耐火材料CrAlB外文文献

耐火材料耐火材料CrAlBCrAlB外文文献外文文献 Aepted ManuscriptStudy of structural electronic optical and thermal properties of refractory material CrAlB Anugya Rastogi Priyanka Rajpoot U P VermaPII S0254 0584 18 30147 0DOI 10 1016 j matchemphys 2018 02 043Reference MAC20394To appearin Materials Chemistryand PhysicsReceivedDate 25NovemberxxRevised Date 4February2018Aepted Date 22February2018Please citethis articleas A Rastogi P Rajpoot U P Verma Studyofstructural e lectronic optical andthermal properties ofrefractorymaterial CrAlB Materials Chemistryand Physics 2018 doi 10 1016 j matchemphys 2018 02 043 This isa PDFfile ofan uneditedmanuscript thathas beenaepted forpublication As aservice toourcustomers weare providingthis earlyversion of the manuscript The manuscriptwill undergocopyediting typesetting and reviewof theresulting proof before it is publishedin itsfinal form Pleasenote thatduring the production processerrors maybe discoveredwhich couldaffect thecontent and alllegaldisclaimers that apply to the journalpertain MANUSCRIPT ACCEPTEDACCEPTEDMANUSCRIPTGRAPHICAL ABSTRACTFigure Partial DOSfor3s and3p statesof aluminumatom MANUSCRIPT ACCEPTEDACCEPTED MANUSCRIPTStudyof Structural Electronic Optical andThermal Propertiesof RefractoryMaterial CrAlB Authors Anugya Rastogi 1 Priyanka Rajpoot 2 U P Verma School ofStudies inPhysics Jiwaji University Gwalior 474011 India e mail 1anugyarastogi physics gmail 2priyankarajpoot47 gmail upv udai gmail these authorscontributed equallyto thiswork ABSTRACTThe structural electronic optical and thermal properties of ternarytransition metalboride CrAlB are studiedusing fullpotential linearizedaugmented planewave methodin the framework of the density functional theory The exchange correlation potentialis solvedusing themodified Perdew Burke Ernzerhof generalizedgradient approximation PBEsol GGA The structuralparameters areoptimized to obtain equilibrium lattice constant bulk modulus and itspressure derivative The calculatedband structure density of states andelectronic charge density show that the material possessesmetallic natureand havecovalent bandcharacter Optical spectracalculations such as thereal and imaginary part of dielectrionstant refractive index extinction coefficient reflectivity absorption coefficient conductivity and loss function areperformed within the photon energy rangeof0 40eV In thiscase the obtained plasma frequency corresponds to24 12eV For radiationabove this energy theproperty of CrAlB changesfrom metallicto dielectric The calculationsof the thermal propertiesusing Gibb s programhave beenperformed in the range0 5000K at0 20and50GPa ofpressure The studiesof optical and thermal properties showthat it is aneligible candidatefor optoelectronicdevices and thedevices working at high temperature The resultsfor CrAlB are reported for the first timeas neitherCrAlB has been synthesizednor anytheoretical calculationhas beenperformed tillso far Keywords Layered structure First principles Structural properties Electronic structure Optical properties Thermal propertiesIntroduction Transitionmetals suchas nitrides borides andcarbides arethe hardestmaterials andhave extremelyhigh melting points thus they are regarded as refractorymaterials 1 These binary transition metalsare alsoregardedasUltra High Temperature Ceramics UHTCs as they have applicationsin hypersonicvehicles 2 plasma arcelectrodes cutting tools furnace elements and high temperature shielding 3 However the obstaclethat hamperthe applicationsof binarytransition metalborides areintrinsic MANUSCRIPT ACCEPTEDACCEPTED MANUSCRIPTbrittleness which shows that theyhave lowfracture toughness low damagetolerance poor resistanceto chemicaldegradation at high temperature 4 poor thermalfatigue resistance and difficultyin machininginto sharpor plexshapes 2 Aluminum layer inserted intobinarytransition metals toform ternarylayered structure 5 improves theirbrittleness andmakes themcorrosion resistant Ultra high temperatureceramics possessesdual characteristics i e of metalas well as ofceramics As metaltheyhavegood thermalconductivity thermal shockresistanceandmachinability as ceramicstheyaregood oxidationresistant Because ofabove twoproperties CrAlB is aneligible candidatefor largeindustrial applications 6 Aording to literature survey no experimentaland theoreticalwork has been reportedon ternaryChromium AluminumBoride CrAlB therefore it wasthought that it isworthwhile toreport theab initio calculationswithin densityfunctional theoryto predictthe structural electronic optical and thermalpropertiesof CrAlBkeeping inmind usabilityof ternarylayered poundcontaining Allayer Technical detailsThe calculationsin thepresent workhave beencarried within theframework ofdensityfunctionaltheory DFT The fullpotential linearizedaugmented planewave FP LAPW method has been used to solveKohn Sham equationsas implemented in Wien2k code 7 Modeling theXC interactionsis themain difficultyof DFT The mostmonly usedGGA functionalis theone proposedby Perdew Burke and Ernzherhof PBE It almostalways overestimatesthe lattice constants ofsolids while LDAconsistently underestimatesthem In bothcases the typicalerrors amountto1 2 of the lattice parameters A seriesof alternativeGGA functionalhave beenproposed toovere thisproblem One of them is the PBEsol 8 functional It isseen asrevised versionsof PBEspecifically adaptedfor solids 9 In thismanuscript theexchange andcorrelation energy has beenobtained usingthe PBEsol GGA functional The atomicmuffin tinradii werechosen suchthat the optimized valuesneither overlapwith eachother northe corecharge leaksout of the sphere The planewave cutoffwas decidedby RMT K max 7 0 where RMT is the smallestmuffin tin radius andK maxis themaximum value of thelattice vectorof the basis set The expansionof thewave functionswas settol 10inside the muffin tinspheres The numberof k points inthe irreduciblewedge ofBrillouin zonewas fixedto7 7 6k point on thebasisof convergedvalue of the total energy as a function of k points for the sameset of the unit cell inputs The calculationswere stoppedonly when the total energy andthe chargeof thesystem reachedthe convergentlimit of the orderof10 4Ry and10 3e respectively After thisconverged values of the total energy with respectto differentunit cell volume wereused toobtain equilibriumcell parameters Now corresponding to equilibriumlattice constantsself consistentcycle SCF was pletedtoobtainband structure and densityof statesplots andalso toplete optical properties calculations Further obtained sets oftotalenergyand cell volume wereused to determine thetemperature effectson CrAlBby usingquasiharmonic Debyemodel asimplementedinMANUSCRIPT ACCEPTEDACCEPTEDMANUSCRIPTGIBBS code 10 This modelgenerates Debye temperature D V and obtainsthe non equilibrium Gibbsfunction G V P T and minimizeG to derivethe thermalequation ofstate V P T In thequasi harmonic Debyemodel the non equilibrium Gibbsfunctions G V P T is writtenas Here E V is the totalenergyper unit cell PV istheproductof hydrostaticpressure andunit cellvolume and Avib isthe Helmholtzfree energy 10 12 For anisotopic solidthe Debye temperature D isexpressed as D 6 f where Misthemolecular massper formulaunit and B Sistheadiabatic bulk modulus Details onf can befound inRefs 10 12 Further B Sis approximatedby thestatic pressibilityas BS B V V P T with respectto volumeV as P T 0Thus throughthe Quasiharmonic Debyemodel one cancalculate thethermal quantitiesat differenttemperature and pressure from the calculatedE V dataat T 0and P 0 The standardthermodynamic relationsare thenusedtoderive othermacroscopic properties Results andDiscussion GeometryOptimization andStructural PropertiesThe space group of ternary chromiumaluminium borideis Cmcm spacegroupno 63 5 In thisstructure atomic positionsare takenas Cr 0 0 4149 0 25 Al 0 0 1943 0 25 and B 0 0 03360 0 25 The optimization of geometrywas obtainedby calculatingthe totalenergy as a function of threevariables u b a andV where urepresents the internal coordinatesof theatoms a andb representthelattice parameters andV isrelated tothe volumeof the unitcell It wasdone intwo steps In firststep the internalgeometry of the cellwas optimizedby theprocedure ofgeometry minimizationwhere theforces actingbetween theatoms areminimized The processwas repeateduntil thechange inthe averageforce fallsbelow1mRyd Bohr In secondstep theb a ratiooptimizationof the crystalenergy wasdone forthe unitcellvolumeV andc a ratio Different values ofb a werechosen forfixed volumeand thena polynomialwas fittedtodetermiheoptimizedb a ratio Once the value ofb a isdecided correspondingtodifferent volumes thetotalenergyhasbeen calculated The conversedMANUSCRIPT ACCEPTEDACCEPTEDMANUSCRIPTvalues of themuffin tinradiusused inthe calculationsare2 30 1 90and1 54Bohr respectively for Cr Al and B Using theobtainedsetswe havedetermined the equilibrium volumeV o the bulkmodulus Bo andthe pressurederivative of the bulkmodulus by fittingthetotalenergy as a function of volumeV totheMurnaghan equationofstate 13 Corresponding totheequilibriumlatticeparameterstheobtainedcrystal structureof CrAlBhasbeenshown in fig 1 a It isthe trigonalprism likestructureandpossesses4formulas perunitcell The optimizedequilibriumlatticeparameters aregiven in table1 The lengthof variousbonds in CrAlB shown in fig 1 a are listedintable2 Table1 Equilibrium latticeparameters of CrAlB obtainedusing differentapproximations Approximation Method LatticeConstants V0 3 E0 Ry B0 GPa B0 a bc LSDA3 0257013 259522 93126117 603 5261 902233 724 0821PBEsol GGA3 0512113 371352 95599120 601 5267 854222 204 0277PBE GGA3 0750213 475662 97905123 446 5274 416210 824 0255Table2 Bond Length in in CrAlB Bond Plane to planeOut ofplane Cr B Y X2 2282 234Cr Cr Z X2 9512 758Cr Al Y Z2 8902 570Al Al X Z2 9512 563Al B Y X2 150 B B Y X 1 740MANUSCRIPT ACCEPTEDACCEPTEDMANUSCRIPT Figure1 a The unitcell structure b Electronic charge density plotsof CrAlB at ambientcondition andcontour plotin 110 plane and c 3D representationof electronihargedensity Electronic PropertiesThe band structure total andpartial densityof statesof CrAlB are shown in fig 2 a and fig 2 b 2 e In fig 2 a the valanceband overlapsthe conductionband atFermi levelwhich indicatesmetallic nature of CrAlB From fig 2 c it isevident thatnear Fermilevel main contributionin PDOS plot isdue to3 d statesof chromiumatom andless contributionof3p and2p statesof AlandB atoms The chargedensity shownin fig 1 b and1 c gives theinformation about the probabilisticmeasure ofpresence ofan electronat aspecific point It revealsthe densityassociated with the chemicalbond andthe areas where chargedensities arepositive andnegative andalso theaumulation anddepletion of electronic charges The covalentbond predictsabout theaumulation ofchange between the sharingatoms whereasthe ionicbond predictsaboutthe natureof the chargedensity atthe atomicpositions i e positive andnegative 14 The unitofelectronihargedensityise 3within thecrystallographic plane 110 Chromium hashigh electrondensity paredto Aluminumand Boron There existsstrong covalentbond between B Batomsand Al Al atoms This bondingbetween Al Al atomresults intoAl layerinthe pound MANUSCRIPT ACCEPTEDACCEPTEDMANUSCRIPTwhich isless strongthan B B bond 15 The figurealso predictsthat bondsbetweenB Cr Al Cr and Al Barecovalent innature Figure2 a Electronic BandStructure of CrAlBat ambient pressureand temperature b Total densityof states DOS states eV c Partial DO