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PhysicaB358(2005)77–85Electronicstructure,latticeconstant,opticalandmechanicalpropertiesforNaCl-structuredTi–Al–NbydensityfunctionaltheoryYingyuanTeng,ShenglongZhu,FangyingZhang,MingshengLi,FuhuiWang,WeitaoWuStateKeyLaboratoryforCorrosionandProtection,InstituteofMetalResearch,ChineseAcademyofSciences,WenchuiRoad62,Shenyang110016,ChinaReceived14September2004;accepted19December2004AbstractTheelectronicstructure,latticeconstant,opticalandmechanicalpropertiesofNaCl-structuredTi–Al–Ncompoundswerestudiedbydensityfunctionaltheorywiththeplanewavepseudopotentialmethod.ThecalculationresultsindicatedthatinaNaCl-structuredTiNcontainingdilutesolventAl,thecalculatedformingenergyofthepaireddefectsofsubstituteAlforTi+Nvacancyis1.7325eVperpairofdefects,whilethatofthepaireddefectsofsubstituteAlforN+Tivacancyis10.62eVperpairofdefects.Inotherwords,theenergeticallypreferredoccupationsitesofAlatomsareTisites.InrelationtothereferencesystemofTiN,thesubstituteAlatomsforTiincreasedthechargetransfertoNatoms,whileAlforNdecreasedit.Ontheotherhand,thesubstituteAlforTiexhibitscationicwhilethoseforNexhibitanionic.TheadditionofAlintothecubicTiNresultedinmuchuniversefeatureoftherefractoryindexinthevisiblelightregime.ThecalculatedreflectivityindicatesthatTiNiscolorfulwhile(Ti3Al)N4isgray.Thesmallerlatticeconstant,lowerelasticproperties(theelastictensor,bulkmodulusandYoungmodulus)andhigherhardnessofNaCl-structure(Ti3Al)N4,thanthoseofTiN,werediscussedintermsofeffectsofthesubstituteAlforTionitselectronicstructure.r2005ElsevierB.V.Allrightsreserved.PACS:70.15.Mb;71.20.b;62.20.xKeywords:Densityfunctionaltheory;Ti–Al–Ncompound;Electronicstructure;Mechanicalproperties;Opticalproperties1.IntroductionThegold-coloredTiNcoatingsarewidelyusedashardcoatingforcuttingtoolsduetoitshighARTICLEINPRESSwww.elsevier.com/locate/physb0921-4526/$-seefrontmatterr2005ElsevierB.V.Allrightsreserved.doi:10.1016/j.physb.2004.12.029Correspondingauthor.Tel.:+8602423904856;fax:+8602423893624.E-mailaddress:yyteng@imr.ac.cn(Y.Teng).elastichardnessanddurability.However,itspooroxidationresistanceattemperaturesabove4501Climiteditsapplicationindrymachining.Inordertoseekforbettercoatingswithnotonlyexcellentmechanicalperformancebutalsofavorableoxida-tionresistance,someternaryandmulti-layerfilmssuchasTiAlN,TiZrNandTiN/Tiweredeveloped[1–5].Amongthem,NaCl-structuredTiAlNcoat-ingshavebeenattractedmuchmoreattentionasaresultoftheirbetteroxidationresistanceatelevatedtemperaturesandhardness[6].Ti1xAlxNcoatingsproducedbyvariousvacuumdepositiontechniquesholdeitherNaCl-typecubicstructureatloweraluminumcontent(e.g.xp0.64)orZnS-typehexagonalstructureforhighx.LatticeparametersofcubicTi1xAlxNuniformlyde-creasedwithrespecttoalllatticespacingwithincreasingxvalues,whileanisotropiclatticeexpansionandshrinkageofhexagonalTi1xAlxNwereobservedwiththea-andc-axes[7].ThechangesoflatticeconstantsweresupposedtobereferredtothesmalleratomicAlradiusthanTi.Ontheotherhand,theirhardness,adhesivestrengthandwearresistantincreasedforloweraluminumcontent(e.g.xp0:25)anddecreasedforhigherx[8].Thechangesinthechemicalcompositionmightresultinthevariationsoftheelectronicstructure.Theinfluenceoftargetcomposition,nitrogenpartialpressure,substratetemperatureandbiaspotentialduringdepositionontheelectronden-sitiesandrelativeenergyshiftsoftheoccupiedandunoccupiedvalenceelectronenergystates(mole-cularorbitalderivedfromN(2p),O(2p),Ti(3d/4s)andAl(3p)electronstates)weredeterminedbyXPSandEELSinasynergisticapproach[9].SeveraltheoreticalstudiesofTiNhavebeenreportedusingawidevarietyoftheoreticalapproaches[10,11].Itslatticeconstants,andbulkmodulushavealsobeentheoreticallyestimated[12–14].ForTi1xAlxN,therelationshipbetweentheelectronicstructureandmechanicalpropertiesisnotwellunderstoodtheoreticallyduetolackofinformationaboutitselectronicstructure.Iva-novskyandSabiryanov[15]calculatedthechangesofthetotaldensityofstates(TDOS)andlocaldensityofstates(LDOS),ofthechargedistribu-tionandthenatureoftheinteratomicinteractionsoccurringwiththeintroductionofAlatomsintositesoftheTiNmetallicsublatticeusingtheso-callednon-empiricaldiscrete-variationalmethod.Inthisarticle,theelectronicstructureandmechanicalpropertiesforTiN,Ti–Al–NandAlNwillbestudiedbydensityfunctionaltotalenergycalculations,aimingtorevealthepreferredoccupationsiteofAlindilutesolutionofcubicTi–Al–NandtoprovidetheoreticalunderstandingtheinfluenceofAlontheequilibriumlatticeconstants,opticalandmechanicalpropertiesofTi1xAlxN.2.ModelandcomputedetailsTotalenergycalculationsbasedondensityfunctionaltheorywerecarriedoutusingaplane-wavebasissetfortheexpansionofthesingleparticleKohn–Shamwavefunctions,asimple-mentedintheCASTEPpackage[16].TheVan-derbiltultrasoftpseudopotentials(USPP)[17]wereselectedtodescribeioniccoresinteraction.ThevalanceelectronsforN,Ti,andAlwere2s22p3,3s23p63d24s2and3s23p1,respectively.Theexchange-correlationfunctionalwasdescribedbythegeneralizedgradientapproximationofPerdewBurkeErnzerhofformula(GGA-PBE)[18].ThegeometryoptimizationwasperformedbyBFGSmethod(Broyden–Fletcher–Gold

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