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1、REVIEWSOFMODERNPHYSICS,VOLUME84,APRIL–JUNE2012LatticeinstabilitiesinmetallicelementsGo¨ranGrimvallDepartmentofTheoreticalPhysics,KTHRoyalInstituteofTechnology,AlbaNovaUniversityCenter,SE-10691Stockholm,SwedenBlankaMagyari-Ko¨peDepartmentofElectricalEngineering,StanfordUniversity,Stan
2、ford,California94305,USAVidvudsOzolin,sˇDepartmentofMaterialsScienceandEngineering,UniversityofCalifornia,LosAngeles,California90095-1595,USAKristinA.PerssonAdvancedEnergyTechnology,LawrenceBerkeleyNationalLaboratory,Berkeley,California94720,USA(published4June2012)Mostmetallicelement
3、shaveacrystalstructurethatiseitherbody-centeredcubic(bcc),face-centeredclosepacked,orhexagonalclosepacked.Ifthebcclatticeisthethermodynamicallymoststablestructure,theclose-packedstructuresusuallyaredynamicallyunstable,i.e.,haveelasticconstantsviolatingtheBornstabilityconditionsor,mor
4、egenerally,havephononswithimaginaryfrequencies.Conversely,thebcclatticetendstobedynamicallyunstableiftheequilibriumstructureisclosepacked.Thisstrikingregularityessentiallywentunnoticeduntilabinitiototal-energycalculationsinthe1990sbecameaccurateenoughtomodeldynamicalpropertiesofsolid
5、sinhypotheticallatticestructures.Afterareviewofstabilitycriteria,thermodynamicfunctionsinthevicinityofaninstability,Bainpaths,andhowinstabilitiesmayariseordisappearwhenpressure,temperature,and/orchemicalcompositionisvariedarediscussed.Theroleofdynamicalinsta-bilitiesintheidealstrengt
6、hofsolidsandinmetallurgicalphasediagramsisthenconsidered,andcommentsaremadeonamorphization,melting,andlow-dimensionalsystems.Thereviewconcludeswithextensivereferencestotheoreticalworkonthestabilitypropertiesofmetallicelements.DOI:10.1103/RevModPhys.84.945PACSnumbers:63.20.dk,64.10.+h
7、,62.20.DCONTENTSB.Calculationofelasticconstants955C.Softmodesasprecursorstostructuralchanges955I.Introduction946V.PressureEffects957II.LatticeInstabilities947A.Generalaspects957A.Phonondispersioncurves947B.Pressure-inducedinstabilitiesatT¼0K957B.Elasticconstants948C.P-Tphasediagramw
8、ithalatticei
