K, Rb) compounds: = Comparative (X Ab initio calculations study of Optical cubic, and orthorhombic structures of XCaCl Optik

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Abderrahim Hadj Larbi

^a,b,c,∗

, Said Hiadsi

^a

, Moufdi Hadjab

^b,c

, M.A. Saeed

^d,e

aLaboratoiredeMicroscopeElectroniqueetSciencesdesMatériaux,Universitéd’OrandesSciencesetdelaTechnologieMohamed Boudiaf,DépartementdeGéniePhysique,BP1505,Elm’naouar,Oran,Algerie

bResearchCenterinIndustrialTechnologiesCRTI,P.O.Box64,Cheraga,16014,Algiers,Algeria

cThinFilmsDevelopmentandApplicationsUnit–(UDCMA),Setif,Algeria

dDepartmentofPhysics,FacultyofScience,UniversitiTeknologiMalaysia,Skudai,81310,JohorBahru,Malaysia

eDivisionofScienceandTechnology,UniversityofEducation,Lahore,Pakistan

a rt i c l e i n f o

Articlehistory:

Received26February2018 Accepted28March2018

Keywords:

DFT FP-LAPW Perovskites Opticalparameters Scintillators

a b s t ra c t

ThestudypredictstheopticalpropertiesofcubicandorthorhombicstructuresofXCaCl3

(X=K,Rb)perovskitecompoundsthroughelectronicbandstructurecomputationwithin theframeworkofdensityfunctionaltheory(DFT).Thegroundstatefunctionsarecomputed employingfullpotentiallinearizedaugmentedplanewave(FP-LAPW)method.Improved bandgapvaluesandtheelectronicaswellasopticalpropertieswerecalculatedbyTranand BlahamodiﬁedBecke–Johnson(mBJ)functional.Thestudiedcompounds’densityofstates revealsthatCl-pstatesdominatethevalenceband.Tounderstandtheopticalproperties, andpredictingtheopticallyisotropicnatureofthesematerials,therealandimaginaryparts ofdielectricfunction,refractiveindex,absorptioncoefﬁcient,andenergylossspectraare plotted.Thepresentstudyshowsagreatpotentialutilizationinceramicscintillators.

1. Introduction

Overthepastfewdecades,therehasbeenahugeincreaseinthequantityofhalidescintillatorsbecauseoftheirdesired properties:highlightyield,energyresolution,fastdecay,thermalstability.Itcanbeusedasdetectorsofradiationindifferent technologicaldevices,andformedicaldiagnostics[1–6].InorganichalideperovskitesofthetypeABX3(A=alkali,B=alkali- earth,X=halide)typeiswidelyusedscintillators,andplayingagreatpartinthedevelopmentofdevicesfordetectionof ionizingradiation.ItwasfoundthatKCaCl₃,andRbCaCl₃ alkali-halidecrystalsshowedsimilartransitionpatterns,being cubicattemperatureabove635^◦CforKCaCl3,300^◦CforRbCaCl3,andorthorhombicstructuresatroomtemperatureforthe bothcompounds[7,8].Inrecentyears,variousapproachesandworkshavebeenpublished,whereasthepropertiesofcubic structuresofKCaCl₃,andRbCaCl₃perovskiteswerecalculated[9,10].Theluminescencepropertiesofvariousimpuritiesin thesecompoundswerealsoinvestigated[11–16].Astudywasconductedtoknowthebehaviorofanotherhalideperovskites KCaF₃,RbCaF₃[17].

Accordingtoauthors’bestknowledge,notheoreticalcalculationsoftheorthorhombicstructureofKCaCl₃,andRbCaCl₃ compoundswerecarriedoutusingabinitioapproach.Theobjectiveofthepresentcomparativestudyistounderstandthe

∗ Correspondingauthorat:LaboratoiredeMicroscopeElectroniqueetSciencesdesMatériaux,Universitéd’OrandesSciencesetdelaTechnologie MohamedBoudiaf,DépartementdeGéniePhysique,BP1505,Elm’naouar,Oran,Algerie.

E-mailaddress:Abderrahim.hadjlarbi@univ.usto.dz(A.HadjLarbi).

https://doi.org/10.1016/j.ijleo.2018.03.128

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Fig.1.Crystalstructureforcubic,andorthorhombicstructuresofXCaCl3(X=K,Rb)compounds.

opticalpatternsoftransitioninorthorhombicandcubicperovskitesXCaCl₃,whereX=K,Rbthroughthecalculationsofthe structural,electronic,andopticalproperties.

2. Computationaldetails

WeemployedtheFP-LAPWmethod,basedondensityfunctionaltheory(DFT)[18,19],implementedinthepackage Wien2k[20],toperformallcalculations.First,weusedthegeneralizedgradientapproximation(GGA-PBE)tooptimize crystalstructuresandcomputeelectronicbands[21].Furthermore,weappliedthemBJapproximationformoreaccuracyin calculationofbandsstructuresandopticalproperties[22].Theplanewavecut-offenergyis−6Rydtoseparatethevalence andcorestates.ThematrixsizeR_mt×K_max=9,whereK_maxistheplane’swavecutoff,R_mtisthesmallestofallatomicsphere radii.TheradiiofK,Rb,ClandCaatomicsphereweresetto2.4,2.4,2.4and2.2a.u.,respectively.Themaximumnumber lforpartialwavesinsidethemufﬁn-tinsphereswasexpandeduptolmax=10.Thek-integrationovertheBrillouinzone wasselectedbyusingMonkhorst-Packmethod[23].Wehaveused10×10×10kmeshintheirreduciblewedgeoftheBZ forthecubicstructure,and11×7×11fortheorthorhombicstructure.Theself-consistentcalculationisconsideredtobe convergedwhenthetotalenergydifferenceislessthan0.0001Ryd.Theelectronicconﬁgurationsforallchemicalatomsare asfollows:3s²3p⁶4s¹forK,4s²4p⁶5s¹forRb,3s²3p⁶4s²forCa,and3s²3p⁵forCl.

3. Resultsanddiscussion 3.1. Structuralproperties

TheXCaCl₃(X=K,Rb)compoundsinvestigatedherehavecubicstructureofspacegroupPm-3m(no.221)athightem- perature,andorthorhombic structurePnma(no.62)ata lowertemperature[7,8].Thecrystalstructuresareshown in Fig.1.

Table1

OptimizedinternalatomicpositionsfromtotalenergyminimizationusingFP-LAPWforcubic,andorthorhombicstructures.

(a)Cubicstructures

KCaCl3 RbCaCl3

Atom x y z x y z

X 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Ca 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000

Cl 0.0000 0.5000 0.5000 0.0000 0.5000 0.5000

(b)Orthorhombicstructures

KCaCl3 RbCaCl3

Atom x y z x y z

X 0.4371 0.2500 0.0155 0.4419 0.2500 0.0164

Ca 0 0 0 0 0 0

Cl1 0.1984 0.0506 0.3043 0.2060 0.0420 0.2945

Cl2 0.5328 0.2500 0.6005 0.5152 0.2500 0.5820

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Othercalc. a(A^o) 5.410[9] 5.420[10] – –

b(A^o) 5.410 5.420 – –

c(A^o) 5.410 5.420 – –

␣=␤=␥(^o) 90 90 90 90

B(GPa) 23.830[9] 26.080[10] – –

B’ 4.296[9] 3.850[10] – –

Table3

CalculatedbandgapofXCaCl3(X=K,Rb)compoundsineVusingPBE,andTB-mBJfunctionals.

KCaCl3(Cubic) RbCaCl3(Cubic) KCaCl3(Ortho) RbCaCl3(Ortho)

PBE 4.811 4.921 5.531 5.452

TB-mBJ 7.125 7.003 7.287 7.132

Othercalc. 4.734[9] 5.03[10] – –

Fig.2. Bandstructureandtotaldensityofstates(TDOS)calculatedforcubicandorthorhombicstructuresofKCaCl3,andRbCaCl3,usingTB-mBJfunctional.

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Fig.3.Partialdensityofstates(PDOS)calculatedforcubicandorthorhombicstructuresofKCaCl3,andRbCaCl3,usingTB-mBJfunctional.

Fig.4. Real(upperpanel)andimaginary(lowerpanel)partsofdielectricconstantscalculatedforcubicandorthorhombicstructuresofKCaCl3,andRbCaCl3, usingTB-mBJfunctional.

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Fig.5.Refractiveindex(n),andextinctioncoefﬁcients(k)forcubicandorthorhombicstructuresofKCaCl3,andRbCaCl3.

First,weoptimizedthelatticeparameters,andusingGGA-PBEapproximationtorelaxtheinternalatomicpositions (Table1).Inordertorelaxtheatomicpositions,theexperimentallatticeparameterswereusedasinputandthenatomic positionswereoptimizedbyminimizingtheforcesonatoms.Tocalculatethelatticeconstants,bulkmodulus(B₀)and pressurederivativeofthebulkmodulus(B₀),theBirch–Murnaghan’sequationofstate[24]wasusedandcomputedvalues oftheseparametersalongwiththepreviousstudiedexperimentalandtheoreticalonesaregiveninTable2.Thestudied latticeparametersagreewellwiththepreviousones[9,10].

Thepresentcomputedresults(Table2)agreewellwiththeprevioustheoreticalcalculationandexperimentalmea- surements.Tothebestofauthors’knowledge,notheoreticalandexperimentaldataoforthorhombicstructuresofthese compoundsavailabletocomparewiththepresentwork.

3.2. Electronicproperties

Withtheoptimizedstructures,wecalculatedthebandstructureofthecubicandorthorhombicperovskites,XCaCl3(X=K, Rb),usingtwofunctionals(PBE,TB-mBJ).Thebandstructures,usingTB-mBJalone,areshowninFig.1,andtherelatedband gapsaregiveninTable3(forbothfunctional).

Fromthetable,itcanbeseenthatTB-mBJvaluesaresuperiorcomparedtotheunder-estimatedPBE-GGAcalculations.For theorthorhombicstructures,andduetothelackofanypreviousexperimentalortheoreticalinvestigations,nocomparison ispossible.Theresultsrevealthatallstudiedcompoundsareinsulatorshavingindirectbandgapbetweenthevalenceband maximumatRsymmetrypointandtheconductionbandminimumat symmetrypointforthecubicstructures,anda directbandgap−fortheorthorhombicstructures.

Fig.2showsthedensitiesofstatesofcubicandorthorhombicXCaCl₃(X=K,Rb)withTB-mBJapproximation.Forthecubic phaseofKCaCl3,thebottommostvalencebandisextendedfrom−12.9to−12.4eVandmainlycorrespondstoCl-sstates hybridizedwithCa-pandK-p.Thesecondregionfrom−12to−11.8eVisformedprimarilyfromtheK-pstateshybridized withCl-sstates.ThethirdregionthatisnearertoFermilevel,rangingaround−2.2eVto0eVhavepredominantlyCl-p characterwithverylesscontributionfromtheCa-sandCa-p.ForRbCaCl3 (cubicphase),thebottomregionisextending around−12.9to−12.4eVdominatedmostlybyCa-pstates.Thetopmostbandregionspreadingfrom−2.1to0eVisbecause ofhybridizationoftheCl-p,Ca-p,andCa-sstates(lesscontributionfromCa)(Fig.3).

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Fig.6. AbsorptionspectraforcubicandorthorhombicstructuresofKCaCl3,andRbCaCl3.

FortheorthorhombicphaseofKCacl3,thebottommost,middle,andtopofthevalencebandsarearound−12.7to−12.2eV,

−11to−10.7eV,and−1.8to0eV,respectively.ThebottomregionisdominatedbytheCl-sstateswithlesscontribution fromtheCa-p,andK-pstates,whilethemiddleregionisdominatedbyK-phybridizedwiththeCl-sandCl-pstates.For thetopofthevalencebandregion,thecontributionismainlyfromthehybridizationofCl-p,Ca-s,Ca-p,K-p,K-sstates(the contributionislessfromCaandK).IncaseofRbCaCl₃,thebottomofthevalencebandregionextendsfrom−12.7to−12.3eV andisdominatedmostlybytheCl-sstateshybridizedwiththeCa-p,andRb-pstates.Themiddleofthevalencebandregion, extendsfrom−8.1to−7.8eV,isdominatedbytheRb-pstateshybridizedwiththeCl-p,andCl-sstates.Theregionnearthe Fermilevelspreadingfrom−1.8to0eV,isduetohybridizationoftheCl-p,Ca-p,Ca-s,Rb-pandRb-d(lesscontributionfrom CaandRb).

Forthebothstructures(thecubic,andtheorthorhombic),conductionbandisessentiallydominatedbyRb-dstatesfor theRbCaCl₃compounds,andhybridizedwithK,Ca,andClfortheKCaCl₃.

Inthecaseofcubicphase,andamongthebandregions,thelowestbandisdominatedbyCl-sstatesinthetwocompounds (KCaCl₃,andRbCaCl₃),andthecontributionofX-p(X=K,Rb)statesinthemiddleregioncanbeseenonlyinKCaCl₃.Thetop ofthevalencebandiscreatedmostlyofCl-p,whereasCa-pandCa-sstatesarepresentinKCaCl3,andRbCaCl3.

Inthecaseoforthorhombicphaseofthebothcompounds,Cl-sstatesaredominantinthelowestbandregion,andX-p (X=K,Rb)statesinthemiddleregionwiththepresenceofthechlorinestates.Forthetopmostregion,thetwocompounds havemainlythesamecharacterhavingcontributionmostlyofCl-pbecauseofthehighelectronegativityofchlorinewhen comparedtootherelements.

3.3. Opticalproperties

Theunderstandingoftheopticalpropertiesofthesecompoundsisthesecondstepafterstudyingitselectronicstructure.

Inthissection,weusedtheTB-mBJfunctionaltocalculatetheopticalpropertiesofthestudiedcompoundsbecauseofthe enhancedband-gapvalues.Thecalculationsneedadensemeshofkpoints,weuse21×21×21forthecubicstructure, and14×9×14fortheorthorhombicstructure.Tothebestofourknowledge,therearenoexperimentaldataavailableto compareourresults.

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Fig.7.Electronenergylossfunctionforcubic,andorthorhombicstructuresofKCaCl3,andRbCaCl3.

Thereisadirectrelationbetweenthecomplexdielectricfunctionandtheenergybandstructureofsolids.Theoptical propertiesofXCaCl₃(X=K,Rb)aredescribedbythecomplexdielectricfunctionε=ε₁+iε₂[25].Fig.4showsthecalculated real(dispersive)partε1andtheimaginary(absorptive)partε2asafunctionofthephotonenergy.

Intheimaginarypartofthedielectricconstantε₂,whichisrelatedtotheelectronictransitionsfromtheoccupiedto theunoccupiedstates[26].Fig.4(a,andb)showsasetofpeaksfrom8.11eVto15.73eV,and8.02eVto15.96eVforcubic structureofKCaCl3,andRbCaCl3respectively.ThesepeaksarisemainlyduetothetransitionfromCl-pstatestoconduction band.Atahigherenergy,andduetothetransitionfromCl-s,andX(X=K,Rb)-pstatestohigherenergylevelsofconduction band,weobservepeaksaround23eV–27.44eV,and19.56eV–27.42eVforKCaCl3,andRbCaCl3respectively(Fig.4a,b).For theorthorhombicstructure,wecansee(Fig.4c,andd)peaksfrom7.77eVto16.30eVforKCaCl3,and7.71eVto16.33for RbCaCl₃.ThesepeaksalsoarisefromthetransitionofCl-pstatestoconductionband.Athigherenergy,weobservepeaks around22.67–27.30eV,and19.30–27.30eVforKCaCl₃,andRbCaCl₃respectively,whichalsomaybeduetothetransition fromCl-s,andX(X=K,Rb)-pstatestohigherenergylevelsofconductionband.

InFig.5,wecanseetherefractiveindex(forallcompounds),alongthethreedifferentdirections.Thestaticrefrac- tiveindicesn(0) arefoundtobeequalto1.52,and1.50forthecubicstructureofXCaCl₃(X=K,Rb),respectively.Forthe orthorhombicstructure,theFig.5(b)showstheisotropicnatureinthelowenergyrangeofthesecompounds,andwefound thatthecalculatedn(0) areequalto1.53,and1.54(averagevaluesalongthethreedirections)forKCaCl3,andRbCaCl3respec- tively.Thevaluesoftherefractiveindicesarefoundtopursueanoppositedirectiontothebandgapfortheorthorhombic structuresofthesecompounds(bandgapdecreasesfromKCaCl₃toRbCaCl₃).Onthecontrary,itfollowsasametrendtothe bandgapforthecubicstructures.

Theabsorptioncoefﬁcient˛(Fig.6)iscalculatedfromthedielectricfunction(wecanseethattheimaginarypartε₂in Fig.4isproportionaltotheabsorptioncoefﬁcient˛),andobservedintherangearound7–30eV(intheultraviolet),itshows whencompoundsabsorbtheincidentbeam.Wenoticethattherearehighabsorptionspeaksathighenergies.Forthecubic structuresofthesecompounds,theopticalgapisaround7.2eV,belowthisvaluethereisnoresponsefromthesematerials, whereasfortheorthorhombicstructures,theopticalgapisaround7.3eV.

TheelectronenergylossspectraL(Fig.7)representtheenergylossperunitlengthofthefastelectronacrossthecom- pound.Weobserve,athighenergies,peaksaround28.7eVforthecubicstructuresofKCaCl3andRbCaCl3,29.1eVforthe orthorhombicstructures.Atenergiesaround15.6–26.3eV,wecanseetwobroadpeaksforKCaCl₃,andonepeakforRbCaCl₃

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compounds.Thesenotablepeaksaredeﬁnedasplasmonpeaks,whichrepresentthechargecollectiveoscillationsofthefree electronsinthecrystal.

Fromtheopticalinvestigationoftheorthorhombicstructureofbothcompounds,wecanseetheisotropicnatureinthe lowenergyregionthoughbeingstructurallyanisotropicwhichisnecessaryfortheceramicscintillators.

4. Conclusions

Inthiswork,wehavestudiedthestructural,electronic,andopticalpropertiesofthecubicandorthorhombicstructureof XCaCl₃(X=K,Rb),applyingtheFP-LAPWmethodintheframeworkofDFT.First,weinvestigatedthestructuralpropertiesof thecompoundsincubicandorthorhombicphases,withtherelaxationoftheinternalatomicpositions.Ourresultsagreewell withtheexperimentaldata,andothertheoreticalcalculations.Second,wecalculatedtheelectronicandopticalpropertiesof thesematerialswithTB-mBJfunctionalwhichimprovetheresultscomparedtotheGGA-PBEapproximation.Thetopmost regionofthevalencebandforthebothcompounds,andforthecubicandorthorhombicstructureisdominatedbyCl-p states.Finally,theopticalresultsrevealtheisotropicnatureofthesecompoundsthoughbeingstructurallyanisotropicin thecaseoftheorthorhombicstructures,whichisnominatedtobebettercandidatesfortheceramicscintillators.

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