Thermodynamic Equilibrium and Stability of Materials

464 Pages·2021·5.182 MB·English

by  Long-Qing Chen

Long-Qing Chen
Thermodynamic
Equilibrium
and Stability
of Materials
Thermodynamic Equilibrium and Stability
of Materials
Long-Qing Chen
Thermodynamic Equilibrium
and Stability of Materials
Long-QingChen
DepartmentofMaterialsScienceandEngineering
DepartmentofMathematics
DepartmentofEngineeringScienceandMechanics
MaterialsResearchInstitute
ThePennsylvaniaStateUniversity
UniversityPark,PA,USA
ISBN978-981-13-8690-9 ISBN978-981-13-8691-6 (eBook)
https://doi.org/10.1007/978-981-13-8691-6
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Preface
Thisbookonthermodynamicsofmaterialsisintendedasatextbookforjunior/senior
undergraduatestudentsandfirst-yeargraduatestudentsinmaterialsscienceandengi-
neering and related fields as well as a reference for researchers who would like to
refreshtheirunderstandingofbasicthermodynamicsandneedtoderivethermody-
namicrelationsfortheirresearch.Imadeaconsciousefforttoexplainthethermo-
dynamic concepts and quantities using plain languages. The focus of this book is
onthefundamentalsofthermodynamicsandtheirapplicationstogenericthermody-
namicsystemsandprocessesratherthanspecificmaterialssystems.Areaderafter
finishing the book is expected to achieve a high-level fundamental understanding
of thermodynamics and acquire the analytical skills of applying thermodynamics
to determining materials equilibria under different thermodynamic conditions and
computingdrivingforcesformaterialsprocesses.
Oneofthepurposesforwritingthisbookistosharemyownunderstandingofther-
modynamicsthroughnearly30yearsofteachingthermodynamicsofmaterialsatthe
PennsylvaniaStateUniversity.Myunderstandingofthermodynamicshasprimarily
been based on reading “Scientific Papers of Josiah Willard Gibbs” which laid the
foundationofthermodynamicsandillustratedthetruemathematicalrigorandbeauty
ofthermodynamics.1Ialsobenefitedgreatlyreadinganumberofmodernthermody-
namicsbooks,includingThermodynamicsandanIntroductiontoThermostatistics
by Herbert B. Callen2, Thermodynamics and Its Applications by Michael Modell
andRobertC.Reid3,ModernThermodynamics:FromHeatEnginestoDissipative
StructuresbyDilipKondepudiandIlyaPrigogine4,TheDynamicsofHeatbyHans
1J. Willard Gibbs, “On the Equilibrium of Heterogeneous Substances,” Transactions of the
ConnecticutAcademy,III.pp.108–248,October1875–May1876,and343–524,May1877–July
1878.
2HerbertB.Callen,“ThermodynamicsandanIntroductiontoThermostatistics,”SecondEdition,
Wiley,1985.
3MichaelModellandRobertC.Reid,“ThermodynamicsanditsApplications,”SecondEdition,
PrenticeHallPTR,1983.
4DilipKondepudiandIlyaPrigogine,“ModernThermodynamics:FromHeatEnginestoDissipa-
tiveStructures,”FirstEdition,JohnWiley&Sons,1998.
v
vi Preface
U.Fuchs5,andPhaseEquilibria,PhaseDiagramsandPhaseTransitionsbyMats
Hillert6.
There are several existing excellent textbooks specifically devoted to applica-
tionsofthermodynamicstomaterialsscienceandengineering,e.g.,Introductionto
ThermodynamicsofMaterialsbyDavidR.GaskellandDavidE.Laughlin7,Ther-
modynamicsofMaterialsbyDavidV.Ragone8,andThermodynamicsinMaterials
SciencebyRobertDeHoff9.Thenaturalquestionwouldbe“whyanothertextbook
onthermodynamics?”Itrytoanswerthisquestionbyemphasizingseveral,whichI
believe,ratheruniquefeaturesofthisbook:
(cid:129) EntropySandchemicalpotentialµ,consideredbymanyastwoofthemostdiffi-
cultandabstractconceptstofullycomprehendinthermodynamics,areintroduced
veryearlyinChap.1aspartofthedefinitionsandterms,emphasizingtheanalog
ofchemicalpotentialµtotemperatureT andpressurepasaformofpotential,
andtheanalogofStovolumeV andamountofchemicalsubstanceNasatypeof
matter.Allsevenbasicthermodynamicvariables(U,S,V,N,T,p,µ)associated
withasimplethermodynamicsystemasdefinedbyGibbsareseparatedintothree
categories:energy(U),matter(S,V,N),andpotential(T,p,µ),emphasizingnot
onlytherelationsbutalsothedifferencesamongthethreetypesofthermodynamic
quantities:energy,matter,andpotential.
(cid:129)
Thediscussiononthefirstlawofthermodynamicsisprimarilyfocusedonopen
systems rather than closed systems as it was done in essentially all modern
textbooks on thermodynamics of materials. Open systems, by definition, allow
exchangesofallthreekindsofmatter(entropy,volume,andchemicalsubstance)
and thus the exchanges of the three forms of energy (thermal, mechanical, and
chemical)betweenasimplesystemanditssurrounding.Oneofthebenefitsfor
discussingthefirstlawofthermodynamicsusingopensystemsistheearlyintro-
ductionanddiscussionofchemicalpotentialintermsofchemicalenergyorthe
Gibbsfreeenergyperunitamountofmatterorthederivativesofdifferentther-
modynamic potential energy functions with respect to the amount of substance
underdifferentthermodynamicconditions.
(cid:129)
Thesecondlawofthermodynamics,anotherconceptoftenperceivedtobedifficult
in thermodynamics, is quantified by directly connecting the amount of entropy
producedtotheamountofthermodynamicenergydissipatedordrivingforce,and
thusallowingonetoquantitativelycalculatetheamountofentropyproducedin
any given irreversible thermodynamic process using thermodynamic quantities
5Hans U. Fuchs, “The Dynamics of Heat: A Unified Approach to Thermodynamics and Heat
Transfer,”SecondEdition,Springer-VerlagNewYork,2010.
6M. Hillert, “Phase Equilibria, Phase Diagrams and Phase Transformations,” Second Edition,
CambridgeUniversityPress,Cambridge,2008.
7DavidR.GaskellandDavidE.Laughlin,“IntroductiontotheThermodynamicsofMaterials,”
SixthEdition,CRCPressLLC,2018.
8DavidV.Ragone,“ThermodynamicsofMaterials,”VolumeIandII,JohnWiley&Sons,Inc.,
1995.
9RobertDeHoff,“ThermodynamicsinMaterialsScience,”CRCPressLLC,2006.
Preface vii
associated with the system of interest. In the existing literature, the connection
betweenentropyincreaseandenergydissipationisoftendiscussedinirreversible
thermodynamics10.
(cid:129)
Thebookfullyembraces,ratherthanshiesawayfrom,themathematicalbeauty
and rigor of Gibbs thermodynamics throughout the book by emphasizing the
importanceoffundamentalequationofthermodynamicsfromwhichallthermo-
dynamic properties of a material can be derived. However, a reader with basic
first-yearundergraduatecalculusskillsisexpectedtobeabletogetthroughthe
book without too much difficulty. It offers detailed descriptions of the step-by-
stepproceduresforcomputingallthethermodynamicpropertiesfromthefunda-
mentalequationofthermodynamicsortheconstructionoffundamentalequations
of thermodynamics in different alternative functional forms based on a set of
common, experimentally measurable thermodynamic properties. The emphasis
ofthechapteronthebriefintroductiontostatisticalthermodynamicsisalsoonthe
connectionbetweenthemicroscopicinteractionsinasystemandthefundamental
equationofthermodynamicsassociatedwiththesystem.
(cid:129)
By far, the most emphasized concept of this book is chemical potential and its
applicationstomaterialsscienceandengineering.Notonlytheconceptofchem-
icalpotentialisintroducedattheverybeginningofthebooktogetherwithtemper-
atureandpressure,butalsoessentiallyalltheapplicationsofthermodynamicsare
discussed based on the concept of chemical potentials, e.g., phase equilibria in
single-componentsystemsaswellasbinaryormulticomponentsolutions,chem-
icalreactionequilibria,andlatticeandelectronicdefectsincrystals,andmulti-
physicsproblemsincludingcouplingamongchemistry,mechanics,andelectricity.
OnecanevendiscusschemicalreactionequilibriawithoutusingthetermofGibbs
free energy. The thermodynamic driving force for the reaction 2A+B = A B
2
can be perfectly described by the difference between the chemical potential of
theinitialstate(thereactants)withchemicalpotentialµr =2µ +µ (inthe
A2B A B
state of mixture of A and B) and the chemical potential of the final state (the
product)µp = µ (intheformofacompoundormolecule,A B).Itisthe
A2B A2B 2
chemicalpotentialthatdeterminesthestabilityofchemicalspecies,compounds,
andphasesandtheirtendencytochemicallyreacttoformnewspecies,transform
tonewphysicalstates,andmigratefromonespatiallocationtoanother.There-
fore,itisthechemicalpotentialdifferencesorgradientsthatdriveessentiallyall
materialsprocessesofinterest.
(cid:129)
The book avoids or at least minimizes the use of terms such as molar Gibbs
freeenergyorpartialmolarGibbsfreeenergybecausemolarGibbsfreeenergy
ofamaterialorpartialmolarGibbsfreeenergyofacomponentispreciselythe
chemicalpotentialofthecorrespondingmaterialorthecorrespondingcomponent
regardlessofwhetherthematerialisasingleormulticomponentsystem.Thereis
acommonmisconceptionintheliteraturethatthestatement,“molarGibbsfree
energyofasystemisequaltoitschemicalpotential,”ortheequation,G/N=µ,
10SybrenR.deGrootandPeterMazur,“Non-EquilibriumThermodynamics,”DoverPublications,
Inc.,New.York,1984.
viii Preface
whereGisGibbsfreeenergy,N isnumberofmolesofchemicalsubstance,and
µisitschemicalpotential,isonlytrueforsingle-componentsystems.Potentials
areuniforminahomogeneoussystematequilibrium,andtheyarealsouniform
withinaheterogeneoussystemifthecorrespondingtypesofmatterareallowed
tofreelyflowortransportacrosstheinterfacesamongthedifferenthomogeneous
regions regardless of the external thermodynamic conditions. Molar Gibbs free
energyofasystematagivenoverallcompositionisuniforminbothhomogeneous
andheterogeneoussystemsinwhichallthechemicalspeciesareallowedtofreely
redistributeacrosstheinterfacesbetweenthedifferenthomogeneous regionsor
phases and the whole system is in thermodynamic equilibrium. Therefore, the
molarGibbsfreeenergyofamulticomponentsystemisapotential,thechemical
potential.ThispointwasalsopointedoutintheoriginalpaperbyGibbsaswellas
inthebookbyHillert.AccordingtoGibbs,forthepurposeofdefiningchemical
potential,“anychemicalelementorcombinationofelementsingivenproportions
may be considered a substance, whether capable or not of existing by itself as
a homogeneous body.” One can define the chemical potential of a component
by“choosingasoneofthecomponentsthematterconstitutingthebodyitself,”
so that the molar Gibbs free energy of a system “may always be considered as
a potential.” According to Hillert, “Actually, one can define a component with
the same composition as the whole system. The chemical potential of such a
componentisequaltoG …”whereG isthemolarGibbsfreeenergy.
m m
(cid:129)
Another feature for this book is the rather extensive discussion on the thermo-
dynamics of electron systems. Existing thermodynamics books in materials are
largelyfocusedonthethermodynamicsofphaseequilibria,andthereisminimal
coverage of thermodynamics of electronic systems. The concept of chemical
potentialorelectrochemicalpotentialofelectronicdefectsisextremelyimportant
forunderstandingthethermodynamicsofmanyprocessesinvolvingelectronssuch
aselectronictransportinthermoelectricsandphotovoltaicsandelectrochemical
reactionsinbatteries,fuelcells,andcorrosion,etc.Thisbookdiscussesthecontri-
butionsofelectronstothermodynamicsbytreatingthemanadditionalchemical,
chargedspecies.
Itshouldbeemphasizedthatafewtopicsthatwereemphasizedinmanyofthe
existingthermodynamicstextbooksarenottreatedindetailinthisbook.Forexample,
althoughtheconceptofelectrochemicalpotentialisintroduced,anditsapplications
inenergyconversionsarebrieflydiscussed,thediscussionsonthermodynamicsof
electrolytesolutionsarenotincluded.Furthermore,theconceptofinterfacialther-
modynamics is touched upon in a number of sections in the book, but there is no
separatechapterdevotedtothistopic.Inaddition„thewholebookhasbeenfocused
onheterogeneousbulksystemsconsistingofseveralhomogeneousregions,andthe
thermodynamics of diffuse interfaces is not discussed. Finally, the book does not
includeanytablesofthermodynamicdatasinceitisnowmucheasierforastudent
todigoutdatadirectlyfromInternetsources.
Foradoptingthebookasatextforanundergraduatecourseinthermodynamicsof
materials,thefollowingsectionsmaybeskipped:2.4.6–2.4.10,2.5.4–2.5.7;3.2,3.3,
Preface ix
3.5–3.6;Chap.4;5.3–5.6;6.3.3–6.3.6;7.8–7.9;8.3–8.5;9.6.3;10.1.2,10.2.1,10.2.4,
10.3,10.4.3–10.4.5;11.9–11.10;12.8,12.10,12.14,12.24,12.26,12.28,12.29.
I would like to acknowledge the help and contributions from many students in
thermodynamics classes over the years, colleagues, current and former graduate
students,andpostdocsforproof-readingthedifferentversionsofbookmanuscript.
In particular, I would like to thank Prof. Jiamian Hu (University of Wisconsin),
Prof. Kasra Momeni (University of Alabama), Dr. Yanzhou Ji (Penn State), Prof.
YuhongZhao(NorthUniversityofChina),Prof.ZijianHong(ZhejiangUniversity),
Mr. Carter Dettor (Penn State), Mr. Erik Furton (Penn State), Dr. Chengchao Hu
(Liaocheng University), Mr. Haowei Zhang (SDIC Unity Capital Co), Ms. Tina J.
Chen (UC Berkeley), Prof. John Mauro (Penn State), Prof. Yi Wang (Penn State),
Ms.SandraElder(PennState),andmanyothers.
ThesolutionstotheexercisequestionswereprimarilyworkedoutbyDr.Yuhui
HuangfromZhejiangUniversitywhovisitedPennStateformorethanayearasa
visitingscholar,andaseparatesolutionmanualwillbepublishedandavailableasa
companiontothistextbook.
Finally,Iwouldliketoexpressmysinceregratitudetomywife,Shuet-funMui,
forherpatienceandunderstandingduringthepreparationofthebookmanuscript.
UniversityPark,USA Long-QingChen
[email protected]
Contents
1 ThermodynamicSystemandItsQuantification .................. 1
1.1 Introduction ............................................ 1
1.2 ThermodynamicSystems ................................. 2
1.3 ThermodynamicVariables ................................ 4
1.3.1 InternalEnergy .................................. 5
1.3.2 Entropy ........................................ 7
1.3.3 Volume ........................................ 7
1.3.4 AmountofChemicalSubstance .................... 8
1.3.5 PotentialsWithinaSystem ........................ 9
1.4 Densities ............................................... 13
1.5 ExtensiveandIntensiveVariables .......................... 15
1.6 ConjugateVariablePairs ................................. 16
1.7 Classical, Statistical, and Nonequilibrium
Thermodynamics ........................................ 17
1.8 Exercises .............................................. 18
2 FirstandSecondLawsofThermodynamics ..................... 21
2.1 ThermodynamicStatesandStateVariables .................. 21
2.2 ThermodynamicProcesses ............................... 23
2.2.1 Spontaneous,orNatural,orIrreversibleProcesses .... 24
2.2.2 ReversibleProcesses ............................. 24
2.3 ThermodynamicSystems ................................. 25
2.4 FirstLawofThermodynamics ............................ 26
2.4.1 First Law of Thermodynamics for Isolated
Systems ........................................ 30
2.4.2 First Law of Thermodynamics for Closed
Systems ........................................ 30
2.4.3 FirstLawofThermodynamicsforReversible
ProcessesinOpenSystems ........................ 32
2.5 SecondLawofThermodynamics .......................... 36
2.5.1 QuantifyingSecondLawofThermodynamics ....... 38
2.5.2 IsolatedSystems ................................. 40
xi