Phase Diagram with Peritectic Reaction

In this example were giving a phase diagram for a platinum-silver alloy. So we're applying temperature degrees centigrade vs. weight percent of silver and we've identified the various regions and then the problem says describe the phases that form and their compositions in this case we mean approximate compositions when a 60-40 liquid is called from 1800 C to 600 C. So we are gonna start here 60/40 in the liquid phase and we're cooling it down also it wants us to explain what the peritectic reaction is and then what phases are present at the end and also how much is there so the end we're at 600 degrees and were here So as we start at 1800 and cool this liquid down remain a liquid till we get to this point at this point we start forming a solid with this composition that solid is alpha and alpha means it's a completely mixed alloy mostly platinum with a small amount of silver So somewhere around 1300 degrees maybe slightly higher than that we're going to start forming an alloy with maybe 6% of silver so around 1300 degrees C we're gonna have 6% silver the rest platinum solid forms and it's in equilibrium with the liquid and the liquid composition of course right at that point is 60% silver. Now as we continue to cool the liquid composition changes. Liquid composition moves along this line and the silver and platinum composition in the alpha solid also changes slightly increasing in silver So when we get to here so we get to slightly below 1200 °c we have the alpha solid but now at about 10% silver and the liquid composition has increased to 66% silver as we cooled down. Once we are at this temperature at this horizontal line now the temperatures gonna remain even though we remove heat and we'll get phase changes and now we start to get this peritectic reaction and that's the case were the alpha solid plus liquid react to make beta solid and beta solid then is this region here that extends all the way up just very this. It extends all the way up to here. The beta solid is a mixture that's enriched in silver and so what we're going to make at this point we're gonna make beta solid with this composition and the alpha solid and liquid gonna react to make beta solid so at the same temperature the alpha solid its composition is 10% silver and the beta solid is about 42% silver. So this is the peritectic reaction for a solid and a liquid react to form a different solid so we're using up some of the liquid using up alpha phase to make this beta phase and we're going to remain at this temperature until all the alpha phase is gone and then we have just this beta phase in equilibrium with liquid So eventually we get to the point still at approximately 1200 C now we just have the liquid plus the beta solid the same compositions here now as we continue to cool now we get into this region here which is liquid plus beta phase so if we pick some point here this is the beta composition over here is the liquid composition an eventually we're gonna get to the point where now we just have beta phase very small temperature range in here we'll just have this orange region this beta phase so approximately 1050 we just have the beta solid we just have that of course it must be at 60% silver since that's the overall composition. Now as we continue to cool and we get into this region now we have two solid phase equilibrium we reform the alpha phase and the beta phase composition increases and as we continue to move down the silver content in the alpha phase is decreasing and the silver content in the beta phase is increasing so we get down to 600 centigrade we have two solid phases the alpha solid and the beta solid now in equilibrium and from the graph roughly estimate that the alpha has 3% silver the beta 75% silver. That last part of the problem then is how much of these two phases do we have and we can just use the lever rule. This distance let me call this "a" this distance "b". The lever rule says that the distance "a" times the amount of the beta phase is equal to the distance "b" times the amount of the alpha phase. So we can just for example with a ruler measure these two distances and get the ratio of the alpha phase to the beta phase When I do that I get that the beta solid amount over the alpha solid is 2.7 which means that if we want to put this in percent amount of beta solid plus alpha solid if it adds up to one then beta is 2.7 times the alpha solid plus the alpha solid is one and so the alpha solid is 0.27 and the beta solid is 0.73. So 73% of the solid is beta 27% is alpha. So when we get to this final here of course we are closer to beta so we have majority beta. In this case 73% and 27% is the alpha phase and that's where we stopped cooling this example This whole region represents these two solid phases in equilibrium