Introduction to phase diagrams

[Music] [Music] welcome to the lecture on introduction to phase diagrams so while discussing the welding metallurgy course we very much need to know about the phase diagrams now I hope that you must have some introductory knowledge about the phase diagrams in your initial courses related to material science and engineering or physical metallurgy so we will have an overview about the phase diagrams and in the subsequent lectures we will also discuss about the phase diagram of ferrous system especially the iron carbon system as well as some of the important non ferrous system also so coming to the introduction about the phase diagrams as you know the phase diagrams are the maps that give the relationship between phases in equilibrium in a system as a function of temperature pressure and Composition so what we you know expect from phase diagram what informations do we expect basically we are in need of engineering alloys we know that in most of the cases the pure metals or pure elements are less significant having less significance as far as the engineering you know use is concerned so what we do is we normally make alloys we have to add a certain element to the parent a terminal element and then we have to see that how it will behave how they are going to behave when they are combined and how the there is strengthening effect or which kind of reactions take place so all that basically as a function of temperature pressure and Composition so we with the change in composition of one element or with the variation of temperature and pressure what you know what kind of phases we are going to get in the equilibrium condition so basically phase diagrams depict about all these things coming to the you know definitions of the different terms like a phase so phase is defined as the physically distinct chemically homogeneous and mechanically separable reasons of a system so that is you know the definition of a phase and you know now if we talk about the gaseous state or you know liquid state or solid state that's what the different states of matter is when we talk about the gaseous phase so since there is mixing at the atomic level so we call it as a single phase similarly if you have a liquid solution in that case we also call it as a single phase now many a times we so that's what we have that is gaseous liquid and the solid they are forming the separate phases you have also independent chemical specie so we will talk about you know components what is component so the independent chemical species that comprise the system are the components of a system so that's what is the definition for a component and it may be elements ions or the compounds so basically there is a well-known rule given by the Gibbs and he has given the rule like F equal to C minus P plus 2 so that is you know the degree of freedom is defined as F so and so f equal to C so the amount of components minus P so that is number of phases in the system and plus 2 but we will see that how that changes because when we are dealing with these elements what happens that in many a times with change in temperature you know we will see that how you know at one point you will see that there are many phases in equilibrium so you know and if you change the parameters like you have the external variables like pressure or temperature or composition in that case how these change in phases you know are incorporated that gets reflected from the phase diagrams so now what we see that normally you have the variable of a system you have normally two external parameters and that is temperature and pressure now if C is the number of component in the system then the number of variables which are required to specify completely the composition of a phase that is equal to C minus one so for if the there are P phases in the system then in that case that will be P into C minus 1 C minus 1 means that if you know the C minus 1 you know components then certainly you know the last component so that's why the number of variables which are required to specify completely the composition of a phase that will be C minus 1 and for P phases you will have P into C minus 1 and if you take the other two external parameters that is temperature and pressure then it becomes P into C minus 1 plus 2 now degree of freedom that is defined as f so it is the independent variable among them and this degree of freedom F it cannot be more than this total number of variables that is you know P into C minus 1 plus 2 now according to Gibbs rule basically F is so Gibbs has given this F as C minus P plus 2 and here you get this F as P into C minus 1 plus two so basically this degree of freedom in that case so this cannot be more than total number of variables so basically C minus P plus two this cannot be more than P into C minus one plus two so what we can make out from this that if there is only one phase present that is P is equal to 1 in that case what you see that so degree of so in that case degree of freedom is equal to the total variable so in that case degree of freedom here it will be C minus 1 plus C plus 1 and in this case also if P is 1 so it will be C minus 1 plus 2 so C plus 1 so degree of freedom will be equal to the total number of variables and as you increase the number of you know variables so number of phases so you know in that case if you increase that in the you know if these number of phases in that you you must have you will see that there is an upper limit to the number of phases that can exist in the equilibrium so basically when you will analyze these equations you will see that how in the multi-component system we have single component system or multi component system then in that case using this formula basically you can see that at any condition at any temperature or pressure you know what will be the degree of freedom so basically how you can change either either you can change pressure or you can change temperature or you can change nothing of them because in that case the conditions will change so that is basically being depicted by these phase diagrams so now what do we will see next will be if you look at the so what we have got from here so if you try to see that if you have if you try to analyze if you see that if your number of phases is suppose one in that case your total number of variables so total you know variable that is CP into C minus one plus two so you will have you know three and if you have you know the degree of freedom so you will see that degree of freedom value will be three now if you go for the number of phases as two so you know now it will be so number of phase becomes you know two here and in that case your this one for a two component system it will be 2 into 2 minus 1 plus 2 so it will be 2 plus 2 that is 4 and for a two component system if you take 2 minus 2 plus 2 so it will be 2 so normally for 3 phases you will have the total variables is 5 and your degree of freedom becomes 1 and similarly you will have for the 4 phases you will have 6 is the total number of variable and the degree of freedom becomes 0 so so that's how you can see that how many phases can be there and at some point you will have the degree of freedom as becoming 0 so we will see that how you analyze the single component system or the multi component system and how you can discuss about you know the different traits of these phase diagrams so coming to the single component system now in this there is no compositional variable and this is basically the pressure temperature diagram for the single component system of iron and what you see that you have different phases that is alpha epsilon gamma delta and all that that is sewn in such cases and now in the case of single component system you can see the different points and you can find that what will be the degree of freedom at different points so now if you talk about so what you see is here this is for the iron and this is very clear that you have these are the solid phases and then you have liquid phase here and then you have gaseous phase at the top so when you if you are in this reason you know in that case P is 1 and this is single component system so if you go to the single component system and when your phase is 1 so degree of freedom will be C minus P plus 2 so C is also 1 and P is also 1 so in that case you will have f as two it means your the degree of freedom is 2 so now basically you can independently vary as long as you are in that single phase region that is in this region or this region or this region or this region so you can basically very either pressure or the temperature independently and you know you know you don't have you know you will be in that phase itself now if you come to when your two phases are in equilibrium suppose and that is normally along a boundary suppose solid and liquid phase is there on that so now in this case you will have two phases in equilibrium so your P will be 2 now F will be C minus P plus 2 C is 1 and P is 2 so now 1 minus 2 plus 2 so your degree of freedom becomes so only one now that means that if you are changing the you can independently change the temperature but then the pressure will automatically change so that you are still in that phase that is your two-phase rhythm that is around normally along the boundaries now if so in that case degree of freedom becomes one now if you talk about you know three phase equilibrium so three phase equilibrium suppose it is at this point suppose say now in that case your phase is three so C minus P plus 2 so P is 3 C is 1 and and so 1 plus 2 minus 3 so in that case it becomes basically F is 0 it means your degree of freedom is 0 so you if either of the you know these parameters if you change either temperature or pressure in that case you are basically going into the different phase region so you will not be at that point so normally that is indicated by a point so that is you know three-phase reason so this is about the single component system now now if you come to a two component system now in this case basically you will have three you know Campu components which are to be looked into as simultaneously one will be temperature another is president and the third is composition now that cannot that can be seen only on the 3 dimensional graph so what we do normally is that we ignore the pressure we take only temperature and composition so basically the Gibbs phase rule that is F equal to C minus P plus 2 so in that case that plus 2 will be replaced with plus 1 because we are ignoring the pressure because pressure does not presently seem to not do much of the changes so ultimately your you know for two-component system the failed diagram looks like this so f equal to C minus P plus 1 now what we see is that normally we can go for a phase diagram of one system where there is a complete liquid and solid solubility so in that case this is how the phase diagram looks like so what we will see that what we are seeing here that in this case you have this as the liquidus line and this is the solidus line this is the liquid and this is the solid so normally this is typically for that type of phase diagram where there are two materials two components you know have the solid as well as the liquid complete solubility in them now what is you know clear from this you can see that when you are decreasing the temperature from this point at this point the whole you know domain is liquid now when you come to the this zone this is the this is the liquidus line and this is the solidus line so the solidus line is separating that solid part with the liquid plus solid zone and the liquidus line is separating the liquid part with the liquid plus solid zone so when it is coming you know below this the temperature is coming below this point in that case the solid will crystallize out and so what we see is that apart from liquid you have also crystallized solid you know phases so and then you have liquid also and once the temperature reaches below this solidus line in that case it completely becomes solid state now what we need to know in this case is that you can see that you have two components one component has the melting temperature at this point another component has melting temperature at this point and as this component percentage increasing you can see that it's liquidus temperature will be going on changing now in this case we need to know a few things one is the you know when we are coming to different points then the solid which will crystallize and now this solid will have what composition and also what will be you know its fractional you know part that is formed so you know basically this is known as the tie line and this tie line is basically talking about the composition so the tie line will tell you the what will be the composition of the liquid and what will be the composition of the solid so based on the tie line you know so tie line is you know meeting here and at this point liquid is point here and the soilless point here so depending upon the tile and touching your liquid as and the solid compositions will be so that's what do you see if you have the melt of composition C not when it reaches to this point at this point this tie line is Ricci is cutting touching the liquidus line at this point so corresponding to this point this is the composition of the liquid so at this point you have liquid as well as the solid zone now the liquid zone will have the composition CL and the solid formed will have the composition CS and accordingly when you are coming at this point is completely solidified it will have the composition of C naught so the tie line will tell you the composition of the phases now another thing is that what will be the amount of solid formed a particular temperature so that is you know being calculated with the help of liver rule now the liver rule tells that you know if you have this this point you take as a fulcrum of the liver so the fraction this upon whole will be the you know part of this solid and the fraction this upon the whole will be telling you about the part of the liquid which is there so basically the line it is you know touching the liquidus line so this part this fraction will be the fraction of the solid form and this fraction will be equal to the fraction of the liquid so that you know these are the two things which we know from these you know phase diagrams the tie line and the lever rule these two you know principles are used to find the composition as well as the amount of the solid or liquid you know phases which are there so that is formed now in this case also we can apply this gives phase rule to find the degree of freedom and if you look at the reason that is if you take the single-phase reason that either solid or liquid in that case you know now that is if you put component is 2 so 2 minus 1 plus 1 so that will be degree of freedom will be 2 so you can in independently very either pressure so you will have three variables here composition of so temperature composition of phase one and composition of phase two so you know you can vary any of the two independently you know so that it is there whereas if you go to the two-phase region again in the two-phase region basically you will have two minus two plus one so there will be only once if you vary one so one of the composition will be changed so it is the same way it can be interpreted as you know we have seen in the case of binary system now in this case of proof complete solubility in the binary system you don't see a point where the degree of freedom is 0 so that's what is seen now when we talk about these you know binary systems now in such cases now what we see that we see many times the invariant reactions and you know so what happens that if you look at the phase diagrams these are the different invariant reactions which are taking place at a particular temperature and you have the different invariant reactions are like eutectic eutectoid peritectic peritectoid monotectic monitor twirl and syntactic so mostly you will have the first 5 which you will normally be looking at now in this case you will have the you know transformation from one phase to others so liquid will be converting to alpha plus beta that is in the case of you know this you will see at many places you will have the eutectic reaction taking place the liquid is there and it will be solidifying at a particular temperature and it will make mixture of two you know solid phases alpha and beta so normally what you see is in the case of iron carbon system it is at about 11 37 degree centigrade or 11 40 degree centigrade in that case the liquid is basically so if you look at so we will deal with you know the iron carbon system and what we will see so now now in this case so this way you know so this is 11 37 degree centigrade now in this case here this is at four point percent of carbon so here basically you will have the austenite plus cementite these two mixtures in this side you will have gamma and they said you will have fe3c so that will be formed and you will have this side as the liquid so that is your eutectic reaction and and in many cases in many systems you will come across so while cooling the liquid will be converting to two solid you know mixtures liquid really is converted to alpha plus beta similarly when you heat the alpha plus beta will be heated analytical ultimately at a particular temperature your liquid will be fought similarly in the case of eutectoid reaction you will have alpha converting to beta plus gamma you have a solid phase and this when you are cooling so it is giving you the beta plus gamma phase so this is happening in the case of iron carbon system also and in this case the you know austenite while being cooling it will lead to the ferrite plus cementite so that's how you know this you have these eutectoid reaction taking place apart from that you have peritectic reaction where the liquid plus alpha so that upon cooling will so liquid plus one solid phase will give you the another solid phase and while if you heat the solid phase will you know be converting to one liquid plus one solid phase so that is your peritectic reaction similarly in peritectoid reaction you will have two solid phases and that will be once you cool in that case it will be giving you another solid phase and reversibly it will be going on for the while you heat it so accordingly as you see these you know you must have the understanding about these things that when you are cooling so in this case at this point these reactions take place and you are getting liquid to alpha plus beta alpha to beta plus gamma so alpha plus liquid 2 beta similarly alpha plus beta 2 gamma alpha plus a liquid will be 2 alpha plus and the liquid alpha 1 is alpha 2 plus beta and similarly liquid 1 plus liquid 2 will be on cooling will be making you the Alpha so these are the you know different invariant reactions and they will be you know we will be facing these invariant reactions you know as we discuss the different types of you know the phase diagrams either beat for the ferrous system or the non ferrous system now you will also know you may also come across certain type of phase diagram when the solid solubility is limited in that case and also the melting point of the you know components they are not vastly different in that case a you know eutectic type of phase diagram will be obtained and that will be so if you can have the typical example which you can see will be basically the lead tin phase diagram and what you see in this case the the phase diagram will be like this so what you see here now in this case you will have so this is type of you know phase diagram which is there for the lead tin so you will have PV and SN now in this case what you see this is the example of the so this point what you see so you will have this is the alpha phase and this is your beta phase so you know what you see is your this point so this is your liquid and this is something like 327 degree centigrade and you will have this case is this is to 32 degrees and agreed now in this case what you see is this portion will be liquid plus alpha and similarly this will be liquid plus beta now in such systems and here it will be alpha plus beta now this point as we discussed this point will be your eutectic point because this liquid composition when it comes at this point so after this point when it solidifies it will make you the alpha plus beta now in these cases you have liquidus line so Lupita's line will be the the line between the liquid and the liquid plus alpha zone so your this line that is boundary between L and L plus alpha so boundary between L and L plus alpha so that will be you know the liquid as 1 similarly liquid as 2 will be boundary between L and alpha L plus beta so that will be your liquid as 2 similarly you will have solidus line and solidus line will be the basically solid as 1 and solid as 2 now solidus line is normally between alpha and you know l plus alpha so you will have alpha and alpha plus alpha similarly beta and L plus beta that will be your sorriness line so this is your liquidus line this is your solidus line apart from that you have also Solvers lines so you will have liquidus line you will have solid solidus line and also you have solvus line and the solvus line is basically s so solvus line is basically boundary between alpha and alpha plus beta so these lines alpha and alpha plus beta or beta and alpha plus beta so these lines are known as the solvers lines so you know normally you must know that in such cases what these lines are known as so these will be your liquidus lines Ln L L plus alpha similarly L and L plus beta you will have liquidus lines similarly you will have the Alpha solid phase and L plus alpha that line so that will be alpha and L plus alpha will be your solidus line here also you have cell in a slide and then if you talk about you know the alpha and alpha plus beta zone or beta and beta alpha plus beta zone in that case these lines will be talking about the solvers lines so these are some of the characteristics of the phase diagrams and we will be discussing about the phase diagrams of faris system as well as nonferrous system because we need to have you know some overview or you know you must be able to rephrase what we have studied in our earlier years and then this basically knowledge will be utilized when we talk about other metal welding metallurgical considerations or points when we go and study the different phenomena so that's about the you know phase diagram and we will further read about we will for the study about you know or interact about these phase diagrams of ferrous as well as non-ferrous systems in our subsequent lectures thank you very much [Music] you [Music]