Domnich.2011.JACerS.pdf

Boron Carbide: Structure, Properties, and Stability under Stress

Vladislav Domnich, Sara Reynaud, Richard A. Haber, and Manish Chhowalla

Department of Materials Science and Engineering, Rutgers, The State University of New Jersey,Piscataway, NJ 08854

Boron carbide is characterized by a unique combination ofproperties that make it a material of choice for a wide rangeof engineering applications. Boron carbide is used in refractoryapplications due to its high melting point and thermal stability;it is used as abrasive powders and coatings due to its extremeabrasion resistance; it excels in ballistic performance due to itshigh hardness and low density; and it is commonly used innuclear applications as neutron radiation absorbent. In addi-tion, boron carbide is a high temperature semiconductor thatcan potentially be used for novel electronic applications. Thispaper provides a comprehensive review of the recent advancesin understanding of structural and chemical variations in boroncarbide 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 arealso discussed.

I. Atomic Structure, Stoichiometry, and Polytypism

THE atomic structure of boron carbide has been exten-sively discussed in the literature.18 The primary struc-tural units of boron carbide are the 12-atom icosahedralocated at the vertices of a rhombohedral lattice of trigonalsymmetry (R3m space group), and the 3-atom linear chainsthat link the icosahedra along the (111) rhombohedral axis,as illustrated in Fig. 1. This structure can also be describedin terms of a hexagonal lattice based on a nonprimitive unitcell, in which case the [0001] axis of the hexagonal latticecorresponds to the [111] rhombohedral direction (Fig. 1).The presence of icosahedra within the boron carbide struc-ture is a consequence of elemental borons ability to formcaged structures of a variety of sizes5,9; the icosahedra inboron carbide are essentially two pentagonal pyramidsbonded together.10 As such, two types of chemically distinctsites, polar and equatorial, are possible within an individualicosahedron. The polar sites correspond to those atoms thatlink the icosahedra together. The polar atoms within the cage

are also the three atoms from each of the two planes oppo-site one another in the crystal structure. The equatorial siteson the other hand are those to which the 3-atom chains arebonded, and these sites form a hexagonal chair within theicosahedron (Fig. 1).Information on the crystal symmetry of boron carbide is

readily available from diraction measurements; however,the exact site occupancies by carbon and boron atoms arestill debated. This is due to the similarity in both electronicand nuclear scattering cross-sections for boron and carbon(11B and 12C isotopes),11,12 which makes it dicult to distin-guish these two atoms by most characterization techniques.From the crystal symmetry considerations, two stoichiome-tries have been originally proposed as candidates for thestable phase of boron carbide: (i) the carbon rich B4C(or B12C3) compound, with the idealized structural congura-tion (B12)CCC,

13,14 where (X12) represents the icosahedralatoms and XXX stands for the chain atoms, and (ii) theB13C2 (or B6.5C) compound, described by an idealized (B12)CBC structural formula, where the center chain carbon atomis replaced by boron.15,16 Formation of additional intermedi-ate phases with crystal symmetry other than R3m, such as amonoclinic modication of B13C2,

17 has also been reported.These variations have been reected in several versions of theBC phase diagram reported in the literature1823; Fig. 2shows examples of the two more commonly used phase dia-grams.20,21 There is agreement in the community about theexistence of a wide range of solid solubility for carbon in thestable phase and a homogeneous range extending from~8 at.% C to ~20 at.% C,3,2224 although synthesis of a sin-gle crystal with the B3.2C stoichiometry, corresponding to24 at.% C has also been reported.25 Beyond ~20 at.% C, amixture of stable phase boron carbide and carbon is oftenencountered, which has a eutectic point at ~30 at.% C of2350C20; but the latter has also been debated to be aslow as 2240C.21 Low carbon content phases (i.e. below8 at.% C) are generally agreed to be solid solutions of thestable phase boron carbide and pure boron.The rhombohedral lattice parameters for the carbon-rich B4C

compound are a = 5.16 A and a = 65.7, with minor variationsdepending on the extent of the investigation.2,13,14,2633

Converted into the more easily worked with hexagonal latticeparameters, B4C has values of a0=5.60 A, c0 = 12.07 A, andan axial ratio of c0/a0 = 2.155.

3 Due to the dierence inatomic radii of carbon and boron, B-rich boron carbideshave slightly expanded lattices. Using precision structural

D. J. Greencontributing editor

Manuscript No. 29735. Received May 25, 2011; approved August 27, 2011.Author to whom correspondence should be addressed. e-mail: manish1@rci.

rutgers.edu

3605

J. Am. Ceram. Soc., 94 [11] 36053628 (2011)

DOI: 10.1111/j.1551-2916.2011.04865.x

2011 The American Ceramic Society

Journal

Feature

characterization of high-purity boron carbides spanning theentire homogeneity range, Aselage et al. established a corre-lation between lattice parameters and stoichiometry.33 Asillustrated in Fig. 3(a), the a parameter experiences a steadyincrease toward more boron-rich stoichiometries, whereas achange in the slope at ~13 at.% C is observed for the com-positional dependence of the c parameter. Further, neutronpowder diraction data11,34 show that the chain bond lengthin boron carbides at 13 at.% C is reduced by 2%3% com-pared to that in boron- and carbon-rich material [Fig. 3(b)].These experimental observations can be understood in termsof the formation of an intermediate B6.5C conguration andthe change in the mechanisms for incorporation of carbonatoms into the lattice that occurs at 13.3 at.% C composi-tion, as discussed below.Despite the absence of experimental methods that can unam-

biguously pinpoint the positions of boron and carbon atoms inthe lattice, various atomic congurations have been suggestedfor boron carbide based on theoretical modeling4,3546 and theavailable experimental data obtained by nuclear magneticresonance,4750 neutron11,34,51 and X-ray2,3133,52 diraction,infrared30,5356 and Raman5661 spectroscopy, and X-rayabsorption12 and scattering62,63 techniques. Possible combina-

tions of such structural elements as B12, B11C, B10C2, andB9C3 icosahedra and CCC, CBC, CCB, CBB, BCB, and BBBchains, as well as the nonlinear chains that include four boronatoms and chains with vacancies, have been suggested in thesestudies.The results of the theoretical energy minimization consis-

tently indicate that the (B11C)CBC structure is preferred tothe (B12)CCC at the carbon-rich end of the homogeneityrange.4,36,37,39,40,4345,64 Because of the existence of nonequiv-alent atomic positions within the icosahedra, two variants of(B11C)CBC should be considered: the polar (B11C

p) congu-ration, where one of the boron atoms in the icosahedron issubstituted by carbon in the polar site, and the equatorial(B11C

e) conguration, where the substitution occurs in theequatorial site. The polar conguration is found to be ener-getically preferred to the equatorial one in all studies wherethe two structures have been modeled within the same calcu-lation framework.35,40,45,65 It should be also noted that thesubstitution of carbon into the icosahedron induces smallmonoclinic distortions in the R3m symmetry, amounting to1.8% and 0.5% of the lattice parameter and to 1.0% and0.1% of the rhombohedral angle for the polar and the equa-torial congurations, respectively.39

Fig. 1. Boron carbide lattice showing correlation between the rhombohedral (red) and the hexagonal (blue) unit cells. Inequivalent lattice sitesare marked by arrows.

Fig. 2. Phase diagram of boron carbide after (a) Ekbom and Amundin,20 depicting B13C2 as the stoichiometrically stable phase and presumingthe presence of several low temperature phases, and (b) Beauvy,21 depicting the more widely accepted B4C as the stoichiometrically stable phase,with solid solutions with B and C on each respective side.

3606 Journal of the American Ceramic SocietyDomnich et al. Vol. 94, No. 11

From an experimental viewpoint, the possibility that(B11C)CBC is the true structural representation of the B4Cstoichiometry was originally inferred,47 and later corrobo-rated,48,66 by nuclear magnetic resonance (NMR) observa-tions. However, concurrent NMR studies by other groupsoered alternative interpretations, including structures withchains consisting only of carbon atoms,49 and chains withtwo carbon atoms substituted by boron.50 In part, these dis-crepancies stemmed from the lack of agreement on theassignment of specic NMR peaks to either the chain centerC atom or to the C atom in the polar icosahedral site. Theo-retical simulation of NMR spectra in (B11C

p)CBC, (B11Ce)

CBC, and (B12)CCC congurations based on density func-tional theory (DFT) helped to resolve this issue.64 It wasfound that the best correlation between the theoretical andthe experimental NMR spectra for the B4C stoichiometrycould be achieved for the B4C structure consisting of allCBC chains and a mixture of (B12), (B11C

p), and (B10C2p)

icosahedra in the ratio of 2.5/95/2.5, with the two C atomsin the latter structure located in the antipodal polar sites.In a related study that employed a similar modeling

framework,39,65 comparison of theoretically simulated andexperimental Raman and infrared spectra of B4C alsoimplied that (B11C

p)CBC is the true representation of boroncarbide at this stoichiometry. Further, the presence of theboron atom in the B4C chain has been inferred fromX-ray2,31,32 and neutron diraction34,51 data, owing to theobservation of the lower scattering at the chain centers, andfrom X-ray absorption12 and scattering62,63 observations.Thus, the majority of theoretical and experimental investiga-tions agree that (B11C

p)CBC is the preferred atomic congu-ration for the B4C stoichiometry.It should be noted that even higher estimations for the car-

bon-rich edge of the homogeneity range have been discussed.Konovalikhin et al. reported successful synthesis of singlecrystal boron carbide with ~24 at.% C.25 To account forhigher carbon content in this compound, the proposed struc-tural conguration included a distribution of CBC chainsand (B11C), (B10C2), and (B9C3) icosahedra, with the hypo-thetical (B9C3)CBC conguration limiting the range of stableboron carbide compounds at 33 at.% C.25,46 However, thelatter nding is in contradiction with an established concept

that due to the internal bonding constraints, the maximumnumber of carbon atoms that can substitute boron in the ico-sahedra is two.67 Following this concept and assuming(B10C2)CBC as the most carbon-rich conguration of boroncarbide, the theoretical limit for the carbon-rich edge of thehomogeneity range should not exceed 25 at.% C.There is a lack of agreement in the scientic community

on the nature of the structural changes in boron carbide atdecreasing carbon concentrations. While it is generallyaccepted that the carbon atoms substitute boron atoms inthe rhombohedral lattice, dierent views exist on whether thechain or the icosahedral atoms are preferentially substituted.Based on entropic and energetic considerations, Emin conjec-tured that preferred substitution occurs in the chain sites.36

According to this theory, the number of CBB chains in thestructure will increase until all material is comprised of the(B11C)CBB units, which corresponds to the B6.5C stoichio-metry at 13.3 at.% C. For lower carbon concentrations, thesubstitution will take place within the icosahedra, renderingthe idealized (B12)CBB conguration for the most boron-richB14C stoichiometry at 6.7 at.% C. This model provides basisfor a consistent interpretation of the observed trends in thecompositional dependence of electrical and thermal transportproperties,6874 elastic properties,75 structural data,33

and vibrational frequencies and intensities incurred fromRaman and infrared (IR) measurements.53,58,59,76

An alternative interpretation of the available X-ray dirac-tion (XRD) data maintains that carbon is preferably replacedby boron in the icosahedral sites.32,77,78 In this model, thenumber of (B12) icosahedra in the material increases as thecomposition approaches 13 at.% C from the carbon-rich end;the structural conguration for the stoichiometric B6.5C phaseis given as (B12)CBC; and the substitution of boron into thechain sites occupied by carbon occurs in the 813 at.% C rangeof compositions. This view is also supported by the DFT cal-culations, which consistently indicate that the (B12)CBC con-guration is more stable than the (B11C)CBB one, both fromthe energy minimization considerations and from a better cor-relation with the experimental lattice parameters.4,38,40,43

Comparative DFT calculations of the free energy and thestructural parameters of various possible congurations ofchain and icosahedral units for dierent boron carbide stoichi-ometries have been reported by several authors.4,40,43 Fanchiniet al.40 observed that the calculated free energies for a numberof dierent atomic congurations, referred to as polytypes, fallinto a small disorder potential of DV 0.2 eV (Fig. 4), corre-sponding to typical temperature variations encountered duringboron carbide synthesis.3 Based on this consideration, Fanchiniand co-workers proposed that various boron carbide polytypeswith energy dierences smaller than the disorder potential cancoexist at any given boron carbide composition.40

In practice, the structure of as synthesized boron carbide ismore disordered than indicated by the idealized modelspresented above. Theoretical calculations predict (B12)BC( for vacancy) to be the most stable conguration at theboron-rich end of the homogeneity range.43 Renement of theXRD data for B9.5C implies that at this composition, up to25% of CBC chains are statistically replaced by the 4-atomBBBB units, where the two central atoms of the unit lie near aplane normal to the threefold axis, bonding to the two termi-nal unit atoms and to the three icosahedral atoms.52 Neutrondiraction observations give evidence of the presence of non-linear chains with a displaced central atom, as well as chainswith a vacancy in the central chain site, along with the regularCBC and (possibly) CBB chains and icosahedral units in themore boron-rich compositions.11,34 Interpretation of the IRabsorption spectra and analysis of the resulting phonon oscil-lator strengths indicate statistical distribution of several struc-tural elements, e.g., (B12) and (B11C) icosahedra, CBC andCBB chains, as well as chainless units, at all compositionswithin the homogeneity range, as illustrated in Fig. 5.54 How-ever, it should be noted that the results of such calculation are

Fig. 3. Dependence of (a) hexagonal lattice parameters a and c,and (b) the chain bond length of boron carbide on carbon content.Lines serve as guides to the eye. Data from (a) X-ray diractionmeasurements by Aselage et al.33 and (b) neutron powder diractionmeasurements by Morosin et al.11,34

November 2011 Structure and Stability of Boron Carbide under Stress 3607

contingent upon the specic assumptions made during thederivation of the model, and other variations of the composi-tional dependencies of the structural elements that form boroncarbide have also been reported.55,79

The presence of defects is essential for boron carbides. Asshown by Balakrishnarajan et al.,42 disorders in the atomicarrangement are a part of the ground-state properties ofboron carbide, and are not due to entropic eects at hightemperatures. This is not unique for boron carbide, butrather a common property of boron-rich solids. In b-rhom-bohedral boron, for example, the presence of intrinsic defectshas been shown to result in macroscopic residual entropy,suggesting that b-boron could be characterized as a frus-trated system.80 The case of boron carbide may be on linewith this research.

Finally, a crucial issue that structural experimental andtheoretical data do not take into account is the presence offree carbon in as-synthesized boron carbide. That is, all poly-crystalline boron carbides contain impurities in the form offree carbon that can exist as either amorphous carbon orintra-granular graphitic inclusions, as shown by a systematiccharacterization of hot-pressed boron carbide ceramics byChen et al.81

II. Electronic Structure, Electronic and Optical Properties

Early work by Lagrenaudie established that boron carbidewas a p-type semiconductor with an estimated band gap of1.64 eV.82 This is much smaller than the band gap of othersemiconductor ceramics, e.g., Eg ~ 3 eV as in silicon carbide.Other estimations for the band gap of boron carbide havealso been reported. Werheit et al. measured an indirect gapof 0.48 eV83 by optical measurements; the same groupreported in a later work a band gap of 2.09 eV, suggestingthat a wide range of gaps could be identied in the boroncarbide structure within the stoichiometric range of B4.3CB11C.

84 Larger band gaps, typically exceeding 3 eV, are con-sistently obtained in theoretical band structure calculations,suggesting that the models do not adequately account for thedisorder in the material which could give rise to midgapstates.35,37,38,64,85,86 Examples of the calculated electronicdensity of states (DOS) showing estimated band gaps for the(B12)CCC

86 and the (B12)CBC85 atomic congurations are

given in Fig. 6. One important observation is that the pres-ence of an intermediate gap state in (B12)CCC, according tocalculations by Dekura et al.,86 results in a smaller band gapof only 1.56 eV in this structure. In the case of (B12)CBC,Calandra et al. report that 88% of total DOS at the Fermilevel arise from the icosahedra; in particular, boron atoms inpolar positions give the largest contribution to the conduc-tion processes.85

Electronic band structure calculations conrm the semicon-ducting nature of boron carbide for the stoichiometric B4C

Fig. 4. Gibbs energies (Gi) and the relative abundancesfi / exp Gi=DV of selected boron carbide polytypes correspondingto the disorder potential of DV = 0.2 eV (dash line), after Fanchiniet al.40 Stability range for a segregated boron-amorphous carbon(B12) + a-C phase is also shown.

Fig. 5. Distribution of chain and icosahedral structural units acrossthe homogeneity range in boron carbide obtained from the analysisof IR absorption data by Werheit and co-workers. Reproduced fromKuhlmann et al.,54 with permission; 1992 Elsevier.

Fig. 6. Calculated electronic DOS for (a) (B12)CCC86 and (b) (B12)

CBC85 polytypes of boron carbide. An intermediate gap state isformed in (B12)CCC. The top of the valence band is taken as theenergy origin. The Fermi level is located at zero for (B12)CCC whileit is at 0.52 eV for (B12)CBC.


with 48 valence electrons.35,37,86 However, more boron-richcompounds, characterized by valence electron deciencies areconsistently found to be metallic.35,38,85 This is a direct conse-quence of the band theory stating that a crystal with oddnumber of valence electrons must be a metal, independent ofthe calculation method.5 Figure 7 shows electronic bandstructures calculated by Kleinmans group for the (B11C)CBCand the (B12)CBC congurations.

37,38,87 As follows from anexamination of Fig. 7, the main dierence between the twostructures is the position of the Fermi level, which indicatesthe semiconducting nature of (B11C)CBC and the metallicnature of (B12)CBC. For the (B12)CCC conguration, as illus-trated in Fig. 6, a distinct feature of the band structure is thepresence of the gap state of nonbonding character, predomi-nantly arising from the p orbital of the central C atom in thechain.86 This may explain the origins for B4C refusal ofassuming the (B12)CCC atomic conguration.Experimentally, boron carbide was found to be a semicon-

ductor throughout the entire homogeneity range, with itselectronic properties dominated by the hopping-type trans-port.68,88,89 The direct current (dc) conductivity of boron car-bide as a function of carbon content, as measured by severalgroups,68,8992 is presented in Fig. 8. Qualitatively, the maxi-mum in conductivity occurs at ~13 at.% C, corresponding tothe B6.5C stoichiometry. This observation, as well as similartrends in the compositional dependences of other boron car-bide properties (e.g., structural parameters, see Fig. 3), havebeen attributed to dierent mechanisms for boron substitu-tions into the lattice sites occupied by carbon atoms, as dis-cussed in Section I. Several related models have been alsoproposed in the literature for explaining boron carbide trans-port properties.Emin advanced a charge transport model based on the

small bipolaron hopping mechanism.9396 In this model, thecharge carriers in boron carbide are pairs of holes that moveby a succession of thermally activated phonon-assisted hopsbetween electronic states on inequivalent B11C icosahedra.The pairing of the holes on B11C icosahedra is viewed as aresult of the disproportionation reaction, 2(B11C)

0 ?(B11C)

+ (B11C)+, resulting in the formation of an electron-

decient (B11C)+ icosahedron, which is a chemical equivalent

of a bipolaron. This theory, together with an associatedstructural model36 (Section I), was able to interpret theobserved compositional, temperature and pressure depen-dence of boron carbide conductivity, as well as the variations

in Hall mobility, Seebeck coecient, dielectric constants, andmagnetic susceptibility of boron carbide with temperatureand carbon concentration.68,72,74,92,97,98

However, it is important to note that the apparent correla-tion of the experimental data with the Emins transportmodel is contingent upon several factors. Crucial for theinterpretation of the compositional dependencies of physicalproperties (e.g., electrical conductivity, Fig. 8) in terms ofsmall bipolaron hopping is Emins conjecture that the struc-ture of the B6.5C compound is described by the (B11C)CBBatomic conguration, providing sucient concentrations ofthe (B11C) units required for the formation of bipolarons atthis stoichiometry. However, as discussed in Section I, thereis no direct empirical evidence in support of this structuralmodel. Moreover, both the renement of XRD data and theresults of all available theoretical ab initio calculations sup-port an alternative structural model, which predicts gradualsubstitution of the icosahedral carbon atoms with boron

Fig. 7. Calculated energy bands for (a) the (B11C)CBC and (b) the (B12)CBC polytypes of boron carbide. The solid and the dash bandsrepresent states that are, respectively, even and odd under reection in a vertical plane. Zero energy corresponds to Fermi level. Reproducedfrom Kleinman,87 with permission; 1991 American Institute of Physics.

Fig. 8. Compositional dependence of dc conductivity in boroncarbide at dierent temperatures. Data from (a) Samara et al.92; (b)Werheit et al.90,91; (c) Wood et al.68; (d) Schmechel et al.89


as the carbon concentration changes from 20 at.% to13.3 at.%. In this model, the preferred atomic congurationfor the B6.5C compound is given by the (B12)CBC formula,providing very limited availability of the (B11C) units, whichis exactly opposite to the requirements of Emins theory.Other inconsistencies of the small bipolaron hopping modelfor boron carbide, such as an overestimate of carrier concen-trations and the evidence for multiple activation energies inthe temperature dependence of electric conductivity, havealso been discussed in the literature.99

An alternative interpretation of boron carbide transportproperties has been proposed by Werheit and co-work-ers.79,89,100,101 They suggest that the semiconducting nature ofboron carbide arises from the structural disorder throughoutthe entire homogeneity range. The intrinsic defects associatedwith disorder are proposed to be Jahn-Teller distortion of theicosahedra,100 missing or incomplete occupation of specicatomic sites, statistical occupation of equivalent sites, or anti-site defects.54,55,79 Werheit maintains that the defects in boroncarbide generate split-o valence states in the band gap,which exactly compensate electron deciency of the idealizedstructures (e.g., (B12)CBC) that are theoretically found to bemetallic. According to Werheit,101 high concentration of gapstates near the valence band is responsible for the low p-typeelectrical conductivity in boron carbide. In addition to theelectrical conductivity in extended band states, hopping-typeconduction in localized gap states is predicted by this model.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, such as the one illustrated in Fig. 5. However, thismodel suers from the lack of independent verication. Thedistribution of structural elements, as proposed by Werheitand co-workers,54,55,79 relies entirely on the interpretation ofspecic bands in the IR absorption spectra of boron carbideobtained by the same group. It will be discussed in Section IIIthat alternative interpretations oered in the literature of theIR data provide alternative explanations to Werheits analy-sis. In addition, their model requires a pre-selection of struc-tural elements that Werheit and co-workers limit to (B12) and(B11C) icosahedra and CBC, CBB, and BB chains. As dis-cussed in Section I, while neutron diraction data give evi-dence for vacancies in the central chain site, other possibleatomic congurations, such as the (B10C2) icosahedra, theCB chains, the nonlinear chains, the 4-atomic boron unitsreplacing the chains, etc., may also be present in boron car-bide at varying stoichiometries. Accounting for these addi-tional structural elements would inevitably alter Werheitscompositional distribution curves, such as the one shown inFig. 5.The origin of disorder in boron carbide has been investi-

gated using quantum chemical methods by Balakrishnarajanet al.,42 who analyzed the nature of the molecular orbitalscorresponding to the (B12) icosahedra and CBC chains andinteractions among them in the most symmetric (B12)CBCstructure. They also studied the eect on the bonding ofadding or removing an electron from the unit cell. The cal-culations have shown that the addition of electrons expandsthe unit cell, elongating and weakening all bonds. In partic-ular, the carbon atoms tend to change hybridization fromsp2 to sp3 as the total molecular charge is increased. Thisgroup also studied the changes in the bonding nature withthe varying carbon content, concluding that partial substitu-tion of carbon by boron atoms creates inevitable disorderbecause it is energetically and entropically favored. In par-ticular, calculations indicate that disorder is localized at thecarbon sites and the bonding of B/C covalent network indefective boron carbide is stronger than in the stoichiome-tric electron-precise B4C.

42 The localization of the electronicstates arising from the B/C disorder therefore leads to semi-conducting nature of boron carbide throughout its entirecompositional range.

The electronic states discussed above determine the opticalproperties of boron carbide and therefore can be probedusing optical techniques. Optical constants of hot-pressedboron carbide with a presumed B4C stoichiometry, calculatedby Larruquert et al. via reectance measurements in theextreme ultraviolet spectral region are listed in Table I.102

Werheit et al. measured dielectric functions of boron carbidesamples with varying history and stoichiometry, as illustratedin Fig. 9.103 A number of critical points for interband transi-tions identied from the data in Fig. 9 indicate that the bandgap of boron carbide does not exceed 2.5 eV. This work alsodemonstrated that the imaginary part of the dielectricfunction reached maximum near ~13 at.% C, which was cor-related by the authors to the highest structural disorder inboron carbide at the B6.5C stoichiometry.

103

The absorption coecients obtained from optical trans-mission measurements on B4.3C samples with varying degreesof structural disorder104,105 are shown in Fig. 10. Opticalabsorption in a single crystal (a 3000 cm1) is higher thanthat in polycrystalline samples; however, the correlation of awith structural disorder cannot be unambiguously establishedbecause a more ordered polycrystalline sample obtained byhot isostatic pressing (HIP) shows lower absorption belowthe absorption edge than the less ordered commercial sampleobtained by hot pressing (HP). The increase in absorptioncoecient toward lower energies in the single crystal datahas been attributed to charge carriers,105 in correlation withboth the hopping-type and the Drude-type transport.Werheit and co-workers have identied several indirect tran-sitions between 0.47 and 3.58 eV via deconvolution of theabsorption edge shown in Fig. 10.104,105 They assign suchprocesses to transitions between various electronic stateswithin the band gap.Feng et al. used nonresonant X-ray Raman scattering

(XRS) technique along with site-specic ab initio calculationsto detect substitutional disorder in carbon-rich boron car-bide.62 The results of this study show that boron preferen-tially occupies the chain center site generating a delocalizedp-type exciton. Enlarged view of the near-edge region for theboron XRS spectrum of B4C shown in Fig. 11 identies theexciton related feature at ~1 eV. Werheit compared theseXRS results with their optical absorption data (Fig. 10) andfound good agreement between the two; he also proposedthat the higher absorption of the single crystal boron carbidein the range of 1.01.5 eV (Fig. 10) must be due to smallerconcentrations of extrinsic structural distortions resulting inhigher probability of exciton generation compared to thepolycrystalline material.84

Figure 12 shows the photoluminescence spectrum of apolycrystalline B4.23C sample measured by Schmechel et al.using the excitation energy of 2.4 eV.106 The features at 1.56and 1.5695 eV in the photoluminescence versus photonenergy dependence have been attributed to the indirect recom-bination of free excitons in the center B atom in CBC andCBB chains, respectively.84 Further, Werheit et al. reportedphotoluminescence measurements on a set of isotope-enrichedboron carbide samples spanning the entire homogeneity rangeusing an excitation energy of 1.165 eV.107 They assigned the

Table I. Optical Constants of Hot-Pressed Boron Carbide102

Wavelength (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 2.05


various luminescence peaks to the presence of localized gapstates and the resulting transitions between such states andthe energy bands. Combining the optical absorption, photolu-minescence, and charge transport data for electron transitionenergies, Werheit proposed an energy band schematic consist-ing of a 2.09 eV band gap, several disorder induced interme-diate gap states extending 1.2 eV above the valence bandedge, excitonic level at 1.56 eV above the valence band edge,and an electron trap level around 0.27 eV below the bottomof the conduction band, as shown in Fig. 13.84,107,108

III. Lattice Dynamics and Vibrational Properties

For a boron carbide crystal of R3m symmetry, group theorypredicts the following representation for the normal modesof lattice dynamics:109

5A1g 2A1u 2A2g 6A2u 7Eg 8Eu: (1)

The 12 modes of A1g and Eg symmetry are Raman active, the14 modes of A2u and Eu symmetry are IR active, and the A1uand A2g modes are optically inactive. By removing zero-fre-quency modes, the number of IR active modes becomes 12.109

For boron carbide polytypes that deviate from true R3m sym-metry, e.g., when a carbon atom is introduced into the icosa-hedron, the above selection rules are not valid and a highernumber of modes is expected in the experimental spectra.

The Raman and IR frequencies have been calculated forthe (B12)CBC polytype from parametric tting of the valenceforce constants,109,110 and for the (B12)CBC, (B12)CCC,(B11C

p)CBC, and (B11Ce)CBC polytypes from ab initio DFT/

DFPT calculations.65,111 In Figs. 14 and 15, theoretical pre-dictions for the IR and Raman active modes in the (B12)CBCand (B11C

p)CBC polytypes are compared with the experimentalspectra for boron carbide of matching stoichiometries, i.e.,B6.5C and B4C, respectively. It is immediately recognized thatthe use of simplied models for the evaluation of the forceconstants109 do not yield reliable frequencies. Indeed, unam-biguous identication of specic IR and Raman bands isimpractical in this case [Figs. 14(a) and 15(a)]. On the otherhand, for mode frequencies calculated by ab initio pseudopo-tential modeling by Lazzari et al.65, correlation with experi-ment is very good [Figs. 14(b) and 15(b)]. In this work, notonly frequencies but also relative peak intensities have beencorrectly predicted in the calculated IR absorption spectrumof (B11C

p)CBC, by accounting for the experimental mixing of

Fig. 9. (a) Real and (b) imaginary parts of the dielectric functionof boron carbide with dierent stoichiometry. Reproduced fromWerheit et al.,103 with permission; 1997 Elsevier.

Fig. 10. Absorption coecient versus photon energy measured onthe (111) surface of a single crystal, on a high quality HIPpolycrystalline sample, and on a commercial HP polycrystallineboron carbide ceramic. All samples are of the B4.3C stoichiometry.Data from Werheit et al.104,105

Fig. 11. Fragment of an XRS spectrum of polycrystalline boroncarbide for a momentum transfer of 1.05 A1 (dots) and thebackground of icosahedral B atoms (solid line) calculated for the(B12)CBC atomic arrangement. Data from Feng et al.

62


polarizations for the A2u and Eu modes.65 Surprisingly,

another ab initio study performed by Shirai et al.,111 based 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 observation that the IR modes shift to lower fre-quencies when a carbon atom is substituted by a boron atomin the icosahedra due to shortening of bond lengths.There have been some eorts to correlate the specic IR

and Raman modes to the atomic structure of boron carbide.According to Vast et al.,39 the IR active Eu mode at396 cm1 originates from the torsion of the CBC chain; theRaman active Eg mode at 480 cm

1 arises from chain rota-tion perpendicular to the (111) plane; and the Raman activeEg mode at 535 cm

1 is due to the libration of the (B11C)icosahedron. The atomic displacements from lattice dynamicscalculated by Shirai et al.112 are commonly referenced byexperimentalists for peak assignments. Shirais model predictsa Raman active A1g mode at 1080 cm

1 originating from thebreathing vibrations of the (B12) icosahedron; an IR activeEu mode at 1040 cm

1 resulting from complex atomic dis-placements due to chain bending, and antisymmetric stretch-ing of an icosahedron; an IR active Eu mode at 487 cm

1

Fig. 12. Photoluminescence spectrum of polycrystalline boroncarbide acquired at the excitation energy of 2.4 eV.106 Squares,experimental results; dash lines, recombination models of freeexcitons: IE E E0p exp E E0=kBTe , with E0 = 1.56 eV(1.5695 eV) and the exciton temperature Te = 46 K; solid lines,averaged experimental results, before and after substracting the1.56 eV model t. Reproduced from Werheit,84 with permission;2006 Institute of Physics.

Fig. 13. Schematic of the structure of gap states in boron carbidedeveloped by Werheit.84,107,108

Fig. 14. Comparison of experimental and theoretical infraredabsorption spectra of boron carbide: (a) FTIR on hot-pressedB6.5C

55 versus parameterized valence force model109 and ab initiocalculation111 for (B12) CBC; (b) FTIR on hot pressed B4.3C

55

versus ab initio calculation for (B11Cp)CBC.65,111 Solid lines: Eu

modes; dash lines: A2u modes.

Fig. 15. Comparison of experimental and theoretical Ramanspectra of boron carbide: (a) dispersive Raman (laser excitations 1.59and 2.41 eV) on hot-pressed B6.5C (this work) versus parameterizedvalence force model for (B12)CBC;

109 (b) dispersive Raman (1.59 eV;2.41 eV) on hot-pressed B4C (this work) versus ab initio calculationfor (B11C

p)CBC.65 Solid lines: Eg modes; dash lines: A1g modes.


originating from chain bending; a Raman active Eg mode at335 cm1 resulting from atomic displacements due to chainrotation and wagging of an icosahedron; and a Raman activeEg mode at 172 cm

1 originating from rotation of an icosa-hedron. Both the parametric tting model of Shirai et al.and the results of ab initio calculations by Vast and co-work-ers agree in assigning an IR active A2u mode at ~1600 cm

1

to the antisymmetric stretching of the CBC chain.4,112

Vast and co-workers have also reported theoretical estima-tions for phonon density of states (PDOS) of the (B12)CBCcompound.85 According to this work, the icosahedral modesare responsible for most of the contribution to total PDOS atfrequencies below 1130 cm1, with the exception of the fea-tures between 200 and 450 cm1, where notable contributionfrom the chain modes involving vibrations of boron atoms isobserved, and the feature at 1040 cm1, which has a signicantcontribution to PDOS from the vibrations of carbon atoms inthe chain (Fig. 16). Also, this model predicts that the high fre-quency feature at 1555 cm1 arises from the chain modes thatinvolve vibrations of both boron and carbon atoms.85

(1) Infrared Spectroscopy ObservationsThe infrared spectra of boron carbide have been studiedextensively by the group of Werheit 5456,105,113 Typical FTIRdata of absorption index, k, are shown in Fig. 14 for twoboron carbide stoichiometries associated with dierent struc-tural congurations: the carbon-rich B4.3C compound andthe intermediate B6.5C compound. Werheit et al. attributethe observed band at ~1600 cm1 to CBC chain stretching,the band at 410 cm1 to CBC chain bending, and all theremaining bands to intra-icosahedral vibrations in boron car-bide.54,113 Further, this group has interpreted the appearance

of bands at 380 and 1450 cm1 in more boron-rich composi-tions (Figs. 14 and 17) as new modes originating fromstretching and bending of the chains that contain a C atomin the central site, such as the BCB or the CCC chains.55

The eect of isotope substitutions on the frequencies of IRactive modes in boron carbide has also been investi-gated.30,53,55,56 The isotope-dependent frequency shifts of IRmodes in boron carbide composed of 10B4.3

12C at the B4.3Cstoichiometry are shown in Fig. 18. The large frequency shiftof the ~1600 cm1 IR absorption band with both 10B and13C isotopic substitutions imply substantial involvement ofboth B and C in this mode, which, combined with high fre-quency, indicates sti bonding between boron and carbonatoms. Further, Aselage et al. challenged assignment of thisband to stretching of the chain CB bond, arguing that sucha strong bond should form between boron and carbon atomsin the polar sites of the neighboring icosahedra.59 However,as shown by Calandra et al.,85 high frequency chain modesthat involve vibrations of both B and C atoms are predictedby ab initio calculations, which supports Werheits assign-ment of the ~1600 cm1 IR absorption band to the CBCchain stretching.

(2) Raman Spectroscopy ObservationsThe Raman spectra of boron carbide are characterized by aseries of bands extending from 200 to 1200 cm1.

5861,114

There are conicting assignments of the observed Ramanbands to vibrations of icosahedra and the 3-atom linearchains.4,39,5761,109,115 Analysis of this is further complicatedby the observed intensity dependence of the low-frequencybands on the excitation wavelength (energy).114 TypicalRaman spectra of two surfaces of a B4.3C single crystal as afunction of laser energy are shown in Fig. 19.The group of Tallant, Aselage, and Emin5759 studied iso-

tope and carbon content dependencies of boron carbidesusing the 514.5 nm (2.41 eV) laser. They assigned the twonarrow bands at 480 and 535 cm1 to the stretching vibra-tions in the soft CBC chains. The intensity of both bands

Fig. 16. Contribution from (a) chain modes and (b) icosahedralmodes to PDOS calculated for the (B12)CBC polytype.

85 Experimental(c) Raman spectra (hot-pressed sample; laser energy 1.96 eV) and (d)FTIR absorption spectra56 of the B6.5C compound are shown forreference.

Fig. 17. Compositional dependence of the high frequency modesin the IR absorption spectra of boron carbide. Reproduced fromKuhlmann et al.,54 with permission; 1992 Elsevier.


was found to diminish progressively with the decrease in car-bon content, which was attributed to the gradual replace-ment of the CBC chains with the CBB chains. At the sametime, the two bands at 270 and 320 cm1 were found todecrease in intensity with the decrease in carbon content, anda new narrow band at ~375 cm1 was found to appear andbecome more pronounced in the spectra of more boron-richcompounds. This latter feature was attributed to the appear-ance of the BBB chains at very low carbon concentrations.Further, according to this group,5759 the dependency of thehigh-frequency bands on carbon isotope and carbon concen-tration suggests that carbon atoms are present within icosa-hedra at all compositions.The group of Werheit56,60,61,115,116 studied isotopic and

compositional dependencies of boron carbide using the1070 nm (1.16 eV) laser. This group maintains that the spectra

acquired at higher laser energies are either coupled with theelectronic states or are able to excite only surface phonons,due to the high absorption coecient of boron carbide abovethe absorption edge,108,115 which the Werheit group places at3.5 eV.104 At long excitation wavelength, the two bands at 270and 320 cm1 become the primary features of the observedRaman spectra (Fig. 19). Following theoretical analysis ofShirai and Emura109, Werheit assigns these two bands to rota-tions of the CBC and CBB chains accompanied by waggingmodes of the icosahedra. Werheits group also nds that theintensities of the two bands at 270 and 320 cm1 diminish withthe decrease in the carbon content, in agreement with theobservations of Tallant, Aselage, and Emin.According to ab initio DFT/DFTP calculations, no vibra-

tional modes should be present in boron carbide at frequen-cies below 400 cm1.39,65 Vast and co-workers argued thatthe Raman bands observed in the experimental spectra at 270and 320 cm1 arise from a lift in the selection rules inducedby structural disorder and must reect the DOS for acousticphonons due to the x4 scaling law for scattering intensity atlow frequencies.4 However, this theory is in conict with thefollowing empirical observations: (i) the two bands at 270 and320 cm1 are present in the anti-Stokes Raman spectra,108

which reects their true Raman nature; (ii) the intensity ofthe two bands at 270 and 320 cm1 increases with decreasinglaser frequency (Fig. 19), which invalidates the x4 scalinglaw argument; and (iii) these bands are equally present inhot-pressed ceramics and in high purity single crystals (cf.Figs. 15 and 19), which questions their dependence on thestructural defects and imperfections. Thus, the true nature ofthe bands at 270 and 320 cm1 in the Raman spectrum ofboron carbide is still to be established.The origin of the bands at 270 and 320 cm1 can be

understood from the viewpoint of boron carbide being afrustrated system, as discussed in Section I. In a frustratedcrystal, a perfectly ordered conguration with high symmetryis characterized by the formation of nonbonding states, asillustrated in Fig. 6. These nonbonding states can form thestrong covalent bond by breaking the symmetry, at the costof losing a covalent bond in another place. Formation of astrong local bond brings about an associated weak bond,and these weak bond or weak angle forces may be responsi-ble for the appearance of low-frequency modes in the Ramanspectra of boron carbide. The primitive-cell calculations(such as the ones by Lazzari et al.65 and by Shirai et al.111),on the other hand, would completely eliminate such uctua-tions over the crystal.Assignment of the 480 cm1 band to chain rotation per-

pendicular to the (111) plane, implied by ab initio calcula-tions of Lazzari et al.,65 has been experimentally conrmedby the observations made on oriented boron carbide singlecrystals. As shown in Fig. 19, the intensity of the 480 cm1

band diminishes with respect to other Raman bands whenthe sample is rotated from the (111) orientation, when thescattering geometry is aligned with the 3-atom chain, to the(210) orientation, when the scattering geometry is at ~25angle to the 3-atom chain. This would be expected for avibrational mode where maximum atomic displacementsoccur in directions perpendicular to the chain axis, such asthe discussed CBC chain rotation mode.39

The Raman spectrum of boron carbide at higher frequen-cies (from 600 to 1200 cm1) is characterized by a number ofbroad bands that are believed to originate predominantlyfrom the vibrations within the icosahedral units.39,58 Follow-ing Shirais mode assignments,112 the major band at1088 cm1 is referred to in some literature as the icosahedralbreathing mode, or IBM. However, analysis of the Ramanactive modes for (B11C)CBC [Fig. 15(a)] and the PDOS for(B12)CBC (Fig. 16), theoretically calculated by the Vastsgroup,65,85 indicate that several modes originating from boththe chains and the icosahedra may contribute to the broadfeature around 1080 cm1.

Fig. 18. Isotope-dependent frequency shift of the IR active modesin B4.3C boron carbide, related to

10B4.312C. Data from Werheit

et al.56

Fig. 19. Raman spectra of B4.3C single crystal acquired atexcitation wavelengths of 515 nm (2.41 eV), 633 nm (1.96 eV), and780 nm (1.59 eV). Left panel: (111) surface. Reproduced fromDomnich et al.,114 with permission; 2002 American Institute ofPhysics. Right panel: (210) surface (this work).


Further insight into the nature of the Raman bands is pro-vided by hydrostatic compression experiments reported bydierent groups.117119 Pressure dependence of band frequen-cies in the Raman spectra measured by Guo et al.,119 up to36 GPa are shown in Fig. 20. The phonon dispersion underpressure is described in terms of mode Gruneisen parametersci, dened by

ci @ lnxi@ lnV

BTxi

@xi@P

; (2)

where xi is the mode phonon frequency, BT is the isothermalbulk modulus, V is the volume, and P is the pressure. Sec-ond-order polynomial tting of the data in Fig. 20 yields thevalues for ci listed in Table II.The 1088 cm1 Raman band shows weak dependence on

pressure (c1088 = 0.59), suggesting high stiness of the associ-ated vibrations. In view of the experimentally observed highercompressibility of icosahedra with respect to the unit cell,120

this questions the assignment of the 1088 cm1 band tobreathing vibrations of icosahedra, as proposed in someworks.58,121 The largest Gruneisen parameter of 1.38 isobserved for the Raman band at 1000 cm1 (Table II). Tak-ing into account the results of ab initio calculation by Lazzariet al.,65 which predict a Raman active mode with the A1g sym-metry (consistent with the icosahedron breathing) at1000 cm1, one might be tempted to identify this band asIBM. However, the 1000 cm1 band vanishes from theRaman spectra above 20 GPa (Fig. 20), whereas the icosahe-dra have been shown to be stable to at least 100 GPa underhydrostatic compression.120,122 Splitting and sharpening of thehigh frequency bands becomes apparent at pressures in excessof 20 GPa;117119 the bands at 932 and 1154 cm1 become dis-cernible in the Raman spectra only above 10 GPa (Fig. 20).Selected band intensities with respect to the 1088 cm1

band are shown in Fig. 21, calculated using the Raman spec-tra acquired by Guo et al.119 at laser excitation wavelengthsof 515 nm (2.41 eV) and 633 nm (1.96 eV). The intensity ofthe 535 cm1 band decreases with pressure faster than theintensity of the 480 cm1 band, indicating dierent origins ofthese bands in accordance with Lazzaris calculations.65 Ofparticular interest is the feature at 270 cm1, which showsanomalous intensity dependence on pressure, peaking at~2530 GPa and falling o rapidly thereafter, a trend remi-niscent of a resonance-type enhancement. However, thisbehavior is independent on laser excitation energy, which

questions possible assignment of this band to a resonanceprocess. Another peculiarity of the two low-frequency bandsat 270 and 320 cm1 is their negative pressure dispersion, asevidenced by their Gruneisen parameters of c274 = 1.90 andc321 = 0.89 (Table II). Pressure softening of zone-boundaryacoustic phonons is a common feature of tetrahedral semi-conductors that accounts for the negative thermal expansioncoecients usually found at low temperatures in these mate-rials.123 Soft acoustic phonons are also believed to induceshear instabilities leading to amorphization in quartz124,125

and coesite.126 However, ultrasonic measurements show thatthe Gruneisen parameters for the longitudinal and transverseacoustic modes in boron carbide are positive, cL = 1.21 andcT = 0.33,

127 which is in conict with the assignment of the270 and 320 cm1 bands to disorder-induced acoustic pho-nons as endorsed by Lazzari et al.65

Because amorphous/graphitic carbon inclusions are com-monly present in commercial boron carbide, it is importantto discuss the lattice dynamics properties associated withthese forms of carbon. The nature of the Raman spectra ofgraphitic and amorphous carbon was investigated by Ferrari

Fig. 20. Pressure dependence of band frequencies in the Ramanspectra of single crystal B4C acquired at the laser energy of 2.41 eV.The best least-square ts are shown by solid lines. Analysis is basedon the Raman spectra reported by Guo et al.119

Table II. Frequencies at Zero Pressure xi,One-Phonon Quadratic Pressure Coecients (d2xdP2),and Gruneisen Parameters ci for Raman Active Modes in

the B4C Single Crystal

xi (cm1) 12

d2xidP2

(cm1Pa2) ci

274 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 0.32

The values are obtained from best least-squares ts to measured pressure

shifts of the Raman bands acquired at the laser energy of 2.41 eV by Guo

et al.119 The bulk modulus of B4C, required to compute ci, is taken fromManghnani et al.117

Fig. 21. Pressure dependence of band intensities in the Ramanspectra of single crystal B4C acquired at the laser energy of (a)2.41 eV and (b) 1.96 eV. Lines serve as guides to the eye. Analysis isbased on the Raman spectra reported by Guo et al.119


et al.128 A typical Raman spectrum of amorphous carbon isshown in Fig. 22. According to the literature, the graphite-like, also called tangential G band (1589 cm1), derives fromthe in-plane stretching vibration of the double C=C bonds(sp2 carbon), and has the E2g symmetry. In the ideal case ofa large single crystal graphitic domain, the G band is theonly one to appear. The disorder-induced D band ( 13001360 cm1) is originating from the breathing vibrations ofthe sixfold aromatic rings in nite graphitic domains. Themechanism responsible for the appearance of the D band isthe formation of an electron-hole pair caused by laser excita-tion and followed by one-phonon emission. It has beenshown that the activation of the D band always requires anelastic defect-related scattering process;128 the D band isindeed observed in sp2 bonded carbons containing vacancies,impurities or other symmetry-breaking defects. The D modeis of the A1g symmetry and involves a phonon near the Kzone boundary.Tuinstra and Koenig noted that the ratio of the intensity

of the D band with respect to the G band varies inverselywith the size of the graphitic clusters.129 This relation waslater modied by Ferrari and Robertson to account fordomains with increased electron connement:128

IDIG

CkL

L[ 20A Tuinstra and Koenig129

(3)

IDIG

CkL

1=2L\20A Ferrari and Robertson128

(4)

Here, constant C(k) depends on the laser wavelength (e.g., C(515 nm) = 40 A), and L is the diameter of the sp2 domain.The G band originating from carbon inclusions may be

responsible for the occurrence of a feature at ~1580 cm1 inthe Raman spectra of boron carbide, as the ones shown inFig. 15. Alternative explanation for the origin of this bandhas been oered by Werheits group.60,116 They argued thatsubstitution of a boron atom for the end carbon atom in theCBC chain should lead to modied selection rules that wouldmake stretching vibrations in the CBB chain Raman active.This is a valid assumption noting that the calculated fre-quency of the antysymmetric stretching mode in the CBCchain is placed around 1600 cm1 (Figs. 14 and 16), and the~1580 cm1 feature is commonly observed in the Ramanspectra of high purity single crystal boron carbide samplesthat are presumably free of carbon inclusions (Fig. 19).

IV. Atomic Bonding, Elastic and Mechanical Properties

Elastic and mechanical properties of boron carbide are deriv-ative of such characteristics of atomic bonding as localizationand delocalization, ionicity and covalence of the bonds andelectron density in inter-atomic regions. In particular, higherstiness and hardness is associated with more localized cova-lent bonds and higher inter-atomic electron density. Fourtypes of atomic bonds can be identied for boron carbide inthe R3m symmetry (Fig. 1): (i) the intrachain bond, whichconnects the end atom and the center atom in the 3-atomchain and has a p character; (ii) the chain-icosahedron bond,which connects the end atom in the 3-atom chain to an atomin the equatorial site of the icosahedron; (iii) the intericosahe-dral bonds, which connect atoms in the polar sites of neigh-boring icosahedra and originate from sp hybridized orbitals;and (iv) the highly delocalized intraicosahedral sp2 bonds,which connect atoms within the icosahedron. Renement ofX-ray and neutron diraction data shows that the intrachainbond has the shortest length at all stoichiometries; it is fol-lowed by the chain-icosahedron bond, the intericosahedralbond, and the intraicosahedral bonds.34,51,52,77,130 For bondsof similar nature, the bond length is inversely related to thebond stiness, which implies that the intrachain bonds arethe most rigid ones and the intraicosahedral bonds are themost compliant ones in boron carbide. This nding is sup-ported by the available theoretical calculations of bondstrength/hardness for several possible congurations of boronand carbon atoms in the stoichiometric B4C andB6.5C.

35,41,45,131 The comparable magnitudes of the inter- andthe intraicosahedral bond strengths were used as the basisfor Emins classication of boron carbide as inverted molecu-lar solid, or a solid composed of strongly bound molecularunits (icosahedra).132

The relative strength of the inter- and the intraicosahedralbonds has been related to the question of the compressibilityof the icosaherdral units with respect to the unit cell. Highpressure neutron diraction studies give direct evidence thatthe icosahedra are 23% more compressible than the interico-sahedral space.120 Compositional variation of longitudinalsound velocities75 and pressure dependence of electrical resis-tivity97 in boron carbide can also be interpreted in terms ofsoft icosahedra. Contradictory to these observations, theoret-ical simulations of the elastic properties of boron carbide athigher pressures predict lower compressibility of the icosahe-dra with respect to the unit cell.65,133 Based on these results,Lazzari et al. argued that the intericosahedral bonds areweaker than the intraicosahedral ones, and challenged thenotion of inverted molecular solid for boron carbide.65 How-ever, as noted by Shirai et al.,111 these arguments did nottake into consideration the fact that per each bond that con-nects an icosahedron to the surrounding lattice, there are tenbonds that connect atoms within the icosahedron. Becauseall available bonds contribute to the elastic deformationunder hydrostatic compression, the 10-fold prevalence of theintraicosahedral bonds would result in lower compressibilityof the icosahedron with respect to the lattice around it, eventhough individually intericosahedral bonds may be stronger.The rigidity of the intrachain bond has also been debated,

as evidence of signicant displacements of the chain centeratom in the direction perpendicular to the threefold axis,coming from X-ray and neutron diraction measure-ments,11,34,78 implied weak bonding between the chain centerand the chain terminal atoms. Some researchers proposedthat the weakness of this bond should arise from its presum-ably ionic character.134 This apparent discrepancy with theconventional understanding and the results of theoreticalmodeling was addressed by Shirai,5 who noted that the calcu-lated restoring force against the displacement perpendicularto the bond axis would constitute only 10% of the bondstretching force, yielding a low energetic barrier for the chaincenter atom to move in the plane normal to the bond axis,

Fig. 22. Raman spectrum of amorphous/graphitic carbon withcharacteristic D and G bands.


and at the same time preserving a strong force constant foratomic displacement in the axial direction. Additional evi-dence that supports the notion of intrachain bond softnesscomes from the spectral position of the bands at 480 and535 cm1 observed in the Raman spectra of boron carbide,which are assigned to stretching vibrations in the CBC chainsby researchers who endorse Emins structural model.59 Thelow frequency of these bands implies a weak force constant.However, assignment of these two bands to the CBC chain-stretching mode is questionable in view of a more recent theo-retical analysis of the vibrational properties of boron carbideby Vast and co-workers,39,65 who have demonstrated thatbetween the two bands in question, only the 480 cm1 bandwas associated with the linear chain, and even this band hadits origin in chain rotation and not in chain stretching, as dis-cussed in Section III. As such, neither the Raman band at480 cm1 nor the one at 535 cm1 would carry informationon the axial rigidity of the intrachain bond.Theoretical calculations nd that the C11 elastic constant is

higher than the C33 constant for both (B12)CBC (nominalB6.5C stoichiometry) and (B11C)CBC (nominal B4C stoichi-ometry) structural congurations.135 This shows good agree-ment with a similar trend in the experimentally measuredvalues of C11 and C33 obtained on a B5.6C single crystal(Table III).136 The commensurable magnitudes of C11 and C33are at odds with the intuitive expectation that due to the align-ment of the stronger intericosahedral bonds with the rhombo-hedral lattice vectors, the stiness of the boron carbide crystalshould be higher along the [001] direction rather than on the(001) plane, i.e., C11 should be lower than C33. Shirai et al.

133

explained this apparent contradiction in terms of internalrelaxation of the boron carbide lattice under external stress.They noted that the distortion of the icosahedra due to theircompressibility anisotropy should result in slight deviations ofthe intericosahedral bonds from the 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. The presence of a sti intrachain bond will not preventthis relaxation because the chain itself is supported by bondsthat lie near the (001) plane, and the stress is absorbed in thiscase by the chain-icosahedron bonds.The anisotropy of boron carbide elastic properties was

investigated on a B5.6C single crystal using resonant ultra-sound spectroscopy by McClellan et al.136 Youngs modulusE was found to be orientation independent when measured onthe (111) plane (basal plane in hexagonal notation), but variedsignicantly when measured on prismatic (parallel to the [111]direction) and pyramidal planes (Fig. 24). The global maxi-mum and minimum Youngs moduli for the B5.6C single crys-tal were found to be Emax = 522 GPa and Emin = 64 GPa,yielding an anisotropy ratio of Emax/Emin = 8.1. The globalmaximum Youngs modulus was found to align with the [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 thebasal plane of the same crystal was found to be 165 GPa and

orientation independent; when measured on pyramidal andprismatic planes, shear modulus varied from the globalminimum of Gmin = 165 GPa to the global maximum ofGmax = 233 GPa (Gmax along the [201] direction), yielding ananisotropy ratio of Gmax/Gmin = 1.4 (Fig. 25).Elastic properties of boron carbide have been shown to

change with carbon content.3 Table IV lists selected literaturedata for elastic moduli and Poissons ratio of polycrystallinesamples with dierent stoichiometries,75,117,120,136138 alongwith the theoretically calculated values of bulk modulus forthe (B12)CBC and (B11C)CBC congurations.

41,45,65,135

Although caution should be exerted when comparing datafor samples of dierent origin, the general trend is that thestiness of boron carbide decreases at lower carbon concen-trations. Compositional variations in Poissons ratio do notfollow this trend and span the range of 0.17 to 0.21, asreported by dierent groups.3,117,136 Some of the earliermechanical tests performed on hot-pressed boron carbidesuggested that Youngs modulus increased with decreasingcarbon concentrations.23,139 Gieske et al. used ultrasonictechniques to measure elastic properties of the samples withvarying stoichiometries and observed a decrease in elasticmoduli with the decrease in carbon concentration.75 One

Table III. Elastic Constants of Boron Carbide

Elastic constant

Cij, GPa

McClellan et al.136 (exp.) Lee et al.135 (calc.)

B5.6C B6.5C B4C

11 542.8 500.4 561.833 534.5 430.2 517.744 164.812 130.6 125.3 123.613 63.5 73.9 69.614 7.7 17.8

Fig. 23. Deformation of boron carbide icosahedra under stressafter Shirai et al.133 The intericosahedral bond (thick solid line) isdeected from the lattice direction [100] by an angle u.

Fig. 24. The orientation dependence of the Youngs modulus forB5.6C single crystal. Reproduced from McClellan et al.,

136 withpermission; 2001 Springer.


particularity of Gieskes data is the observed change in slopein the Youngs modulus versus at.% C dependence at carbonconcentrations of ~13 at.%, corresponding to the B6.5C stoi-chiometry. Shear and bulk moduli exhibited a similar behav-ior, as shown in Fig. 26. A direct correlation can be drawnbetween these observations and a kink in the carbon depen-dence of the c lattice parameter (Fig. 3), which is believed tobe indicative of the distinct mechanisms for substitution ofboron atoms into the icosahedral and the chain units thattake place at the boron- and the carbon-rich sides of theB6.5C composition.Manghnani et al. investigated the pressure dependence of

the elastic moduli of polycrystalline boron carbide up to2.1 GPa, nding a nearly linear relationship as shown inFig. 27.117 The measured bulk moduli were consistent with

the values obtained by Nelmes et al. in high pressure neutrondiraction studies on boron carbide.120 The pressure depen-dence of boron carbide bulk properties can be understoodfrom the inverted molecular solid concept described above.In contrast to the elastic moduli that are intrinsic proper-

ties of the material and derive from atomic bonding, mechan-ical properties (hardness, strength, fracture toughness, etc.)strongly depend on such external factors as quality and sizeof the sample, size of the grains, porosity, presence of defectsand aws, conditions of loading, etc. This is one of the rea-sons for signicant variations in the reported hardness valuesfor boron carbide. Generally, Knoop hardness is used as areference, with tests under a 200 g loading resulting in avalue of HK200 between 29 and 31 GPa.

1,3,24 Vickers hard-ness of boron carbide is generally ~30% higher, although the

Fig. 25. The orientation dependence of the shear modulus for B5.6Csingle crystal. Reproduced from McClellan et al.,136 with permission;2001 Springer.

Table IV. Compositional Dependence of Elastic Moduli andPoissons Ratio in Boron Carbide

Stoichiometry

at.%

C

Bulk modulus

[GPa]

Youngs

modulus

[GPa]

Shear

modulus

[GPa]

Poissons

ratio

exp. calc. exp. exp. exp.

B4C 20.0 247c

235e

199d

246e

234g

248h

239j

220d

472c

462e

448b

441a

200c

197e

188a

0.18c

0.17e

0.21b

B4.5C 18.2 237c 463c 197c 0.17c

B5.6C 15.2 236c

237f462c

460f197c

195f0.17c

0.18f

B6.5C 13.3 231c 217g

227i446c 189c 0.18c

B7.7C 11.5 178c 352c 150c 0.17c

B9C 10.0 183c

130c319c

348c150c

132c0.21c

0.16c

(a)Schwetz and Grellner137

(b)Murthy138

(c)Gieske et al.75

(d)Nelmes et al.120

(e)Manghnani et al.117

(f)McClellan et al.136

(g)Lee et al.135

(h)Lazzari et al.65

(i)Guo et al.41

(j)Aydin and Simtek45

Fig. 26. The carbon content dependence of elastic moduli of hot-pressed boron carbide. Lines serve as guides to the eye. Data fromGieske et al.75

Fig. 27. Pressure dependence of bulk modulus B, Youngs modulusE, and shear modulus G in hot pressed boron carbide. Lines arelinear ts to the data. Respective pressure coecients are shown inparentheses. Reproduced from Manghnani et al.,117 with permission;2000 Universities Press (India) Limited.


values of VH100 as high as 47 GPa have been reported in thesamples prepared by chemical vapor deposition (CVD) tech-nique.140 In nanoindentation measurements on B4.3C singlecrystals, Berkovich hardness values of 4142 GPa have beenmeasured by dierent groups.114,141 This impressive hardnessranks boron carbide as third overall hardest material known,behind diamond and cubic boron nitride. Several worksreport that boron carbide hardness increases with the carboncontent until the edge of the homogeneity range isreached;26,140,142,143 at carbon concentrations in excess of20%, hardness rapidly falls o due to precipitation of thecarbon phase from the B4C solid solution.

140

Boron carbide is characterized by exure strength valueson the order of 350 MPa.1,3,24 Density of boron carbidevaries with carbon concentration as = 2.422 g/cm3 +0.0048[at.% C], with a commonly reported value of 2.52 g/cm3 corresponding to the B4C stoichiometry.

1 This combina-tion of high strength and low density makes boron carbideone of the most attractive structural materials known. Asexpected of both a ceramic and a strong material, boroncarbide has relatively low fracture toughness. Values of KICfor boron carbide are given at ~1.3 MPam1/2.1,3,144

There is considerable interest in the application of boroncarbide as lightweight armor material due to its exceptionalhardness, outstanding elastic properties and low theoreticaldensity. From the ballistic viewpoint, of particular interest isthe response of boron carbide to shock loading. However,available shock loading data show that the performance ofboron carbide at high velocity, high pressure impact is muchlower than that expected from its superior static mechanicalproperties. The shear strength of boron carbide in theshocked state (Fig. 28) falls o rapidly above the HEL,145,146

indicating premature failure of the material as the shockstress reaches a threshold value of ~20 GPa. This behavior issimilar to the shock response of single crystal Al2O3,

147,148

where the drop in the shear strength has been linked to astress-induced phase transformation, and is markedly dier-ent from the shock response of other armor ceramic materi-als, such as SiC149151 and polycrystalline Al2O3,

147,149,152

which are characterized by the deformation hardening thatcommences immediately above the HEL. Apart from a possi-ble phase transformation, the anomalous decrease in shearstrength of boron carbide beyond the HEL may be related toa catastrophic propagation of microcracks and other micro-

structural defects, leading to materials collapse behind theelastic precursor wave.

V. Stress-Induced Structural Instability

The possibility of a phase transformation in boron carbideunder shock loading has been discussed in the literature to aconsiderable extent. Figure 29 shows the available experi-mental shock compression data for boron carbide of varyingstarting density as reported by dierent authors.146,153158

Grady159,160 identies three distinct regions in the hydrody-namic equation of state of boron carbide, each correspond-ing to the hydrodynamic compression of a particular phase:an ambient phase, a second phase that exists in the pressurerange of 2535 to 4555 GPa, and a third phase beyond 4555 GPa [Fig. 29(a)]. Vogler et al.146 note that a possiblephase transition may correspond to the intercept pointbetween the hydrostatic and the hydrodynamic compressioncurves which occurs at ~40 GPa in boron carbide[Fig. 29(b)]. Mashimo and co-workers discuss three regionsin the Hugoniot compression data: a region of predomi-nantly elastic deformation below the HEL (~20 GPa), aregion of mostly isotropic compression from ~20 to 38 GPa,and a region of isothermal compression that extends beyond38 GPa.158 An onset of a phase transformation in boron car-bide, according to this group, corresponds to a kink in theHugoniot compression curve between the isotropic and theisothermal compression regimes [Fig. 29(c)]. Both Vogleret al.146 and Zhang et al.158 also report that the ambient bulksound velocity in boron carbide is signicantly higher thanthe shock velocity at the intercept pressure, which is consis-tent with the concept of a phase transformation. Anotherpossible piece of evidence for a shock-induced phase changein boron carbide, according to Vogler et al., is a very steepdrop in particle velocity observed during initial unloading inrelease experiments, which could be associated with a reversetransformation that occurs immediately upon unloading.146

All the results discussed above are highly suggestive of aphase transformation in boron carbide under shock loading,albeit not entirely conclusive.The damage mechanism responsible for the failure of

boron carbide under shock loading has been directly assessedby Chen et al.161 High resolution transmission electronmicroscopy (HR TEM) analysis of boron carbide ballistictargets subjected to supercritical impact velocities and pres-sures in excess of 2023 GPa revealed the formation of 23 nm wide intragranular amorphous bands that occurredparallel to specic crystallographic planes and contiguouswith the apparent cleaved fracture surfaces (Fig. 30). At sub-critical impacts, the amorphous bands were never observed;instead, a relatively high density of stacking faults and mi-crotwins suggested plastic deformation of the material undershock loading.161

Stress-induced structural transformation of boron carbidehas been reported in static indentation,114,141,162 dynamicindentation,163,164 and scratching experiments.162,165 Fig. 31shows an example of HR TEM observations of large amor-phized zones formed within the indentation contact area andin the scratch debris in B4.3C single crystal.

162 Within theamorphous zone, nanosized grains of crystalline materialwith retained orientation are present, which could indicatehighly anisotropic deformation of boron carbide under stress.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.162 Electron energy loss spectroscopy (EELS) observa-tions indicate that the amorphous structure such as theboxed area 2 in Fig. 31(b) shows a dierent carbon K edgecompared to the crystalline lattice. The appearance of anenhanced p* peak in the carbon K edge implies sp2 bonding,i.e., carbon double bonding in the material. Unlike the car-bon edge, the core-loss edge of boron shows little fundamen-

Fig. 28. Shear strength of boron carbide in the shocked state,estimated from reshock and release experiments. Line serves as aguide to the eye. Reproduced from Vogler et al.,146 with permission;2004 American Institute of Physics.


tal changes.162 Therefore, it is inferred that the boron atomsretain their chemical state, while the chemical state of carbonis partially modied during indentation.These observations are corroborated by extensive Raman

spectroscopy data collected on boron carbide samples sub-jected to high stresses associated with various types of con-tact-loading situations.114,141,162,163,165 Indication of thestructural changes is evidenced by the appearance of high-frequency bands at 1330, 1520, and 1810 cm1 in the Ramanspectra of indented boron carbide (Fig. 32). The alterationsof the Raman spectra are independent on the quality of thestarting material: identical bands are observed in the single

crystals and in the polycrystalline samples after indentationat comparable loads [Figs. 32(b) and (e)]. Also shown inFig. 32(d) is the Raman spectrum of a carbonaceous inclu-sion in polycrystalline boron carbide; such inclusions arecommon in hot-pressed samples and are not to be confusedwith the Raman features of the transformed amorphousboron carbide.Spectral position of the 1330 and 1520 cm1 bands, as

well as the dispersive character of the 1330 cm1 band(Fig. 33), imply the correlation of these bands with, respec-tively, the D and the G bands of amorphous/graphitic car-bon. However, this explanation may be in conict with the

Fig. 30. (a) Boron carbide ballistic target that comminuted during impact and (b) an HR TEM image of a fragment produced by a ballistic testat impact pressure of 23.3 GPa. The lattice images on either side of the band in (b) correspond to the 101 direction of crystalline boron carbide,and the loss of lattice fringes in the band indicates localized amorphization. Reproduced from Chen et al.,161 with permission; 2003 TheAmerican Association for the Advancement of Science.

Fig. 29. Shock compression data on boron carbide as reported by Wilkins,153 McQueen et al.,154 Pavlovskii,155 Gust and Royce,156 Grady,157

Vogler et al.,146 and Zhang et al.158 (symbols) and selected model representations accounting for phase transformations (lines). (a) Gradysmodel:160 dash lines, hydrodynamic compression curves for phase I (below 2535 GPa), phase II (2535 GPa to 4555 GPa), and phase III(beyond 4555 GPa); solid line, a composite hydrodynamic compression curve. (b) Model of Vogler et al.146: dash line, extrapolation ofhydrostatic compression data of Manghnani et al.117; solid line, mean pressure from reshock and release experiments.146 (c) Model of Zhanget al.158: dash line, isothermal compression curve; dot line, isotropic compression curve; solid line, Hugoniot compression curve. Suggested phasetransition (PT) points and the Hugoniot elastic limit (HEL) for boron carbide are indicated by arrows.


following observations: (i) the intensity of the D band of dis-ordered carbon increases with the increasing excitation wave-length,166 while the band at ~1330 cm1 does not show suchdependence;114 (ii); the G band is a prominent band in allcarbon structures involving sp2 bonding167 and the D/Gintensity ratio in disordered/amorphous carbon never exceeds2.5,128 whereas the intensities ratio for the bands at ~1330and ~1520 cm1 varies in the range of 45 at room tempera-

Fig. 31. Plain view TEM micrographs of (a) a 100 mN Berkovich indent and (b) scratch debris in single crystal B4.3C. (c,d) Magnied highresolution lattice images of the boxed areas in (a,b) showing the presence of amorphous material. Reproduced from Ge et al.,162 with permission;2004 Elsevier.

Fig. 33. Dependence of the most prominent band in the Ramanspectra of indented single crystal B4.3C (squares) on laser excitationenergy in comparison with a similar dependence of the D band ofdisordered carbon (circles, data from Pocsik et al.166). Lines arelinear ts to the data. Reproduced from Domnich et al.,114 withpermission; 2002 American Institute of Physics.

Fig. 32. Raman spectra of (a) pristine and (b) indented singlecrystal B4.3C, and (c) pristine and (e) indented polycrystalline hot-pressed boron carbide. Raman spectrum of a graphitic inclusion inpolycrystalline boron carbide is shown in (d).


ture;114,141 and (iii) the position of the band at ~1520 cm1

(Fig. 32) is strongly downshifted compared to the G band ofgraphite.167 It is also important to note that the Raman bandat ~1520 cm1 that appears in the deformed material is notnecessarily related to the 1570 cm1 band in the Ramanspectra of pristine boron carbide [Fig. 32(a)], which has beenattributed in the literature to the presence of carbonaceousinclusions in boron carbide samples, or, alternatively, to thevibrations of the CBB chains.60,116

Changes in the Raman spectra indicative of formation ofthe amorphous material are also observed for the samplessubjected to dynamic loading, ranging from scratching[Fig. 34(a)] to ballistic impact [Figs. 34(c) and (d)]. Ge et al.noted that annealing of the scratch debris with the laserbeam leads to appearance of the G band in the Raman spec-trum of amorphous boron carbide [Fig. 34(b)], implyinggraphitization of the transformed material.162 Eect of tem-perature on the Raman features of amorphous boron carbidewas systematically studied by Yan et al.141 While cryogenictemperatures were found to have no eect on the Ramanspectra, the main features of the amorphous boron carbide(bands at 1330, 1520, and 1810 cm1) were graduallydecreasing under heating until their nal disappearance at400C500C, as shown in Fig. 35. This was accompanied bya gradual increase in the intensity of the G band at1586 cm1. Yan et al. argued that the stress-induced amor-phization of boron carbide could be mainly accomplishedthrough the structural change of the CBC chains, with thesmall amount of boron in the chains residing in the aromaticrings by substituting carbon, and the (B11C) icosahedra pre-serving their structure. Further, this group associated thequalitative changes that occurred in the Raman spectraaround ~500C with the rapid coagulation of the small sp2

bonded carbon clusters that had presumably formed duringroom-temperature indentation, and formation of larger-sizecarbon domains.141

However, this structural model for amorphous boron car-bide resides on an assumption that the 1330 and 1520 cm1

bands are identical to the D and the G bands of carbon; thisis not necessarily true for the reasons discussed above. As anadditional argument against this assumption, deconvolutionof the high frequency bands in the Raman spectra in Fig. 35shows that the intensity of the 1520 cm1 feature in the spec-trum of amorphous boron carbide decreases independentlyof the graphitic G band that appears at 1586 cm1 at ele-vated temperatures; in the temperature range of 300C450C, both these bands are present in the spectra, indicatingtheir dierent origins. Generally, the Raman spectra ofamorphous boron carbide and amorphous/graphitic carbonare qualitatively dierent in terms of band frequencies, bandwidths, and relative band intensities, as evidenced from adirect comparison of the Raman spectra in Figs. 32(d) and(e). A mere appearance of graphitic D and/or G bands instressed boron carbide should not be necessarily interpretedas a sign of amorphization; rather, the presence of a smallerband at 1810 cm1 must be used as a reliable indication of acompleted structural transformation.Interestingly, the Raman spectra of amorphous boron car-

bide lms prepared by magnetron sputtering168,169 exhibitdistinctly dierent features and resemble a broadened spec-trum of crystalline boron carbide with the major band cen-tered around 1100 cm1 (Fig. 36). In addition, the bands at~1330 cm1 and ~1520 cm1 are never observed in amor-phous boron carbide lms.169 This suggests the possibility foran existence of two distinct forms of amorphous boron car-bide consisting of a distorted icosahedral network and dier-ent arrangements of carbon and boron atoms that link theicosahedra together.This problem was addressed in a theoretical study of

amorphous boron carbide by Ivashchenko et al.44 In thiswork, two forms of amorphous BC networks, one based ona 120-atom rhombohedral B4C cell (a-120), and the otherone based on a 135-atom hypothetical cubic B4C cell (a-135),were simulated by means of molecular dynamic (MD) meth-ods. The a-120 conguration was found to consist of disor-dered icosahedra composed mainly of boron atomsconnected by topologically disordered BC and CC net-works. The structure of the a-135 conguration was found tobe similar to the one of a-120, but it was lacking the eight-fold coordinated atoms, implying a less random amorphous

Fig. 34. Raman spectra of hot-pressed boron carbide subjected to(a,b) scratching162 and (c,d) ballistic impact. Scratch debrisconsistently shows evidence of amorphous material (a), and is foundto graphitize upon annealing (b). Most analyzed locations on theballistic fragment surfaces yield spectra similar to (c); however,formation of amorphous material can also be observed, as evidencedby the Raman spectrum in (d).

Fig. 35. Eect of annealing on the evolution of the Raman spectraof a hardness indent in single crystal B4.3C. The spectra wereacquired at temperatures ranging from 25C (ambient) to 600C. Anambient-temperature spectrum of a pristine B4.3C surface is shownfor reference. Reproduced from Yan et al.,141 with permission;2006 American Institute of Physics.


network. The simulated phonon densities of states for thetwo amorphous networks are compared with the experimen-tal Raman spectra obtained on indented boron carbide crys-tals and those measured on amorphous boron carbide lmsin Fig. 37. In the calculated PDOS, the band at 1800 cm1 ismissing in both the a-120 and the a-135 congurations. Forthe a-120 network, the two PDOS bands at 1290 and1450 cm1 resemble the two prominent features in theRaman spectra of indented boron carbide [Fig. 37(a)], andthe band at 750 cm1 correlates with the increased density ofthe icosahedral modes in the PDOS calculated for the crys-talline (B12)CBC form, as shown in Fig. 16(b). In contrast,the PDOS of the a-135 network shows a general correlationwith the broad features in the Raman spectra of amorphousboron carbide lms [Fig. 37(a)]. These results provide basisfor a thesis that the stress-induced transformation of boroncarbide proceeds via destruction of the linear chains, forma-tion of topologically disordered BC and CC networks fromthe chain C and B atoms, distortion of the icosahedral (B12)and (B11C) units, and rearrangement of these structural ele-ments into a randomly interconnected amorphous network.

The driving force for such structural collapse is still to beestablished. Yan et al. addressed this issue from the experi-mental position.118 A complete set of experiments usingquasi-hydrostatic and quasi-uniaxial compression up to50 GPa, followed by depressurization to ambient pressure,was conducted on a boron carbide single crystal, and in situRaman spectroscopy was engaged to detect possible highpressure phase transformations. It was observed that underhydrostatic compression, the material remained a perfect sin-gle crystal without visible surface relief and cracking; no evi-dence of amorphization was detected in the samples loadedhydrostatically after pressure release. The results were signi-cantly dierent when the single crystal boron carbide wassubjected to uniaxial loading and unloading. In this case, thedepressurized samples were found to be broken into a num-ber of smaller fragments; evident cracks, surface relief, andshear bands could be observed optically; and the formationof amorphous material was evidenced by in situ Raman spec-troscopy at 1316 GPa during unloading of the samples thathad been previously loaded to pressures in excess of 25 GPa.Further, Raman spectroscopy analysis of the fully depressur-ized samples revealed spectral features typical for stressamorphized material as observed in indentation and scratch-ing experiments, i.e., the bands at ~1330, ~1520, and~1820 cm1. These results emphasized the importance ofnonhydrostatic stresses for the stability of boron carbide athigh pressure.Theoretical simulations by the same group indicated a

drastic volume change of the hypothetical (B11C)CBC unit

Fig. 37. Comparison of the calculated PDOS of the amorphousa-120 and a-135 structures44 with the experimental Raman spectra ofthe indented boron carbide (this work) and an amorphous boroncarbide lm prepared by magnetron sputtering.169

Fig. 36. Raman spectra of boron carbide lms deposited bymagnetron sputtering at temperatures of 700C, 900C, and 970C.168

Crystallization of the lms occurs at temperatures above 900C.

Fig. 38. Ab initio simulation of the stabilization of B11C(CBC)under hydrostatic and uniaxial compression. (a) Compressed volumeversus pressure. The square data represent the volume change withhydrostatic pressure, and the circle data correspond to the volumechange with uniaxial stress along the CBC atomic chain. (b) Atomiccongurations of the B4C unit cell at various pressurescorresponding to data points in (a). Reproduced from Yan et al.,118

with permission; 2009 American Physical Society.


cell at the destabilization pressure of 19 GPa (consistentwith the HEL of 1520 GPa) due to the bending of theCBC chain (Fig. 38).118 At higher pressures, the chaindeformation was found to continue until the (B11C)CBClattice was irreversibly distorted. It was suggested that thecentral boron atom of the chain could bond with the neigh-boring atoms in the icosahedra forming a higher energystructure. The release of this energy during depressurizationwas proposed to be responsible for the collapse of theboron carbide structure and the formation of localizedamorphized bands.118

Theoretical investigation of phase stability in boron car-bide polytypes at elevated pressures was conducted byFanchini et al.40 The free energies for several boron carbidecongurations were calculated under increasing hydrostaticpressure at room temperature. The results indicated that theenergetic barrier for pressure-induced amorphization ofboron carbide was by far the lowest for the hypothetical(B12)CCC polytype, which was found to be

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