meaning of line HE : i) line shared by phase fields of B+L, C+L, B+C+L

1. H B C b c E F G a A • meaning of line HE : i) line shared by phase fields of B+L, C+L, B+C+L ii) comp path of in the phase field of B+C+L iii) along this line, B and C are in with the melt (L) AFEG : phase field of A BHEF : " B CGEH : " C for a melt whose comp falls within the primary phase field of (for example) B, the first (primary) crystal to appear on cooling is B • projection

2. congruent melting • binary joins and Alkemade lines - binary join : a line connecting pts representing comps of crystals in the ternary (why binary join? ∵behaving like a system) - Alkemade line : a join having a boundary line joins : A-B, B-BC, BC-C, B-C, A-C, A-BC Alkemade lines : A-B (wE), B-BC (tE), BC-C (sD), A-C (rD), A-BC (ED) * B-C join is not an Alkemade line (no common boundary) → implying that there is no phase field of  Alkemade theorem : the intersection of a boundary line (or extension) with its corresponding Alkemade line (or extension) represents on the boundary line while on the Alkemade line

3. Fig. 6.19. System A-B-C with isotherms added. Fig. 6.20. isothermal section at 700°C Fig. 6.21. Isothermal section at 600°C. Fig. 6.22. isothermal section at 400°C Fig. 6.23. isothermal section at 300°C isothermalsections

4. cooling path: study in the ternary with a congruently melting binary AB compound

5. P2 P1 1) X belonging to ∆ (comp triangle) A-C-AB, final solidification at E1 L → (at TX) L+C → (along e1E1) L+C+A → A+C+AB at E1 2) Y within ∆ A-C-AB, finally at E1 L → (at TY) L+AB → (along e2E1) L+AB+A → AB+A+C at E1 3) Z within ∆ B-C-AB, finally at E2 L → (at TZ) L+B → (along e3E2) L+B+AB → B+AB+C at E2 cf) at E1 and E2, three boundary lines are approaching within a 360° range and thus the ternary liq disappears L → A+C+AB (E1) or L → B+C+AB (E2) thereby becoming invariant pts if the lines are within a 180° range → one of the phases will dissolve (or resorb) and becoming a invariant pt in an isoplethal analysis of the ternary i) the comp is in what primary field? or on a boundary line or join? ii) the comp is in which comp triangle? or on a join which is one side of a comp triangle? iii) what invariant pt is associated with a particular comp triangle?

6. cooling path: isoplethal study in the ternary with a congruently melting AB compound but a join P E

7. cooling path: isoplethal study in the ternary with a congruently melting AB compound but a non-binary join P E

8. why non-binary?: the primary phase field of B exists on AB-C, however, it cannot be described by a combination of AB and C • according to Alkemade theorem → intersection of EP with C-AB being located on an extension of EP → T decreases from P to E X : L → (at TX) L+B → (along e4P) L+B+C → (at P) B+C+AB Y : L → (at TY) L+B → (along e4P) L+B+C → (along PE) L+C+AB → (at E) C+A+AB check points !!!! 1) draw a vertical pseudo-binary diagram along C-AB 2) what happens on cooling at the point, P (explain the answer: L → C+AB+L → A+C+AB)

9. ternary cooling path for an melting binary compound AB the comp pt of the incongruently melting binary compound falling outside of its primary field so, the first solid (Xtal) on cooling at comp BC is not a BC phase but a phase of , in this case

10. [I] X : belong to Δ A-C-BC, thus final solidification at D (A-C-BC) L → (at TX) L+C → (along HD) L+A+C → (at D) A+C+BC Solid starting from C → moving to K via M → finally jumping from K to its original comp X (A+C+BC) when L reached D, invariant peritectic

11. [II] Y : belonging to Δ A-C-AB, thus final solidification at E (A-C-AB) L → (at TY) L+B → (along GP) L+B+C → (along PE) L+C+AB → finally L+C+AB ⇒ A+C+AB at E Solid starting from B → moving to R → jumping from R to J then moving to M via K → finally jumping to original comp Y (A+C+AB) when L reached E, invariant eutectic

12. [III] Z : ∈ Δ A-B-BC comp. triangle, thus final solidification at E (A-B-BC) L → (at TZ) L+C → (along KR) L+C+BC → (at R) its corresponding solid is now BC only (all the C portion disappeared, so-called resorb) → (on RG) L+BC → (along GE) L+A+BC → finally L+A+BC ⇒ A+B+BC at E Solid starting from C → moving to BC → staying at BC for a while (when L is on RG) → moving from BC to F (on A-BC) → finally jumping to original comp Z (A+B+BC) when L reached E, invariant eutectic

13. A [IV] K1 K2 K3 E1 K : comp on an Alkemade line of A-BC L →(at TK)L+C → (along RP) L+A+C → at P, the solid part composed of A+C and the rxn of A+C+L ⇒ A+BC (zero amount of C) occurring K K1 K3 K2 temp of E1 const T line temp of P

14. [V] recurrent crystallization : very strong curvature of pP, exaggerated case of [III] X : L → (at TX) L+B → (along KR) L+AB+B (at R, B completely resorbed) → (on an extension of AB-R-R’) L+AB → (at R’) contact with AB+B again (due to high curvature) ∴ (along R’P) L+AB+B → (along PE) L+AB+C → finally at E, L+AB+C ⇒ AB+C+A