Lecture 22

We will start lecture 22 and today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid solution and evolution of phase diagram. Today's topic is free energy and composition plots for binary solution, solid slash liquid this is G A naught liquid, this is G B naught liquid, this is G B naught solid, it was a T m B to T m A. T 2 equal to T m b. Blue line G 2 G 1 del G mix for solid solution in blue. G 2 G 1 del G mix for liquid solution, it will be green. So, G 2 G 1 del G mix for solid solution in blue. G 2 G 1 del G mix for liquid solution in blue. So, G 2 G 1 del G mix for solid solution in blue. a liquid a will be stable. So, that means, G a liquid naught I can arbitrarily choose this one as 0. For b liquid b about solid b both will coexist or they have both are stable fine equilibrium G b naught liquid equal to G b solid equal to 0 reference point is 0. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, G 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 del G mix for solid solution in blue. So, for a at T, T 2 G 1 a liquid will be stable. R x B equal to 1, G 2 S equal to G 2 liquid G B naught solid G B naught liquid equal to G 2 liquid. So, liquid pure B and solid pure B will co-exist pure metal B air melting point root T 2, that means, if I see the equilibrium, at this point my solid and liquid B will reach equilibrium. That means, I can understand the equilibrium with a dot and in the rest of the compositions, all of them will be liquid stable. That means, at a second condition. This is very important, equilibrium point. Solid and liquid composition pure B, that means, x B equal to 1. This indicates solid and liquid, both equilibrium and composition x B equal to 1, right? T versus x B just based on a two phase equilibrium. Now, let us see what will happen in T1, now in T1 what I will do is the same plot G versus T this is G A naught solid, this is G A naught liquid, G B naught solid, G B naught liquid, this is T M B, this is T M A fine. T 4 equal to T M A sorry melting point of A and it is less than T M B, melting point of B. T versus T versus X B pure A, pure B, X B equal to 1, X A equal to 1, T1, T2 or T2 melting point of B. solid solution, green line the liquid solution mixed or unmixed condition irrespective of that it has 0, for liquid for pure B, G B S is less than G B liquid. for pure A, G A L equal to S G B solid G B naught liquid, T equal to T 4 of course, for pure A, G A naught liquid, T equal to T 4 of course, see this is del G mix. This is G2 for solid, this is G3 for solid, this is G4, this is G5, this is G6, this is G6, this is G7, this is G8, this is G9, this is G10, this is G11, this is G12, this is G11. For all compositions XA equal to 1, 1 G2 solid equal to G1 solid, and delta G mix solid equal to 0 and this is equal to G A naught solid and this is equal to G A naught liquid right. So, that means, at x equal to and pure when pure A is there, then solid phase and liquid phase of course, composition to have a pure A both will be equilibrium. So, A greater than 0 equal to 1, G 2 solid is less than G 2 liquid, liquid solution stable condition 1, liquid stable till this point and then here solid and liquid B under equilibrium fine. A point set a solid and liquid, solid A liquid A equilibrium at solid will be stable solution, liquid stable liquid liquid solution. So, that means, 2 point 2 phase equilibrium composition plot. . T 5 less than T m a less than T m b ok, temperature 2nd T 2, 3rd T 4, 4th T 5, T 5. In T 5 reference value at T 5 of course, 1 atmosphere pressure P equal to 1 atmosphere. At T 5 G for B, pure B, G B naught solid is less than G B naught liquid that means, G B naught solid equal to 0. For A, pure A, G A naught solid is less than G A naught a liquid, this will be liquid, G A naught solid equal to 0, G A naught solid, this is G A naught liquid, G B naught liquid, G B naught liquid, pure B, this is pure ok, T 14, T 15, T 16, T 17, T 18, T 19, T 20, T 21, T 22, T 23, T 24, T 25, T 26, T 27, T 28, T 29, T 30, T 31, T 32, T 33, T 34, T 35, T 36, T 37, T 38, T 39, T 40, T 40, T 41, T 42, T 43, T 44, T 45, T 46, T 47, T 48, T 49, T 50, T 51, T 52, T 53, T 52, T equilibrium hierarchy or free energy hierarchy. So, X B greater than equal to 0 and 1 G 2 S is less than G 2 L, solid solution will be stable, solid solution stable condition 5, solid solution at all composition except X A equal to 1, 4th condition, liquid solution stable at all compositions except X B equal to 1 or liquid solution stable at all conditions this is condition 1, this is condition 2, this is condition 4, this is condition 5. At A due to point A due to point 2 phase equilibrium, point number let us say m and n, m and n 2 phase equilibrium, m composition pure A, n composition pure B, fine. So, at A due to point A due to point B due to point C due to point D due to point C, this is condition 1, this is condition 2, this is condition 3, this is condition 4, this is