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1、Chapter 1. Thermodynamics and Phase DiagramsProf. Dr. X.B. ZhaoDepartment of Materials Science and EngineeringZhejiang University1Chapter 1 : Thermodynamics and Phase DiagramsHomogeneous Systemwith the same physical and chemical propertiesHeterogeneous Systembeing made of several phases1.0.1 Thermod
2、ynamics Systems2Chapter 1 : Thermodynamics and Phase DiagramsqOpen System can exchange mass, heat and work with its surroundingsqClosed System no mass exchange, heat and work exchange possibleqIsolated Systemno mass, no heat, no work exchange3Chapter 1 : Thermodynamics and Phase DiagramsA. Energy, H
3、eat and WorkThe energy of an isolated system is constantThe work done on a thermally isolated system is independent of the type of work and the route1.0.2 The First Law of Thermodynamics4Chapter 1 : Thermodynamics and Phase Diagramsisolated systemW = 0, E = const.closed systemD DE = Q + WQ 0, system
4、 receives heatQ 0, work is done on the systemW 0, D DS D DS eadiabatic process : D DS e = 0, D DS = D DS iirr. adiabatic process : D DS 0rev. adiabatic process : D DS = 011Chapter 1 : Thermodynamics and Phase DiagramsThe Second Law of ThermodynamicsThe entropy of a closed system can not decrease.Cla
5、usius:Heat can not flow automatically from cold side to hot side.perpetualmachinestype IPlanck:Such a process is impossible if its only result were to exchange heat to work.type II12Chapter 1 : Thermodynamics and Phase DiagramsMr. Tompkins in PaperbackG. GamowCambridge University Press, 1965Heat can
6、 not flow automatically from cold side to hot side !13Chapter 1 : Thermodynamics and Phase DiagramsPhase :a portion of the system whose properties and composition are homogeneous, and is physically distinct from each other.A given system can exist as a mixture of one or more phases, which can change
7、 into a new phase or mixture of phases.Why ? the initial state of the system is unstable relative to the final state1.1 Equilibrium in a Closed System14Chapter 1 : Thermodynamics and Phase DiagramsHow is system stability measured ? by its Gibbs free energy (at const. T and P)G = H - - TS(1.1)H: a me
8、asure of the heat content of the system ( H = U + PV )S : a measure of the randomness of the systemlow T : TS small, solids are most stable(strongest atomic binding, low H)high T : TS dominates, liquids or gases are stable (atoms more free, high S)15Chapter 1 : Thermodynamics and Phase DiagramsStabl
9、e, Metastable and UnstableGdG = 0BACdG = 0dG = 0an arbitrary state parameterBACStable: graphite, single crystal siliconMetastable: diamond, amorphousUnstable: super-cooling liquid (nucleation)BAC16Chapter 1 : Thermodynamics and Phase DiagramsPossibility and Realizability : Thermodynamics and Kinetic
10、sGBACG1G2Energy HumpD DG = G2 G1 H solidsince G = H - TSG liquid G solid at low TG liquid G solid at high TTmD DHmat Tm : H liquid - H solid = D DHmG liquid = G solidsolidstableliquidstableHG22Chapter 1 : Thermodynamics and Phase Diagrams1.2.2 Effect of Pressureg-irond-iron-irone-ironliquid ironTPCl
11、ausius-Clapeyron equationg gd da ae eLTPL Sd d g gg g a aD DV- - -+ +D DH- - - -dp/dt+ + +- -23Chapter 1 : Thermodynamics and Phase DiagramsTmTD DGGGSGLFree energiesat Tm1.2.3 The Driving Force for SolidificationG L = H L - - TS LG S = H S - - TS SD DG = D DH - TD DS = 0for most metalsL R (8.3 J mol
12、-1K-1)at T with small D DT , ( Tm - - T = D DT )can be ignored, D DH & D DS independent on T difference on 24Chapter 1 : Thermodynamics and Phase Diagrams1.3 Binary Solutions1.3.1 The Gibbs Free Energy of Binary SolutionsXA mole AXB mole BXA + XB = 1MIX1 mole A+BG1 = GAXA + GBXBG2 = G1 + D DGmixD DG
13、mix : mixing free energyD DGmix = D DHmix - TD DSmix 25Chapter 1 : Thermodynamics and Phase Diagrams1.3.2 Ideal SolutionsD DHmix = 0 D DSmix = - -R ( XAlnXA + XBlnXB )D DGmix = RT ( XAlnXA + XBlnXB )Note: Since XA and XB are 1, D DSmix is positive,D DGmix is negative.XB01Molar free energy GGAGBG 0D
14、DGmixAt higher temperatureLow THigh Tmixing free energy D DGmixXB01the absolute free energy is not of interest!26Chapter 1 : Thermodynamics and Phase Diagrams1.3.3 Chemical PotentialMulti-ComponentSystemdnAconstant T and Ptotal free energy of the system : G G + dGif dnA small enough, dG proportional
15、 to dnA, or : dG = mAdnADefinition:Chemical potential , orPartial molar free energyNote:G: total free energy of the systemG: molar free energy (one mol)27Chapter 1 : Thermodynamics and Phase Diagramsgeometric meaning of chemical potentialABXBm mAm mBGGBGART lnXAfor ideal solutionRT lnXBfor ideal sol
16、utionGtangent line at XB28Chapter 1 : Thermodynamics and Phase DiagramsDHmix : calculated from the nearest neighbor bonds and their bond energies1.3.4 Regular Solutionsideal solution :DHmix = 0 , not true for most (if not all) solutionsregular solution : a simplification of real solutions with DHmix
17、 0 ABABABABAAABBABBBAABA-AA-BB-Be eABA-Be eBBB-Be eAAA-Aenergybond29Chapter 1 : Thermodynamics and Phase DiagramsA-AB-BBeforemixingBBAAA-BBABAA-BAftermixinge eAA + e eBB2e eABEnergy change per A-B bond : e e = e eAB - - (e eAA + e eBB)AB bonds per mol : PAB = Na z XAXBTherefore : D DHmix = w w XAXB
18、, where w w = Na ze e 0D DHmixXB1w w 30Chapter 1 : Thermodynamics and Phase Diagramsw w e eABA-B bond preferredXBD DHmixTD DSmixD DGmixw w 0, High TXBD DHmixTD DSmixD DGmixw w 0e eAA, e eBB 0, High TXBTD DSmixD DHmixD DGmixw w 0, Low T31Chapter 1 : Thermodynamics and Phase Diagrams1.3.5 ActivityIdea
19、l Solutions A = GA + RT lnXA B = GB + RT lnXBReal Solutions A = GA + RT lnaA B = GB + RT lnaBABXBm mAm mBGGBGART lnaAfor real solutionRT lnaBfor real solutionGtangent line at XBD DGmix32Chapter 1 : Thermodynamics and Phase DiagramsDefinition of activity coefficient : g g = a / XXNiFeNiaNiRaoults law
20、Herrys law1873KHerrys law:g gB B = aB B / XB B const.Raoults law:g gA A = aA A / XA A 1dilute solutionof Ni in Fedilutesolutionof Fein NiHerrys law and Raoults law apply toall solutions when sufficiently dilute33Chapter 1 : Thermodynamics and Phase DiagramsXZnPbZnaZn1080K1180KRaoults law34Chapter 1
21、: Thermodynamics and Phase DiagramsABb ba aNear pure A : a a phaseNear pure B : b b phaseSolution X0 ? X 0if a a1 + b b1a a1b b1Lever Ruleamount of a a1:amount of b b1:Molar free energy of a a1 + b b1:free energy will be decreased If pure a a (or b b ) a a + b b 1.4 Equilibrium in Heterogeneous Syst
22、ems35Chapter 1 : Thermodynamics and Phase DiagramsCondition of Equilibrium in a Heterogeneous SystemABX 0b ba a11For alloy X 0 : G0 G0 G1 , (1+1) is more stable However, G can be minimized if the alloy consists e and eeePQWhat are point P and Q ?P, Q are two common tangent points on both G curvesfor
23、 alloy between andGe on the common tangent is minimum36Chapter 1 : Thermodynamics and Phase DiagramsHeterogeneous EquilibriumCondition of Equilibrium in a Heterogeneous System continue : about the common tangent lineABa aPand :Chemical potentials of component A and B in phase with the composition of
24、 and :Chemical potentials of component A and B in phase with the composition of b bQ37Chapter 1 : Thermodynamics and Phase Diagrams1.5.1 A Simple Phase DiagramABTLSA and B are completely miscible in both the solid and liquid states and are both are ideal solutions, such as Si-Ge, Au-Ag systems.T1T1:
25、 GL GS, liquid is the stable phase;ABGT2T2: GL = GS for pure A, melting temperature for A;T3LST3T3: GS GL when xB GL when xBx2, liquid stable, for x1 xB 0, Au and Ni atoms dislike each otherq at higher temperature (solid): DGmix= DHmix - - TDSmix 0, miscibility gap: (Au) + (Ni)q even above the gap:
26、Au, Ni repel each other, solid disrupted below 1064 C, a minimum melting pointq other systems: Cu-Pb, Cu-Ni, Cu-Mn, NiO-CoO, SiO2-Al2O3, etc. spinodal decomposition39Chapter 1 : Thermodynamics and Phase Diagrams1.5.3 Co-Sb SystemEutectic ReactionDHmix 0, the miscibility gap extends into the liquidPe
27、ritectic Reaction, DHmix 1%, the solid solution can not be treated as a dilute solution.modifying39601.4CuAg85203.0FeCu21605480217059005120432047900.811.80.772.51.72.51.4CdNiSbCoSiPbAgsolutePbPbPbAuAlAgCusolvent45Chapter 1 : Thermodynamics and Phase Diagrams1.6.2 The influence of particle sizes on t
28、he solid solubilityBulk a aSolid solution a a: atomic weight M, density r, interface energy gSpherical a a particlerdm(gram)dG = ?Bulk free energy change:Free energy change caused by the increase of the surface area of the particleIn the equilibrium condition, dG1 = dG2For a dilute solution (Thomson
29、-Freundlich equation):Significantly if r 100 nm46Chapter 1 : Thermodynamics and Phase Diagrams1.6.3 The solid phase lineBLTT1xAxSolid phase linexLHypotheses a a: dilute regular, L : idealB in the dilute phase , (Hentys law): (1)Since is regular solution: (2)B in the ideal solution L: (3)Equilibrium,
30、 Eq.(1) = Eq.(3) : (4)Where DGmB is the free energy when 1 mol pure B melts at temperature TDHmB : melting heat of pure B TmB : melting point of pure B47Chapter 1 : Thermodynamics and Phase Diagrams (5) A in a phase obeys Raoults Law L is a ideal solutionSimilar to Eq.(5), we have: (6)Can be obtaine
31、d from thermodynamic handbooks,x and xL can be then calculated from Eq.(5) and Eq.(6).48Chapter 1 : Thermodynamics and Phase Diagrams1.7 Thermodynamics during Phase Transformations1.7.1 NucleationLiquidSolid a aP T1GxxSolution x is cooled from liquid phase to T1.Y0SxSLxLxS x 0 at T1. (A and B atoms
32、dislike each other). Any solution between xA and xB will be decomposed into xA and xB at T1.T0XB-TD DSmixD DHmixD DGmixw w 0, Low TKBKAx1dxdG10xxFor solution x2 between KA and KB : any fluctuation will lead to a decrease of free energy and thus the solution will be automatically decomposed.x2dG20x2dG20 dx60Chapter 1 : Thermodynamics and Phase DiagramsEnd of Chapter 161Chapter 1 : Thermodynamics and Phase Diagrams
