 phase transitions of end members, binary or ternary compounds SiO 2 :  -cristobalite → (1470°C) tridymite → (870°C)  -quartz AC :  -AC → ( 1000°C)  -AC ABC :  -ABC → ( 1100°C)  -ABC, the transf temp line is wrong ! the temp of transf be as it is in the pure one, two or three comp phase

 review and summary of factors in the isoplethal study 1.what is the original ? 2.the original comp in which ? or on a boundary line or invar pt? 3.in which ? 4.where is the associated pt? and where it finally ? 5.in moving toward a boundary line in a primary field, it moves on a line away from the primary field comp pt and the lever rule applied 6.when the crystallization path intersects the boundary line, do two phases crystallize together or does one phase resorb? use to the boundary 7.when the liq proceeds on boundary line, what is the corresponding ? 8.be alert for cases where one phase is completely resorbed 9.be alert for cases where the crystallization path goes through a reaction pt (U, R) or a peritectic pt (P) 10.during final crystallization, above the temp of the invar pt and below 11.be careful to determine what phases crystallize or resorb at a peritectic pt 12.the phase analysis diagram may be constructed for help i) be able to follow the cooling paths at fixed comp ii) be able to draw isothermal sections at various temp iii) be able to draw vertical sections, very difficult !

liquid immiscibility ternary T1T1 L1L1 L2L2 A+B L 1 +L 2  K ( pt)  the immiscible region narrowed by adding comp, C K

real examples of monotectic system

 a typical case of liq miscibility gap in the ternary K’ (max temp) in the binary, but can be in the ternary a dome removed tie line ? tie line difficult to know the exact trajectory but should be inside the dashed line passing the pt, K

1) comp, Y : finally at E, A+B+C initially btw T 1 & T 2, L → (at T Y ) L+C → (at pt, a, T 2 ) Liq touches the dome → (at T 3 ) C+L 1 (comp, b’ )+L 2 (comp, b’’ ) → (at T 4 ) still inside C + L 1 (comp, c’ ) + L 2 (comp, c” ) → (at T 5 ) C+L 1 +L 2 ⇒ C+L(d”) again in a 2-phase region → (until T 9 ) still inside C+L and at T 9, touching the C+B+L → (along 9-E) C+B+L and finally at E, C+B+L ⇒ A+B+C 2) comp, b : initially in a single L phase → (at T b, when the dome touches the point of b) L 1 +L 2 → (at T 3 ) L 1 +L 2 +C → (at T 5 ) L+C → (along 9-E) L+C+B and finally at E, C+B+L ⇒ A+B+C b b’ b” l2l2 l1l1 c a Y T2T2 T3T3

[L 1 +L 2 ] [C+L 1 +L 2 ][C+L] [B+C+L][A+B+C] [L] b B A C C+L 1 +L 2

 when the miscibility gap covers primary phase fields

l2l2 l1l1  when the miscibility gap covers two primary phase fields isotherms being plotted they are, too note : the tie-lines are isothermal in the miscibility gap ∴ the k’k” line that meets the e 1 E line is isothermal, i.e. 4-phase equil of L 1 +L 2 +A+C X : L → (at T X ) L 1 +L 2 → (somewhere) L 1 +L 2 +C → (at T k ) L 1 (k’)+L 2 (k”)+A+C → here, L 1 disappears → (along k”E) L+A+C → at E, A+B+C Is the temp of the k’kk” line lowest in the miscibility gap ? e1e1 k’ k k” E L 1 +L 2 L 1 +L 2 +A L 1 +L 2 +C k k’kk”

 the cooling study of the alloy (x) assuming T e1 >T e2 >T e3 >T E X L K L2L2 L1L1 T k’k”