Previous PDF in this issueNext PDF in this issue

Article start

SolidStateCommunications151(2011)1349–1354Contents lists available atSciVerse ScienceDirectSolidStateCommunicationsjournal homepage:www.elsevier.com/locate/sscFirstprinciplesstudyonthestructural,electronic,andelasticpropertiesofNa–AssystemsH.B.Ozisika,b,∗,K.Colakoglua,E.Deligozb,H.OzisikbaGaziUniversity,FacultyofScience,PhysicsDepartment,06500,Teknikokullar,Ankara,TurkeybAksarayUniversity,FacultyofArtsandScience,PhysicsDepartment,68100,Campus,Aksaray,Turkeya r t i c l e i n f oArticlehistory:Received5February2011Receivedinrevisedform5May2011Accepted14June2011byD.D.SarmaAvailableonline23June2011Keywords:D.MechanicalpropertiesD.ElectronicbandstructureD.Phasetransitiona b s t r a c tWe have performed the first principles calculation by using the plane-wave pseudopotential approachwith the generalized gradient approximation for investigating the structural, electronic, and elasticpropertiesNa–Assystems(NaAsinNaP,LiAsandAuCu-typestructures,NaAs2inMgCu2-typestructure,Na3As in Na3As, Cu3P and Li3Bi-type structures, and Na5As4in A5B4-type structure). The latticeparameters, cohesive energy, formation energy, bulk modulus, and the first derivative of bulk modulus(tofittoMurnaghan’sequationofstate)oftherelatedstructuresarecalculated.Thesecond-orderelasticconstantsandtheotherrelatedquantitiessuchasYoung’smodulus,shearmodulus,Poisson’sratio,soundvelocities,andDebyetemperaturearealsoestimated.©2011ElsevierLtd.Allrightsreserved.1. IntroductionAlkali metal pnictides are member of the family of Zintlphase which has drawn attention of scientists in inorganicresearch for many years [1,2]. These materials show differentphysicalandchemicalpropertiesdependingonthestructureandchemical composition [2–4]. They possess a band gap range from0.1 eV up to 2.5 eV for different stoichiometry and structures.This important property is used in thin film and photocathodeapplication [5,6]. Some alkali pnictides are, also used in crystalgrowthtechniques[7–9].There are many studies on alkali pnictides, but most ofthem are on the compounds of the alkali metals with Sb andBi elements. It has been reported only few recent theoreticalor experimental works on Na–As compounds [2,10–18]. Thestructural parameters, melting points, standard enthalpies, andentropies of formation of the synthesized Na–As compoundsare investigated in orthorhombic NaP, hexagonal Na3As, andCu3P structures [10]. Brauer and Zintl [11] analyzed the crystalstructure of Na3As using the X-ray method. Mansmann [12]studiedcrystalstructureofNa3AsinCu3P-typestructure.Inearlyworks, the melting point and enthalpy of formation for Na3Aswere determined calorimetrically [13,14]. In a very recent work,∗Correspondingaddress:GaziUniversity,DepartmentofPhysics,06500,Ankara,Turkey.Tel.:+903122021458;fax:+903122122279.E-mailaddresses:havva.bogaz@gazi.edu.tr,havvabogaz@gmail.com(H.B.Ozisik).Burtzlaffetal.[2]obtainedthestructuralparametersofmonoclinicNaAs compound. The phase transition from the Na3As structureto the Li3Bi structure was estimated by Beister et al. [15]. Hafnerand Range [16] synthesized the Na3As compound in the P63cmspace group and investigated structural properties and revisionsproposed by Brauer and Zintl [11], experimentally. Theoretically,less attention has been paid to these compounds and there areonlyfewworksonthehalf-metallicferromagnetismofNaAsinzincblende[17]androcksaltstructures[18].Here,weaimtoinvestigatethestructural,electronic,andelasticproperties of Na–As compounds for different stoichiometries andstructures (NaAs in NaP, LiAs and AuCu-type structures, NaAs2in MgCu2-type structure, Na3As in Na3As, Cu3P and Li3Bi-typestructures, and Na5As4in A5B4-type structures) in detail andinterpretthesalientresults.DetailedcrystallographicparametersoftheconsideredstructuresaregiveninTable1.Thelayoutofthispaperisasfollows:ThemethodofcalculationisgiveninSection2.TheresultsandoverallconclusionarepresentedanddiscussedinSections3and4,respectively.2. Method of calculationAll calculations have been carried out using the Vienna abinitio simulation package (VASP) [19–22] based on the densityfunctional theory (DFT). For the exchange and correlation termsin the electron–electron interaction, Perdew–Burke–Ernzerhof(PBE)[23]wasusedwithinthegeneralizedgradientapproximation(GGA). The electron–ion interaction was considered in the form0038-1098/$–seefrontmatter©2011ElsevierLtd.Allrightsreserved.doi:10.1016/j.ssc.2011.06.019
1350H.B.Ozisiketal./SolidStateCommunications151(2011)1349–1354Table 1CrystallographicdataforconsideredstructuresofNa–Ascompoundsandthecalculatedatomicpositionsafterlocaloptimizationsontheabinitiolevel(GGA–PBE).CompoundSpacegroup(number)PrototypeAtomSiteGGA–PBE(present)k-gridmeshNaAsP212121(19)orthorhombicNaPNa14a(x1,y1,z1)4a(0.4086,0.9025,0.0450)8×8×5Na24a(x2,y2,z2)4a(0.1487,0.6370,0.3277)As14a(x3,y3,z3)4a(0.2875,0.1349,0.2904)As24a(x4,y4,z4)4a(0.4182,0.4025,0.1235)NaAsP21/c(14)monoclinicLiAsNa14e(x1,y1,z1)4e(0.2189,0.3904,0.3300)8×8×5Na24e(x2,y2,z2)4e(0.2346,0.6634,0.0323)As14e(x3,y3,z3)4e(0.3197,0.8938,0.2895)As24e(x4,y4,z4)4e(0.3120,0.1610,0.1188)NaAsP4/mmm(123)tetragonalAuCuNa1a(0,0,0)1a(0,0,0)8×8×11As1d(1/2,1/2,1/2)1d(0.5,0.5,0.5)NaAs2Fd−3m(227)cubicMgCu2Na8a(1/8,1/8,1/8)8a(0.125,0.125,0.125)6×6×6As16d(1/2,1/2,1/2)16d(0.5,0.5,0.5)Na3AsP63/mmc(194)hexagonalNa3AsNa12b(0,0,1/4)2b(0,0,0.25)10×10×6Na24f(1/3,2/3,z1)4f(0.3333,0.6667,0.5801)As2c(1/3,2/3,14)2c(0.3333,0.6667,0.25)Na3AsFm−3m(225)cubicLi3BiNa14b(1/2,1/2,1/2)4b(0.5,0.5,0.5)7×7×7Na28c(1/4,1/4,1/4)8c(0.25,0.25,0.25)As4a(0,0,0)4a(0,0,0)Na3AsP63cm(185)hexagonalCu3PNa12a(0,0,z1)2a(0,0,0.2871)6×6×6Na24b(1/3,2/3,z2)4b(0.3333,0.6667,0.2231)Na36c(x1,0,z3)6c(0.3015,0,0.5762)Na46c(x2,0,z4)6c(0.3607,0,0.9154)As6c(x3,0,z5)6c(0.3308,0,0.2460)Na5As4C2/m(12)monoclinicA5B4Na14i(x1,0,z1)4i(0.1005,0,0.3866)6×6×6Na24i(x2,0,z2)4i(0.7549,0,0.1630)Na32a(0,0,0)2a(0,0,0)As14i(x3,0,z3)4i(0.4562,0,0.1704)As24i(x4,0,z4)4i(0.3930,0,0.3926)of the projector–augmented–wave (PAW) method [20,24] withplanewaveuptoenergyof450eV.Thek-meshvaluesdeterminedby choosingk-point separation 0.02 Å−1are given inTable 1were found sufficient for the total energy calculations. Structuraloptimization was performed for each structure for all latticeconstants, angles, and internal atomic coordinates until thedifference in total energy and the maximum force were within1.0×10−6eVand1.0×10−4eV/Å,respectively.Foragivenvolumeoftheunitcell,thelatticeparametersaredeterminedinsuchawaythatthetotalenergybecomesaminimum.Thedataoftotalenergyversus volume were fitted using Murnaghan’s equation of state(eos) [25]. Besides the equilibrium volume, this fitting proceduregivestheminimumvalueofthetotalenergyE,theisothermalbulkmodulusBanditspressurederivativeB′attheequilibriumstate.3. Results and discussion3.1. StructuralpropertiesFirst, we have been optimized the volume of the cell and theionic positions of atoms. The obtained parameters were used tocalculateotherphysicalproperties.Thecalculatedatomicpositionsand lattice parameters are listed inTables 1and2along withthe available works for comparison. The crystal total energy iscalculated for different values of lattice constant (at constantb/aandc/a), and fitted in terms of Murnaghan’s eos [25]. (Theenergy–volume curves are not shown here to save space.) Thebulkmodulusanditspressurederivativehavealsobeencalculatedbased on the same Murnaghan’s eos and the results are listed inTable 2. It can be seen that the present lattice parameters are ingood agreement (around 1%) with experimental ones except forNa3As and Li3Bi structures. For these latter structures the latticeconstantsareoverestimatedabout0%–4.4%fromRefs.[10,15]and4.8%fromRef.[15],respectively.As a fundamental physical property, the bulk modulus ofsolidsprovidesvaluableinformationincludingintheaveragebondstrengthsofatomsforthegivencrystals[26].Inthepresentcase,the largest value of bulk modulus (50.9 GPa) is obtained for theMgCu2-typestructure,anditimpliesthatthisstructureistheleastcompressibleoneamongtheothers.The cohesive energy is known as a measure of the strength ofthe forces, which bind atoms together in the solid state. In thiscontext,thecohesiveenergiesofNa–Ascompoundsarecalculatedintheconsideredstructures.Thecohesiveenergies(Ecoh)ofgivenphasesaredefinedasENaxAsycoh=ENaxAsytotal−xENaatom+yEAsatom(1)whereENaxAsytotalisthetotalenergy(informulunit)ofthecompoundat equilibrium lattice constant andENaatomandEAsatomare the atomicenergies of the pure constituents calculated with a large cutoffrmax=15 Å (free atoms). Also from the total energy of thecompoundandtheconstituentelementalsolids(BCCW-type(Im-3m, #229, A2) for Sodium and rhombohedralα-As-type (R-3m,#166, A7) for the Arsenic element), one can find the formationenergyusingtherelationENaxAsyform=ENaxAsytotal−xENasolid+yEAssolid.(2)The calculated cohesive and formation energies are listed inTable 2and they are in good agreement with the values of Refs.[13,14]. These results imply that present compounds possess thenegative formation energy and can easily been synthesized invarious stable phases. The ranking order of cohesive energy withformation energy is the same. Formation energy and cohesiveenergy of NaP (LiAs), MgCu2, Na3As (Cu3P), and A5B4phases are,relatively, higher than the other type of stoichiometry. It is seenfromTable2thattheNaPandLiAshavethesameformationenergy(0.795 eV/f.u.) and similarly, the formation energy for Na3As andCu3Pphases(1.716eV/f.u.)areequal.Thevalueofcohesiveenergyalsoexhibitsthesimilartrend.The phase transition pressures of Na–As compounds arecalculated from the Gibbs free energy at 0 K. The value of phase
Previous PDF in this issueNext PDF in this issue