IOP PUBLISHING SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS Sci. Technol. Adv. Mater. 11 (2010) 023001 (27pp) doi:10.1088/1468-6996/11/2/023001 TOPICAL REVIEW Raman effect in icosahedral boron-rich solids Helmut Werheit1, Volodymyr Filipov2, Udo Kuhlmann1,8, Ulrich Schwarz3, Marc Armbr��ster3, Andreas Leithe-Jasper3, Takaho Tanaka4, Iwami Higashi5, Torsten Lundstr��m6, Vladimir N Gurin7 and Maria M Korsukova7 1 Institute of Physics, University Duisburg-Essen, D-47048 Duisburg, Germany 2 I.N. Frantsevich Institute for Problems of Materials Science of NASU, 03142 Kiev, Ukraine 3 Max-Plank-Institute for Chemical Physics of Solids, D-01187 Dresden, Germany 4 National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 5 Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-01, Japan 6 Institte of Chemistry, Uppsala University, S-75121 Uppsala, Sweden 7 Ioffe Physical���Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia E-mail: helmut.werheit@uni-duisburg-essen.de and helmut.werheit@koeln.de Received 30 November 2009 Accepted for publication 30 March 2010 Published 1 June 2010 Online at stacks.iop.org/STAM/11/023001 Abstract We present Raman spectra of numerous icosahedral boron-rich solids having the structure of ��-rhombohedral, ��-rhombohedral, ��-tetragonal, ��-tetragonal, YB66, orthorhombic or amorphous boron. The spectra were newly measured and, in some cases, compared with reported data and discussed. We emphasize the importance of a high signal-to-noise ratio in the Raman spectra for detecting weak effects evoked by the modification of compounds, accommodation of interstitial atoms and other structural defects. Vibrations of the icosahedra, occurring in all the spectra, are interpreted using the description of modes in ��-rhombohedral boron by Beckel et al. The Raman spectrum of boron carbide is largely clarified. Relative intra- and inter-icosahedral bonding forces are estimated for the different structural groups and for vanadium-doped ��-rhombohedral boron. The validity of Badger���s rule is demonstrated for the force constants of inter-icosahedral B���B bonds, whereas the agreement is less satisfactory for the intra-icosahedral B���B bonds. Keywords: Raman scattering, icosahedral boron-rich solids, ��-rhombohedral boron, ��-rhombohedral boron, ��-tetragonal boron, ��-tetragonal boron, orthorhombic boron structures, YB66, amorphous boron 1. Introduction Raman spectroscopy is a sensitive tool for investigating the phonon spectra of crystalline solids and their modification due to changes in the chemical composition or presence of structural imperfections. This is particularly important in 8 Present address: Pirelli Deutschland GmbH, D-64747 Breuberg. the case of icosahedral boron-rich solids containing different types of such structural imperfections. i. Natural boron consists of 18.83% isotope 10B and 81.17% 11B, which have a considerable mass difference of 8.7%. Usually, these isotopes are assumed to be statistically distributed in the lattice, but a preferred occupation of specific sites might be conceivable as well. 1468-6996/10/023001+27$30.00 1 �� 2010 National Institute for Materials Science Printed in the UK

Sci. Technol. Adv. Mater. 11 (2010) 023001 Topical Review ii. The B12 icosahedra are slightly distorted owing to the Jahn���Teller effect, thus reducing their symmetry from Ih to D3d in the rhombohedral structures. iii. Most of these atomic arrangements exhibit intrinsic defects of unoccupied or partially occupied regular atomic sites. iv. Carbon has a high affinity to boron. Therefore, carbon impurities are usually found in boron and boron compounds. In the icosahedra, carbon atoms preferably occupy polar sites. Therefore, they induce a specific distortion of the icosahedra, as revealed by the anisotropic changes in the structure of ��-rhombohedral boron and boron carbide [1, 2]. Structural distortions are important for the electronic properties of icosahedral boron-rich solids. In some cases, they are even responsible for the semiconducting properties of these materials, in contrast to the metallic behavior of idealized structures predicted by theoretical calculations [3, 4]. Deviations from the ideal crystal structures lift the symmetry selection rules and induce the Raman activity of modes that are normally inactive. Attributing such Raman signals to vibrations of specific atoms or atomic arrangements may yield information on specific structural defects. However, defect-induced changes in the Raman spectra are relatively weak. Therefore, in this paper, we specifically emphasize the importance of a high signal-to-noise ratio for studying structural defects by Raman spectroscopy. The periodicity of crystals is abruptly terminated at the surface. This modifies the bulk properties within a distorted layer of rearranged atoms. Therefore, when investigating bulk phonons, it must be ascertained that Raman scattering within this layer does not essentially contribute to the measured spectra. Beilby layers or adsorbed layers on the surface can aggravate this problem. As shown below, Raman spectra of boron carbide can be affected accordingly. In this review, we present, compare and discuss the Raman spectra of numerous icosahedral boron-rich structures belonging to various structure groups. Such comparison requires spectra obtained under the same experimental conditions, including equipment, sample preparation, spectral resolution, excitation energy, etc. Therefore, most spectra shown in this review were newly reproduced often with improved spectral resolution and signal-to-noise ratio. A few Raman spectra of icosahedral boron-rich solids are taken from literature. 2. Experimental details In an earlier Raman study of icosahedral boron-rich compounds, we have carefully tested different methods of sample preparation [5]. Accordingly, the Raman spectra in this study, as far as measured using the Jobin���Yvon Labram spectrometer, were obtained on freshly cleaved samples, ensuring clean and undamaged surfaces. However, the crystallographic orientation was not controlled and the relative intensity of Raman peaks can be slightly affected by polarization effects. Most spectra were recorded under ambient conditions, using a Jobin���Yvon Labram spectrometer and the blue line of an Ar ion laser (487.987 nm, 2.546 eV). The spectral resolution was approximately 1.5 cm-1 and the excitation power was about 15 mW. Some spectra were acquired using a Bruker Fourier-transform (FT) Raman spectrometer with Nd:YAG laser excitation (1064 nm, 1.1654 eV, power 1.5 W) at a spectral resolution of approximately 2 cm-1. Both these acquisition methods can induce unwanted ancillary effects. The excitation energy of the Ar ion laser (2.546 eV) considerably exceeds the band gap energy in most icosahedral boron-rich solids. Because of the high absorption coefficient at 2.546 eV, the penetration depth of the exciting light can become so small that a narrow region below the surface of the sample is preferably excited. This experimental condition caused controversy in the past discussions of the Raman spectra of boron carbide. The problem of Raman excitation in the surface region in materials like boron carbide, where the interband transitions determine the penetration depth of the exciting laser light, can be avoided using a sufficiently low excitation energy, like that of the Nd:YAG laser in FT-Raman spectroscopy. This was demonstrated by Werheit et al [6] by applying different excitation energies to the very same sample and was further elaborated in a recent work [7]. A disadvantage of FT-Raman spectroscopy is the high excitation intensity of the Nd:YAG laser, which can raise the sample temperature. This might affect the spectra in such materials as ��-rhombohedral boron, where phase transitions occur near room temperature. The considerably different excitation energies and laser intensities in both methods may result in different interactions with electrons and electronic states. Therefore electron-resonance effects and luminescence radiation cannot be excluded. In this study, background radiation in the spectra was approximated by a straight line and subtracted from the measured spectra. 3. Results 3.1. Icosahedra The high symmetry of the regular icosahedron shown in figure 1 is characterized by inversion and twofold, threefold and fivefold rotation axes. The fivefold rotation axis is incompatible with translation symmetry, and therefore, icosahedra are distorted in crystal structures. Franz and Werheit [8] demonstrated that the reason for this distortion is the Jahn���Teller effect. The latter reduces the icosahedral group Ih to the subgroup D3d, which corresponds to the space group R ��m. 3 This naturally explains the existence of ��-rhombohedral and ��-rhombohedral boron structure groups with the space group R3m. In those structures, one of the three-fold rotation axes of the icosahedron coincides with the crystallographic c-axis. The intra-icosahedral B���B distances summarized in table 1 suggest that the icosahedra are also distorted in other 2

Sci. Technol. Adv. Mater. 11 (2010) 023001 Topical Review Table 1. Intra- and inter-icosahedral B���B distances in the icosahedra of various icosahedral boron-rich solids. Intra- and inter-icosahedral B���B distances (��) Bond �� -rh. B Boron B 6 As �� -rh. B �� -B 28 Amorphous LiAlB 14 �� -AlB 12 �� -AlB 12 YB 66 YB 66 [ 26 ] carbide [ 11 ] [ 12 ]/[ 13 ] [ 14 , 15 ]/ B [ 80 ] [ 20 ] [ 21 ] central outer icos. [ 27 ] [ 16 ] [ 17 ��� 19 ] icos. [ 22 ] [ 22 ] Polar triangle 1.751 1.814 1.81 1.782(4) 1.75���1.95/1.80 1.62���1.91 1.8002(5) 1.736���1.863 1.735���1.864 1.726 1.808 Equatorial 1.784 1.767 1.750(3) 1.8640(5) Polar���equatorial 1.807 1.808 1.760(3) 1.8479(5) Polar���equatorial 1.800 1.795 1.756(4) 1.7842(5) Inter-icosahedral 1.671 1.721 1.77 1.678/1.72 1.64 1 . 678 a 1.7237(5)���1.8474(5) 1.686���1.813 1.649���1.843 1.624, 1.725, 1.823 a The inter-icosahedral bond length is not explicitly given in [ 17 , 18 ]. However, the close similarity of the diffraction pattern with that of �� -rhombohedral boron justifies using the value of this crystalline solid, in particular because the inter-icosahedral bond is preferably radially oriented along the fivefold rotation axis of the icosahedron. This value is used for model calculations in [ 19 ] as well. Figure 1. Icosahedron twofold, threefold and fivefold rotation axes are indicated. groups of icosahedral boron-rich structures. The determining role of the Jahn���Teller effect and other structural distortions in the electronic properties of these solids was shown by Schmechel and Werheit [9] who considered the splitting of electronic states calculated by Fujimori and Kimura [10]. The electron density distributions in the icosahedra of ��-rhombohedral boron and boron carbide are very similar as demonstrated by Hosoi et al [23]. Therefore, bonds and vibration spectra are expected to be closely related (see figure 7 and the text below). Vibrations of the isolated regular icosahedron were calculated by Beckel and Vaughan [24]. However, they can be considerably altered in crystal fields. For ��-rhombohedral boron, the simplest icosahedral boron-rich solid, the phonon frequencies were determined by Beckel et al [29], and in better agreement with the experimental Raman spectra reported by Vast et al [35]. As parts of the Raman spectra of all icosahedral boron-rich solids are significantly determined by vibrations of the icosahedra, the variation of the bond distances summarized in table 1 will be used for the spectral analysis below. 3.2. ��-rhombohedral boron structure group 3.2.1. ��-rhombohedral boron. ��-rhombohedral boron has the simplest crystal structure among icosahedral boron-rich solids [25]. One slightly distorted B12 icosahedron is positioned at each of the eight rhombohedral vertices of the rhombohedral unit cell (figure 2). The associated lattice parameters are 5.0643 �� and �� = 58.0962���, or, in hexagonal description, a = 4.9179 and c = 12.5805 �� [26, 27]. There are two independent atomic positions: six equivalent polar atoms in the idealized structure (black circles in figure 2) form the upper and lower triangles of the icosahedron. In between, there are six equatorial atoms (bright circles in figure 2) arranged in a puckered hexagon. For B���B distances, see table 1. According to group theory, 10 Raman-active modes (4 A1g singlets and 6 Eg doublets) are expected for ��-rhombohedral boron with D3d point symmetry [28, 29]. In total, 30 nonzero modes with 20 distinct crystal vibration frequencies (barring accidental degeneracy) are predicted [29]. 3

Sci. Technol. Adv. Mater. 11 (2010) 023001 Topical Review Figure 2. ��-rhombohedral boron���idealized unit cell with one icosahedron at each vertex. The first experimental Raman spectrum of ��-rhombohedral boron, showing 12 peaks, was published by Richter and Ploog [30] and was subsequently confirmed by other authors [31���35]. Polarization-resolved measurements [33] provided information on the symmetry of the observed modes. FT-Raman spectra were also obtained [34]. Initial theoretical simulations of the Raman spectrum of ��-rhombohedral boron [29, 36] were not satisfactory. Later ab initio lattice dynamics calculations by Vast et al [35] yielded very good agreement between mode frequencies and measured Raman spectrum and an unambiguous assignment of all significant observed features. Finally, Shirai and Katayama-Yoshida [37] studied the phonon spectrum of ��-rhombohedral boron from the viewpoint of anharmonic effects. They calculated the phonon spectrum by evaluating the anharmonic force constants of individual bonds obtained from the pressure dependence of phonon frequencies. For the phonon dispersion curves, see [37]. In table 2, the frequencies of the experimentally determined Raman modes (figure 3) are compared with the theoretical results obtained by ab-initio calculation [35] and by preferably considering the anharmonicity of vibrations [37]. For most phonon modes, the agreement with the experimental data is slightly better for ab-initio results than for anharmonic calculations. Despite these theoretical improvements, the initial calculations of Beckel et al [29] remain important because they contain a detailed description of the specific movements of atoms and atomic groups in the different modes (see below). Figure 3 shows the high-resolution (���1.5 cm-1) Raman spectrum of ��-rhombohedral boron measured in this study. Long data accumulation resulted in a high signal-to-noise ratio and enabled the detection of weak spectral features. As a result, several weak Raman bands were found in addition to the well-known modes. Moreover, the second-order Raman spectrum of ��-rhombohedral boron was not reported before, to the best of our knowledge. The anti-Stokes spectrum measured for Raman shifts below 1000 cm-1 confirms the Stokes Raman peaks in this spectral range. Assuming equivalent bonding of isotopes, the isotope-dependent shift of vibration modes corresponds to m(10 B)/m(11 B) = 0.96. In particular, this holds for individual atoms. For larger atomic clusters, the mass difference of vibrating groups of atoms is reduced by the statistical distribution of isotopes. This effect is observed for the 527 cm-1 mode, which corresponds to the rotation of the rigid B12 icosahedra [29], and it explains the narrow width of this line. A detailed theoretical investigation of this problem by Shirai and Katayama-Yoshida [37, 38], ignoring the effect of isotope distribution, showed that among many factors, including anharmonicities, temperature is most important. As an essential new aspect concerning lattice dynamics of boron-rich structures, it was stated that the anharmonicities of individual bonding angles are rather large. 10B/11B isotope effects in form of split modes are mostly expected at high frequencies, which are associated with small assemblies of moving atoms. Figure 4 shows the highest-frequency region of the one-phonon Raman spectrum. Instead of the two Raman-active phonons, as predicted theoretically [35], four strong peaks are clearly discernable (Nos 13���16 in table 2) and probably two very weak ones at 1094 and 1238 cm-1. Polarization-resolved measurements by Tallant et al [33] assigned one of the main peaks to an Eg mode (doublet) and three others to A1g (singlet) symmetry. Beckel et al [29] described the movement of atoms in these modes as follows. The Eg mode (No. 13) is a mixture of two vibration modes of the B12 cluster, having frequencies ��1 and ��2. For ��1, all six external two-center bonds of the icosahedra are compressed simultaneously. For ��2 (at a given moment) two of the six are compressed, two are stretched and two are unstrained. The effect of ��1 is prevalent. The A1g modes predominantly originate from the radial movement of the polar atoms belonging to the triangles of the icosahedra, which induce double stress and double compression of the strong two-center bonds between the icosahedra. This movement is mixed with an intra-icosahedral vibration where the polar triangles move in opposite vertical directions, while the puckered hexagon breathes through a horizontal atomic displacement. Accordingly, the vertical movement of the polar triangle atoms is amplified and the motion of hexagon atoms is reduced. Therefore, there is little internal hexagon strain and external three-center bond strain in the vibration. According to Beckel���s description, the triplets of polar atoms are essentially involved in the A1g mode (No. 15, and 16). The radial movement of triangle atoms means double stretch and double compression of the strongest bonds, which are the inter-icosahedral two-centered bonds. Hence, triplets of boron atoms must be considered for explaining a possible isotope-dependent frequency shift of this mode. The frequency ratio of the peak maximum at 1187 cm-1 and the 1201 cm-1 shoulder, ��1/��2 = 0.988, agrees well with the value [(2m(10B) + m(11B))/(m(10B) + 2m(11B))]1/2 = 0.986. This isotope distribution has a relatively high probability in comparison with that of a 10B triplet vibrating against a 11B triplet. Nevertheless, the shift to the very weak maximum at 1238 cm-1 with ��1/��2 = 0.9588 agrees well with the 4

Sci. Technol. Adv. Mater. 11 (2010) 023001 Topical Review Table 2. Frequencies and halfwidths of Raman peaks in ��-rhombohedral boron (in cm-1): new results compared with theoretical and experimental results of Vast et al [35] and theoretical calculations by Shirai et al [37]. Raman frequencies of B4.3C boron carbide are partly matched to ��-rhombohedral boron frequencies, and are partly specific to B4.3C. ��-rhombohedral boron B4.3C boron carbide This work Vast et al [35]: Shirai et al [37] Matched Specific Halfw. Remark Theory Exp. Halfw. Theory Halfwidth to ��-rh. B for B4.3C 1st order Raman lines 1 494 Very weak 270 2 527 2.9 Eg 529 525 0.8 Eg 497 0.1% 0.5 321 3 552 Very weak 417 4 589 605 Eg 608 586 Eg 572 0.62% 3.5 477 5 694 408 A1g 708 692 5 A1g 710 0.9% 6.4 529 6 713 5.9 Eg 729 708 Eg 743 0.85% 6.3 575 7 750 652 8 778 7.1 Eg 790 774 7 Eg 818 0.86% 7.0 9 795 10.8 A1g 815 793 11 A1g 759 0.6% 4.6 727 10 873 7.7 Eg 890 870 8 Eg 884 0.89% 7.8 797 11 934 18.8 A1g 947 925 22 A1g 965 1.2% 11.6 864 12 1094 Very weak 13 1125 11.0 Eg 1138 1122 15 Eg 1169 1.2% 14.0 928 14 1160 1001 15 1187 11B A1g 1192 1186 24 A1g 1191 1.7% 20.2 1076 16 1201 10B 17 1238 Very weak 2nd order Raman lines 201 1300 202 1409 203 1464 Shoulder 204 1492 205 1533 206 1582 207 1630 208 1663 209 1710 210 1783 211 1827 212 2262 213 2328 214 2389 value [(3m(10B))/(3m(11B))]1/2 = 0.9592. Raman spectra of isotopically enriched ��-rhombohedral boron should be used to verify the above assignment. However, by anticipating the results for orthorhombic borides presented below, the attribution of the 1187/1201 cm-1 pair to the boron isotopes becomes questionable���they are shifted, but an accordingly separated pair of equally strong bands occurs, which contrasts to the abundance ratio 10B/11B ��� 1/4. While the calculated A1g mode (1192 cm-1) is close to the experimental position (1187 cm-1) there is a larger discrepancy for the Eg mode: 1138 and 1125 cm-1, respectively. The theoretical value 1138 cm-1 is in between the 1125 and 1160 cm-1 peaks. This suggests splitting of the Eg doublet, an assumption which is not supported by the polarization-resolved measurements [33]. Comparison of Raman and absorption spectra in figure 4 brings an alternative interpretation. The Raman peaks at 1201 and 1238 cm-1 coincide with absorption maxima and thus can be attributed to luminescence due to electronic transitions between gap states. The increasing absorption slope can well be fitted to Lucovsky���s theory [39] of deep-level-to-band transitions, yielding 0.126 eV as the ionization energy of the deep level. Further investigation is required for deciding between these interpretations. According to Beckel et al [29], the 934 cm-1 mode (No. 11) involves distortions of the polar triangles as well as of the equatorial hexagon, where two of the six bonds are stretched. The 873 cm-1 line (No. 10) is essentially an isolated icosahedral mode, which mainly stresses the equatorial and the slant bonds of the icosahedron. The strongest peak at 795 cm-1 (No. 9) is attributed to the external three-centered bonds, which are compressed at an instant when two-centered bonds are stressed. Internally, the triangle and vertical bonds are most strained. The 694 cm-1 mode (No. 5) is assumed to be almost unaffected by the crystalline two- or three-centered forces, which explains its weakness. In this mode, the three northern-hemisphere ring atoms move south, and the southern atoms move north. In this movement, the slant bonds are equally and simultaneously stretched. Strain of the three-centered bonds is assumed to be mostly responsible for 5