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1、4INTERNAL STABILITY4. INTERNAL STABILITY -EQUILIBRIUM -Chord role Phase diagramTheory of Phase Transformation in Metals124L. Lu (2010) 4.1. Introduction to phase diagramspgPhase diagrams illustrate equilibrium phase presented in differentconditions. There are basically two kinds of phase diagrams, n
2、amely,binary and ternary phase diagrams.Binary refers to two elements while ternary to three elements. Abinary phase diagram can be expressed by a 2D graph while ternaryy pgpygpyis represented by a 3D graph.Theory of Phase Transformation in Metals125L. Lu (2010) 4.1.1 Binary phase diagramy pgWilliam
3、 D CallisterTheory of Phase Transformation in Metals126L. Lu (2010) William D CallisterWilliam D CallisterTheory of Phase Transformation in Metals127L. Lu (2010) William D CallisterWilliam D CallisterTheory of Phase Transformation in Metals128L. Lu (2010) William D Callister4 1 2Ternary phase diagra
4、m4.1.2 Ternary phase diagramGT TiTi lBACTernary phase diagrams (F 1.40 & 1.41, Porter & Eaterling)Theory of Phase Transformation in Metals129L. Lu (2010) Ternary phase diagrams (F 1.40 & 1.41, Porter & Eaterling)4 2Equilibrium4.2. EquilibriumIf elements A and B do not have the same crystal structure
5、s in their pure state at a given T, two energies must be considered.cGBfGmixaa bbbGmixABXXXTheory of Phase Transformation in Metals130L. Lu (2010) Chord RoleThe molar free energy of a two-phase system as function ofcomposition of the total system is given by the chord connecting thecomposition of th
6、e total system, is given by the chord connecting themolar free energy points of the two constituent phases.fGMolar free energy of ef G( + )?o aee e e gy o a two phase mixture. (F 1.26, Porter & Easterling)d Gg)d gabc BX0 BX BXABTheory of Phase Transformation in Metals131L. Lu (2010) BBXBXBAB BX BXWi
7、th pure componentSolutions of componentsGGXBXBTheory of Phase Transformation in Metals132L. Lu (2010) (F 1.27, Porter & Eaterling) 0G 0GG 0GGG 0GGGG1G 1G 1G eG0 eGGGAX0X0ABABGe B1X 01eX 0eABABConsider now allay X0, G0 G0G1, material contains 1+ 1is more stableHoweverG can be minimized if the materia
8、l contains thestable. However, G can be minimized if the material contains the composition eand e.GGGe Tm,Aand Tm,BT Tm(A) T2 Tm(B) T3GGT1T2abcdXBS lidSolidLiquidT1GT3T2T3 3ABTheory of Phase Transformation in Metals144L. Lu (2010) 4.3.2. ImmiscibilityGM = RT (xAlnxA+xBlnxB) + xAxB4000450030003500J)x
9、AxB150020002500Hm(JA B500100015000 00.20.40.60.81XTheory of Phase Transformation in Metals145L. Lu (2010) XBxB500000.20.40.60.81-1500-1000-500K-1)-2500-2000opy (J K-3500-3000EntroRT (xAlnxA+xBlnxB)5000-4500-4000-5000Theory of Phase Transformation in Metals146L. Lu (2010) xBGM = RT (xAlnxA+xBlnxB) +
10、xAxB000.20.40.60.81B-100)-300-200(J/mol)-500-400 Gm-600500-700xB,1xB,2Theory of Phase Transformation in Metals147L. Lu (2010) G1200 K0)21(1 B BBBMxxxRTxG1000 K 1000 K800 K1000 K800 KT1+ 212500 KxBxBMiscibility gapTheory of Phase Transformation in Metals148L. Lu (2010) 4.3.3. Spinodal pointsG112GGM 2
11、1122BABM xxRTxGx xBTheory of Phase Transformation in Metals149L. Lu (2010) TS id l li1+ 212Spinodal line1 2xBMiscibility gap with spinodal lineTheory of Phase Transformation in Metals150L. Lu (2010) http:/math gmu edu/sander/movies/spinum htmlTheory of Phase Transformation in Metals151L. Lu (2010) h
12、ttp:/math.gmu.edu/ sander/movies/spinum.html4.3.4 Systems with a Miscibility gap(F 1.30, Porter & Eaterling)yy g pLiquid:GGTT2Liquid: Approximately idealSolid:abcdXBGGT1T2Solid: Hmix 0Ad BabcdBSolidLiquidA and B: Dislike each otherqu dLiquidT1T2GabcdT3Complete soluteLiquidadSolidT3 ee ffABTheory of
13、Phase Transformation in Metals152L. Lu (2010) If a system with a miseibility gap is considered, the solid phase Hmix 0, i,e. the A and atoms dislike each other. Therefore at low T3, thefree energy curve for the solid assumes a negative curvature in themiddle, and the solid solution is most stable as
14、 a mixture of twophases + The effect of a positive Hin sold is alreadyphases + . The effect of a positive Hmixin sold is alreadyapparent at higher temperature where it gives rise to a minimummelting point mixture.Theory of Phase Transformation in Metals153L. Lu (2010) 4.3.5Simple eutectic system(F 1
15、.32, Porter & Eaterling)T1T2T3GGGSLSLSLLLAAABBB+ 1L1L+1LL+T5T4SLLT1T2TGGatureS SL+L+T3 T4T5TemperaAAABBB1L+1L+11+The formation of a eutectic system is associated with Hmix. Ifis much larger than zero, the miscibility gap can extend into the liquid phase where eutectic reaction takes placeS mixHTheory of Phase Transformation in Metals154L. Lu (2010) place.(F 1.33, Porter & Eaterling) T1T2T3LLL LTAAABBBT1T4L T2T3T4Theory of Phase Transformation in Metals155L. Lu (2010) AABB(F 1.34, Porter & Eaterling)T1T2T3 ll+lllll+ +lAAABBB T1T4T5llT5T4T3T2lll+l l+T5
