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2.2.PhaseDiagramsofModelOxides…
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underconditionsofweaksupersaturationisobserved-thisisgrowthdue
tothepresenceofscrewdislocationsforminggrowthpyramidsonthesur-
faceofthecrystal.Basedonthisassumptionsuchphenomenaaskinetics
ofsteps,theirinstability,formationofbunchesofsteps,rougheningofthe
surface,normalandlateralcrystalgrowthwerebroadlydiscussedinthe
literature.Adetaileddescriptionofthesetheoriescanbefoundin[2],[3]
2.2.PhaseDiagramsofModelOxides.Major
ChallengesinCrystalGrowthofStoichiometric
OxideCrystals
2.2.1.GibbsPhaseRule
ForagivensystemcontainingCcomponentsthenumberofthecoexisting
phasesPandthenumberofdegreesoffreedom,F,thatthesystemhas
inequilibriumareconnectedbythefollowingequation:
P
+1
F
C
+
2
(2.12)
Inaone-componentsystemitmeansthatatthesocalledtriplepoint
inwhichthreephasesexistthereisnodegreeoffreedom(F=0).Eutectic
pointsarealsoinvariantduetotheexistenceofthreephases(liquidand
twocrystallinephases).Inthecaseoftwophasesinequilibrium,forex-
amplesolidandliquid,thechangeofthetemperatureofthesystemresults
inthechangeofthepressure,thereforeonlyonedegreeoffreedomexists.
Gibbsphaseruleinitsclassicalformtakespressureandtemperatureasthe
independentvariables.Whenconstantpressureiskept,thenumberofin-
dependentvariablesisreducedbyone.Ontheotherhand,theGibbsfree
energymaydependonotherfieldssuchaselectricworkdensityofpolar-
izedcrystalorelasticenergystoredinadeformedsolid[4].Crystallization
ofepitaxiallayersofSrTiO
3ondiferentsubstrates,duetolatticemis-
match,cancausediferentstraininas-grownthinsinglecrystallinelayer.
UnderrelativelysmallstrainandathighTthematerialremainsparaelectric
(cubicphase).Underlargestrain,themateriallowersitssymmetryandbe-
comesferroelectric.Intheintermediateregioncoexistenceofbothphases
isobserved,despiteconstantpressure.