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Chemical Thermodynamics of Materials Macroscopic and Microscopic Aspects Svein Stølen DepartmentofChemistry,UniversityofOslo,Norway Tor Grande DepartmentofMaterialsTechnology,NorwegianUniversityof ScienceandTechnology,Norway with a chapter on ThermodynamicsandMaterialsModellingby Neil L. Allan SchoolofChemistry,BristolUniversity,UK Chemical Thermodynamics of Materials Chemical Thermodynamics of Materials Macroscopic and Microscopic Aspects Svein Stølen DepartmentofChemistry,UniversityofOslo,Norway Tor Grande DepartmentofMaterialsTechnology,NorwegianUniversityof ScienceandTechnology,Norway with a chapter on ThermodynamicsandMaterialsModellingby Neil L. 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Contents Preface xi 1 Thermodynamic foundations 1 1.1 Basic concepts 1 Thermodynamicsystems 1 Thermodynamicvariables 2 Thermodynamicprocessesandequilibrium 3 1.2 The first law of thermodynamics 4 Conservationofenergy 4 Heatcapacityanddefinitionofenthalpy 5 Referenceandstandardstates 8 Enthalpyofphysicaltransformationsandchemicalreactions 9 1.3 The second and third laws of thermodynamics 12 Thesecondlawandthedefinitionofentropy 12 Reversibleandnon-reversibleprocesses 12 ConditionsforequilibriumandthedefinitionofHelmholtzandGibbsenergies 13 Maximumworkandmaximumnon-expansionwork 15 Thevariationofentropywithtemperature 16 Thethirdlawofthermodynamics 17 TheMaxwellrelations 18 PropertiesoftheGibbsenergy 20 1.4 Open systems 24 Definitionofthechemicalpotential 24 Conditionsforequilibriuminaheterogeneoussystem 25 Partialmolarproperties 25 TheGibbs–Duhemequation 26 References 27 Further reading 27 2 Single-component systems 29 2.1 Phases, phase transitions and phase diagrams 29 Phasesandphasetransitions 29 Slopesofthephaseboundaries 33 PhasediagramsandGibbsphaserule 36 v vi Contents Field-inducedphasetransitions 37 2.2 The gas phase 39 Idealgases 39 Realgasesandthedefinitionoffugacity 40 Equationsofstateofrealgases 42 2.3 Condensed phases 44 Variationofthestandardchemicalpotentialwithtemperature 44 Representationoftransitions 47 Equationsofstate 52 References 54 Further reading 55 3 Solution thermodynamics 57 3.1 Fundamental definitions 58 Measuresofcomposition 58 Mixturesofgases 59 Solidandliquidsolutions–thedefinitionofchemicalactivity 60 3.2 Thermodynamics of solutions 60 Definitionofmixingproperties 60 Idealsolutions 63 Excessfunctionsanddeviationfromideality 64 3.3 Standard states 67 Henry’sandRaoult’slaws 68 RaoultianandHenrianstandardstates 70 3.4 Analytical solution models 73 Dilutesolutions 73 Solutionmodels 74 Derivationofpartialmolarproperties 77 3.5 Integration of the Gibbs–Duhem equation 79 References 83 Further reading 83 4 Phase diagrams 85 4.1 Binary phase diagrams from thermodynamics 85 Gibbsphaserule 85 Conditionsforequilibrium 88 Idealandnearlyidealbinarysystems 90 Simpleeutecticsystems 96 Regularsolutionmodelling 98 Invariantphaseequilibria 102 Formationofintermediatephases 103 Meltingtemperature:depressionorelevation? 106 MinimizationofGibbsenergyandheterogeneousphaseequilibria 109 4.2 Multi-component systems 109 Ternaryphasediagrams 109 Quaternarysystems 115 Ternaryreciprocalsystems 116 4.3 Predominance diagrams 117 References 125 Further reading 125 Contents vii 5 Phase stability 127 5.1 Supercooling of liquids – superheating of crystals 128 5.2 Fluctuations and instability 132 Thedrivingforceforchemicalreactions:definitionofaffinity 132 Stabilitywithregardtoinfinitesimalfluctuations 133 Compositionalfluctuationsandinstability 135 ThevanderWaalstheoryofliquid–gastransitions 140 Pressure-inducedamorphizationandmechanicalinstability 143 5.3 Metastable phase equilibria and kinetics 149 Phasediagramsreflectingmetastability 149 Thermalevolutionofmetastablephases 150 Materialsinthermodynamicpotentialgradients 152 References 153 Further reading 155 6 Surfaces, interfaces and adsorption 157 6.1 Thermodynamics of interfaces 159 Gibbssurfacemodelanddefinitionofsurfacetension 159 Equilibriumconditionsforcurvedinterfaces 163 Thesurfaceenergyofsolids 164 Anisotropyandcrystalmorphology 165 Trendsinsurfacetensionandsurfaceenergy 167 Morphologyofinterfaces 171 6.2 Surface effects on heterogeneous phase equilibria 175 Effectofparticlesizeonvapourpressure 176 Effectofbubblesizeontheboilingtemperatureofpuresubstances 177 Solubilityandnucleation 179 Ostwaldripening 180 Effectofparticlesizeonmeltingtemperature 181 Particlesize-inducedphasetransitions 185 6.3 Adsorption and segregation 186 Gibbsadsorptionequation 186 Relativeadsorptionandsurfacesegregation 189 Adsorptionisotherms 191 References 193 Further reading 195 7 Trends in enthalpy of formation 197 7.1 Compound energetics: trends 199 Preludeontheenergeticsofcompoundformation 199 Periodictrendsintheenthalpyofformationofbinarycompounds 202 Intermetalliccompoundsandalloys 210 7.2 Compound energetics: rationalization schemes 211 Acid–baserationalization 211 Atomicsizeconsiderations 214 Electroncountrationalization 215 Volumeeffectsinmicroporousmaterials 216 7.3 Solution energetics: trends and rationalization schemes 218 Solidsolutions:strainversuselectrontransfer 218 Solubilityofgasesinmetals 220 Non-stoichiometryandredoxenergetics 221 Liquidsolutions 223 viii Contents References 226 Further reading 227 8 Heat capacity and entropy 229 8.1 Simple models for molecules and crystals 230 8.2 Lattice heat capacity 233 TheEinsteinmodel 233 Collectivemodesofvibration 235 TheDebyemodel 241 Therelationshipbetweenelasticpropertiesandheatcapacity 244 Dilationalcontributionstotheheatcapacity 245 Estimatesofheatcapacityfromcrystallographic,elasticandvibrational characteristics 247 8.3 Vibrational entropy 248 TheEinsteinandDebyemodelsrevisited 248 Effectofvolumeandcoordination 250 8.4 Heat capacity contributions of electronic origin 252 Electronicandmagneticheatcapacity 252 Electronicandmagnetictransitions 256 8.5 Heat capacity of disordered systems 260 Crystaldefects 260 Fastionconductors,liquidsandglasses 261 References 264 Further reading 266 9 Atomistic solution models 267 9.1 Lattice models for solutions 268 Partitionfunction 268 Idealsolutionmodel 269 Regularsolutionmodel 271 Quasi-chemicalmodel 276 Florymodelformoleculesofdifferentsizes 279 9.2 Solutions with more than one sub-lattice 285 Idealsolutionmodelforatwosub-latticesystem 285 Regularsolutionmodelforatwosub-latticesystem 286 Reciprocalionicsolution 288 9.3 Order–disorder 292 Bragg–Williamstreatmentofconvergentorderinginsolidsolutions 292 Non-convergentdisorderinginspinels 294 9.4 Non-stoichiometric compounds 296 Massactionlawtreatmentofdefectequilibria 296 Solidsolutionapproach 297 References 300 Further reading 301 10 Experimental thermodynamics 303 10.1 Determination of temperature and pressure 303 10.2 Phase equilibria 305 10.3 Energetic properties 308 Thermophysicalcalorimetry 309 Thermochemicalcalorimetry 313 Electrochemicalmethods 319