welcome to my youtube channel modi mechanical engineering tutorials so in this video i would like to explaining in details on cooling co4 binary alloy which forming a solid solutions so in this case of the binary alloy that means it will be the two component systems so that will be having let's take a one examples so metal a metal a that will be having a melting point around 1000 degree centigrade and metal be 700 degree centigrade so here that will be the binary alloy that will be made of the a and b so which forms or new materials or you can say new solid solutions a b so that will be the talking about the how the cooling curve of this binary a b materials it will be going to be changed so for better understanding of the cooling cow so as you can see it will be making the one plot so here that will be the x axis that will be representing as a time and this y axis it will be representing as a temperature in degree centigrade so for making a cooling curve for binary metal alloy a and b as you can see so according to the range of the melting point of both the binary alloys so here that will be the maximum is 1000 so let's take on points onto the y-axis 200 400 600 800 1000 one two double zero and one four double zero and the x x-axis that will be the time so according to the given melting point of a and b so just you can make a point for a so that will be the point a so just you can make a one dotted line melting point of a materials and according to the given conditions or given assumptions metal b that will be having a melting point around 700 so just you can make a point at 700 so here so once again make a one horizontal dotted line so that would be representing as a melting point of b so for the cooling cows that will be the equilibrium conditions like that from higher temperature to slow cooling at your room temperature how it will be going to be change the different kind of phases with respect to the different temperatures with respect to time so that time temperature and phase it will be representing as a cooling cow and here that will be the two component system so it will be called as a binary alloy and forming a solid solution or you can see single phase solid solutions so as you can see here at higher temperature so we are considering at one four zero zero degree centigrade temperatures so we all know at higher temperatures both the metals a and b which will be into the liquid phase so at your above the melting point of both the metals so here that would be the melting point of a and b so the highest that will be the one thousands or you can considering as more than 1000 degree centigrade both the matters it will be in the form of the liquid state so in any binary alloy in the form of liquid state which will be having a 100 solubility say at point a which will be representing as a 100 percent liquid material so for any composition of a or b that will be following such kind of cooling cause for the binary alloy so let's take at point a and that will be representing as a hundred percent liquid now according to the cooling cost that will be the slow cooling with respect to the time so just you can see cooling of binary metal a b so up to the point b so that point or you can say that cooling lines which will be intersect the line of the melting point of any of the two materials so which will be having a higher melting point first that will be the starting point of the solidification or by the cooling of ab materials to the room temperatures so first of all that will be intersecting at one point which will be having a higher melting point so here the metal a which will be having a higher melting point around 1000 degree centigrade so around 1000 degree centigrade that will be the starting point of the solidifications as you can see so at point b it will be the temperature at which the solid tiny particles it being forms so for understanding the microstructure at point b so just you can see these particles it will be called as a formation of nuclei or you can say that will be the tiny particles or you can say starting point of the solidifications so basically at metal a which will be having a higher melting point or can say around 1000 for a so this nuclei it will be from metal a materials so in general case which metal of a and b which will be having a higher melting point that will be the point of the stratification you can say that will be the starting point of the solidifications so at point b the starting point of the solidifications here with the example of metal a once again the cooling towards the room temperatures you can see so from b for slow coolings so from b to c it will be look like this because of the both the metals that will be having a different melting points so once again the solidifications it will be going on up to the point c so point c that will be the temperature of your another metals so here that will be the melting point of metal b so around 700 degree centigrade so point c that will be representing as an endpoint of solidification so if you want to talk about the microstructure at point c so let us see at point c so what happened at point c as you can see so that will be representing as a endpoint of the solidifications or you can see from b to c all the liquid form of a and b that will be converting into hundred percent solid so at point c that will be 100 percent solid so it will be making a alternate layer of metal a and metal b so during b to c all the liquid form of a and b which will be converting into the solid so just you can see for a 2b regions so here for a to b regions or can say a to b solidification process that will be 100 percent liquid but which liquid that will be a plus b and for b to c here that will be liquid plus solid for a plus b and just you can see for third or you can see from c point to d point you can see from second melting point of the any metal towards the room temperature so that would be point number d which will be also considering as a hundred percent solid of a material plus b material so that will be the similar kind of structure is being formed at point d but just it will be the rearrangement of the structure of the solid materials of a and b so up to c to d that will be 100 percent solid of a plus b so in the cooling of the binary alloy so just change into the middle area or you can say from b to c regions so in case of the previous theory of the solidification of your metal or you can say single metal so that would be constant temperature solidification process but here b2c that will be not at your constant temperature process so now we will see or you can say we will validate this cooling code for binary alloy by gibbs phase rule so let us see the gibbs phase rule so according to the gibbs phase ruler can say modified equations of the gibbs phase rule so modified equations that would be considering as a constant pressure process so over all the cooling process or you can say heating process it always performing at one atmospheric constant pressure so we are always using the modified gibbs rule so and that will be p plus f that will be equal to c plus 1 where p that will be representing the number of phases f that will be degree of freedom and c it will be the number of component systems so let us start with the different regions of a b b c and c d now for region a to b and apply the gibbs phase rule so p plus f that will be equal to c plus 1 so just you can take p over here a to b that will be 100 percent liquid we already discussing that of a and b or you can say at your liquid state both the matters it will be in the form of the single phase so p is equal to 1 then f we need to identify and see here that will be the binary alloy so always c that will be having a 2 so 2 plus 1 so just you can see f is equal to 2 so just you can note down f is equal to 2 for the a to b regions so what it means to it will be having a two variables it will be effect onto the phase so here the two variables one is the temperature so temperature and composition it will be changing without changing the liquid phase so just again so it means that temperature and composition is changing without changing the liquid phase so during a to b it will be not changing the liquid to any other phase so just it will be drop down the temperature and it will be if you are also changing the weight percentage of a and b so this line it might be change right now talking about b2c regions and apply the gibbs phase rule so for b2c regions it will be having the two phase liquid plus solid so p is equal to 2 plus f see once again that will be the two component systems because of the binary plus one so finally you will get f is equal to 1 so f is equal to 1 that means that it will be having a single variables so according to the cooling curve of the binary load for b2c regions only temperature it will be dropped down because at your point number b that will be representing at the starting point of the solidifications so once it will be start the solidification process so it will be fixed the compositions so only temperature is going to be change with respect to time and our liquid phase that will be converting into the hundred percent solid at point number c so b2c that will be only having a single degree of freedom and that will be temperature now apply for the c2d regions once again p is equal to 1 because that would be the hundred percent solid one plus f see that will be the two plus one so f is equal to two so just you can note down f is equal to two so similarly the temperature it will be changing from 700 to the room temperatures or you can say temperature is dropped down compositions it will be also changed or you can say rearrangement of the solid structure without changing the solid phase so this cooling curve of binary alloys which will be also validated by the gibbs phase rule so i hope you understand this theory for the cooling of the binary alloy to forming a solid solutions so basically solid solutions it will be having a different kind of tendency so here that will be the case of the solubility of both the metals a and b which will be having a hundred percent solubility which each other into the liquid state as well as into the solid state if that solubility it will be changed so that will be having a different graphical representations or you can see cooling cause so i hope you understand this theory so if you like this then subscribe and share modi mechanical engineering tutorials thank you so much and keep watching