Treść książki

Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
2.1.TheoryofCrystalGrowth
31
Inamany-particlessystem,theinternalenergyU(thesocalledstate
function,dependentonlyonphysicalparametersofthesystemandinde-
pendentonthewayinwhichthesystemreachedthegivenstate)decreases
whenequilibriumisreached.Otherstatefunctionstobenamedareentropy,
enthalpy,andfreeenergy.Accordingtothefirstlawofthermodynamics:
'U
1
QW
-
(2.1)
Thechangeintheinternalenergyofaclosedsystemisequaltothe
amountofheatQsuppliedtothesystemminustheamountofworkWdone
bythesystemonitssurroundings.
Ontheotherhand,entropySshouldincreasetoreachequilibrium.The
entropyisdefinedbyBoltzmann’sformula
SklnM
=
(2.2)
wherekistheBoltzmannconstant,andMisthenumberofthepossible
statesofthesystem.
UsingUandSaswellastemperatureT,pressureP,andvolumeV
wecandefinetwostatefunctionsusefulindescribingequilibriumofthe
many-particlesystems.HelmholtzfreeenergyFdefinedas
F
1
UTS
-
whileGibbsfreeenergyGisdescribedas
G
1
UPVTS
+
-
HereenthalpyHequalsto
H
1
UPV
+
(2.3)
(2.4)
(2.5)
Fgoestotheminimumwhenthemany-particlesystemreachesequilibrium
underaconstanttemperaturewithoutchangingthevolumewhileGgoesto
minimumatequilibriumunderaconstanttemperaturewhenpressuredoes
notchange.Inotherwords
dF0
1
(
T,Vconstant
)
dG
1
0
(
T,Pconstant
)
(2.6)
(2.7)
Anydisturbanceofthesystemfromtheequilibriumdiminishesentropy
(dS<0),butincreasesfreeenergy(dF>0,dG>0).
AnincrementoftheGibbsfreeenergyofthemulti-particlesystem,
composedofonekindofparticle,byaddingofonemolofparticlesis
definedasthechemicalpotentialu.Ifthesystemiscomposedofdiferent