浙江大學(xué)材料熱力學(xué)與動(dòng)力學(xué)ppt課件

1、 Chapter 1. Thermodynamics and Phase DiagramsProf. Dr. X.B. ZhaoDepartment of Materials Science and EngineeringZhejiang University Homogeneous Systemwith the same physical and chemical propertiesHeterogeneous Systembeing made of several phases1.0.1 Thermodynamics Systems q Open System can exchange m

2、ass, heat and work with its surroundingsq Closed System no mass exchange, heat and work exchange possibleq Isolated Systemno mass, no heat, no work exchange A. Energy, Heat and Work The energy of an isolated system is constant The work done on a thermally isolated system is independent of the type o

3、f work and the route1.0.2 The First Law of Thermodynamics isolated systemW = 0, E = const.closed systemDE = Q + WDE = Q + WQ 0, system receives heatQ 0, work is done on the systemW 0, DS DS eadiabatic process : DS e = 0, DS = DS iirr. adiabatic process : DS 0rev. adiabatic process : DS = 0 The Secon

4、d 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 II Mr. Tompkins in PaperbackG. GamowCambridge Un

5、iversity Press, 1965Heat can not flow automatically from cold side to hot side ! Phase :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

6、or mixture of phases.Why ? the initial state of the system is unstable relative to the final state1.1 Equilibrium in a Closed System How 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 measur

7、e 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) Stable, Metastable and UnstableGdG = 0BACdG = 0dG = 0an arbitrary state parameterBACStable: graphite, single crystal

8、siliconMetastable: diamond, amorphousUnstable: super-cooling liquid (nucleation)BAC Possibility and Realizability : Thermodynamics and KineticsGBACG1G2Energy HumpDG = G2 DG = G2 G1 0 : only possible for the transformation from B to A G1 H solidsince G = H - TSG liquid G solid at low TG liquid G soli

9、d at high TTmDHmDHmat Tm : H liquid - H solid = DHmG liquid = G solidsolidstableliquidstableHG 1.2.2 Effect of Pressureg-irond-irona-irone-ironliquid ironTPVPGT= = Clausius-Clapeyron equationVTHdTdPD DD D= = eqeqg gd da ae eLTPL Sd d g gg g a aD DV- - -+ +D DH- - - -dp/dt+ + +- - TmTDGDGGGSGLFree en

10、ergiesat TmmmTLTHS= =D D= =D D1.2.3 The Driving Force for SolidificationG L = H L - TS L G S = H S - TS SDG = DH - TDS = 0DG = DH - TDS = 0for most metalsL R (8.3 J mol-1K-1)at T with small DT , ( Tm - T = DT )SLppCC- -can be ignored, DH & DS independent on T difference on mmTTLTLTLGD D= =- - D

11、D 1.3 Binary Solutions1.3.1 The Gibbs Free Energy of Binary SolutionsXA mole AXB mole BXA + XB = 1MIX1 mole A+BG1 = GAXA + GBXBG2 = G1 + DGmixDGmix : mixing free DGmix : mixing free energyenergyDGmix = DHmix - TDSmix DGmix = DHmix - TDSmix 1.3.2 Ideal SolutionsDHmix = 0 DHmix = 0 DSmix = -R ( XAlnXA

12、 + XBlnXB )DSmix = -R ( XAlnXA + XBlnXB )DGmix = RT ( XAlnXA + XBlnXB )DGmix = RT ( XAlnXA + XBlnXB )Note: Since XA and XB are 1, DSmix is positive,DGmix is negative.XB01Molar free energy GGAGBG 0DGmiDGmix xAt higher temperatureLow THigh Tmixing free energy DGmixXB01the absolute free energy is not o

13、f interest! 1.3.3 Chemical PotentialMulti-ComponentSystemdnAconstant T and Ptotal free energy of the system : G G + dGif dnA small enough, dG proportional to dnA, or : dG = mAdnAijnTPiijnG=,mDefinition:Chemical potential , orPartial molar free energyNote:G: total free energy of the systemG: molar fr

14、ee energy (one mol) geometric meaning of chemical potentialABXBmAmAmBmBGGBGART lnXAfor ideal solutionRT lnXBfor ideal solutionGtangent line at XB DHmix : calculated from the nearest neighbor bonds and their bond energies1.3.4 Regular Solutionsideal solution :DHmix = 0 , not true for most (if not all

15、) solutionsregular solution : a simplification of real solutions with DHmix 0 ABABABABAAABBABBBAABA-AA-BB-BeABeABA-BeBBeBBB-BeAAeAAA-Aenergybond A-AB-BBeforemixingBBAAA-BBABAA-BAftermixingeAA + eBBeAA + eBB2eABEnergy change per A-B bond : e = eAB - (eAA + eBB)AB bonds per mol : PAB = Na z XAXBTheref

16、ore : DHmix = w XAXB , where w = Na ze 0DHmixDHmixXB1w w ( () )BBAABAmixmixmixlnlnXXXXRTXXSTHG+ + += =- -= =w wD DD DD Dw 0w eAA, eBB eABeABA-B bond A-B bond preferredpreferredXBDHmixDHmixTDSmixDGmixDGmixw 0, High Tw 0, High TXBDHmixDHmixTDSmixDGmixDGmixw 0, Low Tw 0w 0eAA, eBB eABeAA, eBB 0, High T

17、w 0, High TXBTDSmixDHmixDHmixDGmixDGmixw 0, Low Tw 0, Low T 1.3.5 ActivityIdeal SolutionsA = GA + RT lnXAB = GB + RT lnXBReal Solutions A = GA + RT lnaAB = GB + RT lnaBABXBmAmAmBmBGGBGART lnaAfor real solutionRT lnaBfor real solutionGtangent line at XBDGmixDGmix Definition of activity coefficient :

18、g = a / X0.00.20.40.60.81.00.00.20.40.60.81.0XNiFeNiaNiRaoults lawHerrys law1873KHerrys law:gB = aB / XB const.Raoults law:gA = aA / XA 1dilute solutionof Ni in Fedilutesolutionof Fein NiHerrys law and Raoults law apply toall solutions when sufficiently dilute 0.00.20.40.60.81.00.00.20.40.60.81.0XZn

19、PbZnaZn1080K1180KRaoults law BGAGABb ba aNear pure A : a phaseNear pure B : b phaseSolution X0 ? b0Ga0GX 0if a1 + b1b1Ga1G1X1Xa1a1b1b1Lever Ruleamount of a1:( () ) ( () )1101XXXX- - -amount of b1:( () ) ( () )1110XXXX- - -Molar free energy of a1 + b1:11110111011GXXXXGXXXXG- - -+ +- - -= =1Gfree ener

20、gy will be decreased If pure a (or b ) a + b 1.4 Equilibrium in Heterogeneous Systems Condition of Equilibrium in a Heterogeneous SystemAGABb0G1Gb1Ga0Ga1GX 0b ba a1X1Xa1b1BGFor alloy X 0 : G0 G0 G1 , (1+1) is more stable However, G can be minimized if the alloy consists e and eeGeGeXbeeGeXaePQWhat a

21、re point P and Q ?P, Q are two common tangent points on both G curvesfor alloy between andGe on the common tangent is minimumeXeX Heterogeneous EquilibriumCondition of Equilibrium in a Heterogeneous System continue : about the common tangent lineAGABa aeXPamBamAamAamBand :Chemical potentials of comp

22、onent A and B in a phase with the composition of eXbmAand :Chemical potentials of component A and B in b phase with the composition of bmBeXBGeXb bQbmBbmAB B B A A A m mm mm mm mm mm m= = = = = 1.5.1 A Simple Phase DiagramABTLSA and B are completely miscible in both the solid and liquid states and a

23、re 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 -

24、 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 decomposition 1.5.3 Co-Sb System 0 10 20 30 40 50 60 70 80 90 100 atomic percent antimon

25、y 0 10 20 30 40 50 60 70 80 90 100 weight percent antimony 200 400 600 800 1000 1200 1400 1600 temperature, C 1495C 1121C 1202C 1113C 1065C 931C 876C 623C 377C 422C 630.755C 2.5 25.5 (a-Co) (e-Co) b (Sb) g g d L Sb Co Eutectic ReactionDHmix 0, the miscibility gap extends into the liquidPeritectic Re

26、action, DHmix 1%, the solid solution can not be treated as a dilute solution.RTHRSxxBB21lnD D- -D D= =- -a aa amodifying39601.4CuAg85203.0FeCu21605480217059005120432047900.811.80.772.51.72.51.4CdNiSbCoSiPbAgsolutePbPbPbAuAlAgCusolventRSBDRHBD 1.6.2 The influence of particle sizes on the solid solubi

27、lityBulk aSolid solution a: atomic weight M, density r, interface energy gSpherical a particlerdm(gram)dG = ?Bulk free energy change:()=m-m=aaRTMdmMdmdGrrln1Free energy change caused by the increase of the surface area of the particlerdmrdrdAdmdrrdVr=p=r=p=28,42rdmdAdGrg=g=22In the equilibrium condi

28、tion, dG1 = dG2RTrMaarrg=2lnFor a dilute solution (Thomson-Freundlich equation):RTrMxxrrgaa2lnln+=Significantly if r 100 nm 1.6.3 The solid phase lineBLTaT1xaAxSolid phase linexLHypotheses a: dilute regular, L : idealB in the dilute phase a, (Hentys law):00lnlng+m=maaaRTxRTBB (1)Since a is regular solution:0lnlng=g=aaRTRTHBD (2)B in the ideal solution L:LLBLBxRT ln0+m=m (3)Equilibrium, Eq.(1) = Eq.(3) :()RTHGRTHxxBmBBBLBLaaaa-=-m-m=ln00DDD (4)Where DGmB is the free energy