Designing a Family of Aluminum-Containing Fluoroborate Crystals with Enhanced Birefringence and Second-Harmonic Generation Coe ffi cient

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pubs.acs.org/JPCCArticleDesigningaFamilyofAluminum-ContainingFluoroborateCrystalswithEnhancedBirefringenceandSecond-HarmonicGenerationCoefficientsBasedontheFirst-PrinciplesMethodsYangZhong,ZhenpengHu,TongqingSun,*YongfaKong,*andJingjunXuCiteThis:J.Phys.Chem.C2021,125,7431−7438ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Rb3Al3B3O10F(orRbAlBO3.33F0.33)isanF-deficientcrystalgrownathightemperatureandreportedtobeapotentialultravioletordeepultraviolet(DUV)nonlinearopticalcrystal.However,thesystematicstudyofallpossiblecrystalstructuresandopticalpropertiesofMAlBO3F(M=K,Rb,andCs)withtheidealstoichiometricratiohasneverbeenreported.Inthepresentwork,afamilycontaining16differentcrystalstructuresofMAlBO3F(M=K,Rb,andCs)withlargebirefringenceandsecond-harmonicgeneration(SHG)coefficientswaspredictedbythefirst-principlesmethod.AllthesestructuressatisfydynamicstabilityandBornelasticstability.ThemaximumbirefringenceofMAlBO3F(M=K,Rb,andCs)is0.07,whichiscomparabletothebirefringenceofKBe2BO3F2.ThemaximumSHGcoefficientofMAlBO3F(M=K,Rb,andCs)is−0.68pm/V,whichisabout1.74timesthatofKDP(d36(KDP)=0.39pm/V).Inaddition,thepotentialcorrelationbetweenthebirefringenceofMAlBO3F(M=K,Rb,andCs)andthestackingmodesoftheopticalfunctionalunits(BO3andAlO3ForAlO3F2coordinationpolyhedra)inthecrystalhasbeenrevealed.ThisprovidesuswithusefulcluesforthesearchofDUVMαAlβBγOδFεcrystalswithlargebirefringence.1.INTRODUCTIONtherearefewstudiesontheMαAlβBγOδFεsystem.TheThecoredevicesofall-solid-statedeepultraviolet(DUV)birefringenceofBaAlBO3F2(BABF),arepresentativecrystalof21,22lasersaretheDUVnonlinearoptical(NLO)crystals,whichtheMαAlβBγOδFεsystem,isonly0.042.BABFcannotgenerateDUVcoherentlightbelow200nmthroughfrequencycangenerateDUVcoherentlightdirectlythroughfrequency1−3conversionduetoitslowbirefringence.However,Liuetal.conversion.However,DUVNLOcrystalsneedtomeethaverecentlysynthesizedthecrystalofCsAlB3O6F,whoseseveralstrictrequirementsatthesametime:hightransparencybirefringenceis0.09andlargeenoughtoachieveDUVphase-intheDUVregion(bandgap>6.2eV);sufficientlylarge23matching.Thissuggeststhatmanyundiscoveredcrystalsinsecond-harmonicgeneration(SHG)coefficients(dij>0.39pm/V);andenoughbirefringencetoachievephasematching.4theMαAlβBγOδFεsystemmayhaveahigherbirefringenceandDownloadedviaUNIVOFCALIFORNIASANTABARBARAonMay16,2021at12:03:03(UTC).Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.betteropticalpropertiesthanthoseofBABF.Atpresent,KBe2BO3F2(KBBF)istheonlyDUVNLOcrystalZhaoetal.havereportedapotentialDUVNLOcrystal5,6thathaspracticalapplications.However,thehightoxicityofRb3Al3B3O10FwhosepowderSHGeffectisabout1.2timesBeisnotfriendlytotheenvironmentandhumanhealth.In24thatofKDP.Fluorinehasstrongvolatilityathighaddition,itisdifficulttogrowalargehigh-qualityKBBFcrystaltemperatures,whichoftencausesthegrownfluorine-becauseofitsseverelayergrowthhabit.Therefore,thesearchcontainingcrystalstructuretobeF-deficient.Ifwedividetheforaberyllium-freeDUVNLOcrystalhasneverbeenstopped,numberofeachatomintheabovechemicalformulaby3,webuttrialanderrorexperimentalapproachesarenotsuitableforcangetanequivalentnewchemicalformula:RbAlBO3.33F0.33.thehigh-throughputexplorationofDUVNLOmaterials.ThisnewchemicalformulaisobviouslyF-deficient.SomeFFortunately,predictingthestructuresandpropertiesofDUVatomsinthecrystalwerevolatilizedathightemperatures.TheNLOmaterialsbythefirst-principlesmethodcangreatlyshortenthematerialdevelopmentcycleandhasgraduallybecomeanewpatternofDUVNLOmaterialexploration.7−13Received:January16,2021Inrecentyears,someberyllium-freefluoroboratecrystalsRevised:March15,2021thatcanbeusedaspotentialDUVNLOmaterialshavebeenPublished:March26,2021successfullygrown,suchasMB4O6F(M=NH4,Na,Rb,and14−20Cs)andMB5O7F3(M=Ca,Sr).TheresearchinrecentyearshasbeenmainlyfocusedontheMαBβOγFδsystem,but©2021AmericanChemicalSocietyhttps://doi.org/10.1021/acs.jpcc.1c004127431J.Phys.Chem.C2021,125,7431−7438

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlenegativechargecarriedbythevolatilizedFatomswasrules,adjacentcoordinationpolyhedratendnottosharetooreplenishedbythenegativechargeoftheexcessOatoms.Ifmanyvertices.AsthenumberofthesharedverticesbetweensomemeasuresaretakentoavoidthevolatilizationofFatomstwoadjacentcoordinationpolyhedraincreases,thedistanceduringthecrystalgrowth,itistheoreticallypossibletogrowabetweenthecationsatthecenteroftheadjacentcoordinationstoichiometriccrystalwithanidealchemicalformulaofpolyhedrawillbereduced;then,thecoulombrepulsionRbAlBO3F.Kangetal.havereportedapredictedcrystal25betweenthecationswillincreasegreatly.AccordingtostructureofKAlBO3F.However,ourstructurepredictionresultsindicatethatthecrystalstructureofKAlBOFreportedPauling’sfifthrule,crystalstendtocrystallizeinahighly3byKangetal.isonlyoneofthemetastablestructuresofsymmetricalmannertoreducethenumberofuniquestructuralKAlBO3Fbutnottheground-statecrystalstructurewiththeunits.lowestenergy.DuetotheaboveconstraintsofPauling’srulesontheWehavepredicted16stablecrystalstructuresofMAlBO3Fstructureofinorganiccrystals,crystallographicparametersof(M=K,Rb,andCs)inthepresentwork,amongwhichsometheground-stateandmeta-stablestructuresareconstrainedincrystalshaveasignificantlyhigherbirefringencethanthatofasubspacebyPauling’srules,sowedonothavetosearchforBABFcrystalsandexcellentSHGeffects.Byanalyzingthetheground-stateandmeta-stablestructureintheentirestructuralcharacteristicsofthepredictedMAlBO3F(M=K,configurationspace.TocoverthepossiblecandidatesthatRb,andCs)crystals,wefoundthatBO3andAlO3ForAlO3F2willrelaxtotheground-stateandmeta-stablestructures,thecoordinationpolyhedrahavefourtypicalstackingmodesinthecrystal.ItisworthnotingthattherangeofthebirefringenceofcandidateswithfullycoordinatedpolyhedraaregeneratedthesecrystalsiscloselyrelatedtothestackingmodesandthatfromtheMCiterationwithconstraintsonthecrystalthebirefringencesofthesecrystalsindifferentstackingmodessymmetry,interatomicdistances,coordinationnumberofhaveobviousdifferences.WhentheMAlBO3F(M=K,Rb,eachcation,andthenumberofsharedverticesbetweenandCs)crystalstructureisinthemostadvantageousstackingcoordinationpolyhedra.Differentfromcommoniterativemode,itsbirefringencecanreachabout0.07,whichismuchoptimizationschemesinwhichtheabinitiocalculationsathigherthanthatofBABF.Thisenlightensusthatinadditioneachiterationrelyontheresultfromapreviousiteration,thetolookingfornewopticalfunctionalunits,wecanalsoadjustmethodinPAMCARSpreparesallcandidatesbeforetheabthestackingmodeoftheexistingopticalfunctionalunitsinainitiocalculationsstart.Asaresult,theabinitiostructuralcrystaltoincreaseitsbirefringencetogenerateshortercoherentlight.relaxationscanbemassivelyparallelized.Inthepresentwork,thecandidatestructuresofMAlBO3F2.COMPUTATIONALDETAILS(M=K,Rb,andCs)thatmeetPauling’srulesweregeneratedThetraditionalcrystalstructurepredictionmethodistosearchbyPAMCARSandrelaxedbytheViennaAbinitioSimulation32,33forthelowestenergystructuredirectlythroughthePackage(VASP).Thestructureconstraintsusedin26−28mathematicalglobaloptimizationalgorithm.However,PAMCARSaregiveninTableS1intheSupportingthecomputationalcomplexityofthismethodwillincreaseInformation.K3s23p64s1,Rb4s24p65s1,Cs5s25p66s1,Oexponentiallyasthenumberofelementsinthecrystal2s22p4,Al3s23p1,B2s22p1,andF2s22p5statesweretreatedasincreases.Therefore,thisstrategyisonlysuitableforpredictingvalencestates.Theexchangeandcorrelationinteractionofcrystalswithasmallnumberofelements.ManyDUVNLOelectronswasapproximatedbygeneralizedgradientapprox-crystalswithexcellentperformanceoftenhave4−5elements;34imationofthePerdew−Burke−Ernzerhoffunctional.Thetherefore,traditionalcrystalstructurepredictionmethodshavecut-offenergyofthewavefunctionofelectronswas500eV.encounteredabottleneckinthepredictionofDUVNLOcrystals.ItiswellknownthatthestructuresofinorganicTheconjugategradientdescentalgorithmwasusedtorelaxthecrystalsobeyPauling’srules,29,30whichcanbeusedtodesignshapesandatomicpositionsofthecandidatestructures.TheinorganicDUVNLOcrystals.Thisisashortcutwhichcanforceconvergencecriterionforthestructurerelaxationwasreducethecomputationalamountrequiredtopredictthe0.01eV/Å.Theopticalpropertieswerecalculatedwithintheinorganiccrystalstructures.Wehavereportedanalgorithmindependentparticleapproximationandthesecond-ordercalledPauling’srule-guidedMonteCarlo(MC)searchnonlinearsusceptibilities(χ(2))weregivenbythefollowing31abc(PAMCARS)andthecorrespondingsoftware,whichpredict35,36equationstheground-stateandmeta-stableinorganiccrystalstructuresofagivencompositionbycombininganMCsearchinthe(2)(2)(2)χχ=+(VE)χ(VH)configurationspaceconstrainedbyPauling’sruleswithababcabcabcinitiostructuralrelaxations.AccordingtoPauling’sfirstrule,thecoordinationnumberof(2)dkacationisrelatedtoitsradius.Thelargertheradiusoftheχabc(VE)=−∑∑∫3Pabc()BZ4πmn∈∈VB,lCBcation,thehigherthecoordinationnumberofthecation.SincelooDabc()ktheradiusofacationdoesnotvarymuchindifferentcrystals,nlmmthecoordinationnumberofacationisoftenacertainvalueorooωωωωω22()(()kk+−())(kk()2)nlmlmnmlmwithinacertainrangeindifferentcrystals.AccordingtoabcPauling’ssecondrule,inorganiccrystalsshouldmeetlocal−Dmnl()k222electricalneutrality.Therefore,aminimumdistanceshouldbeωωωωωlm()(2kkkklm()−−nm())(lm())keptbetweentheatomswiththesamesignofchemicalvalence16Dabc()k|oomnltoavoidlocalchargeaccumulationthatbreaksthelocal+}222ooelectricalneutrality.AccordingtoPauling’sthirdandfourthωωωωωnm()(2kkkklm()−−nm())(nm()4)~7432https://doi.org/10.1021/acs.jpcc.1c00412J.Phys.Chem.C2021,125,7431−7438

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure1.StablecrystalstructuresofMAlBO3F(M=K,Rb,andCs).(2)dkTable1.StructureandEnergyInformationoftheCrystalχabc(VH)=∑∑∫3Pabc()ml,V∈∈BCnBBZ4πStructuresofMAlBO3F(M=K,Rb,andCs)looabccrystalsasymmetrycellformulaunits(Z)energy/Z(eV)Dlmn()kmooωωωωω22()(()kk+−())(kk()2)KABF-IP6̅c22−47.44nnlnlnmnlKABF-IIP6̅1−47.43abc−Dmnl()kKABF-IIIPmc212−47.30222ωωωωωnl()(2kkkknl()−−nm())(nl())RABF-IP32−47.4116Dabc()k|ooRABF-IIP632−47.41mnl+}RABF-IIIP31−47.40222ooωωωωωnm()(2kkkknl()−−nm())(nm()4)~RABF-IVP212−47.36RABF-VP3c12−47.36abcabcDpmnl()Imkk=[()()()pkpk]RABF-VIR33−47.34mnnllmRABF-VIIPmc212−47.07Here,ωnm(k)=En(k)−Em(k)arethetransitionenergiesatRABF-VIIIP1̅2−47.06thereciprocalpointkbetweenthestateslabeledbymandn.CABF-IP32−47.38pa(k)=⟨ψ(k)|∇|ψ(k)⟩isthemomentummatrixelementmnmanCABF-IIP632−47.38betweentheBlochstatesψm(k)andψn(k).CABF-IIIP3c12−47.27CABF-IVP31−47.273.RESULTSANDDISCUSSIONCABF-VP1̅2−46.99aThescatterplotoftheenergyoftherelaxedcandidateKAlBO3F,RbAlBO3F,andCsAlBO3FareabbreviatedasKABF,structuresofMAlBO3F(M=K,Rb,andCs)isshowninRABF,andCABF,respectively.FigureS1intheSupportingInformation.ThreestablecrystalstructuresofKAlBO3F,eightstablecrystalstructuresofexample,themaximumenergydifferenceamongthethreeRbAlBO3F,andfivestablecrystalstructuresofCsAlBO3FKAlBO3Fcrystalstructuresisonly0.02eV/atom.Mostofthewerepredicted,asshowninFigure1.ThecrystallographicpredictedcrystalstructuresofMAlBO3F(M=K,Rb,andCs)parametersofthesecrystalsarelistedinTableS2inthehaveNLOactivity,exceptfortwocentrosymmetriccrystalsSupportingInformation.Table1liststhestructureandenergy(RbAlBO3F-VIIIandCsAlBO3F-V).AhexahedralstructureofinformationofthepredictedcrystalstructuresofMAlBOF(MAlOFisformedaroundeachAl3+ioninthethreestable332=K,Rb,andCs).ThestructureofKAlBO3FreportedbyKangKAlBO3Fcrystalstructures.Thedistancebetweentheatomic25+etal.isKAlBO3F-II,listedinTable1.TheenergyoflayersinthecrystalincreasesastheionicradiusofM(M=K,KAlBOF-IIishigherthanthatofKAlBOF-I,sothestructureRb,andCs)increases,asshowninFigure2.Al3+ionscannot33reportedbyKangetal.isoneofthemetastablestructuresofformbondswiththeupperandlowerF−ionsatthesametimeKAlBO3F.ItcanbeseenfromTable1thattheenergyinthecrystalstructuresofRbAlBO3FandCsAlBO3F.Thus,differencebetweenthestablecrystalstructuresofthesameonlyatetrahedralstructureofAlO3Ftendstobeformedcomponentisverysmall.TakingtheKAlBOFcrystalasanaroundeachAl3+ioninthecrystalstructuresofRbAlBOFand337433https://doi.org/10.1021/acs.jpcc.1c00412J.Phys.Chem.C2021,125,7431−7438

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure2.DistancebetweentheatomiclayersinthreetypicalcrystalstructuresofMAlBO3F(M=K,Rb,andCs).Figure3.Phononspectraandtheelasticstrainenergycurves.Phononspectraof(a)KAlBO3F-I,(b)RbAlBO3F-I,and(c)CsAlBO3F-I.Theelasticstrainenergycurvesof(d)KAlBO3F-I,(e)RbAlBO3F-I,and(f)CsAlBO3F-Iunderdifferentstrains.37CsAlBO3F.Asaresult,thecrystalstructuresofRbAlBO3Fandhexagonalsystem,theseelasticcomponentsneedtomeettheCsAlBO3FarenotisomorphicwiththatofKAlBO3F.followingconditionsAstablecrystalstructureneedstosatisfydynamicstability37CCCC>||,22<(CCC+),>0,C>0andBornelasticstability.ThephononspectraofMAlBO3F-I1112133311124466(M=K,Rb,andCs)areshowninFigure3a−c.Thephonon(2)spectraofotherpredictedstablecrystalstructuresofMAlBO3F(M=K,Rb,andCs)areshowninFigureS2intheSupportingTheelasticstrainenergyperunitvolumeforthetrigonalInformation.Theabsenceofimaginaryfrequenciesinallthecrystalsystemisphononspectraindicatesthatallthepredictedcrystal12121212structuresaredynamicallystable.TheelasticcoefficientsofUCCCC()εεεεε=+++111112333444MAlBOF(M=K,Rb,andCs)werealsocalculatedtocheck22223theelasticstabilityofthecrystals.KAlBO3F-Ibelongstothe++++1CCCCε21ε2εεεε44566612121313hexagonalcrystalsystem.RbAlBO3F-IandCsAlBO3F-Ibelong22tothetrigonalcrystalsystem.Theelasticstrainenergyperunit++−+CCCC1414εε1323εε1424εε1456εε(3)volumeforthehexagonalcrystalsystemcanbeexpressedas1111whereC11,C12,C13,C14,C33,C44,andC66areseven2222UCCCC()εεεεε=+++111112333444componentsoftheelasticmatrixofthetrigonalcrystalsystem.2222Accordingtothenecessaryandsufficientelasticstability1212conditionforthetrigonalsystem,37theseelasticcomponents++++CCCC445ε666ε1212εε131εε322needtomeetthefollowingconditions+C1323εε(1)212CCC11>||12,044>,C13

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure4.Electronicstructuresandrefractiveindexcurves.Thebandstructuresof(a)KAlBO3F-I,(b)RbAlBO3F-I,and(c)CsAlBO3F-I.ThePDOSof(d)KAlBO3F-I,(e)RbAlBO3F-I,and(f)CsAlBO3F-I.Therefractiveindexcurvesof(g)KAlBO3F-I,(h)RbAlBO3F-I,and(i)CsAlBO3F-I.Accordingtoeqs1and3,theelasticcoefficientsofcrystalsisintherangeof6.1−6.4eV.ThebandgapofMAlBO3F-I(M=K,Rb,andCs)wereobtainedbyfittingKAlBO3FismuchhigherthanthatofMAlBO3F(M=Rb,Cs),thestrainenergycurvesunderdifferentstrains,asshowninwhereasthebandgapsofRbAlBO3FandCsAlBO3FareveryFigure3d−f.TheelasticmatricesofallcrystalsofMAlBO3Fclose.TheMAlBO3F(M=K,Rb,andCs)crystalexhibits(M=K,Rb,andCs)arelistedinTableS3intheSupportingexcellentNLOproperties.Forexample,themaximumSHGInformation.Itcanbeverifiedbyeqs3and4thatMAlBO3F-IcoefficientsofKAlBO3F-II,RbAlBO3F-I,andCsAlBO3F-IVare(M=K,Rb,andCs)meetstheBornelasticstabilitycriterions.intherangeof1.45−1.74×d36(KDP).AsshowninFigureSimilarly,wehaveverifiedthatallpredictedcrystalsmeetthe4d−f,thestatesofMAlBO3F(M=K,Rb,andCs)neartheBornelasticstabilitycriteriaaccordingtotheelasticmatricesbandgaparemainlycontributedbyB,O,andFatoms.ThislistedinTableS3intheSupportingInformation.indicatesthattheopticalpropertiesofMAlBO3F(M=K,Rb,38,39TheHSE06hybridfunctionalwasusedtocalculatetheandCs)crystalsaremainlydeterminedbytheBO3bandstructureandpartialdensityofstates(PDOS)ofcoordinationpolyhedraandarealsoaffectedbytheFatomsMAlBO3F(M=K,Rb,andCs).TheenergybandstructuresintheAlO3F2orAlO3Fcoordinationpolyhedra.Therefore,itandPDOSsofMAlBO3F-I(M=K,Rb,andCs)areshownincanbeexpectedthatdifferentstackingmodesofBO3andFigure4a−f.ThebandgapsofKAlBO3F-I,RbAlBO3F-I,andAlO3F2orAlO3FcoordinationpolyhedrainthecrystalwillCsAlBO3F-Iare7.2,6.1,and6.1eV,respectively.ThecausethedifferencesintheopticalpropertiesofMAlBO3F(Mconductionbandminimums(CBMs)ofMAlBO3F-I(M==K,Rb,andCs)crystals.K,Rb,andCs)arealllocatedatpointG.Table2liststhebandMostofthepredictednon-centrosymmetricMAlBO3F(M=gapsandopticalpropertiesofallpredictednon-centrosym-K,Rb,andCs)crystalsbelongtothetrigonalandhexagonalmetriccrystals.ThebandgapofKAlBO3Fcrystalsisinthecrystalsystems.ThestackingofBO3andAlO3F2orAlO3Frangeof6.7−7.2eV,thebandgapofRbAlBO3Fcrystalsisincoordinationpolyhedrainthecrystalmainlypresentsfourtherangeof5.9−6.5eV,andthebandgapofCsAlBO3Fmodes:α,β,γ,andδ(asshowninFigure5a−d).Intheαand7435https://doi.org/10.1021/acs.jpcc.1c00412J.Phys.Chem.C2021,125,7431−7438

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleTable2.OpticalPropertiesandtheStackingModesofthecanbeinferredthatthebirefringenceofBABFisaround0.04.Non-centrosymmetricCrystalStructuresofMAlBO3F(M=Coincidentally,theexperimentallymeasuredbirefringenceof21K,Rb,andCs)BABFis0.042,whichisingoodagreementwithourtheoreticalanalysis.EgapstackingaThechangeinthebirefringenceofthecrystalswithdifferentcrystals(eV)Δn@1064nmdij@1064nm(pm/V)modesstackingmodesispotentiallyrelatedtothechangeintheKAlBO3F-I7.20.062d22=−0.36αeffectivemassoftheelectronsinthesecrystals.TheeffectiveKAlBO3F-II7.20.062d11=−0.68,d22=0.40αmasstensorofelectronscanshowtheanisotropyofelectronKAlBO3F-III6.70.070d15=0.00,d24=0.42,αd33=−0.33motion,whichoftencausetheanisotropyofrelatedphysicalRbAlBO3F-I6.10.041d11=0.57,d15=−0.12,γpropertiesinthematerial.Thepolarizationofthematerialisd22=0.04,d33=−0.12mainlycontributedbytheelectronsattheCBM.Therefore,weRbAlBO3F-II6.10.041d15=−0.10,d33=−0.12γcalculatedtheeffectivemassoftheelectronsatCBMintheRbAlBO3F-III6.40.046d11=−0.58,d15=−0.08,βMAlBO3F(M=K,Rb,andCs)crystalswithα,β,γ,andδd22=−0.23,d33=−0.10stackingmodes,respectively,asshowninFigure6.TheRbAlBO3F-IV5.90.032d14=−0.11,d16=0.11,d22=0.14,d23=−0.27RbAlBO3F-V6.50.051d15=−0.06,d22=0.22,βd33=−0.04RbAlBO3F-VI6.20.036d11=0.52,d15=0.13,δd22=−0.36,d33=0.08RbAlBO3F-VII6.50.068d15=0.01,d24=0.61,αd33=−0.56CsAlBO3F-I6.10.035d11=0.59,d15=−0.24,γd22=0.03,d33=−0.54CsAlBO3F-II6.10.035d15=0.22,d33=0.53γCsAlBO3F-III6.40.045d15=0.16,d22=0.22,βd33=0.30CsAlBO3F-IV6.40.045d11=−0.60,d15=0.17,βd22=−0.27,d33=0.30aThestackingmodeofRbAlBO3F-IVisnotgiveninthetablesincethestackingmodeofRbAlBO3F-IVisunrepresentativeandquiteFigure6.EffectivemassoftheelectronsattheCBMandthedifferentfromthoseoftheothercrystals.birefringenceinthecrystalswithdifferentstackingmodes.βstackingmodes,BO3coordinationpolyhedraandAlO3F2oreffectivemassoftheelectronwascalculatedbyfittingtheAlO3Fcoordinationpolyhedraarestackedalongseparateaxes.followingequationIntheγstackingmode,BO3andAlO3FcoordinationÄÅÅÉÑÑ2polyhedraarestackedalternatelyalongthesameaxis.IntheÅÅÅÅ1ÑÑÑÑ1∂En()k=δstackingmode,BO3,AlO3F,andMO3F3coordinationÅÅÅÅm*()kÑÑÑÑℏ2∂∂kkÇnÖabab(5)polyhedraarestackedalternatelyalongthesameaxis.Thebirefringences(Δn)ofMAlBO3F(M=K,Rb,andCs)whereEn(k)istheenergyeigenvalueofthenthBlochstateincrystalswithdifferentstackingmodeshaveobviousdifferences.theBrillouinzone.TheeffectivemasstensorofanelectroncanThebirefringenceofthecrystalwiththeαstackingmodeisinshowthestrengthofthecrystalfieldactingontheelectron.therangeof0.062−0.070,thebirefringenceofthecrystalwithSincethesecrystalsareuniaxial,thecalculatedeffectivemassoftheβstackingmodeisintherangeof0.045−0.051,thetheelectronalongthexandydirections(m*x(k)andm*y(k))birefringenceofthecrystalwiththeγstackingmodeisintheareequalwithinthenumericalerror,whichindicatesthattherangeof0.035−0.041,andthebirefringenceofthecrystalwithcrystalfieldisequalalongthexandydirectionsofthecrystal.theδstackingmodeisabout0.036.InthecrystalstructureofTherefore,thecontributionofelectronstothepolarizationinBABF,BO3andAlO3F2coordinationpolyhedraarestackedthexandydirectionsisthesame.Inaddition,Figure6showsalternatelyalongthesameaxis,asshowninFigure5e.Thisthatm*x(k)andm*y(k)arenotsensitivetothewaythecrystalsstackingmodeislabeledwithεandissimilartotheγstackingarestacked,butm*z(k)changessignificantlywiththestackingmode.Thus,thebirefringenceofBABFmaybesimilartothatmodes.Asthedifferencebetweenm*z(k)andm*x(k)decreases,oftheMAlBO3F(M=Rb,Cs)crystalwiththeγstackingtheelectronsbehavemoresimilarlyinalldirections;then,themode.AccordingtotherangeofthebirefringenceoftheanisotropyofthepolarizationinthecrystalsdecreasesandasaMAlBO3F(M=Rb,Cs)crystalwiththeγstackingmode,itresult,thebirefringence(Δn)ofthecrystaldecreases.IntheFigure5.FivestackingmodesinMAlBO3F(M=K,Rb,andCs)andBABF.7436https://doi.org/10.1021/acs.jpcc.1c00412J.Phys.Chem.C2021,125,7431−7438

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlecrystalwiththeαstackingmode,thedifferencebetweenProgramofChina(2019YFA0705000),andtheProgramform*x(k)andm*z(k)isthelargestandthecorrespondingChangjiangScholarsandInnovativeResearchTeaminbirefringenceisthelargest.However,inthecrystalwiththeδUniversityofChina(IRT_13R29),the111ProjectofChinastackingmode,thedifferencebetweenm*x(k)andm*z(k)isthe(grantno.B07013).smallestandthecorrespondingbirefringenceisthesmallest.■4.CONCLUSIONSREFERENCES(1)Peng,Q.-J.;Zong,N.;Zhang,S.-J.;Wang,Z.-M.;Yang,F.;Inconclusion,wehavepredicted16stablecrystalstructuresofZhang,F.-F.;Xu,Z.-Y.;Zhou,X.-J.DUV/VUVAll-Solid-StateLasers:MAlBO3F(M=K,Rb,andCs)usingPAMCARSandVASPTwentyYearsofProgressandtheFuture.IEEEJ.Sel.Top.Quantuminthepresentwork.ThedynamicandBornelasticstabilitiesofElectron.2018,24,1602312.thesestructuresweretestedbyphononspectraandelastic(2)Xuan,H.;Igarashi,H.;Ito,S.;Qu,C.;Zhao,Z.;Kobayashi,Y.coefficients.TheBO3andAlO3ForAlO3F2coordinationHigh-Power,Solid-State,DeepUltravioletLaserGeneration.Appl.Sci.polyhedrainMAlBO3F(M=K,Rb,andCs)crystalshavefour2018,8,233.typicalstackingmodes.Thebirefringences(Δn)ofMAlBO3F(3)Tran,T.T.;Yu,H.;Rondinelli,J.M.;Poeppelmeier,K.R.;(M=K,Rb,andCs)crystalswithdifferentstackingmodesHalasyamani,P.S.DeepUltravioletNonlinearOpticalMaterials.haveobviousdifferences.ThemaximumbirefringenceoftheChem.Mater.2016,28,5238−5258.(4)ShivHalasyamani,P.;Rondinelli,J.M.TheMust-haveandNice-KAlBO3Fcrystalwithαstackingmodecanreach0.07,whichisto-haveExperimentalandComputationalRequirementsforFunc-comparabletothebirefringenceofKBBF.MAlBO3F(M=K,tionalFrequencyDoublingDeep-UVCrystals.Nat.Commun.2018,9,Rb,andCs)crystalsalsohaveexcellentNLOproperties,and2972.themaximumSHGcoefficientsofmanyMAlBO3F(M=K,(5)Chen,C.T.;Wang,G.L.;Wang,X.Y.;Xu,Z.Y.Deep-UVRb,Cs)crystalsaremuchhigherthanthatofKDP.TheNonlinearOpticalCrystalKBe2BO3F2Discovery,Growth,OpticalsuccessfulpredictionofMAlBO3F(M=K,Rb,andCs)PropertiesandApplications.Appl.Phys.B:LasersOpt.2009,97,9−crystalswithexcellentopticalpropertiesleadsustobelievethat25.MαAlβBγOδFε(M=K,Rb,Cs,Mg,Ba,Ca,...)crystalsmay(6)Cyranoski,D.MaterialsScience:China’sCrystalCache.Naturehavemassiveuntappedpotentialthatawaitsfurtherresearch.2009,457,953−955.(7)Lin,Z.;Jiang,X.;Kang,L.;Gong,P.;Luo,S.;Lee,M.-H.First-■principlesMaterialsApplicationsandDesignofNonlinearOpticalASSOCIATEDCONTENTCrystals.J.Phys.D:Appl.Phys.2014,47,253001.*sıSupportingInformation(8)Rondinelli,J.M.;Kioupakis,E.PredictingandDesigningOpticalTheSupportingInformationisavailablefreeofchargeatPropertiesofInorganicMaterials.Annu.Rev.Mater.Sci.2015,45,https://pubs.acs.org/doi/10.1021/acs.jpcc.1c00412.491−518.Computationaldetailsandadditionalresults(PDF)(9)Bian,Q.;Yang,Z.;Wang,Y.;Mutailipu,M.;Ma,Y.;Pan,S.Computer-AssistedDesignofaSuperiorBe2BO3FDeep-UltravioletNonlinear-OpticalMaterial.Inorg.Chem.2018,57,5716−5719.■AUTHORINFORMATION(10)Bian,Q.;Yang,Z.;Wang,Y.;Cao,C.;Pan,S.PredictingGlobalCorrespondingAuthorsMinimuminComplexBerylliumBorateSystemforDeep-ultravioletTongqingSun−SchoolofPhysicsandTheMOEKeyFunctionalOpticalApplications.Sci.Rep.2016,6,34839.LaboratoryofWeak-LightNonlinearPhotonics,Nankai(11)Zhang,B.;Tikhonov,E.;Xie,C.;Yang,Z.;Pan,S.PredictionofUniversity,Tianjin300071,P.R.China;Email:suntq@FluorooxoborateswithColossalSecondHarmonicGeneration(SHG)CoefficientsandExtremelyWideBandGaps:Towardsnankai.edu.cnModulatingPropertiesbyTuningtheBO3/BO3FRatioinLayers.YongfaKong−SchoolofPhysics,TheMOEKeyLaboratoryAngew.Chem.,Int.Ed.2019,58,11726−11730.ofWeak-LightNonlinearPhotonics,andTEDAInstituteof(12)Zhang,B.;Zhang,X.;Yu,J.;Wang,Y.;Wu,K.;Lee,M.-H.AppliedPhysics,NankaiUniversity,Tianjin300071,P.R.First-PrinciplesHigh-ThroughputScreeningPipelineforNonlinearChina;Email:kongyf@nankai.edu.cnOpticalMaterials:ApplicationtoBorates.Chem.Mater.2020,32,6772−6779.Authors(13)Yang,Z.;Tudi,A.;Lei,B.-H.;Pan,S.EnhancedNonlinearYangZhong−SchoolofPhysics,NankaiUniversity,TianjinOpticalFunctionalityinBirefringenceandRefractiveIndex300071,P.R.China;orcid.org/0000-0002-4855-6310DispersionoftheDeep-UltravioletFluorooxoborates.Sci.ChinaZhenpengHu−SchoolofPhysics,NankaiUniversity,TianjinMater.2020,63,1480−1488.300071,P.R.China;orcid.org/0000-0002-8469-1683(14)Shi,G.;Wang,Y.;Zhang,F.;Zhang,B.;Yang,Z.;Hou,X.;Pan,JingjunXu−SchoolofPhysics,TheMOEKeyLaboratoryofS.;Poeppelmeier,K.R.FindingtheNextDeep-UltravioletNonlinearWeak-LightNonlinearPhotonics,andTEDAInstituteofOpticalMaterial:NH4B4O6F.J.Am.Chem.Soc.2017,139,10645−AppliedPhysics,NankaiUniversity,Tianjin300071,P.R.10648.(15)Zhang,Z.;Wang,Y.;Zhang,B.;Yang,Z.;Pan,S.PolarChinaFluorooxoborate,NaB4O6F:APromisingMaterialforIonicCompletecontactinformationisavailableat:ConductionandNonlinearOptics.Angew.Chem.,Int.Ed.2018,57,https://pubs.acs.org/10.1021/acs.jpcc.1c004126577−6581.(16)Wang,Y.;Zhang,B.;Yang,Z.;Pan,S.Cation-TunedSynthesisNotesofFluorooxoborates:TowardsOptimalDeep-UltravioletNonlinearTheauthorsdeclarenocompetingfinancialinterest.OpticalMaterials.Angew.Chem.,Int.Ed.2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