老师课件材料热力学第七章

1StatisticalThermodynamics任课教师：刘伟材料科学与工程系第六章（1）2经典热力学－平衡态热力学TAPAVAUAHASAGA过程：W、Q状态A状态B准静态过程非准静态过程TBPBVBUBHBSBGB密度、温度、压强不均匀不能用状态函数来表示！G标准态1.定义(体系、函数、材料性能)2.热力学定律3.热力学关系式4.热力学平衡1.热力学定义2.热力学定律4.热力学平衡3.热力学关系式统计热力学非平衡热力学材料性能3经典热力学－平衡态热力学G温度压力单组元二组元多组元相变热力学相图热力学界面热力学关键问题：如何构造G自由能函数？G曲线随温度、压力和成分如何变化？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波函数局限在空间不同范围，彼此没有重叠。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.体系每一个分立的能量本征值称为能级量子化的能量本征值的集合组成本征能谱，构成能级的分布。14DegenerateWaveFunctionsQuantumStatesN-FoldDegenerate体系的运动状态称为量子态，用波函数来描述。属于同一能级的不同量子态数称为该能级的简并度。15PopulationsPopulationTheaveragenumberofparticlesthathavetheenergyibythenameniIfthesystemisclosed:EnergyLevelsDegeneratePopulations16Macrostates17宏观状态（宏观态）的确定是要求规定每个能级上有多少个粒子，而不关心是哪些粒子。规定每个粒子在哪一个能级上，如果能级是简并的，同一个能级上有多个量子态，那么还要确定每个粒子处于哪个能级的哪个量子态上。181920212223Microstates微观状态的确定是规定每个粒子在哪一个能级上，如果能级是简并的，同一个能级上有多个量子态，那么还要确定每个粒子处于哪个能级的哪个量子态上。一种宏观态对应的微观状态数，也就是一种分布对应的微观状态数。体系的每一个微观态对应着一个特定的宏观态，而一个宏观态对应多个微观态。24Microstates25Microstates26Microstates27Microstates28Microstates29MicrostatesDoesadistributionchangemakeamacrostatehavemoreorfewermicrostates?30Microstates31Microstates32Microstates33ProbabilitiesMacrostate1Macrostate2N1N2>P1P2>Thetotalprobabilityoffindingamicrostatethatcorrespondstothemacrostatewithmoremicrostatesishigher.Macrostateswithfewermicrostatesassociatedwiththemarelessprobablesincetherearefewerdetailedwaysofconfiguringthesystemtocomeupwiththatmacrostate.34ProbabilitiesProbabilitiesofthedifferentwaysIcandistributeenergyEintheenergylevelsi

ofaclosedsystemofNidenticalparticles.Findingthemostlikelyconfigurationofasystem,thatisthemostlikelymacrostateIneedtodeterminewhichmacrostatehasthemostmicrostatesandalsohastherighttotalenergyandnumberofparticles.Tofindthismacrostatewecanmaximizethefunction:35BoltzmannDistribution36BoltzmannDistribution37BoltzmannDistribution38BoltzmannDistribution39BoltzmannDistribution40BoltzmannDis