BoronCarbide:Structure,Properties,andStabilityunderStressVladislavDomnich,SaraReynaud,RichardA.Haber,andManishChhowallaDepartmentofMaterialsScienceandEngineering,Rutgers,TheStateUniversityofNewJersey,Piscataway,NJ08854Boron carbide is characterized by a unique combination ofproperties that makeit amaterial of choicefor awiderangeofengineeringapplications. Boroncarbideisusedinrefractoryapplicationsduetoitshighmeltingpointandthermal stability;it isusedasabrasivepowdersandcoatingsduetoitsextremeabrasionresistance; itexcelsinballisticperformanceduetoitshigh hardness and lowdensity; and it is commonly used innuclear applications as neutron radiation absorbent. In addi-tion, boroncarbide is ahightemperature semiconductor thatcanpotentiallybe usedfor novel electronic applications. Thispaper provides acomprehensivereviewof therecent advancesinunderstandingofstructural andchemical variationsinboroncarbide and their inuence on electronic, optical, vibrational,mechanical, and ballistic properties. Structural instability ofboron carbide under high stresses associated with externalloading and the nature of the resulting disordered phase arealsodiscussed.I. AtomicStructure,Stoichiometry,andPolytypismTHE atomic structure of boron carbide has been exten-sivelydiscussedinthe literature.18The primarystruc-tural units of boron carbide are the 12-atomicosahedralocatedat thevertices of arhombohedral latticeof trigonalsymmetry(R3mspace group), andthe 3-atomlinear chainsthat linktheicosahedraalongthe(111) rhombohedral axis,as illustratedinFig. 1. This structurecanalsobedescribedintermsof ahexagonal latticebasedonanonprimitiveunitcell, in which case the [0001] axis of the hexagonal latticecorresponds to the [111] rhombohedral direction (Fig. 1).The presence of icosahedrawithinthe boroncarbide struc-ture is a consequence of elemental borons ability toformcaged structures of a variety of sizes5,9; the icosahedra inboron carbide are essentially two pentagonal pyramidsbondedtogether.10Assuch, twotypesof chemicallydistinctsites, polarandequatorial, arepossiblewithinanindividualicosahedron. Thepolarsitescorrespondtothoseatomsthatlinktheicosahedratogether.Thepolaratomswithinthecagearealsothethreeatomsfromeachof thetwoplanesoppo-siteoneanotherinthecrystal structure. Theequatorial sitesontheotherhandarethosetowhichthe3-atomchainsarebonded, andthese sites forma hexagonal chair withintheicosahedron(Fig. 1).Informationonthe crystal symmetryof boroncarbide isreadily available fromdiraction measurements; however,the exact site occupancies by carbonandboronatoms arestill debated. This is duetothesimilarityinbothelectronicandnuclear scattering cross-sections for boronandcarbon(11Band12Cisotopes),11,12whichmakesitdiculttodistin-guishthese twoatoms bymost characterizationtechniques.Fromthe crystal symmetry considerations, twostoichiome-tries have been originally proposed as candidates for thestable phase of boron carbide: (i) the carbon rich B4C(orB12C3)compound,withtheidealizedstructuralcongura-tion (B12)CCC,13,14where (X12) represents the icosahedralatoms and XXXstands for the chain atoms, and (ii) theB13C2(or B6.5C) compound, describedbyanidealized(B12)CBCstructural formula, wherethecenterchaincarbonatomisreplacedbyboron.15,16Formationofadditional intermedi-atephaseswithcrystal symmetryotherthanR3m, suchasamonoclinicmodicationof B13C2,17has alsobeenreported.ThesevariationshavebeenreectedinseveralversionsoftheBC phase diagramreported in the literature1823; Fig. 2showsexamplesof thetwomorecommonlyusedphasedia-grams.20,21There is agreement inthe communityabout theexistenceofawiderangeofsolidsolubilityforcarboninthestable phase and a homogeneous range extending from~8at.%Cto~20at.%C,3,2224althoughsynthesisof asin-gle crystal with the B3.2Cstoichiometry, corresponding to24at.%Chas alsobeenreported.25Beyond~20at.%C, amixture of stable phase boroncarbide andcarbonis oftenencountered, which has a eutectic point at ~30at.%Cof2350C20; but the latter has also been debated to be aslow as 2240C.21Low carbon content phases (i.e. below8at.%C) are generallyagreedtobe solidsolutions of thestablephaseboroncarbideandpureboron.The rhombohedral lattice parameters for the carbon-rich B4Ccompound are a=5.16Aand a=65.7, with minor variationsdepending on the extent of the investigation.2,13,14,2633Convertedintothemoreeasilyworkedwithhexagonallatticeparameters, B4Chasvalues of a0=5.60A , c0=12.07A , andan axial ratio of c0/a0=2.155.3Due to the dierence inatomic radii of carbon and boron, B-rich boron carbideshave slightly expanded lattices. Using precision structuralD.J.GreencontributingeditorManuscriptNo.29735.ReceivedMay25,2011;approvedAugust27,2011.Author to whom correspondence should be addressed. e-mail: manish1@rci.rutgers.eduJ.Am.Ceram.Soc.,124(2011)DOI:10.1111/j.1551-2916.2011.04865.x2011TheAmericanCeramicSocietyJournalFeaturecharacterizationof high-purityboroncarbides spanningtheentirehomogeneityrange, Aselageetal. establishedacorre-lation between lattice parameters and stoichiometry.33AsillustratedinFig. 3(a), theaparameter experiences asteadyincrease towardmore boron-richstoichiometries, whereas achangeintheslopeat ~13at.%Cis observedfor thecom-positional dependence of the c parameter. Further, neutronpowderdiractiondata11,34showthatthechainbondlengthinboroncarbidesat 13at.%Cisreducedby2%3%com-paredtothat inboron- andcarbon-richmaterial [Fig. 3(b)].Theseexperimental observationscanbeunderstoodintermsof theformationof anintermediateB6.5Ccongurationandthe change inthe mechanisms for incorporationof carbonatoms intothe lattice that occurs at 13.3at.%Ccomposi-tion,asdiscussedbelow.Despite the absence of experimental methods that can unam-biguously pinpoint the positions of boron and carbon atoms inthelattice,variousatomiccongurationshavebeensuggestedfor boron carbide based on theoretical modeling4,3546and theavailable experimental data obtained by nuclear magneticresonance,4750neutron11,34,51andX-ray2,3133,52diraction,infrared30,5356and Raman5661spectroscopy, and X-rayabsorption12andscattering62,63techniques.Possiblecombina-tions of suchstructural elements as B12, B11C, B10C2, andB9C3icosahedraandCCC,CBC,CCB,CBB,BCB,andBBBchains, as well as the nonlinear chains that include four boronatoms and chains with vacancies, have been suggested in thesestudies.Theresults of thetheoretical energyminimizationconsis-tentlyindicate that the (B11C)CBCstructure is preferredtothe (B12)CCCat the carbon-rich end of the homogeneityrange.4,36,37,39,40,4345,64Becauseoftheexistenceofnonequiv-alentatomicpositionswithintheicosahedra, twovariantsof(B11C)CBCshouldbeconsidered: thepolar(B11Cp) congu-ration, whereoneof theboronatoms intheicosahedronissubstitutedby carboninthe polar site, andthe equatorial(B11Ce) conguration, where the substitution occurs in theequatorial site. Thepolarcongurationisfoundtobeener-geticallypreferredtotheequatorial oneinall studies wherethetwostructureshavebeenmodeledwithinthesamecalcu-lationframework.35,40,45,65It shouldbe alsonotedthat thesubstitution of carbon into the icosahedron induces smallmonoclinic distortions inthe R3msymmetry, amountingto1.8%and0.5%of the lattice parameter andto1.0%and0.1%oftherhombohedral angleforthepolarandtheequa-torialcongurations,respectively.39chain sites icosahedralpolar sites icosahedralequatorial sites [0001] [10 0]1[01 0]1[100] [010] [001] Fig. 1. Boroncarbidelatticeshowingcorrelationbetweentherhombohedral (red)andthehexagonal (blue)unitcells. Inequivalentlatticesitesaremarkedbyarrows.(b) (a)Fig. 2. Phasediagramofboroncarbideafter(a)EkbomandAmundin,20depictingB13C2asthestoichiometricallystablephaseandpresumingthepresenceofseverallowtemperaturephases, and(b)Beauvy,21depictingthemorewidelyacceptedB4Casthestoichiometricallystablephase,withsolidsolutionswithBandConeachrespectiveside.2 JournaloftheAmericanCeramicSocietyDomnichetal.From an experimental viewpoint, the possibility that(B11C)CBCis the true structural representationof the B4Cstoichiometry was originally inferred,47and later corrobo-rated,48,66by nuclear magnetic resonance (NMR) observa-tions. However, concurrent NMRstudies by other groupsoered alternative interpretations, including structures withchains consisting only of carbon atoms,49and chains withtwocarbonatomssubstitutedbyboron.50Inpart, thesedis-crepancies stemmed from the lack of agreement on theassignment ofspecicNMRpeakstoeitherthechaincenterCatomortotheCatominthepolaricosahedral site. Theo-retical simulationof NMRspectra in(B11Cp)CBC, (B11Ce)CBC, and(B12)CCCcongurations basedondensity func-tional theory (DFT) helped to resolve this issue.64It wasfoundthat the best correlationbetweenthe theoretical andthe experimental NMRspectra for the B4Cstoichiometrycould be achieved for the B4Cstructure consisting of allCBCchains anda mixture of (B12), (B11Cp), and(B10C2p)icosahedraintheratioof 2.5/95/2.5, withthetwoCatomsinthelatterstructurelocatedintheantipodalpolarsites.In a related study that employed a similar modelingframework,39,65comparison of theoretically simulated andexperimental Raman and infrared spectra of B4C alsoimpliedthat (B11Cp)CBCisthetruerepresentationof boroncarbide at this stoichiometry. Further, the presence of theboron atom in the B4C chain has been inferred fromX-ray2,31,32and neutron diraction34,51data, owing to theobservationof thelowerscatteringat thechaincenters, andfrom X-ray absorption12and scattering62,63observations.Thus, themajorityof theoretical andexperimental investiga-tionsagreethat(B11Cp)CBCisthepreferredatomiccongu-rationfortheB4Cstoichiometry.Itshouldbenotedthatevenhigherestimationsforthecar-bon-richedgeofthehomogeneityrangehavebeendiscussed.Konovalikhin etal. reported successful synthesis of singlecrystal boron carbide with ~24at.%C.25To account forhighercarboncontentinthiscompound, theproposedstruc-tural conguration included a distribution of CBCchainsand(B11C), (B10C2), and(B9C3) icosahedra, withthe hypo-thetical (B9C3)CBCcongurationlimitingtherangeofstableboroncarbide compounds at 33at.%C.25,46However, thelatter ndingis incontradictionwithanestablishedconceptthat due tothe internal bondingconstraints, the maximumnumberofcarbonatomsthatcansubstituteboronintheico-sahedra is two.67Following this concept and assuming(B10C2)CBCas themost carbon-richcongurationof boroncarbide, thetheoretical limit for thecarbon-richedgeof thehomogeneityrangeshouldnotexceed25at.%C.There is alackof agreement inthe scientic communityonthenatureof thestructural changes inboroncarbideatdecreasing carbon concentrations. While it is generallyaccepted that the carbon atoms substitute boron atoms intherhombohedrallattice,dierentviewsexistonwhetherthechainortheicosahedral atomsarepreferentiallysubstituted.Basedonentropicandenergeticconsiderations,Eminconjec-turedthat preferredsubstitutionoccurs inthe chainsites.36Accordingtothis theory, thenumber of CBBchains inthestructure will increase until all material is comprisedof the(B11C)CBBunits, whichcorresponds tothe B6.5Cstoichio-metryat 13.3at.%C. Forlowercarbonconcentrations, thesubstitutionwill takeplace withintheicosahedra, renderingtheidealized(B12)CBBcongurationforthemostboron-richB14Cstoichiometryat6.7at.%C. Thismodel providesbasisfor aconsistent interpretationof theobservedtrends inthecompositional dependenceofelectrical andthermal transportproperties,6874elastic properties,75structural data,33and vibrational frequencies and intensities incurred fromRamanandinfrared(IR)measurements.53,58,59,76AnalternativeinterpretationoftheavailableX-raydirac-tion(XRD)datamaintainsthatcarbonispreferablyreplacedby boroninthe icosahedral sites.32,77,78Inthis model, thenumber of (B12) icosahedrainthe material increases as thecompositionapproaches13at.%Cfromthecarbon-richend;the structuralconguration for the stoichiometricB6.5C phaseisgivenas(B12)CBC; andthesubstitutionof boronintothechain sites occupied by carbon occurs in the 813 at.% C rangeofcompositions.ThisviewisalsosupportedbytheDFTcal-culations, whichconsistentlyindicatethatthe(B12)CBCcon-gurationismorestablethanthe(B11C)CBBone,bothfromthe energy minimization considerations and from a better cor-relation with the experimental lattice parameters.4,38,40,43ComparativeDFTcalculationsof thefreeenergyandthestructural parameters of various possible congurations ofchain and icosahedral units for dierent boron carbide stoichi-ometries have been reported by several authors.4,40,43Fanchinietal.40observed that the calculated free energies for a numberof dierent atomic congurations, referred to as polytypes, fallinto a small disorder potential of DV 0.2eV (Fig. 4), corre-sponding to typical temperature variations encountered duringboron carbide synthesis.3Based on this consideration, Fanchiniand co-workers proposed that various boron carbide polytypeswithenergydierencessmallerthanthedisorderpotentialcancoexist at any given boron carbide composition.40Inpractice,thestructureofassynthesizedboroncarbideismore disordered than indicated by the idealized modelspresented above. Theoretical calculations predict (B12)BC(for vacancy) tobe the most stable congurationat theboron-rich end of the homogeneity range.43Renement of theXRDdatafor B9.5Cimplies that at thiscomposition, upto25%of CBCchains arestatisticallyreplacedbythe4-atomBBBBunits, wherethetwocentral atomsoftheunitlienearaplanenormaltothethreefoldaxis,bondingtothetwotermi-nalunitatomsandtothethreeicosahedralatoms.52Neutrondiractionobservationsgiveevidenceofthepresenceofnon-linearchainswithadisplacedcentral atom, aswell aschainswith a vacancy in the central chain site, along with the regularCBCand(possibly)CBBchainsandicosahedral unitsinthemore boron-richcompositions.11,34Interpretationof the IRabsorptionspectraandanalysisoftheresultingphononoscil-latorstrengthsindicatestatisticaldistributionofseveralstruc-tural elements, e.g., (B12) and(B11C) icosahedra, CBCandCBBchains, as well as chainless units, at all compositionswithinthehomogeneityrange,asillustratedinFig. 5.54How-ever, it should be noted that the results of such calculation are5.595.605.615.625.635.645.655.66(b)ca ()a12.0412.0612.0812.1012.1212.1412.1612.1812.20c ()Boron carbideLattice parameters7 8 9 10 12 11 13 14 15 16 17 18 19 20 211.421.431.441.451.461.47Chain bond Carbon Content (at.%)Bond Length ()(a)Fig. 3. Dependence of (a) hexagonal lattice parameters a and c,and(b) thechainbondlengthof boroncarbideoncarboncontent.Lines serve as guides to the eye. Data from(a) X-ray diractionmeasurementsbyAselageetal.33and(b)neutronpowderdiractionmeasurementsbyMorosinetal.11,34StructureandStabilityofBoronCarbideunderStress 3contingent upon the specic assumptions made during thederivationofthemodel,andothervariationsofthecomposi-tional dependencies of the structural elements that form boroncarbide have also been reported.55,79Thepresenceofdefectsisessential forboroncarbides. AsshownbyBalakrishnarajanetal.,42disorders inthe atomicarrangement are a part of the ground-state properties ofboroncarbide, andare not due toentropic eects at hightemperatures. This is not unique for boron carbide, butrather acommonpropertyof boron-richsolids. Inb-rhom-bohedralboron,forexample, thepresenceofintrinsicdefectshas been shown to result in macroscopic residual entropy,suggesting that b-boron could be characterized as a frus-tratedsystem.80The case of boroncarbide maybe onlinewiththisresearch.Finally, a crucial issue that structural experimental andtheoretical datadonot takeintoaccount is thepresenceoffreecarboninas-synthesizedboroncarbide.Thatis,allpoly-crystalline boroncarbides containimpurities inthe formoffree carbon that can exist as either amorphous carbon orintra-granulargraphiticinclusions, asshownbyasystematiccharacterization of hot-pressed boron carbide ceramics byChenetal.81II. ElectronicStructure,ElectronicandOpticalPropertiesEarly work by Lagrenaudie established that boron carbidewas ap-typesemiconductor withanestimatedbandgapof1.64eV.82This is muchsmaller thanthebandgapof othersemiconductorceramics, e.g., Eg~3eVasinsiliconcarbide.Other estimations for the bandgapof boroncarbide havealsobeenreported. Werheit etal. measuredanindirect gapof 0.48eV83by optical measurements; the same groupreportedinalater workabandgapof 2.09eV, suggestingthat awide range of gaps couldbe identiedinthe boroncarbide structure within the stoichiometric range of B4.3CB11C.84Largerbandgaps, typicallyexceeding3eV, arecon-sistentlyobtainedintheoretical bandstructure calculations,suggestingthatthemodelsdonotadequatelyaccountforthedisorder in the material which could give rise to midgapstates.35,37,38,64,85,86Examples of the calculated electronicdensityofstates(DOS)showingestimatedbandgapsforthe(B12)CCC86and the (B12)CBC85atomic congurations aregiveninFig. 6. Oneimportant observationis that thepres-enceof anintermediategapstatein(B12)CCC, accordingtocalculationsbyDekuraetal.,86resultsinasmallerbandgapof only1.56eVinthis structure. Inthe case of (B12)CBC,Calandraetal. report that 88%of total DOSat theFermilevel arisefromtheicosahedra; inparticular, boronatomsinpolar positions give the largest contributiontothe conduc-tionprocesses.85Electronicband structure calculationsconrm the semicon-ductingnature of boroncarbide for the stoichiometric B4C-6.60 -6.55 -6.50 -6.45 -6.400.40.60.81.0(B12) + a-C (B10Cp2)BCB(B11Cp)CCB(B11Cp)CBB(B12)CBC(B12)CCCRelative AbundanceFree Energy (eV/site)(B11Cp)CBCFig. 4. Gibbs energies (Gi) and the relative abundancesfi / exp Gi=DV ofselectedboroncarbidepolytypescorrespondingtothedisorder potential of DV=0.2eV(dashline), after Fanchinietal.40Stability range for a segregated boron-amorphous carbon(B12)+a-Cphaseisalsoshown.8 10 12 14 16 18 200.00.10.20.30.40.50.60.70.80.91.0 (B11C) (B12) Chainless CBB CBCConcentration of Structural ElementsCarbon Content (at.%)Fig. 5. Distributionofchainandicosahedral structural unitsacrossthehomogeneityrangeinboroncarbideobtainedfromtheanalysisofIRabsorptiondatabyWerheitandco-workers. ReproducedfromKuhlmannetal.,54withpermission; 1992Elsevier.01234(B12)CBC(B12)CCC-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.501234DOS (states/eV/unit cell)Energy (eV)(a)(b)Fig. 6. CalculatedelectronicDOSfor(a) (B12)CCC86and(b) (B12)CBC85polytypes of boron carbide. An intermediate gap state isformedin(B12)CCC. The topof the valence bandis takenas theenergyorigin. TheFermi level islocatedatzerofor(B12)CCCwhileitisat 0.52eVfor(B12)CBC.4 JournaloftheAmericanCeramicSocietyDomnichetal.with48 valence electrons.35,37,86However, more boron-richcompounds, characterizedbyvalenceelectrondecienciesareconsistentlyfoundtobemetallic.35,38,85Thisisadirectconse-quence of the bandtheory stating that a crystal withoddnumberofvalenceelectronsmustbeametal, independentofthe calculation method.5Figure7 shows electronic bandstructurescalculatedbyKleinmansgroupforthe(B11C)CBCandthe (B12)CBCcongurations.37,38,87As follows fromanexaminationof Fig. 7, the maindierence betweenthe twostructures is thepositionof theFermi level, whichindicatesthe semiconducting nature of (B11C)CBCand the metallicnatureof(B12)CBC.Forthe(B12)CCCconguration,asillus-tratedinFig. 6,adistinctfeatureofthebandstructureisthepresenceof thegapstateof nonbondingcharacter, predomi-nantlyarisingfromtheporbitalofthecentralCatominthechain.86This may explain the origins for B4C refusal ofassuming the (B12)CCC atomic conguration.Experimentally, boroncarbidewasfoundtobeasemicon-ductor throughout the entire homogeneity range, with itselectronic properties dominated by the hopping-type trans-port.68,88,89Thedirectcurrent(dc)conductivityofboroncar-bideasafunctionofcarboncontent, asmeasuredbyseveralgroups,68,8992ispresentedinFig. 8. Qualitatively, themaxi-muminconductivityoccursat~13at.%C, correspondingtotheB6.5Cstoichiometry. This observation, as well as similartrendsinthecompositional dependencesof otherboroncar-bideproperties (e.g., structural parameters, seeFig. 3), havebeenattributedtodierent mechanisms for boronsubstitu-tionsintothelatticesitesoccupiedbycarbonatoms, asdis-cussed in SectionI. Several related models have been alsoproposedintheliteratureforexplainingboroncarbidetrans-portproperties.Emin advanced a charge transport model based on thesmall bipolaronhoppingmechanism.9396Inthis model, thechargecarriersinboroncarbidearepairsofholesthatmovebyasuccessionof thermallyactivatedphonon-assistedhopsbetween electronic states on inequivalent B11Cicosahedra.Thepairingof theholes onB11Cicosahedrais viewedas aresult of the disproportionation reaction, 2(B11C)0?(B11C)+(B11C)+,resultingintheformationofanelectron-decient(B11C)+icosahedron,whichisachemicalequivalentof a bipolaron. This theory, together with an associatedstructural model36(SectionI), was able to interpret theobserved compositional, temperature and pressure depen-denceofboroncarbideconductivity,aswellasthevariationsinHall mobility, Seebeckcoecient, dielectricconstants, andmagnetic susceptibility of boron carbide with temperatureandcarbonconcentration.68,72,74,92,97,98However,itisimportanttonotethattheapparentcorrela-tion of the experimental data with the Emins transportmodel is contingent upon several factors. Crucial for theinterpretationof thecompositional dependencies of physicalproperties (e.g., electrical conductivity, Fig. 8) in terms ofsmall bipolaronhoppingisEminsconjecturethat thestruc-tureof theB6.5Ccompoundis describedbythe(B11C)CBBatomic conguration, providing sucient concentrations ofthe(B11C) unitsrequiredfortheformationof bipolaronsatthis stoichiometry. However, as discussedinSectionI, thereis nodirect empirical evidence insupport of this structuralmodel. Moreover, boththerenementofXRDdataandtheresults of all available theoretical abinitiocalculations sup-port analternativestructural model, whichpredicts gradualsubstitution of the icosahedral carbon atoms with boron50-5-10-15Energy (eV)(a)50-5-10-15(b)Fig. 7. Calculatedenergy bands for (a) the (B11C)CBCand (b) the (B12)CBCpolytypes of boron carbide. The solidand the dashbandsrepresent states that are, respectively, evenandoddunder reectioninavertical plane. Zeroenergycorresponds toFermi level. ReproducedfromKleinman,87withpermission; 1991AmericanInstituteofPhysics.8 10 12 14 16 18 2005101520 295 K a 295 K b 450 K c 450 K dDC Conductivity (cm)Carbon Content (at.%)Fig. 8. Compositional dependence of dc conductivity in boroncarbideat dierent temperatures. Datafrom(a) Samaraetal.92; (b)Werheitetal.90,91;(c)Woodetal.68;(d)Schmecheletal.89StructureandStabilityofBoronCarbideunderStress 5as the carbon concentration changes from 20at.% to13.3at.%. Inthis model, thepreferredatomiccongurationfor theB6.5Ccompoundis givenbythe(B12)CBCformula,providingverylimitedavailabilityof the(B11C)units, whichis exactly opposite to the requirements of Emins theory.Other inconsistencies of thesmall bipolaronhoppingmodelforboroncarbide, suchasanoverestimateofcarrierconcen-trations andthe evidencefor multipleactivationenergies inthe temperature dependence of electric conductivity, havealsobeendiscussedintheliterature.99An alternative interpretation of boron carbide transportproperties has been proposed by Werheit and co-work-ers.79,89,100,101Theysuggestthatthesemiconductingnatureofboroncarbidearisesfromthestructural disorderthroughouttheentirehomogeneityrange.TheintrinsicdefectsassociatedwithdisorderareproposedtobeJahn-Tellerdistortionoftheicosahedra,100missing or incomplete occupation of specicatomicsites,statisticaloccupationofequivalentsites,oranti-sitedefects.54,55,79Werheitmaintainsthatthedefectsinboroncarbide generate split-o valence states in the band gap,whichexactlycompensateelectrondeciencyoftheidealizedstructures(e.g., (B12)CBC) that aretheoreticallyfoundtobemetallic. AccordingtoWerheit,101highconcentrationof gapstatesnearthevalencebandisresponsibleforthelowp-typeelectrical conductivity inboroncarbide. Inadditiontotheelectrical conductivityinextendedbandstates, hopping-typeconductioninlocalizedgapstatesispredictedbythismodel.The compositional dependencies of physical properties inboron carbide, such as electrical conductivity shown in Fig. 8,can then be correlated with the total concentration of intrinsicdefects, suchas the one illustratedinFig. 5. However, thismodel suersfromthelackof independent verication. Thedistributionof structural elements, as proposedbyWerheitandco-workers,54,55,79reliesentirelyontheinterpretationofspecicbandsintheIRabsorptionspectraof boroncarbideobtained by the same group. It will be discussed in SectionIIIthatalternativeinterpretationsoeredintheliteratureoftheIRdataprovidealternativeexplanationstoWerheitsanaly-sis. Inaddition, theirmodel requiresapre-selectionofstruc-turalelementsthatWerheitandco-workerslimitto(B12)and(B11C) icosahedraandCBC, CBB, andBBchains. Asdis-cussedinSectionI, while neutrondiractiondatagive evi-dence for vacancies inthe central chainsite, other possibleatomic congurations, such as the (B10C2) icosahedra, theCBchains, thenonlinear chains, the4-atomicboronunitsreplacingthechains, etc., mayalsobepresent inboroncar-bide at varying stoichiometries. Accounting for these addi-tional structural elements would inevitably alter Werheitscompositional distributioncurves, suchas theoneshowninFig. 5.Theoriginof disorder inboroncarbidehas beeninvesti-gatedusingquantumchemical methodsbyBalakrishnarajanetal.,42whoanalyzed the nature of the molecular orbitalscorrespondingtothe (B12) icosahedraandCBCchains andinteractions among themin the most symmetric (B12)CBCstructure. They also studied the eect on the bonding ofaddingor removinganelectronfromtheunit cell. Thecal-culationshaveshownthat theadditionof electrons expandstheunit cell, elongatingandweakeningall bonds. Inpartic-ular, the carbon atoms tend to change hybridization fromsp2to sp3as the total molecular charge is increased. Thisgroupalsostudiedthe changes inthe bonding nature withthevaryingcarboncontent, concludingthat partial substitu-tion of carbon by boron atoms creates inevitable disorderbecause it is energeticallyandentropically favored. Inpar-ticular, calculations indicatethat disorder is localizedat thecarbon sites and the bonding of B/Ccovalent network indefective boroncarbide is stronger thaninthe stoichiome-tricelectron-preciseB4C.42Thelocalizationof theelectronicstatesarisingfromtheB/Cdisorderthereforeleadstosemi-conducting nature of boron carbide throughout its entirecompositional range.Theelectronicstatesdiscussedabovedeterminetheopticalproperties of boron carbide and therefore can be probedusing optical techniques. Optical constants of hot-pressedboroncarbidewithapresumedB4Cstoichiometry,calculatedby Larruquert etal. via reectance measurements in theextreme ultraviolet spectral region are listed in TableI.102Werheitetal. measureddielectricfunctionsofboroncarbidesampleswithvaryinghistoryandstoichiometry,asillustratedinFig. 9.103Anumberofcritical pointsforinterbandtransi-tionsidentiedfromthedatainFig. 9indicatethatthebandgapofboroncarbidedoesnotexceed2.5eV.Thisworkalsodemonstrated that the imaginary part of the dielectricfunctionreachedmaximumnear~13at.%C,whichwascor-relatedby the authors tothe highest structural disorder inboroncarbideattheB6.5Cstoichiometry.103The absorption coecients obtained fromoptical trans-missionmeasurementsonB4.3Csampleswithvaryingdegreesof structural disorder104,105are shown in Fig. 10. Opticalabsorptioninasinglecrystal (a 3000cm1)ishigherthanthatinpolycrystallinesamples; however, thecorrelationofawithstructuraldisordercannotbeunambiguouslyestablishedbecause amore orderedpolycrystalline sample obtainedbyhot isostatic pressing (HIP) shows lower absorption belowtheabsorptionedgethanthelessorderedcommercial sampleobtainedby hot pressing (HP). The increase inabsorptioncoecient toward lower energies in the single crystal datahasbeenattributedtochargecarriers,105incorrelationwithboth the hopping-type and the Drude-type transport.Werheit andco-workershaveidentiedseveral indirect tran-sitions between 0.47 and 3.58eVvia deconvolution of theabsorption edge shown in Fig. 10.104,105They assign suchprocesses to transitions between various electronic stateswithinthebandgap.Feng etal. used nonresonant X-ray Raman scattering(XRS)techniquealongwithsite-specicabinitiocalculationsto detect substitutional disorder in carbon-rich boron car-bide.62The results of this studyshowthat boronpreferen-tiallyoccupies the chaincenter sitegeneratingadelocalizedp-typeexciton. Enlargedviewofthenear-edgeregionfortheboronXRSspectrumof B4CshowninFig. 11identiestheexciton related feature at ~1eV. Werheit compared theseXRSresultswiththeiroptical absorptiondata(Fig. 10) andfound good agreement between the two; he also proposedthatthehigherabsorptionofthesinglecrystal boroncarbideintherangeof 1.01.5eV(Fig. 10) must beduetosmallerconcentrations of extrinsic structural distortions resultinginhigher probability of exciton generation compared to thepolycrystallinematerial.84Figure12 shows the photoluminescence spectrumof apolycrystalline B4.23Csample measuredby Schmechel etal.usingtheexcitationenergyof2.4eV.106Thefeaturesat1.56and 1.5695eV in the photoluminescence versus photonenergy dependence have been attributed to the indirect recom-binationof free excitons inthe center BatominCBCandCBBchains, respectively.84Further, Werheit etal. reportedphotoluminescencemeasurementsona setof isotope-enrichedboroncarbidesamplesspanning theentire homogeneityrangeusinganexcitationenergyof 1.165eV.107TheyassignedtheTableI. OpticalConstantsofHot-PressedBoronCarbide102Wavelength(nm) n(a.u.) k(a.u.)49.0 0.5 0.4154.3 0.45 0.6358.0 0.45 0.7467.2 0.53 1.0274.0 0.60 1.1583.5 0.77 1.4592.0 0.86 1.61104.8 1.11 1.81121.6 1.77 2.056 JournaloftheAmericanCeramicSocietyDomnichetal.various luminescencepeaks tothepresenceof localizedgapstates andthe resultingtransitions betweensuchstates andthe energybands.Combiningtheoptical absorption,photolu-minescence, andchargetransportdataforelectrontransitionenergies,Werheitproposedanenergybandschematicconsist-ingofa2.09eVbandgap, several disorderinducedinterme-diate gap states extending 1.2eVabove the valence bandedge, excitoniclevel at1.56eVabovethevalencebandedge,andanelectrontraplevel around0.27eVbelowthebottomof the conduction band, as shown in Fig. 13.84,107,108III. LatticeDynamicsandVibrationalPropertiesForaboroncarbidecrystal ofR3msymmetry, grouptheorypredicts the following representationfor the normal modesoflatticedynamics:1095A1g2A1u2A2g6A2u7Eg8Eu: (1)The12modesofA1gandEgsymmetryareRamanactive,the14modesofA2uandEusymmetryareIRactive,andtheA1uandA2gmodes areopticallyinactive. Byremovingzero-fre-quencymodes,the number ofIR active modesbecomes12.109For boron carbidepolytypes that deviate from true R3m sym-metry,e.g.,whenacarbonatomisintroducedintotheicosa-hedron, theaboveselectionrulesarenot validandahighernumber of modes isexpected in the experimental spectra.The RamanandIRfrequencies have beencalculatedforthe(B12)CBCpolytypefromparametricttingofthevalenceforce constants,109,110and for the (B12)CBC, (B12)CCC,(B11Cp)CBC, and(B11Ce)CBCpolytypesfromabinitioDFT/DFPTcalculations.65,111InFigs. 14and15, theoretical pre-dictionsfortheIRandRamanactivemodesinthe(B12)CBCand(B11Cp)CBCpolytypes arecomparedwith theexperimentalspectra for boroncarbide of matching stoichiometries, i.e.,B6.5CandB4C,respectively.Itisimmediatelyrecognizedthatthe use of simpliedmodels for the evaluationof the forceconstants109donot yieldreliablefrequencies. Indeed, unam-biguous identication of specic IRand Raman bands isimpractical inthiscase[Figs. 14(a) and15(a)]. Ontheotherhand, formodefrequenciescalculatedbyabinitiopseudopo-tential modelingbyLazzari etal.65, correlationwithexperi-ment is verygood[Figs. 14(b) and15(b)]. Inthis work, notonlyfrequencies but alsorelativepeakintensities havebeencorrectlypredictedinthecalculatedIRabsorptionspectrumof(B11Cp)CBC,byaccountingfortheexperimentalmixingof2 3 4 5 6 7 8 9 10012345678e1Photon Energy (eV) B4.23C B6.28C B8.52C B10.37C2 3 4 5 6 7 8 9 1034567e2Photon Energy (eV)(a)(b)Fig. 9. (a) Real and(b) imaginaryparts of the dielectric functionof boron carbide with dierent stoichiometry. Reproduced fromWerheitetal.,103withpermission; 1997Elsevier.0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.010002000300040005000600070008000900010000HPpolycrystalline ceramicAbsorption Coefficient (cm-1)Photon Energy (eV)B4.3Csingle crystalHIPFig. 10. Absorptioncoecient versus photonenergymeasuredonthe (111) surface of a single crystal, on a high quality HIPpolycrystalline sample, and on a commercial HP polycrystallineboroncarbide ceramic. All samples are of the B4.3Cstoichiometry.DatafromWerheitetal.104,105-4 -2 0 2 4 61112131415Intensity (a.u.)Energy from the Edge (eV)Polycrystalline B4CFig. 11. Fragment of an XRS spectrumof polycrystalline boroncarbide for a momentum transfer of 1.05A 1(dots) and thebackground of icosahedral Batoms (solid line) calculated for the(B12)CBCatomicarrangement.DatafromFengetal.62StructureandStabilityofBoronCarbideunderStress 7polarizations for the A2uand Eumodes.65Surprisingly,anotherabinitiostudyperformedbyShiraietal.,111based onthe same selection of pseudopotentials, yielded IR activemodes that did not correlate well with the experiment(Fig. 14). Nevertheless, the latter work did elucidate animportant observationthat theIRmodes shift tolower fre-quencieswhenacarbonatomissubstitutedbyaboronatomin the icosahedra due to shorteningof bond lengths.There havebeensome eorts tocorrelate the specic IRandRamanmodestotheatomicstructureofboroncarbide.According to Vast etal.,39the IR active Eumode at396cm1originates fromthetorsionof theCBCchain; theRamanactiveEgmodeat 480cm1arises fromchainrota-tionperpendiculartothe(111) plane; andtheRamanactiveEgmode at 535cm1is due tothe librationof the (B11C)icosahedron.Theatomicdisplacementsfromlatticedynamicscalculated by Shirai etal.112are commonly referenced byexperimentalistsforpeakassignments.ShiraismodelpredictsaRamanactiveA1gmodeat1080cm1originatingfromthebreathingvibrations of the (B12) icosahedron; anIRactiveEumode at 1040cm1resulting fromcomplex atomic dis-placementsduetochainbending, andantisymmetricstretch-ing of anicosahedron; anIRactive Eumode at 487cm11.55 1.56 1.57 1.58 1.59010203040506070Intensity (a.u.)Photon Energy (eV)model fitaverage exp. dataFig. 12. Photoluminescence spectrum of polycrystalline boroncarbide acquired at the excitation energy of 2.4eV.106Squares,experimental results; dash lines, recombination models of freeexcitons: IE E E0p exp E E0=kBTe , with E0=1.56eV(1.5695eV) and the exciton temperature Te=46K; solid lines,averaged experimental results, before and after substracting the1.56eV model t. Reproduced fromWerheit,84with permission;2006InstituteofPhysics.conduction band conduction band0.270.065electron trapsexcitonsdeep levelsEnergy(eV)valence band valence band1.5602.091.2conduction band conduction bandvalence band valence bandFig. 13. Schematicof the structure of gapstates inboroncarbidedevelopedbyWerheit.84,107,108400 600 800 1000 1200 1400 1600calc. (B12)CBCIRexp. B6.5Cexp. B4Ccalc. (B11Cp)CBC400 600 800 1000 1200 1400 1600(b)Absorption (a.u.)Wavenumber (cm-1)(a)Shirai 1996Shirai 2000Shirai 2000Lazzari 1999Fig. 14. Comparison of experimental and theoretical infraredabsorption spectra of boron carbide: (a) FTIR on hot-pressedB6.5C55versus parameterized valence force model109and ab initiocalculation111for (B12) CBC; (b) FTIRon hot pressed B4.3C55versus ab initio calculation for (B11Cp)CBC.65,111Solid lines: Eumodes;dashlines:A2umodes.Lazzari 1999calc. (B12)CBCRamanexp. B6.5Cexp. B4Ccalc. (B11Cp)CBCShirai 1996200 400 600 800 1000 1200 1400 1600 1800 20001.59 eVIntensity (a.u.)Wavenumber (cm-1)2.41 eV2.41 eV1.59 eV(a)(b)Fig. 15. Comparison of experimental and theoretical Ramanspectraofboroncarbide:(a)dispersiveRaman(laserexcitations1.59and2.41eV) onhot-pressedB6.5C(this work) versusparameterizedvalenceforcemodel for(B12)CBC;109(b)dispersiveRaman(1.59eV;2.41eV) onhot-pressedB4C(this work) versusabinitiocalculationfor(B11Cp)CBC.65Solidlines:Egmodes;dashlines:A1gmodes.8 JournaloftheAmericanCeramicSocietyDomnichetal.originatingfromchainbending; aRamanactiveEgmodeat335cm1resultingfromatomic displacements due tochainrotationandwaggingofanicosahedron;andaRamanactiveEgmodeat 172cm1originatingfromrotationof anicosa-hedron. Both the parametric tting model of Shirai etal.andtheresultsofabinitiocalculationsbyVastandco-work-ersagreeinassigninganIRactiveA2umodeat~1600cm1totheantisymmetricstretchingoftheCBCchain.4,112Vastandco-workershavealsoreportedtheoreticalestima-tions for phonondensityof states (PDOS) of the(B12)CBCcompound.85Accordingtothiswork, theicosahedral modesareresponsibleformostofthecontributiontototalPDOSatfrequencies below1130cm1, withtheexceptionof thefea-turesbetween200and450cm1, wherenotablecontributionfromthechainmodesinvolvingvibrationsofboronatomsisobserved, and the feature at 1040cm1, which has a signicantcontributionto PDOSfrom thevibrations of carbon atomsinthe chain (Fig. 16). Also, this model predicts that the high fre-quency feature at 1555cm1arises from thechain modesthatinvolve vibrations of both boron and carbon atoms.85(1) InfraredSpectroscopyObservationsThe infrared spectra of boron carbide have been studiedextensivelybythegroupofWerheit5456,105,113TypicalFTIRdata of absorptionindex, k, are showninFig. 14 for twoboroncarbidestoichiometriesassociatedwithdierentstruc-tural congurations: the carbon-rich B4.3Ccompound andthe intermediate B6.5Ccompound. Werheit etal. attributethe observedbandat ~1600cm1toCBCchainstretching,the band at 410cm1to CBCchain bending, and all theremainingbandstointra-icosahedralvibrationsinboroncar-bide.54,113Further, thisgrouphasinterpretedtheappearanceofbandsat380and1450cm1inmoreboron-richcomposi-tions (Figs. 14 and 17) as new modes originating fromstretchingandbendingof thechains that containaCatominthecentralsite,suchastheBCBortheCCCchains.55TheeectofisotopesubstitutionsonthefrequenciesofIRactive modes in boron carbide has also been investi-gated.30,53,55,56Theisotope-dependent frequencyshifts of IRmodes inboroncarbidecomposedof10B4.312Cat theB4.3CstoichiometryareshowninFig. 18. Thelargefrequencyshiftof the ~1600cm1IRabsorptionbandwithboth10Band13Cisotopic substitutions imply substantial involvement ofbothBandCinthismode, which, combinedwithhighfre-quency, indicates sti bonding between boron and carbonatoms. Further, Aselageetal. challengedassignment of thisbandtostretchingofthechainCBbond, arguingthatsuchastrongbondshouldformbetweenboronandcarbonatomsinthepolar sites of theneighboringicosahedra.59However,as shownbyCalandraetal.,85highfrequencychainmodesthatinvolvevibrationsof bothBandCatomsarepredictedby ab initio calculations, which supports Werheits assign-ment of the ~1600cm1IRabsorption band to the CBCchainstretching.(2) RamanSpectroscopyObservationsTheRamanspectraof boroncarbidearecharacterizedbyaseries of bands extending from200 to 1200cm1.5861,114There are conicting assignments of the observed Ramanbands to vibrations of icosahedra and the 3-atomlinearchains.4,39,5761,109,115Analysis of this is further complicatedby the observed intensity dependence of the low-frequencybands on the excitation wavelength (energy).114TypicalRamanspectraof twosurfacesof aB4.3Csinglecrystal asafunctionoflaserenergyareshowninFig. 19.Thegroupof Tallant, Aselage, andEmin5759studiediso-tope and carbon content dependencies of boron carbidesusing the 514.5nm(2.41eV) laser. They assigned the twonarrowbands at 480and535cm1tothe stretchingvibra-tions inthe soft CBCchains. The intensity of bothbands200 400 600 800 1000 1200 1400 1600 1800 (a.u.)Wavenumber (cm-1)icosahedrachainsRamanIRPDOS(d)(c)(a)(b)Fig. 16. Contribution from(a) chain modes and (b) icosahedralmodes to PDOS calculated for the (B12)CBC polytype.85Experimental(c)Ramanspectra(hot-pressedsample;laserenergy1.96eV)and(d)FTIRabsorption spectra56of the B6.5Ccompoundare shownforreference.1200 1300 1400 1500 1600 1700 18008.8 at.% C10.5 at.% C11.2 at.% C13.7 at.% CAbsorption (a.u.)Wavenumber (cm-1)18.9 at.% CIRFig. 17. Compositional dependence of the high frequency modesin the IRabsorption spectra of boron carbide. Reproduced fromKuhlmannetal.,54withpermission; 1992Elsevier.StructureandStabilityofBoronCarbideunderStress 9wasfoundtodiminishprogressivelywiththedecreaseincar-bon content, which was attributed to the gradual replace-ment of theCBCchains withtheCBBchains. At thesametime, the two bands at 270 and 320cm1were found todecreaseinintensitywiththedecreaseincarboncontent,andanewnarrowbandat ~375cm1was foundtoappear andbecomemorepronouncedinthespectraof moreboron-richcompounds. Thislatterfeaturewasattributedtotheappear-ance of the BBBchains at verylowcarbonconcentrations.Further, accordingtothisgroup,5759thedependencyof thehigh-frequencybandsoncarbonisotopeandcarbonconcen-trationsuggests that carbonatoms arepresent withinicosa-hedraatallcompositions.The group of Werheit56,60,61,115,116studied isotopic andcompositional dependencies of boron carbide using the1070nm (1.16eV) laser. This group maintains that the spectraacquiredat higher laser energies areeither coupledwiththeelectronicstates or areabletoexciteonlysurfacephonons,duetothehighabsorptioncoecientofboroncarbideabovetheabsorptionedge,108,115whichtheWerheitgroupplacesat3.5eV.104At long excitation wavelength, the two bands at 270and320cm1become the primaryfeatures of the observedRaman spectra (Fig. 19). Following theoretical analysis ofShirai and Emura109, Werheit assigns these two bands to rota-tionsof theCBCandCBBchainsaccompaniedbywaggingmodesof theicosahedra. Werheitsgroupalsondsthat theintensities of the two bands at 270 and 320cm1diminish withthe decrease in the carbon content, in agreement with theobservations of Tallant, Aselage, and Emin.AccordingtoabinitioDFT/DFTPcalculations, novibra-tional modesshouldbepresent inboroncarbideat frequen-cies below400cm1.39,65Vast andco-workers argued thattheRamanbandsobservedintheexperimentalspectraat270and320cm1arisefromalift intheselectionrulesinducedbystructural disorderandmust reecttheDOSforacousticphononsduetothex4scalinglawforscatteringintensityatlowfrequencies.4However, thistheoryisinconictwiththefollowingempiricalobservations:(i) the twobands at 270 and320cm1are present in the anti-Stokes Raman spectra,108whichreects their true Ramannature; (ii) the intensityofthetwobandsat270and320cm1increaseswithdecreasinglaser frequency (Fig. 19), which invalidates the x4scalinglawargument; and (iii) these bands are equally present inhot-pressed ceramics and in high purity single crystals (cf.Figs. 15 and19), whichquestions their dependence onthestructural defectsandimperfections. Thus, thetruenatureofthe bands at 270and320cm1inthe Ramanspectrumofboron carbide is stillto be established.The origin of the bands at 270 and 320cm1can beunderstood fromthe viewpoint of boron carbide being afrustratedsystem, as discussedinSectionI. Ina frustratedcrystal, aperfectlyorderedcongurationwithhighsymmetryis characterizedby the formationof nonbonding states, asillustratedinFig. 6. These nonbondingstates canformthestrongcovalent bondbybreakingthesymmetry, at thecostof losingacovalent bondinanother place. Formationof astrong local bond brings about an associated weak bond,andtheseweakbondorweakangleforcesmayberesponsi-blefortheappearanceoflow-frequencymodesintheRamanspectra of boron carbide. The primitive-cell calculations(suchastheonesbyLazzari etal.65andbyShirai etal.111),ontheotherhand, wouldcompletelyeliminatesuchuctua-tionsoverthecrystal.Assignment of the 480cm1bandtochainrotationper-pendicular tothe (111) plane, impliedby ab initio calcula-tions of Lazzari etal.,65has beenexperimentallyconrmedbythe observations made onorientedboroncarbide singlecrystals. As showninFig. 19, theintensityof the480cm1banddiminishes withrespect toother Ramanbands whenthe sample is rotatedfromthe (111) orientation, whenthescatteringgeometryis alignedwiththe3-atomchain, tothe(210) orientation, when the scattering geometry is at ~25angle to the 3-atomchain. This would be expected for avibrational mode where maximum atomic displacementsoccur indirections perpendicular tothe chainaxis, suchasthediscussedCBCchainrotationmode.39TheRamanspectrumof boroncarbideat higherfrequen-cies(from600to1200cm1)ischaracterizedbyanumberofbroad bands that are believed to originate predominantlyfromthevibrationswithintheicosahedral units.39,58Follow-ing Shirais mode assignments,112the major band at1088cm1isreferredtoinsomeliteratureastheicosahedralbreathing mode, or IBM. However, analysis of the Ramanactivemodes for (B11C)CBC[Fig. 15(a)] andthePDOSfor(B12)CBC (Fig. 16), theoretically calculated by the Vastsgroup,65,85indicatethatseveral modesoriginatingfromboththe chains andthe icosahedramaycontribute tothe broadfeaturearound1080cm1.-60-50-40-30-20-1001012C10B Frequency shift (cm-1)13CMB11B-60-50-40-30-20-100103 1 2 1 0 1 420 cm-1 625 cm-1 727 cm-1 793 cm-1 866 cm-1 900 cm-1 991 cm-1 1113 cm-1 1624 cm-1 Frequency shift (cm-1)MC10B4.312C11Fig. 18. Isotope-dependent frequencyshift of the IRactive modesin B4.3Cboron carbide, related to10B4.312C. Data fromWerheitetal.56400 800 1200 16001.59 eV1.96 eVIntensity (a.u.)Wavenumber (cm-1)2.41 eV(111) surface400 800 1200 1600Wavenumber (cm-1)(210) surfaceFig. 19. Raman spectra of B4.3C single crystal acquired atexcitationwavelengths of 515nm(2.41eV), 633nm(1.96eV), and780nm (1.59eV). Left panel: (111) surface. Reproduced fromDomnich etal.,114with permission; 2002 American Institute ofPhysics.Rightpanel:(210)surface(thiswork).10 JournaloftheAmericanCeramicSocietyDomnichetal.FurtherinsightintothenatureoftheRamanbandsispro-vided by hydrostatic compression experiments reported bydierentgroups.117119Pressuredependenceofbandfrequen-cies intheRamanspectrameasuredbyGuoetal.,119upto36GPaareshowninFig. 20. ThephonondispersionunderpressureisdescribedintermsofmodeGru neisenparametersci,denedbyci @ ln xi@ ln V BTxi@xi@P ; (2)wherexiisthemodephononfrequency, BTistheisothermalbulkmodulus, Vis thevolume, andPis thepressure. Sec-ond-orderpolynomial ttingofthedatainFig. 20yieldsthevaluesfor cilistedinTableII.The 1088cm1Ramanbandshows weakdependence onpressure(c1088=0.59),suggestinghighstinessoftheassoci-atedvibrations.Inviewoftheexperimentallyobservedhighercompressibilityof icosahedrawithrespect totheunit cell,120this questions the assignment of the 1088cm1band tobreathing vibrations of icosahedra, as proposed in someworks.58,121The largest Gru neisen parameter of 1.38 isobservedfortheRamanbandat1000cm1(TableII). Tak-ingintoaccounttheresultsofabinitiocalculationbyLazzarietal.,65which predict a Raman active mode with the A1g sym-metry (consistent with the icosahedron breathing) at1000cm1, one might be temptedtoidentify this bandasIBM. However, the 1000cm1band vanishes from theRamanspectraabove20GPa(Fig. 20), whereastheicosahe-drahavebeenshowntobestabletoatleast 100GPaunderhydrostatic compression.120,122Splitting and sharpening of thehighfrequencybandsbecomesapparentatpressuresinexcessof 20GPa;117119the bands at 932 and 1154cm1become dis-cernible in the Raman spectra only above 10GPa (Fig. 20).Selected band intensities with respect to the 1088cm1bandareshowninFig. 21,calculatedusingtheRamanspec-traacquiredbyGuoetal.119at laserexcitationwavelengthsof 515nm(2.41eV) and633nm(1.96eV). Theintensityofthe 535cm1band decreases with pressure faster than theintensityofthe480cm1band,indicatingdierentoriginsofthese bands inaccordance withLazzaris calculations.65Ofparticular interest is the feature at 270cm1, whichshowsanomalous intensity dependence on pressure, peaking at~2530GPaandfallingorapidlythereafter, atrendremi-niscent of a resonance-type enhancement. However, thisbehavior is independent on laser excitation energy, whichquestions possible assignment of this band to a resonanceprocess. Anotherpeculiarityof thetwolow-frequencybandsat270and320cm1istheirnegativepressuredispersion, asevidencedbytheirGru neisenparametersof c274= 1.90andc321= 0.89(TableII). Pressuresofteningofzone-boundaryacoustic phonons is acommonfeature of tetrahedral semi-conductorsthat accountsforthenegativethermal expansioncoecientsusuallyfoundat lowtemperaturesinthesemate-rials.123Soft acoustic phonons are also believed to induceshear instabilities leading to amorphization in quartz124,125andcoesite.126However, ultrasonicmeasurementsshowthattheGru neisenparametersforthelongitudinal andtransverseacousticmodes inboroncarbidearepositive, cL=1.21andcT=0.33,127whichis inconict withtheassignment of the270 and320cm1bands todisorder-inducedacoustic pho-nonsasendorsedbyLazzarietal.65Because amorphous/graphitic carboninclusions are com-monlypresent incommercial boroncarbide, it is importantto discuss the lattice dynamics properties associated withtheseforms of carbon. Thenatureof theRamanspectraofgraphiticandamorphouscarbonwasinvestigatedbyFerrari0 5 10 15 20 25 30 352003004005006007008009001000110012009321154Wavenumber (cm-1)Pressure (GPa)10882743211000872729835795479533Fig. 20. Pressure dependence of band frequencies in the Ramanspectraofsinglecrystal B4Cacquiredatthelaserenergyof2.41eV.Thebest least-squaretsareshownbysolidlines. AnalysisisbasedontheRamanspectrareportedbyGuoetal.119TableII. FrequenciesatZeroPressure xi,One-PhononQuadraticPressureCoecients (d2xdP2),andGru neisenParameters ciforRamanActiveModesintheB4CSingleCrystalxi(cm1)12d2xidP2(cm1Pa2) ci274 0.026 1.90321 0.015 0.89415 0.001 0.26479 0.008 0.43533 0.010 0.33729 0.024 0.76795 0.054 1.09836 0.039 1.00872 0.021 0.99932 0.024 1.021000 0.130 1.381088 0.018 0.591154 0.015 0.32The values are obtainedfrombest least-squares ts tomeasuredpressureshifts of the Ramanbands acquiredat the laser energy of 2.41eVbyGuoetal.119The bulk modulus of B4C, required to compute ci, is taken fromManghnanietal.11740608010012014020400 5 10 15 20 25 30 350204083510882743211000932729795479Pressure (GPa)5332040Relative Intensity (% I1088)20040060080010001002005 10 15 20 25 30 35010020083510882743211000932729795479Pressure (GPa)533100200(a) (b)Fig. 21. Pressure dependence of band intensities in the Ramanspectra of single crystal B4Cacquired at the laser energy of (a)2.41eVand(b)1.96eV. Linesserveasguidestotheeye.AnalysisisbasedontheRamanspectrareportedbyGuoetal.119StructureandStabilityofBoronCarbideunderStress 11etal.128Atypical Ramanspectrumof amorphouscarbonisshowninFig. 22. Accordingtothe literature, the graphite-like, alsocalledtangential Gband(1589cm1), derivesfromthe in-plane stretching vibrationof the double C=Cbonds(sp2carbon), andhastheE2gsymmetry. Intheideal caseofa large single crystal graphitic domain, the Gband is theonlyonetoappear. Thedisorder-inducedDband(13001360cm1) is originating fromthe breathing vibrations ofthe sixfold aromatic rings in nite graphitic domains. Themechanismresponsiblefor theappearanceof theDbandistheformationofanelectron-holepaircausedbylaserexcita-tion and followed by one-phonon emission. It has beenshownthat theactivationof theDbandalwaysrequires anelastic defect-related scattering process;128the D band isindeedobservedinsp2bondedcarbonscontainingvacancies,impurities or other symmetry-breakingdefects. TheDmodeis of the A1gsymmetryandinvolves aphononnear the Kzoneboundary.TuinstraandKoenignotedthat theratioof theintensityof the Dbandwithrespect tothe Gbandvaries inverselywiththe size of the graphitic clusters.129This relationwaslater modied by Ferrari and Robertson to account fordomainswithincreasedelectronconnement:128IDIGCkL L[20 A TuinstraandKoenig129(3)IDIGCkL 1=2L\20 A FerrariandRobertson128(4)Here, constantC(k)dependsonthelaserwavelength(e.g., C(515nm)=40A ),andListhediameterofthesp2domain.The Gband originating fromcarbon inclusions may beresponsiblefortheoccurrenceof afeatureat~1580cm1inthe Ramanspectraof boroncarbide, as the ones showninFig. 15. Alternative explanationfor the originof this bandhas beenoeredbyWerheits group.60,116TheyarguedthatsubstitutionofaboronatomfortheendcarbonatomintheCBCchainshouldleadtomodiedselectionrulesthatwouldmakestretchingvibrations intheCBBchainRamanactive.This is a valid assumption noting that the calculated fre-quency of the antysymmetric stretching mode in the CBCchainisplacedaround1600cm1(Figs. 14and16), andthe~1580cm1feature is commonly observed in the Ramanspectra of highpurity single crystal boroncarbide samplesthatarepresumablyfreeofcarboninclusions(Fig. 19).IV. AtomicBonding,ElasticandMechanicalPropertiesElasticandmechanicalpropertiesofboroncarbidearederiv-ativeofsuchcharacteristicsofatomicbondingaslocalizationanddelocalization, ionicityandcovalenceof thebonds andelectrondensityininter-atomicregions. Inparticular, higherstinessandhardnessisassociatedwithmorelocalizedcova-lent bonds and higher inter-atomic electron density. Fourtypesofatomicbondscanbeidentiedforboroncarbideinthe R3msymmetry (Fig. 1): (i) the intrachain bond, whichconnects the endatomandthe center atominthe 3-atomchainandhasapcharacter; (ii) thechain-icosahedronbond,whichconnectstheendatominthe3-atomchaintoanatomintheequatorialsiteoftheicosahedron;(iii)theintericosahe-dral bonds, whichconnect atomsinthepolarsitesof neigh-boringicosahedraandoriginatefromsphybridizedorbitals;and (iv) the highly delocalized intraicosahedral sp2bonds,whichconnect atoms withintheicosahedron. Renement ofX-rayandneutrondiractiondatashowsthattheintrachainbondhas theshortest lengthat all stoichiometries; it is fol-lowed by the chain-icosahedron bond, the intericosahedralbond, andtheintraicosahedral bonds.34,51,52,77,130Forbondsof similar nature, thebondlengthisinverselyrelatedtothebondstiness, whichimplies that the intrachainbonds arethe most rigidones andthe intraicosahedral bonds are themost compliant ones inboroncarbide. This ndingis sup-ported by the available theoretical calculations of bondstrength/hardnessforseveralpossiblecongurationsofboronand carbon atoms in the stoichiometric B4C andB6.5C.35,41,45,131Thecomparablemagnitudesoftheinter-andthe intraicosahedral bond strengths were used as the basisforEminsclassicationofboroncarbideasinvertedmolecu-lar solid, or asolidcomposedof stronglyboundmolecularunits(icosahedra).132Therelativestrengthoftheinter-andtheintraicosahedralbondshasbeenrelatedtothequestionofthecompressibilityof the icosaherdral units withrespect tothe unit cell. Highpressureneutrondiractionstudies givedirect evidencethattheicosahedraare23%morecompressiblethantheinterico-sahedral space.120Compositional variation of longitudinalsoundvelocities75andpressuredependenceofelectrical resis-tivity97inboroncarbidecanalsobeinterpretedinterms ofsofticosahedra. Contradictorytotheseobservations, theoret-ical simulationsof theelasticproperties of boroncarbideathigherpressurespredictlowercompressibilityoftheicosahe-drawithrespect totheunit cell.65,133Basedontheseresults,Lazzari etal. argued that the intericosahedral bonds areweaker than the intraicosahedral ones, and challenged thenotionofinvertedmolecularsolidforboroncarbide.65How-ever, as notedby Shirai et al.,111these arguments didnottakeintoconsiderationthefactthatpereachbondthatcon-nectsanicosahedrontothesurroundinglattice, therearetenbonds that connect atoms withinthe icosahedron. Becauseall available bonds contribute to the elastic deformationunderhydrostaticcompression, the10-foldprevalenceof theintraicosahedral bonds wouldresult inlower compressibilityoftheicosahedronwithrespecttothelatticearoundit, eventhoughindividuallyintericosahedralbondsmaybestronger.Therigidityoftheintrachainbondhasalsobeendebated,as evidence of signicant displacements of the chaincenteratomin the direction perpendicular to the threefold axis,coming from X-ray and neutron diraction measure-ments,11,34,78impliedweakbondingbetweenthechaincenterand the chain terminal atoms. Some researchers proposedthattheweaknessofthisbondshouldarisefromitspresum-ably ionic character.134This apparent discrepancy withtheconventional understanding and the results of theoreticalmodelingwasaddressedbyShirai,5whonotedthatthecalcu-latedrestoringforce against the displacement perpendicularto the bond axis would constitute only 10%of the bondstretchingforce,yieldingalowenergeticbarrierforthechaincenter atomtomoveintheplanenormal tothebondaxis,1000 1200 1400 1600 1800GIntensity (a.u.)Wavenumber (cm-1)DCarbonFig. 22. Raman spectrum of amorphous/graphitic carbon withcharacteristicDandGbands.12 JournaloftheAmericanCeramicSocietyDomnichetal.andat thesametimepreservingastrongforceconstant foratomic displacement in the axial direction. Additional evi-dence that supports the notionof intrachainbondsoftnesscomes fromthe spectral positionof the bands at 480 and535cm1observedinthe Ramanspectraof boroncarbide,whichareassignedtostretchingvibrationsintheCBCchainsbyresearchers whoendorse Emins structural model.59Thelowfrequencyof thesebandsimpliesaweakforceconstant.However, assignment of thesetwobandstotheCBCchain-stretching mode is questionable in view of a more recent theo-retical analysisofthevibrational propertiesofboroncarbideby Vast and co-workers,39,65who have demonstrated thatbetweenthetwobandsinquestion, onlythe480cm1bandwasassociatedwiththelinearchain, andeventhisbandhaditsorigininchainrotationandnotinchainstretching,asdis-cussedinSectionIII. As such, neither the Ramanbandat480cm1nor theoneat 535cm1wouldcarryinformationon the axial rigidity of the intrachain bond.TheoreticalcalculationsndthattheC11elasticconstantishigher than the C33constant for both (B12)CBC(nominalB6.5Cstoichiometry) and(B11C)CBC(nominal B4Cstoichi-ometry) structural congurations.135Thisshowsgoodagree-ment with a similar trend in the experimentally measuredvalues of C11and C33obtained on a B5.6Csingle crystal(TableIII).136The commensurable magnitudes of C11 and C33are at odds with the intuitive expectation that due to the align-mentofthestrongerintericosahedralbondswiththerhombo-hedral lattice vectors, the stiness of the boron carbide crystalshouldbehigheralongthe[001] directionratherthanonthe(001)plane,i.e.,C11shouldbelowerthanC33.Shiraietal.133explained this apparent contradiction in terms of internalrelaxationof theboroncarbidelatticeunder external stress.Theynotedthatthedistortionoftheicosahedraduetotheircompressibilityanisotropy should result in slight deviations ofthe intericosahedral bonds fromthe lattice vectors of therhombohedral unit cell, as illustrated in Fig. 23. To accommo-date deformation under compression along the [001] direction,the sti intericosahedral bonds would choose to rotate insteadof contracting, leading to relaxation of the entire crystal struc-ture. Thepresenceofastiintrachainbondwill notpreventthisrelaxationbecausethechainitselfissupportedbybondsthatlienearthe(001)plane,andthestressisabsorbedinthiscase by the chain-icosahedron bonds.The anisotropy of boron carbide elastic properties wasinvestigatedona B5.6Csingle crystal using resonant ultra-soundspectroscopybyMcClellanetal.136Youngs modulusE was found to be orientation independent when measured onthe (111) plane (basal plane in hexagonal notation), but variedsignicantly whenmeasured on prismatic(parallelto the [111]direction) andpyramidal planes (Fig. 24). The global maxi-mumandminimumYoungsmodulifortheB5.6Csinglecrys-tal were found to be Emax=522GPa and Emin=64GPa,yieldingananisotropyratioof Emax/Emin=8.1. The globalmaximumYoungsmoduluswasfoundtoalignwiththe[111]direction, implying higher stiness of the crystal along thechain axis in response to tension or compression loadingwithin the elastic regime. Shear modulus measured on thebasalplaneofthesamecrystalwasfoundtobe165GPaandorientationindependent; whenmeasuredonpyramidal andprismatic planes, shear modulus varied from the globalminimumof Gmin=165GPa to the global maximumofGmax=233GPa(Gmaxalongthe[201] direction), yieldingananisotropy ratio of Gmax/Gmin=1.4 (Fig. 25).Elastic properties of boron carbide have been shown tochangewithcarboncontent.3TableIVlistsselectedliteraturedataforelasticmoduli andPoissonsratioof polycrystallinesamples with dierent stoichiometries,75,117,120,136138alongwiththetheoreticallycalculatedvalues of bulkmodulus forthe (B12)CBC and (B11C)CBC congurations.41,45,65,135Although caution should be exerted when comparing datafor samples of dierent origin, thegeneral trendis that thestinessof boroncarbidedecreasesat lowercarbonconcen-trations. Compositional variations inPoissons ratiodonotfollowthis trend and span the range of 0.17 to 0.21, asreported by dierent groups.3,117,136Some of the earliermechanical tests performed on hot-pressed boron carbidesuggested that Youngs modulus increased with decreasingcarbon concentrations.23,139Gieske etal. used ultrasonictechniques tomeasureelasticproperties of thesamples withvarying stoichiometries and observed a decrease in elasticmoduli with the decrease in carbon concentration.75OneTableIII. ElasticConstantsofBoronCarbideElasticconstantCij,GPaMcClellanetal.136(exp.) Leeetal.135(calc.)B5.6C B6.5C B4C11 542.8 500.4 561.833 534.5 430.2 517.744 164.812 130.6 125.3 123.613 63.5 73.9 69.614 7.7 17.8~60[100][010]Fig. 23. Deformation of boron carbide icosahedra under stressafter Shirai etal.133The intericosahedral bond(thicksolidline) isdeectedfromthelatticedirection[100]byanangle u.0 10 20 30 40 50 60 70 80 90400420440460480500520540Young's Modulus (GPa)Theta (Degrees)] 2 [11 to 0] 1 [1 from (111)[201] to ] 2 [11 from (132)] 2 [11 to [111] from 0) 1 (1] 1 [22 to 0] 1 [1 from (114)Fig. 24. The orientation dependence of the Youngs modulus forB5.6C single crystal. Reproduced from McClellan etal.,136withpermission; 2001Springer.StructureandStabilityofBoronCarbideunderStress 13particularityofGieskesdataistheobservedchangeinslopeintheYoungsmodulusversusat.%Cdependenceatcarbonconcentrationsof~13at.%, correspondingtotheB6.5Cstoi-chiometry. Shearandbulkmoduli exhibitedasimilarbehav-ior, as showninFig. 26. Adirect correlationcanbedrawnbetweentheseobservationsandakinkinthecarbondepen-denceoftheclatticeparameter(Fig. 3), whichisbelievedtobe indicative of the distinct mechanisms for substitutionofboronatoms intothe icosahedral andthe chainunits thattake place at the boron- and the carbon-rich sides of theB6.5Ccomposition.Manghnani etal. investigatedthe pressuredependence ofthe elastic moduli of polycrystalline boron carbide up to2.1GPa, nding a nearly linear relationship as shown inFig. 27.117The measuredbulkmoduli were consistent withthevaluesobtainedbyNelmesetal.inhighpressureneutrondiractionstudies onboroncarbide.120Thepressuredepen-dence of boroncarbide bulkproperties canbe understoodfromtheinvertedmolecularsolidconceptdescribedabove.Incontrast totheelasticmoduli that areintrinsicproper-tiesofthematerialandderivefromatomicbonding,mechan-ical properties (hardness, strength, fracture toughness, etc.)stronglydependonsuchexternal factors asqualityandsizeofthesample,sizeofthegrains,porosity,presenceofdefectsandaws, conditionsof loading, etc. Thisisoneof therea-sonsforsignicantvariationsinthereportedhardnessvaluesfor boroncarbide. Generally, Knoophardness is usedas areference, with tests under a 200g loading resulting in avalue of HK200between29and31GPa.1,3,24Vickers hard-nessofboroncarbideisgenerally~30%higher, althoughthe0 10 20 30 40 50 60 70 80 90150160170180190200210220230240Shear Modulus (GPa)Theta (Degrees)] 2 [11 to 0] 1 [1 from (111)[201] to ] 2 [11 from (132)] 2 [11 to [111] from 0) 1 (1] 1 [22 to 0] 1 [1 from (114)Fig. 25. TheorientationdependenceoftheshearmodulusforB5.6Csinglecrystal. ReproducedfromMcClellanetal.,136withpermission;2001Springer.TableIV. CompositionalDependenceofElasticModuliandPoissonsRatioinBoronCarbideStoichiometryat.%CBulkmodulus[GPa]Youngsmodulus[GPa]Shearmodulus[GPa]Poissonsratioexp. calc. exp. exp. exp.B4C 20.0 247c235e199d246e234g248h239j220d472c462e448b441a200c197e188a0.18c0.17e0.21bB4.5C 18.2 237c463c197c0.17cB5.6C 15.2 236c237f462c460f197c195f0.17c0.18fB6.5C 13.3 231c217g227i446c189c0.18cB7.7C 11.5 178c352c150c0.17cB9C 10.0 183c130c319c348c150c132c0.21c0.16c(a)SchwetzandGrellner137(b)Murthy138(c)Gieskeetal.75(d)Nelmesetal.120(e)Manghnanietal.117(f)McClellanetal.136(g)Leeetal.135(h)Lazzarietal.65(i)Guoetal.41(j)AydinandSimtek4510 12 14 16 18 20100150200250300350400450500GBEElastic Moduli (GPa)Carbon Content (at.%)Fig. 26. The carboncontent dependence of elastic moduli of hot-pressedboroncarbide. Lines serveas guides totheeye. DatafromGieskeetal.750.5 1.0 1.5 2.0190200210220230240250460470480(1.10)(4.26)EBGElastic Moduli (GPa)Pressure (GPa)(3.85)Fig. 27. PressuredependenceofbulkmodulusB, YoungsmodulusE, and shear modulus Gin hot pressed boron carbide. Lines arelinear ts tothedata. Respectivepressurecoecients areshowninparentheses. ReproducedfromManghnani etal.,117withpermission;2000UniversitiesPress(India)Limited.14 JournaloftheAmericanCeramicSocietyDomnichetal.valuesofVH100ashighas47GPahavebeenreportedinthesamplespreparedbychemical vapordeposition(CVD) tech-nique.140Innanoindentationmeasurements onB4.3Csinglecrystals, Berkovichhardnessvaluesof 4142GPahavebeenmeasuredbydierentgroups.114,141Thisimpressivehardnessranksboroncarbideasthirdoverall hardestmaterial known,behind diamond and cubic boron nitride. Several worksreportthatboroncarbidehardnessincreaseswiththecarboncontent until the edge of the homogeneity range isreached;26,140,142,143at carbon concentrations in excess of20%, hardness rapidly falls odue toprecipitation of thecarbonphasefromtheB4Csolidsolution.140Boroncarbide is characterizedbyexure strengthvalueson the order of 350MPa.1,3,24Density of boron carbidevaries with carbon concentration as =2.422g/cm3+0.0048[at.%C], withacommonlyreportedvalueof 2.52g/cm3correspondingtotheB4Cstoichiometry.1Thiscombina-tionof highstrengthandlowdensitymakes boroncarbideone of the most attractive structural materials known. Asexpected of both a ceramic and a strong material, boroncarbidehas relativelylowfracturetoughness. Values of KICforboroncarbidearegivenat ~1.3MPam1/2.1,3,144Thereis considerableinterest intheapplicationof boroncarbideas lightweight armor material duetoits exceptionalhardness, outstanding elastic properties andlowtheoreticaldensity. Fromtheballisticviewpoint, ofparticularinterestisthe response of boroncarbide toshockloading. However,available shockloadingdatashowthat the performance ofboroncarbideathighvelocity, highpressureimpactismuchlowerthanthat expectedfromitssuperiorstaticmechanicalproperties. The shear strength of boron carbide in theshockedstate(Fig. 28)fallsorapidlyabovetheHEL,145,146indicating premature failure of the material as the shockstressreachesathresholdvalueof~20GPa. Thisbehaviorissimilar tothe shockresponse of single crystal Al2O3,147,148where the dropinthe shear strengthhas beenlinkedtoastress-inducedphasetransformation, andis markedlydier-ent fromtheshockresponseof otherarmorceramicmateri-als, such as SiC149151and polycrystalline Al2O3,147,149,152whichare characterizedby the deformationhardening thatcommencesimmediatelyabovetheHEL.Apartfromapossi-ble phase transformation, the anomalous decrease inshearstrengthofboroncarbidebeyondtheHELmayberelatedtoacatastrophicpropagationof microcracks andother micro-structural defects, leading tomaterials collapse behindtheelasticprecursorwave.V. Stress-InducedStructuralInstabilityThe possibility of aphase transformationinboroncarbideundershockloadinghasbeendiscussedintheliteraturetoaconsiderable extent. Figure29 shows the available experi-mental shockcompressiondataforboroncarbideofvaryingstarting density as reported by dierent authors.146,153158Grady159,160identies three distinct regions inthe hydrody-namicequationof stateof boroncarbide, eachcorrespond-ingtothehydrodynamiccompressionof aparticular phase:anambient phase, asecondphasethat existsinthepressurerangeof2535to4555GPa, andathirdphasebeyond4555GPa [Fig. 29(a)]. Vogler etal.146note that a possiblephase transition may correspond to the intercept pointbetweenthehydrostaticandthehydrodynamiccompressioncurves which occurs at ~40GPa in boron carbide[Fig. 29(b)]. Mashimoandco-workers discuss three regionsin the Hugoniot compression data: a region of predomi-nantly elastic deformation below the HEL (~20GPa), aregionof mostlyisotropiccompressionfrom~20to38GPa,andaregionofisothermal compressionthat extendsbeyond38GPa.158Anonsetofaphasetransformationinboroncar-bide, accordingtothis group, corresponds toakinkintheHugoniot compressioncurve betweenthe isotropic andtheisothermal compression regimes [Fig. 29(c)]. Both Vogleretal.146andZhangetal.158alsoreportthattheambientbulksoundvelocityinboroncarbide is signicantlyhigher thantheshockvelocityat theintercept pressure, whichis consis-tent with the concept of a phase transformation. Anotherpossiblepieceof evidenceforashock-inducedphasechangeinboroncarbide, accordingtoVogler etal., is averysteepdropinparticlevelocityobservedduringinitial unloadinginreleaseexperiments, whichcouldbeassociatedwithareversetransformation that occurs immediately upon unloading.146All the results discussed above are highly suggestive of aphasetransformationinboroncarbideundershockloading,albeitnotentirelyconclusive.The damage mechanism responsible for the failure ofboroncarbideundershockloadinghasbeendirectlyassessedby Chen etal.161High resolution transmission electronmicroscopy (HRTEM) analysis of boron carbide ballistictargets subjectedtosupercritical impact velocities andpres-sures inexcess of 2023GPa revealedthe formationof 23nmwide intragranular amorphous bands that occurredparallel to specic crystallographic planes and contiguouswiththeapparentcleavedfracturesurfaces(Fig. 30). Atsub-critical impacts, the amorphous bands werenever observed;instead, arelativelyhighdensityof stackingfaults andmi-crotwinssuggestedplasticdeformationof thematerial undershockloading.161Stress-inducedstructural transformationof boroncarbidehas been reported in static indentation,114,141,162dynamicindentation,163,164and scratching experiments.162,165Fig. 31showsanexampleof HRTEMobservationsof largeamor-phizedzonesformedwithintheindentationcontactareaandin the scratch debris in B4.3Csingle crystal.162Within theamorphous zone, nanosized grains of crystalline materialwith retained orientation are present, which could indicatehighlyanisotropicdeformationofboroncarbideunderstress.Formation of nanosized oriented amorphous bands similarto the bands observed in ballistically impacted material(Fig. 30) has also been reported for indented boron car-bide.162Electronenergy loss spectroscopy (EELS) observa-tions indicate that the amorphous structure such as theboxedarea2inFig. 31(b) shows adierent carbonKedgecompared to the crystalline lattice. The appearance of anenhancedp*peakinthecarbonKedgeimpliessp2bonding,i.e., carbondoublebondinginthematerial. Unlikethecar-bonedge, thecore-lossedgeofboronshowslittlefundamen-0 10 20 30 40 50 60 70 8005101520strengthlimitShear Strentgth (GPa)Shock Stress (GPa) elasticregimeFig. 28. Shear strength of boron carbide in the shocked state,estimated fromreshock and release experiments. Line serves as aguidetotheeye. ReproducedfromVogleretal.,146withpermission;2004AmericanInstituteofPhysics.StructureandStabilityofBoronCarbideunderStress 15tal changes.162Therefore, it isinferredthat theboronatomsretaintheirchemical state,whilethechemical stateofcarbonispartiallymodiedduringindentation.Theseobservations are corroboratedbyextensive Ramanspectroscopy data collectedonboroncarbide samples sub-jectedtohighstresses associatedwithvarious types of con-tact-loading situations.114,141,162,163,165Indication of thestructural changes is evidencedby the appearance of high-frequencybandsat1330,1520,and1810cm1intheRamanspectraof indentedboroncarbide (Fig. 32). The alterationsof theRamanspectraareindependent onthequalityof thestartingmaterial: identical bands are observedinthe singlecrystals andinthe polycrystalline samples after indentationat comparable loads [Figs. 32(b) and (e)]. Also shown inFig. 32(d) is the Ramanspectrumof acarbonaceous inclu-sion in polycrystalline boron carbide; such inclusions arecommoninhot-pressedsamples andarenot tobeconfusedwith the Raman features of the transformed amorphousboroncarbide.Spectral position of the 1330 and 1520cm1bands, aswell as the dispersive character of the 1330cm1band(Fig. 33), implythecorrelationof these bands with, respec-tively, the Dandthe Gbands of amorphous/graphitic car-bon. However, this explanationmaybe inconict withthe(a) (b)Fig. 30. (a)Boroncarbideballistictargetthatcomminutedduringimpactand(b)anHRTEMimageofafragmentproducedbyaballistictestatimpactpressureof23.3GPa.Thelatticeimagesoneithersideofthebandin(b)correspondtothe

101directionofcrystallineboroncarbide,andthe loss of lattice fringes inthe bandindicates localizedamorphization. ReproducedfromChenetal.,161withpermission; 2003 TheAmericanAssociationfortheAdvancementofScience.0 20 40 60 80 1000.750.800.850.900.951.00PT Experiment Grady (2506 kg/m3) McQueen et al. (1900 kg/m3) McQueen et al. (2400 kg/m3) Vogler et al. (2508 kg/m3) Wilkins (2500 kg/m3) Pavlovskii (2510 kg/m3) Gust & Royce (2503 kg/m3) Zhang et al. (2516 kg/m3)HEL0 20 40 60 80 1000.750.800.850.900.951.00PT0 20 40 60 80 1000.750.800.850.900.951.00PT II-IIIModel Grady Vogler et al. Zhang et al.Relative Volume V/V0Pressure (GPa)PT I-II0 20 40 60 80 1000.750.800.850.900.951.00PT Experiment Grady (2506 kg/m3) McQueen et al. (1900 kg/m3) McQueen et al. (2400 kg/m3) Vogler et al. (2508 kg/m3) Wilkins (2500 kg/m3) Pavlovskii (2510 kg/m3) Gust & Royce (2503 kg/m3) Zhang et al. (2516 kg/m3)HEL0 20 40 60 80 1000.750.800.850.900.951.00PT0 20 40 60 80 1000.750.800.850.900.951.00PT II-IIIModel Grady Vogler et al. Zhang et al.Relative Volume V/V0Pressure (GPa)PT I-II(a)(b)(c)Fig. 29. ShockcompressiondataonboroncarbideasreportedbyWilkins,153McQueenetal.,154Pavlovskii,155Gust andRoyce,156Grady,157Vogler etal.,146andZhang etal.158(symbols) and selectedmodel representations accounting for phase transformations (lines). (a) Gradysmodel:160dashlines, hydrodynamic compressioncurves for phase I (below2535GPa), phase II (2535GPato4555GPa), andphase III(beyond 4555GPa); solid line, a composite hydrodynamic compression curve. (b) Model of Vogler etal.146: dash line, extrapolation ofhydrostaticcompressiondataof Manghnani etal.117; solidline, meanpressurefromreshockandrelease experiments.146(c) Model of Zhangetal.158: dashline, isothermal compressioncurve;dotline, isotropiccompressioncurve;solidline, Hugoniotcompressioncurve.Suggestedphasetransition(PT)pointsandtheHugoniotelasticlimit(HEL)forboroncarbideareindicatedbyarrows.16 JournaloftheAmericanCeramicSocietyDomnichetal.followingobservations: (i)theintensityoftheDbandofdis-orderedcarbonincreaseswiththeincreasingexcitationwave-length,166whilethebandat~1330cm1doesnotshowsuchdependence;114(ii); the Gbandis a prominent bandinallcarbon structures involving sp2bonding167and the D/Gintensityratioindisordered/amorphouscarbonneverexceeds2.5,128whereas the intensities ratiofor the bands at ~1330and~1520cm1variesintherangeof45atroomtempera-(a) (b)(c) (d)Fig. 31. PlainviewTEMmicrographs of (a) a100mNBerkovichindent and(b) scratchdebris insinglecrystal B4.3C. (c,d) Magniedhighresolutionlatticeimagesoftheboxedareasin(a,b)showingthepresenceofamorphousmaterial.ReproducedfromGeetal.,162withpermission;2004Elsevier.1.5 1.8 2.1 2.4 2.7126012801300132013401360Wavenumber (cm-1)Laser Energy (eV)D band of carbonMost prominent band in indented boron carbideFig. 33. Dependence of the most prominent band in the Ramanspectraof indentedsinglecrystal B4.3C(squares) onlaserexcitationenergyincomparisonwithasimilar dependence of the Dbandofdisordered carbon (circles, data fromPo csik etal.166). Lines arelinear ts to the data. Reproduced fromDomnich etal.,114withpermission; 2002AmericanInstituteofPhysics.200 400 600 800 1000 1200 1400 1600 1800 2000Intensity (a.u.)(e)(d)(c)(b)(a)Wavenumber (cm-1)CarboninclusionBoron Carbide2.41 eVSingle crystalPolycrystallineFig. 32. Raman spectra of (a) pristine and (b) indented singlecrystal B4.3C, and(c) pristine and(e) indentedpolycrystalline hot-pressedboroncarbide. Ramanspectrumof agraphiticinclusioninpolycrystallineboroncarbideisshownin(d).StructureandStabilityofBoronCarbideunderStress 17ture;114,141and(iii) the positionof the bandat ~1520cm1(Fig. 32)isstronglydownshiftedcomparedtotheGbandofgraphite.167ItisalsoimportanttonotethattheRamanbandat ~1520cm1that appears inthedeformedmaterial is notnecessarily related to the 1570cm1band in the Ramanspectraofpristineboroncarbide[Fig. 32(a)], whichhasbeenattributedinthe literature tothe presence of carbonaceousinclusions inboroncarbidesamples, or, alternatively, tothevibrationsoftheCBBchains.60,116Changes intheRamanspectraindicativeof formationofthe amorphous material are also observed for the samplessubjected to dynamic loading, ranging from scratching[Fig. 34(a)] toballisticimpact [Figs. 34(c) and(d)]. Geetal.noted that annealing of the scratch debris with the laserbeamleadstoappearanceoftheGbandintheRamanspec-trum of amorphous boron carbide [Fig. 34(b)], implyinggraphitizationof thetransformedmaterial.162Eect of tem-peratureontheRamanfeaturesofamorphousboroncarbidewas systematicallystudiedbyYanetal.141While cryogenictemperatures were found to have no eect on the Ramanspectra, the mainfeatures of the amorphous boroncarbide(bands at 1330, 1520, and 1810cm1) were graduallydecreasing under heating until their nal disappearance at400C500C,asshowninFig. 35.Thiswasaccompaniedbya gradual increase in the intensity of the G band at1586cm1. Yanetal. arguedthat the stress-inducedamor-phization of boron carbide could be mainly accomplishedthroughthe structural change of the CBCchains, withthesmall amountofboroninthechainsresidinginthearomaticringsbysubstitutingcarbon, andthe(B11C) icosahedrapre-serving their structure. Further, this group associated thequalitative changes that occurred in the Raman spectraaround~500Cwiththe rapidcoagulationof the small sp2bondedcarbonclusters that hadpresumablyformedduringroom-temperature indentation, andformationof larger-sizecarbondomains.141However, thisstructural model foramorphousboroncar-bideresidesonanassumptionthat the1330and1520cm1bandsareidentical totheDandtheGbandsofcarbon; thisisnotnecessarilytrueforthereasonsdiscussedabove. Asanadditional argument against this assumption, deconvolutionofthehighfrequencybandsintheRamanspectrainFig. 35showsthattheintensityofthe1520cm1featureinthespec-trumof amorphous boron carbide decreases independentlyof the graphitic Gbandthat appears at 1586cm1at ele-vated temperatures; in the temperature range of 300C450C,boththesebandsarepresentinthespectra,indicatingtheir dierent origins. Generally, the Raman spectra ofamorphous boroncarbide andamorphous/graphitic carbonarequalitativelydierentintermsofbandfrequencies, bandwidths, and relative band intensities, as evidenced fromadirect comparisonof the RamanspectrainFigs. 32(d) and(e). Amere appearance of graphitic Dand/or Gbands instressedboroncarbideshouldnot benecessarilyinterpretedasasignof amorphization; rather, thepresenceof asmallerbandat1810cm1mustbeusedasareliableindicationofacompletedstructuraltransformation.Interestingly, theRamanspectraofamorphousboroncar-bide lms prepared by magnetron sputtering168,169exhibitdistinctlydierent features andresemble abroadenedspec-trumof crystalline boroncarbidewiththemajor bandcen-teredaround1100cm1(Fig. 36). Inaddition, thebands at~1330cm1and ~1520cm1are never observed in amor-phousboroncarbidelms.169Thissuggeststhepossibilityforanexistenceof twodistinct forms of amorphousboroncar-bideconsistingofadistortedicosahedral networkanddier-ent arrangements of carbonandboronatoms that linktheicosahedratogether.This problemwas addressed in a theoretical study ofamorphous boron carbide by Ivashchenko etal.44In thiswork, twoformsofamorphousBCnetworks, onebasedona 120-atomrhombohedral B4Ccell (a-120), and the otheronebasedona135-atomhypotheticalcubicB4Ccell(a-135),weresimulatedbymeansof moleculardynamic(MD) meth-ods. Thea-120congurationwas foundtoconsist of disor-dered icosahedra composed mainly of boron atomsconnected by topologically disordered BCand CCnet-works.Thestructureofthea-135congurationwasfoundtobesimilar totheoneof a-120, but it was lackingtheeight-foldcoordinatedatoms, implyingaless randomamorphous200 400 600 800 1000 1200 1400 1600 1800 2000(d)(c)(b)(a)Intensity (a.u.)Boron Carbide2.41 eVBallistic FragmentsScratch DebrisWavenumber (cm-1)Fig. 34. Ramanspectraof hot-pressedboroncarbide subjectedto(a,b) scratching162and (c,d) ballistic impact. Scratch debrisconsistentlyshowsevidenceofamorphousmaterial (a), andisfoundto graphitize upon annealing (b). Most analyzed locations on theballistic fragment surfaces yield spectra similar to (c); however,formationofamorphousmaterialcanalsobeobserved, asevidencedbytheRamanspectrumin(d).200 400 600 800 1000 1200 1400 1600 1800 2000 indentation25 C100 C200 C300 C400 C450 C500 C600 CIntensity (a.u.)Raman shift (cm-1)pristine area25 CFig. 35. EectofannealingontheevolutionoftheRamanspectraof a hardness indent in single crystal B4.3C. The spectra wereacquiredattemperaturesrangingfrom25C(ambient)to600C. Anambient-temperature spectrumof apristine B4.3Csurface is shownfor reference. Reproduced from Yan etal.,141with permission;2006AmericanInstituteofPhysics.18 JournaloftheAmericanCeramicSocietyDomnichetal.network. The simulated phonon densities of states for thetwoamorphousnetworksarecomparedwiththeexperimen-tal Ramanspectraobtainedonindentedboroncarbidecrys-tals andthosemeasuredonamorphous boroncarbidelmsinFig. 37.InthecalculatedPDOS,thebandat1800cm1ismissinginboththea-120andthea-135congurations. Forthe a-120 network, the two PDOS bands at 1290 and1450cm1resemble the two prominent features in theRamanspectra of indentedboroncarbide [Fig. 37(a)], andthebandat750cm1correlateswiththeincreaseddensityoftheicosahedral modes inthePDOScalculatedfor thecrys-talline (B12)CBCform, as showninFig. 16(b). Incontrast,thePDOSof thea-135networkshowsageneral correlationwiththebroadfeaturesintheRamanspectraof amorphousboroncarbide lms [Fig. 37(a)]. These results provide basisfor athesis that thestress-inducedtransformationof boroncarbideproceedsviadestructionof thelinearchains, forma-tionoftopologicallydisorderedBCandCCnetworksfromthechainCandBatoms, distortionof theicosahedral (B12)and(B11C) units, andrearrangement of thesestructural ele-mentsintoarandomlyinterconnectedamorphousnetwork.Thedrivingforceforsuchstructural collapseisstill tobeestablished. Yanetal. addressedthis issue fromthe experi-mental position.118A complete set of experiments usingquasi-hydrostatic and quasi-uniaxial compression up to50GPa, followed by depressurization to ambient pressure,wasconductedonaboroncarbidesinglecrystal, andinsituRaman spectroscopy was engaged to detect possible highpressure phase transformations. It was observedthat underhydrostaticcompression, thematerial remainedaperfectsin-glecrystal withoutvisiblesurfacereliefandcracking; noevi-dence of amorphizationwas detectedinthe samples loadedhydrostaticallyafterpressurerelease. Theresultsweresigni-cantly dierent when the single crystal boron carbide wassubjectedtouniaxial loadingandunloading. Inthiscase, thedepressurizedsampleswerefoundtobebrokenintoanum-ber of smaller fragments; evident cracks, surface relief, andshear bands couldbeobservedoptically; andtheformationofamorphousmaterialwasevidencedbyinsituRamanspec-troscopyat1316GPaduringunloadingofthesamplesthathadbeenpreviouslyloadedtopressuresinexcessof25GPa.Further, Ramanspectroscopyanalysisofthefullydepressur-ized samples revealed spectral features typical for stressamorphizedmaterial asobservedinindentationandscratch-ing experiments, i.e., the bands at ~1330, ~1520, and~1820cm1. These results emphasized the importance ofnonhydrostatic stresses for the stabilityof boroncarbide athighpressure.Theoretical simulations by the same group indicated adrastic volume change of the hypothetical (B11C)CBCunit200 400 600 800 1000 1200 1400 1600 1800 2000a-120a-BC (indentation)a-135Intensity (a.u.)Wavenumber (cm-1)a-BC (film)PDOSRamanFig. 37. Comparison of the calculated PDOS of the amorphousa-120anda-135structures44withtheexperimentalRamanspectraofthe indented boron carbide (this work) and an amorphous boroncarbidelmpreparedbymagnetronsputtering.169400 800 1200 1600 2000970C900CIntensity (a.u.)Wavenumber (cm-1)700CBoron Carbide FilmsFig. 36. Raman spectra of boron carbide lms deposited bymagnetronsputteringattemperaturesof700C,900C,and970C.168Crystallization of the lms occurs at temperatures above 900C.A BDCE(a)(b)0 10 20 30 40 50 60-0.20-0.15-0.10-0.050.00 Hydrostatic compression Uniaxial compressionRelative Volume, (V-V0)/V0Pressure (GPa)ABCDEFig. 38. Ab initio simulation of the stabilization of B11C(CBC)underhydrostaticanduniaxial compression. (a)Compressedvolumeversus pressure. The squaredatarepresent thevolumechangewithhydrostatic pressure, andthe circle datacorrespondtothe volumechangewithuniaxial stressalongtheCBCatomicchain. (b)Atomiccongurations of the B4C unit cell at various pressurescorrespondingtodatapointsin(a). ReproducedfromYanetal.,118withpermission; 2009AmericanPhysicalSociety.StructureandStabilityofBoronCarbideunderStress 19cell at the destabilization pressure of 19GPa (consistentwith the HEL of 1520GPa) due to the bending of theCBC chain (Fig. 38).118At higher pressures, the chaindeformation was found to continue until the (B11C)CBClattice was irreversibly distorted. It was suggested that thecentral boronatomof thechaincouldbondwiththeneigh-boring atoms in the icosahedra forming a higher energystructure. Thereleaseof this energyduringdepressurizationwas proposed to be responsible for the collapse of theboron carbide structure and the formation of localizedamorphizedbands.118Theoretical investigationof phase stability inboroncar-bide polytypes at elevated pressures was conducted byFanchini etal.40Thefreeenergies for several boroncarbidecongurations were calculated under increasing hydrostaticpressureat roomtemperature. Theresultsindicatedthat theenergetic barrier for pressure-induced amorphization ofboron carbide was by far the lowest for the hypothetical(B12)CCC polytype, which was found to be unstable at67GPa during hydrostatic loading. The collapse of the(B12)CCCstructure was predictedtoresult inasegregationof the (B12) icosahedraandamorphous carboninthe formof 23nmwide bands along the (113) lattice direction, inagreementwiththeTEMobservationsonballisticallyloadedsamplesshowninFig. 30. Anexampleof themost energeti-callyfavoredtransformationpathof the (B11Cp)CBCpoly-type into the (B12) icosahedra and graphitic carbon, asproposed by Fanchini etal.,40is schematically shown inFig. 39fortwodierentvaluesofhydrostaticpressure.Bothmodels discussedabove are opentocriticism. Theresults of Fanchini etal.40predict collapseof the(B12)CCCpolytypeundercompressionat hydrostaticpressuresof only67GPa,butexperimentallytheambientphaseofboroncar-bidehasbeenreportedstableunderhydrostaticcompressionofupto100GPa.118120,122Inlinewiththeavailableexperi-mental work, abinitiomodelingbyanothergroupestimatedtheamorphizationpressureforthe(B12)CCCpolytypetobeat 300GPa,44byfar exceeding the predictions of Fanchinietal.40Moreover, thereiscompellingevidencethatthe(B12)CCCconguration does not exist in nature (e.g., Dekuraetal.;86see also relevant discussion in SectionsI and II).Fanchini etal. alsopredictthedecompositionofthe(B11CP)CBCpolytypeintothe(B12)icosahedraandamorphouscar-bonat ~40GPa,40whichis more inline withthe availableshockcompressionandnanoindentationdataonboroncar-bide, butonceagainndsnoconrmationinthehydrostaticcompressionexperiments. Onthe other hand, the model ofchainbendingunderuniaxial compressionproposedbyYanetal.,118albeittakingintoaccounttheimportanceofnonhy-drostaticloadingforthecollapseofboroncarbide,islackinganempirical validation. This model assumes a transforma-tionintoanewstructureintheloadingstage, andtheinsituRamandataobtainedbythe same groupdonot showanysign of such transformation. Nanoindentation data couldprovideinformationonvolumetricchangesassociatedwithatransformationofthiskind,particularlyinviewofconsistentobservation of the transformed material in the hardnessimprints.170However, a discontinuity or a change in theslope of the loading curve that couldbe associatedwithastress-induced transformation has never been recorded inboron carbide under depth-sensing indentation.114,171Inaddition, thesignsof areversetransformation, evidencedinthe Yans high pressure experiments,118could not be dis-cerned in the nanoindentation unloading curves (Fig. 40).Thismayberelatedtoverysmall volumetricchangesassoci-atedwiththepresumedtransformation, whichisnotsurpris-ing noting the small size of the transformed amorphizedzonesobservedundertheTEM(Figs. 30and31).Additionalexperimental andtheoretical workwill be requiredtofully0 100 200 300 400 500020406080100120140160unloadingloadingunloadingLoad (mN)Indenter Displacement (nm)loadingB4.3C(111) surface100 150 200 250 300 350010203040Mean Contact Pressure (GPa)Contact Depth (nm)Fig. 40. Nanoindentationloadversusdisplacement andmeancontact pressureversuscontact depthcurvesforthe(111) surfaceof B4.3C. Thepressure is highest at the point of initial contact anddecreases to44GPaat the endof the loadingstage. The smoothline prole onbothloadingandunloadingindicatestheabsenceofsuddenvolumetricchangesthatcouldbeassociatedwithaphasetransformation.-0.15-0.10-0.050.000.050.100.150.200 GPa 16 GPa(B12) + Graphite(B12)CCC(B11Ce)CCB(B11Ce)CBCRelative Energy (eV/cell)(B11Cp)CBCTransition PathFig. 39. A schematic route proposed by Fanchini etal.40totransform(B11Cp) CBCinto(B12) andgraphiteat ambient pressureandat 16GPa. The transformationsteps involve migrationof thecarbonatomintheicosahedronfromapolar toanequatorial site,(B11Cp) CBC ? (B11Ce)CBC; migration of the boron atomin thechainfromthe central toa boundary site, (B11Ce)CBC ? (B11Ce)CCB; swappingof theequatorial icosahedral carbonatomwiththeboundaryboronatominthe chain, (B11Ce)CBC ? (B12)CCC; andcoalescence of the obtained CCCchains along the (113) planes,throughrotationoftheiraxisaroundthe[001]direction.20 JournaloftheAmeri