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34
2.GrowthofABO
3andBO
2Crystals
2.2.2.PhaseDiagrams
Singlecrystalgrowthofmanycompoundoxides,duetotheirproperties,
imposesusingofphasediagramstodefinepreciseconditionsofcrystal-
lization,especiallyfrommelts.Inthecaseofincongruentmeltingorthe
presenceofhigh-temperatureirreversible/destructivephasetransitionthe
crystallizationmustbecarriedoutbelowthetemperatureofsuchtransfor-
mationtoobtainthedesiredphase.Alsocongruentlymeltingcompounds
withhightemperaturesofmeltingareeasiertobecrystallizedwhenthereis
apossibilityofloweringthetemperatureofcrystallizationbytheaddition
ofsomecomponents.Thebestsolutioninalldiscussedabovecasesisthe
so-calledself-fluxHighTemperatureSolutionGrowth(HTSG)inwhich
thesolventusedtofluxgrowthisoneofthecomponentsofagivenphase
diagram.Suchasolventdoesnotintroduceotherelementstothecrystal
growthsystemandthereforeischosenunlessotherfactorsmakeitimpos-
sible.Themainobstacleinusingself-fluxistheformationofotherphases
beforereachingthedesirabletemperatureofcrystallization.Sometimes
highviscosityofsuchsolventcanalsolimititsapplications.ACerS-NIST
PhaseEquilibriaDiagramsDatabasegivesdetailedinformationonexisting
compoundsandtheirtransformationsinagivensystemoftwoormore
chemicalcomponents,andthereforeisaveryusefultoolincarryingout
crystalgrowthexperiments[5].
2.2.3.NonstoichiometricOxides
Animportantthermodynamicquantitydescribingnonstoichiometricox-
idesistheactivityofoxygeninthesolidcompound.Itisthechemical
potentialofoxygenp
O2
µ
O
2
1
µ
0
O
2
+
RTlnP
O
2
Herep
0
O2isthechemicalpotentialofoxygeninitsstandardstateand
P
O2istheequilibriumoxygenpressureintheatmospheresurroundingthe
nonstoichiometricoxide.RTlnP
O2isthemeasureoftherelativepartial
molarfreeenergyofoxygen.Thesevaluesdependobviouslyonthetem-
peraturebutalsoonthecompositioninsomecases.Itwasshown[6]that
somenonstoichiometricphasesconsistofawholeseriesoflinephases
(Magnéliphases).Pointdefectstructurespredominateinnonstoichio-
metricphases(connectedtovacanciesandinterstitialpositionsofcat-
ionsoranions).However,insomecompounds,likeTiO
2-xtheexcess
chargeoftheelectronicspeciesiscompensatedbyextendeddefectswith
(2.13)