浙江大学材料热力学与动力学.ppt

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 Thermodynamics 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,Heat 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 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.Clausius: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 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 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 measure 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 DiagramsStable,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 KineticsGBACG1G2Energy 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 ironTPClausius-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-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 DGmix: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 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 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 solutionGtangent 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 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,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 ActivityIdeal 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 lawHerrys 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: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 Systems35Chapter 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 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 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: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: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 liquidPeritectic 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 the 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-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,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 obtained 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 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 TKBKAx1dxdG10 xxFor solution x2 between KA and KB:any fluctuation will lead to a decrease of free energy and thus the solution will be automatically decomposed.x2dG20 x2dG20 dx60Chapter 1:Thermodynamics and Phase DiagramsEnd of Chapter 161Chapter 1:Thermodynamics and Phase Diagrams