老師課件材料熱力學(xué)第七章

1StatisticalThermodynamics任課教師：劉偉材料科學(xué)與工程系第六章（1）2經(jīng)典熱力學(xué)－平衡態(tài)熱力學(xué)TAPAVAUAHASAGA過程：W、Q狀態(tài)A狀態(tài)B準(zhǔn)靜態(tài)過程非準(zhǔn)靜態(tài)過程TBPBVBUBHBSBGB密度、溫度、壓強(qiáng)不均勻不能用狀態(tài)函數(shù)來表示！G標(biāo)準(zhǔn)態(tài)1.定義(體系、函數(shù)、材料性能)2.熱力學(xué)定律3.熱力學(xué)關(guān)系式4.熱力學(xué)平衡1.熱力學(xué)定義2.熱力學(xué)定律4.熱力學(xué)平衡3.熱力學(xué)關(guān)系式統(tǒng)計熱力學(xué)非平衡熱力學(xué)材料性能3經(jīng)典熱力學(xué)－平衡態(tài)熱力學(xué)G溫度壓力單組元二組元多組元相變熱力學(xué)相圖熱力學(xué)界面熱力學(xué)關(guān)鍵問題：如何構(gòu)造G自由能函數(shù)？G曲線隨溫度、壓力和成分如何變化？成分4INTRODUCTIONThermodynamicsisdividedintotwomainsubjects:ClassicalThermodynamicsStatisticalThermodynamicsClassicalThermodynamicsismacroscopicandphenomenalogicalStatisticalThermodynamicsismicroscopic

QuantumbehavioroftheatomsofthematerialsStatisticalmechanicsconcepts,strategiesMathematicalmethodsconnectthemicroscopicbehaviorofmaterialswiththeirmacroscopicproperties.5ClassicalThermodynamicsMacroscopicthermodynamicbehaviorVariouslawsofphysicsMathematicalprinciplesMeasuredpropertiesofamaterial.Thephenomenologicalapproachhastwomainings:First,itdoesnottelluswhyamaterialbehavesthewayitdoes.Forexample,whyenthalpyincreasewhenchangingcondition?ClassicalThermodynamicscannottellus!Thesecondthingwedonotgetfrommacroscopicthermo-dynamicsistheabilitytopredictfromfirstprincipleshowamaterialwillbehave.6StatisticalThermodynamicsRelationshipbetweenClassicalandStatisticalThermodynamics:Macroscopicsystemsareonlythemanifestationofmicroscopicbehavior.Themicroscopicbehaviorgivesusalltheinformationweneedtoanalyzethemacroscopicsystembecausethemacroscopicsystembehavesinanaverageway.Microscopicstates------Quantummechanics7StatisticalThermodynamicsBasicconcepts

Boltzmannstatisticsandpartitionfunction

ConnectingMacroscopicandMicroscopicThermo-dynamics

Ensemblestatistics8StatisticalThermodynamicsBasicConcepts:ParticlesEnergyLevelsPopulationsMacrostatesMicrostatesProbabilities9Particles

InteractingParticlesNon-interactingParticlesBoltzmannStatistics

ClassicalParticlesIdenticalindistinguishableIdenticaldistinguishableLocalizedParticlesNotLocalizedParticlesBose-EnsteinStatisticsFermi-DiracStatisticsEnsembleStatistics10ParticlesTwoparticlesBoltzmannstatisticsAB---------AB---------ABAB---BA---A---BB---A---AB---BA123ThreepossiblequantumstateLocalizedparticles波函數(shù)局限在空間不同范圍，彼此沒有重疊。11ParticlesTwoparticlesBose-Einsteinstatistics123AA---------AA---------AAAA---A---A---AAIdenticalParticlesIdenticalTheoryWaveFunctionSymmetryAntisymmetry（S＝0，1，2，…）NotLocalizedparticles12ParticlesTwoparticlesFermi-Diracstatistics123AA---A---A---AA（S＝1/2，3/2，…）NotLocalizedparticles13EnergyLevelsEnergyLevels:energyisquantized

Spectroscopy-MaterialsemitandabsorblightatcharateristicfrequenciesSemiconductor-conductionandforbiddenbandWiththeenergiesorderedfromlowesttohighestandwhereeachparticleinoursystemcanonlyhaveoneofthesespecifiedenergiesatanygivenpointintime.體系每一個分立的能量本征值稱為能級量子化的能量本征值的集合組成本征能譜，構(gòu)成能級的分布。14DegenerateWaveFunctionsQuantumStatesN-FoldDegenerate體系的運動狀態(tài)稱為量子態(tài)，用波函數(shù)來描述。屬于同一能級的不同量子態(tài)數(shù)稱為該能級的簡并度。15PopulationsPopulationTheaveragenumberofparticlesthathavetheenergyibythenameniIfthesystemisclosed:EnergyLevelsDegeneratePopulations16Macrostates17宏觀狀態(tài)（宏觀態(tài)）的確定是要求規(guī)定每個能級上有多少個粒子，而不關(guān)心是哪些粒子。規(guī)定每個粒子在哪一個能級上，如果能級是簡并的，同一個能級上有多個量子態(tài)，那么還要確定每個粒子處于哪個能級的哪個量子態(tài)上。181920212223Microstates微觀狀態(tài)的確定是規(guī)定每個粒子在哪一個能級上，如果能級是簡并的，同一個能級上有多個量子態(tài)，那么還要確定每個粒子處于哪個能級的哪個量子態(tài)上。一種宏觀態(tài)對應(yīng)的微觀狀態(tài)數(shù)，也就是一種分布對應(yīng)的微觀狀態(tài)數(shù)。體系的每一個微觀態(tài)對應(yīng)著一個特定的宏觀態(tài)，而一個宏觀態(tài)對應(yīng)多個微觀態(tài)。24Microstates25Microstates26Microstates27Microstates28Microstates29MicrostatesDoesadistributionchangemakeamacrostatehavemoreorfewermicrostates?30Microstates31Microstates32Microstates33ProbabilitiesMacrostate1Macrostate2N1N2>P1P2>Thetotalprobabilityoffindingamicrostatethatcorrespondstothemacrostatewithmoremicrostatesishigher.Macrostateswithfewermicrostatesassociatedwiththemarelessprobablesincetherearefewerdetailedwaysofconfiguringthesystemtocomeupwiththatmacrostate.34ProbabilitiesProbabilitiesofthedifferentwaysIcandistributeenergyEintheenergylevelsi

ofaclosedsystemofNidenticalparticles.Findingthemostlikelyconfigurationofasystem,thatisthemostlikelymacrostateIneedtodeterminewhichmacrostatehasthemostmicrostatesandalsohastherighttotalenergyandnumberofparticles.Tofindthismacrostatewecanmaximizethefunction:35BoltzmannDistribution36BoltzmannDistribution37BoltzmannDistribution38BoltzmannDistribution39BoltzmannDistribution40BoltzmannDis