which was drawn at a particular temperature. Now what happens is if we change the temperature of the system this also changes. So this is at a particular temperature at another temperature we can get another PCT curve. So this is let us say at temperature T1, T2, T3 and this is at critical temperature. So this is in the pressure is plotted as a concentration. Now we can see that as the temperature increases this equilibrium pressure this also increases and we are getting the width of the platu which is also reducing. So this width of platu region also decreases as the temperature increases. Now the important thing to be noted here is this platu tells about the miscibility regime of the two phases which is alpha and beta. So as the temperature increases and the platu pressure it increases or the platu width decreases the miscibility region of alpha and beta phase also decreases and this continues till a temperature which is the critical temperature. So TC being the critical temperature and this continues. So the width continues to decrease until it diminishes to 0. So the platu width becomes 0 and the miscibility also reduces to 0 and after that what happens is earlier we have seen there is an alpha region, alpha plus beta region and finally a beta region. So alpha in between we were getting an alpha plus beta region but beyond this critical point there is no two phase region alpha plus beta or alpha is directly converting into beta continuously. So that is the impact of change in temperature on the PCT curves. Now ideally what we should get is that a pressure composition isotherm with a flat platu. So this is how we get the ideal pressure composition temperature isotherm at a particular temperature. Some of the hydrides they still show this flat platu but most of the hydrides there is a sloping platu that is being observed and this continues to change when we plot pressure with the concentration. So this instead of getting a flat platu we are getting a slopey platu and that tells us at this is again at a particular temperature. This is in case of most of the hydrides or this is in the real case we get a sloping platu. Now this tells us that the equilibrium pressure is different here it also changes. So instead of getting a particular equilibrium pressure here different regions of the material that is having a different equilibrium pressure. Now the significance of this sloping platu is that tells us that the different part of the metal or the material or the host matrix that absorbs at different equilibrium pressure. The reason for this sloping platu is the presence of different inhomogeneities into the metal or the presence of different impurities or the presence of different stress. So these are the reasons which gives rise to a sloping platu. And we have to remember that while designing a metal hydride based system we have to consider that what is the actual platu in the case of the metal hydride being selected for that particular application. Now the another deviation from the ideal case is the presence of hysteresis. Now in ideal case what happens is like if we plot the pressure with the concentration during the absorption as we go along the curve and when we reach to the maximum pressure or the maximum absorption occurs if we want to now release hydrogen from the system or if the hydrogen is to be withdrawn from the system then we should be able to trace back the same curve or we should move on to the same curve getting back that hydrogen. The same curve is expected to be retraced back during the desorption process. That means the equilibrium pressure for absorption and desorption is expected to be the same. But in actual practice what happens is for the actual hydrides these absorption this is the absorption curve while during desorption the same curve is not retraced back rather the desorption curve it lies below the absorption curve. So that pressure and concentrations if these are plotted this is let us say absorption curve then after reaching the maximum point or the maximum capacity here if we want to the hydrogen to be released the curve that is obtained during the desorption is different or lower below the absorption curve. So this is the desorption curve or the equilibrium pressure for absorption is not equal to the equilibrium pressure for the desorption here. So the desorption platu pressure here we can see it is lower than the absorption platu pressure and this is known as this effect is known as hysteresis. When the absorption cycle or absorption curve is not matching with the desorption curve in the desorption cycle. So this hysteresis gap occurs between the absorption and desorption cycle. The reason for occurrence of this hysteresis is considered to be the plastic deformations which are not reversible because of the lattice expansion that occurs when hydrogen incorporates into the host metal matrix because of the irreversible plastic deformation in the metal matrix and this is highly undesirable in case of the use on the when metal hydrides are to be used for various applications. The reason being this interferes with the effective storage capacity but this is not an error. This is the intrinsic property of the hydride system and if we do that several times this will be retraced back or this hysteresis will be every time observed and this it is essential that while designing a hydrogen storage system we should consider the presence of this hysteresis that the desorption pressure will be different from the absorption pressure and also there will be a difference in the capacities as well. One more deviation could be that instead of or in certain metal hydrides like in iron titanium type of metal hydride it is observed that instead of having one plattue there are two plattues which are observed. So there is a plattue which is at a lower pressure one plattue at a lower pressure and then there is another plattue that could also be there which is at a higher pressure or higher concentration. Now for example for FETI we can say that there is an alpha phase which gets hydrided to form a beta phase. So that is the beta phase and this beta phase further hydrides to give one more phase which is the gamma phase and thus there are two different plattues existing. So there are two different types of hydrides. These could be monohydride and dihydride and these results into two different plattue regions. So while designing any system that also needs to be considered. Usually the monohydrides these are more so we will see later that the there may be difference in the stability of these hydrides as well and that has to be considered in a hydrogen storage system. Now we have seen that the want half plot or the want half equation in the previous class where the ln of P the pressure it is related to the delta H value. Now this delta H the first term that if we plot ln P with 1 upon T the first term will give us the delta H upon R value which is the slope of the curve. If we draw a straight line of log P with 1 upon T the slope will give us minus delta H upon R while the intercept will be given by delta S upon R. Now this term remains constant and from there we can even get the value of delta H. How is it obtained? Like these are the pressure composition isotherms which are being drawn for different temperatures T1, T2, T3, T4. Now when we get an equilibrium pressure so this is a case of a flat plateau it becomes easier because the equilibrium pressure remains constant throughout the plateau region and we have also seen that as the temperature increases the plateau pressure also increases the plateau width decreases. So equilibrium pressure here is increasing as the temperature is increasing. Now this equilibrium pressure in the middle of the plateau could be used or this value could be used or the equilibrium pressure these series of points of equilibrium pressure at different temperatures can be used to plot log of equilibrium pressure with 1 upon T and this according to this equation will be given by a straight line. So this equilibrium points pressure points when plotted with temperature 1 upon temperature at different temperatures T1, T2, T3, T4 we get a straight line having a slope of minus delta H upon R and in intercept of delta S upon R. So this slope is going to tell us what is the delta H value for that particular material and the intercept will tell us what is the delta S value enthalpy and entropy of formation. Now this it becomes very easy when it is flat plateau however if we have also seen that for in actual practice or for most of the hydride this we get is a sloping plateau. Now how to find the equilibrium pressure corresponding to that which can be used for the want of plot what has been done is when it is a sloping plateau we get a P equilibrium that also changes with the concentration. So instead of being constant it also changes with the concentration. So a particular value of H by M, a particular value of H by M is selected for that particular sloping plateau condition and usually this is taken to be the middle point of the plateau region at different temperatures like here it has been shown for the flat plateau we have taken to be the middle point same can be taken when it is a sloping plateau. So the middle point is taken as the P equilibrium at different temperature even if it is a sloping plateau. Now what if there is a hysteresis so in that case we will have a different P equilibrium for absorption and a different P equilibrium for the desorption case. So in that case if there is a hysteresis either we can consider absorption P equilibrium or desorption but for that we have to be consistent like if for a particular temperature we have taken absorption equilibrium pressure then for the other temperatures also we will have to take the same absorption equilibrium pressure only that means absorption equilibrium pressure only not the we cannot take for others desorption plateau pressure or the equilibrium pressure and that has to be mentioned while reporting the delta H value. So in this way drawing a want of plot we can get the value of delta H and delta S. Now this delta H as we have mentioned this is related to the stability of the metal hydride. If the delta H value is high that means that material or the metal hydride has a higher stability. If it has a higher stability that means we will require low dissociation pressure or high temperature in order to get the hydrogen from the metal hydride system or for the hydrogen release. So as the delta H value is higher that means higher stability and a higher temperature or low dissociation pressure is required for the release of hydrogen. However reverse occurs if like it is delta H value is low that means the system is less stable and we will require higher dissociation pressure or low temperature for the hydrogen release. Now in actual case what is required is neither delta H should be very high nor it should be very low. An optimum or a medium or an intermediate value is required for getting for having a ease of uptake and release of hydrogen from these metal hydride based systems. Now let us understand some of the terminologies which are commonly used in metal hydrides or solid state hydrogen storage systems like the term volumetric hydrogen capacity. The volumetric hydrogen capacity it represents the amount of hydrogen which is being stored in that system or in that material per unit volume that is gram of hydrogen per litre. Now if it is systems based then it will be system volume, if it is for we are reporting for material then it will be considered to be material volume. Now the amount of hydrogen that is being stored per unit volume of the bulk material is being considered when we are talking about the material based volumetric hydrogen storage capacity. Similarly we can use another term which is known as the gravimetric storage capacity and this is the amount of hydrogen which is stored per unit mass of the material. Now it can be expressed in two ways either H by M that is the hydrogen to metal atoms ratio or it can also be expressed in terms of weight percent. So weight percent here the amount of hydrogen or the mass of hydrogen divided by the mass of the material and along with the mass of the hydrogen as well where H by M is the hydrogen to metal atom ratio and correspondingly the molar mass of hydrogen as well as the material being considered. So the mass of or the weight of hydrogen being stored divided by the weight of the material plus weight of hydrogen being stored times that will give into weight percent. So if we consider now consider PCT curve or PCT diagram we can see that this is a typical pressure composition isotherm which is having a sloping platu and then there is a hysteresis as well. So this is let us say the absorption curve and then this is a desorption curve. So there exist a splattu slope there is a hysteresis and then we can identify the different terms in this PCI diagram. Now there are two terms which are related to the capacity here one is the maximum capacity which we can find out if we consider the absorption curve. So this is the maximum that it can take so this the entire this value will give us the maximum storage capacity so H by M maximum however the reversible storage capacity will be lower than this maximum storage capacity and this is the capacity of hydrogen being absorbed and desorbed between the lower and the upper operating pressures of a hydrogen storage. So reversible storage capacity is usually the width of the platu pressure which is being considered so this is in that case the reversible storage capacity given by delta H by M R. The slope of the platu is given by D ln of P upon D H by M the concentration ratio while the hysteresis between the absorption and desorption curves is given by ln pressure of absorption by pressure of desorption. So here in in a single curve we have shown the different terms and their representation in the PCT diagram. Along with that there are many more terminologies which becomes important when we consider the design of hydrogen storage system when we consider different metal hydrides like one of the most important process when metal hydrides are used for storage is the activation. Now usually these metal surfaces they are covered by oxide layers and these oxide layers are of different thickness that depends upon the synthesis method. Now presence of the surface oxide layer that blocks the hydrogen entering into the metal or it acts as a hydrogen barrier layer and does not allow the hydrogen to get into the metal to form metal hydride. So that needs to be broken for that activation is being performed this is also known as first hydrogenation. So activation or first hydrogenation is usually performed at a higher temperature and pressure so that hydrogen can penetrate inside this oxide layer could go through this oxide layer. So what happens is when hydrogen enters into this into the metal lattice there is an expansion and when hydrogen is released there is a contraction when there are several cycles of expansion and contraction occurs the metal it breaks up into the or fine particles metal particles are obtained and that the process of removing the surface oxide increasing the specific surface area creating fresh surfaces or active sites that improves both the activation and kinetics of the process. So when we are considering the design of a storage system that temperature and pressure which are required for activation the high temperature and pressure that we mentioned required for activation that has to be considered or included while we are considering the designing of such system. So the system should be able to bear those temperatures and pressure should be able to handle. Now the another terminology that we use is the kinetics and that we study in several other courses as well. We have seen in the previous class that hydrogenation of metal hydrides is a complex process and it involves several steps that we have seen before. And out of these several steps any of the steps could be a slower step so that slowest step will be the rate determining step or the rate limiting step. And the overall kinetics will be limited by that slowest step. So we can plot the kinetics of a system or a metal hydride by plotting the reaction fraction against time and the dependence of this plot on different temperatures and pressures that will be helpful in finding out the rate limiting step and that has to be considered when we are designing the system. That is important because we will see when we will learn about the designing of the system that heat and mass transport transfer that plays an important role. And metal hydride that plays an important role because one of the reaction that is the forward reaction of formation of metal hydride it is an exothermic process and the reverse reaction is an endothermic reaction. So that means heat is required for the reverse reaction and heat is released for the forward reaction. So there involves the heat of reaction. At the same time the thermal conductivity of the hydride phase is poor. So lot of thermal management is important and needs to be considered when we design a metal hydride based hydrogen storage system. At the same time we have also seen that when hydrogen enters into the metal lattice there is an expansion and when it comes out there is a contraction. So such expansion and contraction can even result into a sort of process which is could be even decrepitation or embrittlement could also be obtained. So the factors that are very important when we consider the kinetics are like what is the sample size which we have selected, whether it is a lump, whether it is a powder, what is the particle size if we have selected even the powder, what are their surface properties, whether the gas which we have used is pure or not, whether there are impurities present in the solid material which we have used the metal. So all these play an important role while determining the kinetics of the process. One more term that we use is the cycle life. Now what is expected when we design a system is that the material which is being used that should have a very high cycle life. By cycle life we mean here that the properties hydrogen storage properties should be consistent over several cycles. That means its capacity, its kinetics, reversibility, platu pressure all should remain constant when we are considering repeated cycling or it should be same during the entire life of use of that material and that system. So the desirable is that the cycle life of material should be high. Now again there are several parameters which govern the cycle life of these materials like this proportionation. Again the expansion contraction of volume if there are any impurities present in the gas if impurities are present then some of the metal hydrates they get poisoned because of these impurities and then their cycle life reduces. Whether there is a particle agglomeration that has happened, are there any structural changes or phase changes involved sometimes there are non-hydriding phases are formed or sometimes there are stable hydrides which are formed which are very difficult to dissolve under normal conditions. So all that can not only reduce the capacity but can also reduce the cycle life of the materials. So what can be done is we can improve by several ways. Substitution is one of the way of improving the cycle life. One more term that is being used is the decrepitation. This decrepitation means this is a self pulverization of the alloy that happens because of the volume change during cycling process. It is also because of the brittle nature of these hydriding alloys and this is very important that needs to be considered while designing a storage system because this decrepitation can change the way these material has been packed. Now with time what will happen is with repeated cycling the particles will break into smaller particles and that may affect that may change the porosity that may affect the gas and heat flow inside the metal hydride bed. These smaller particles they will tend to settle down into the tank or the lower part of the tank and in that case what will happen is when they settle down into the bottom part of the tank during hydrogenation again there will be an expansion of the lattice and that could even lead to after certain time bulging of the tank from the bottom or it can even lead to rapture of the tank. So in this class we have seen that ideal PCT usually have a flat plattue but a real or for most of the hydrides there is a PCT which shows sloping plattue hysteresis or there can be multiple plattues. While designing a system we have to consider all these take into account all these while considering or selection of the metal hydride. We have also seen how to plot went off plot and using that we can find the delta H value which determines the stability of the hydride or the conditions at which the hydrogen will metal hydride will dissociate to release hydrogen and we have also learned the different terminologies which are used in a metal hydride based system. In the next class we will see what are the different metal hydrides which could be used for solid state hydrogen storage thank you.