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:
[email protected].,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