The self-consistent ab initio lattice dynamical method

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1、ComputationalMaterialsScience44(2009)888–894ContentslistsavailableatScienceDirectComputationalMaterialsSciencejournalhomepage:www.elsevier.com/locate/commatsciTheself-consistentabinitiolatticedynamicalmethoda,*abcP.Souvatzis,O.Eriksson,M.I.Katsnelson,S.P.RudinaDepartmentofPhysicsandMaterialsScience,

2、UppsalaUniversity,Box530,SE-75121Uppsala,SwedenbInstituteforMoleculesandMaterials,RadboudUniversityNijmegen,NL-6525EDNijmegen,TheNetherlandscTheoreticalDivision,LosAlamosNationalLaboratory,LosAlamos,NewMexico87545,USAarticleinfoabstractArticlehistory:Wedescribeamethodforcalculatingtemperaturedepende

3、ntphononspectraselfconsistentlyfromfirstReceived16May2008principles.ThemethodcombinesconceptsfromBorn’sself-consistentphononapproachwithabinitioReceivedinrevisedform11June2008calculationsofaccurateinteratomicforcesinasupercell.TestcalculationsonthehightemperatureAccepted12June2008bccphaseofTi,Zr,Hf,S

4、candY,asrepresentativeexamples,reproducetheobservedhightemperatureAvailableonline31July2008phononfrequencieswithgoodaccuracy.Byuseofanembeddedatompotentialwedemonstratethemethod’srelevanceincalculatingapproximatecriticaltemperaturesofsolid–solidphasetransitionsPACS:forthehcptobcctransitioninZr.65.40

5、.DeÓ2008ElsevierB.V.Allrightsreserved.63.20.D71.20.BeKeywords:Self-consistentPhononcalculationAnharmonicPhasetransitionSCAILDPhonon–phononinteraction1.Introductionnonspectraintheharmonicapproximationcanbeefficientlyeval-uatedbyuseofinformationgivenbydensityfunctionaltheory,e.g.,Severalmaterialsappea

6、rincrystalstructureswhichappeartoviaatomicforcesorinlinearresponsetheory[4].However,forthenotbeenergeticallystable.Thebodycenteredcubic(bcc)structurebccphasesoftheelementsmentionedabovethephononspectrainismaybethesimplestandbestknownexample.Intheharmonictheharmonicapproximationrevealimaginaryphononf

7、requenciesapproximation[1]itisanunstablecrystalstructureforthegroupforsomewavevectors[5,6],whichshowsthatthebccphaseisfromIVBelements,fortherare-earthelements,fortheactinides,andalatticedynamicspointo