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First-Principles Study of the Electronic Structure, Optical Properties, and Lattice Dynamics of BC2N Yanlu Li,† Weiliu Fan,*,‡ Honggang Sun,† Xiufeng Cheng,† Pan Li,† Xian Zhao,*,† and Minhua Jiang† State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, China, and School of Chemistry and Chemical Engineering, Shandong UniVersity, Jinan, 250100, China ReceiVed: NoVember 2, 2009; ReVised Manuscript ReceiVed: December 29, 2009
First-principles calculations of the electronic, optical, and lattice dynamic properties of c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N were performed with the density functional theory (DFT) plane-wave pseudopotential method. It is found that the difference in electronic structures and optical properties is arising from the different numbers and species of chemical bonds in the five phases. The vibration analysis shows three main frequency regions arising from different relative movements among the B, C, and N atoms for the five phases. The calculation demonstrates that z-BC2N and t-BC2N have more vibration states and own much higher vibration frequencies. The experimental Raman peak, well reproduced in z-BC2N and t-BC2N, has been assigned to be the serious relative translational movements of C atoms (C1 and C3 for z-BC2N; C2 and C3 for t-BC2N) along the z direction with the other atoms moving slightly. Though the five phases may not display excellent heat capacities in room temperature (about 30 J/mol/K), the high Debye temperatures, reaching about 1700 K, may lead to some research and application interests in the thermodynamic aspect. 1. Introduction Recently, ternary boron carbon nitrogen (B-C-N) compounds have received special attention since they may be a new kind of superhard material with extremely high hardness comparable with diamond1–3 and have great thermal and chemical stability as cubic boron nitride (c-BN).4 Moreover, B-C-N compounds are expected to behave as electronic and optoelectronic devices because their band gaps are thought to be intermediate between semimetallic graphite and insulating hexagonal-BN (h-BN) and can be determined by the atomic composition and atomic arrangement.5,6 Besides, owning to the common properties (short bond length and high coordination number, which together also imply a high atomic density and low ionicity), B-C-N systems may exhibit a number of further prominent characteristics, which holds especially for the vibrational and thermal properties.7,8 Among the ternary B-C-N compounds, diamond-like BC2N (c-BC2N) has gained extensive attention. Despite that several allegedcubicBC2Nmaterialshavebeensuccessfullysynthesized,9,10 the crystal structure of BC2N has still not been conclusively determined. So most experimental and theoretical studies were focused on the structural forms and mechanical properties of BC2N. So far, many possible structures have been predicted, e.g., zinc-blende struc-1-7,11 chalcopyrite (cp-) BC2N,12 tetragonal z-BC2N,13 wurtzite (w-) BC2N,14 body-centered BC2N,15 low-density (LD-) BC2N,16 I-BC2N,17 the short period (C2)n(BN)n (111) superlattice,18 and tetragonal (t-) BC2N.19 Among the proposed structures, the z-BC2N phase was considered to be perhaps a more likely phase due to its simulated X-ray diffraction (XRD) spectrum which agreed well with the experi* To whom all correspondence should be addressed. Tel.: 86-53188366330. Fax: 86-531-88364864. E-mail:
[email protected],
[email protected]. † State Key Laboratory of Crystal Materials. ‡ School of Chemistry and Chemical Engineering.
ment data,13 and the t-BC2N phase was predicted to be another candidate because the simulated XRD and Raman patterns were in excellent agreement with the experimental results.19 However, rarely studies about the optical properties have been reported, although they are of great importance in giving insight into the fundamental physical properties and potential applications. In addition, the knowledge of lattice dynamic properties plays a key role in understanding the structural, phase transition, infrared (IR)/Raman vibration, and thermodynamic properties and the phenomena related to the electron-phonon interaction. Although some IR and Raman investigations of BC2N have been involved,20,21 theoretical studies of thermodynamic properties, such as heat capacity and Debye temperature, have rarely been referenced.21 Systemic studies on lattice dynamics and thermodynamics of BC2N are still of great importance and in demand. In this paper, we pay attention to the more energetically favorable structure of zinc-blende BC2N (struc-1, labeled as c-BC2N), wurtzite BC2N (w3-BC2N, labeled as w-BC2N), cpBC2N, z-BC2N, and t-BC2N. First-principles calculations of the structure and electronic, optical, and lattice dynamic properties are presented. Structural and electronic properties were discussed to provide a sufficient explanation to the difference of the optical and lattice dynamic properties for BC2N polymorphs. Besides, via lattice dynamic calculations, we aim at providing a compelling assignment of the experimental Raman and IR peaks to specific phonons which would allow one to identify the vibrational signature of the different structural units in the crystals. We also discussed the thermodynamic properties, such as constant volume heat capacity and Debye temperature. The remainder of this paper is organized as follows. A brief description of our computational method is given in Section 2. The results and discussion are examined in Section 3, followed by a summary of our conclusions in Section 4.
10.1021/jp9104739 2010 American Chemical Society Published on Web 01/22/2010
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Figure 1. Crystal structures of BC2N. (a) c-BC2N, (b) w-BC2N, (c) cp-BC2N, (d) z-BC2N, and (e) t-BC2N. Boron, carbon, and nitrogen are depicted in pink, gray, and blue, respectively.
TABLE 1: Structural Parameters of BC2N Polymorphs structure
c-BC2N
symmetry
w-BC2N
Pmm2 present
calcd12
cp-BC2N I4j2d
P3m1 exptl30
present
calcd14
present
calcd12
z-BC2N P4j2m exptl9
present
calcd13
t-BC2N P4j21m present
calcd19
a (Å) 2.535 2.536 3.602 2.501 2.501 3.614 3.613 3.642 3.562 3.565 3.576 3.579 b (Å) 2.507 2.510 2.501 2.501 3.614 3.613 3.562 3.565 3.576 3.579 c (Å) 3.604 3.605 4.206 4.205 7.146 7.147 7.163 7.168 7.110 7.116 R (°) 90 90 90 90 90 90 90 90 90 90 β (°) 90 90 90 90 90 90 90 90 90 90 γ (°) 90 90 120 120 90 90 90 90 90 90 V (Å3) 22.90 22.95 22.78 22.78 93.33 93.30 90.87 91.10 90.91 91.15 F (g/cm3) 3.541 3.541 3.561 3.561 3.476 3.478 3.570 3.561 3.568 B0 (GPa) 398.5 383.2 355 407.0 407.5 367.0 364.7 282 404.1 402.7 404.3 422.1 Et (eV/atom) -165.14 -165.1414 -165.38 -165.38 -164.72 -164.7214 -165.34 -165.80 -165.35 -165.80
2. Computational Details The first-principles density functional theory (DFT) calculations22 were employed with the Cambridge Sequential Total Energy Package (CASTEP) code,23 using norm-conserving pseudopotentials24 and a plane-wave expansion of the wave functions. We used the local-density approximation (LDA) with the Ceperley-Alder25 form to describe the exchange and correlation potential. The Monkhorst-Pack scheme k-point sampling was used for integration over the first Brillouin zone.26 The Kohn-Sham energy function was directly minimized via the conjugate-gradient method.22 The convergence criteria for structure optimization and energy calculation were set to ultrafine quality with a kinetic energy cutoff of 770 eV and the k-point meshes of 10 × 10 × 7 for c-BC2N, 12 × 12 × 6 for w-BC2N, 8 × 8 × 10 for cp-BC2N, 7 × 7 × 3 for z-BC2N, and 7 × 7 × 4 for t-BC2N, which cause the tolerance for self-consistent field, energy, maximum force, maximum displacement, and maximum stress to be 5.0 × 10-7 eV/atom, 5.0 × 10-6 eV/atom, 0.01 eV/Å, 5.0 × 10-4 Å, and 0.02 GPa, respectively. For all the equilibrium structures, the Mulliken populations were investigated using a projection of the planewave states onto a linear combination of atomic orbital basis sets,27,28 which is widely used to perform charge transfers and population analysis. The Mulliken overlap populations were integrated by a distance cutoff of 3.5 Å. The phonon frequencies and density of phonon states were calculated from the response to small atomic displacements.29 Infrared spectra are obtained from Born effective charges, dielectric susceptibilities, and phonons at the G point. The relevant formulas for the calculation of the IR spectra are given in Section 3. 3. Results and Discussion 3.1. Geometric Structure and Electronic Properties. The crystal structures of c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and
t-BC2N are shown in Figure 1. The c-BC2N, which is constructed from an eight-atom cubic BN unit cell, is orthorhombic symmetry with the Pmm2 space group after relaxation (as shown in Figure 1a). There are two kinds of nonidentical C atoms, and all the B and N atoms are identical in the unit cell of c-BC2N, forming four types of chemical bond. The w-BC2N, which starts from the four-atom wurtzite BN unit cell, as shown in Figure 1b, has a hexagonal lattice with the P3m1 space group. The number of nonidentical atoms and chemical bonds for w-BC2N is the same as that for c-BC2N. Figure 1c shows the structure of cp-BC2N with the tetragonal symmetry belonging to the space group of I4j2d. In the cp-BC2N structure, all the B, C, and N atoms are identical, so they only form C-N and B-C bonds. The z-BC2N structure (with the 16-atom unit cell) has tetragonal symmetry belonging to the space group of P4j2m (Figure 1d). The t-BC2N phase is a candidate structure by interchanging B and N atoms with each other in the structure frame of z-BC2N, with the same tetragonal symmetry belonging to the P4j21m space group (Figure 1e). There are three kinds of nonidentical C atoms and two kinds of nonidentical N atoms, while all of the B atoms are identical in the unit cell of z-BC2N and t-BC2N. Six kinds of chemical bonds are formed. In Table 1, we list the calculated lattice parameters together with the volume of the unit cell, density, the total energy Et, as well as the bulk modulus B0 of the five phases. Our calculated lattice constants agree well with other theoretical results12–14,19 and are a little smaller than the experimental data,9,30 which indicates that the methods used in our calculations are reliable and reasonable. From Table 1 we can get that w-, z-, and t-BC2N have superiority in total energy and high bulk modulus larger than 400 GPa. The calculated bulk moduli of c-BC2N (398.5 GPa) and cp-BC2N (367.0 GPa) are much higher than the measured ones of 35530 and 282 GPa9 because the experimentally synthesized BC2N is a mixture of crystalline and amor-
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Figure 2. Total and projected density of states of BC2N. (a) c-BC2N, (b) w-BC2N, (c) cp-BC2N, (d) z-BC2N, and (e) t-BC2N.
phous phases, which results certainly in the remarkable decrease of the experimental value of the bulk modulus. The theoretical densities of z-BC2N (3.570 g/cm3) and t-BC2N (3.568 g/cm3) are the highest among all the five configurations and higher than the experimental density (3.358 g/cm3) of the synthesized cubic BC2N.9 The lower total energy, higher bulk moduli, and higher density of z-BC2N and t-BC2N indicate that we should pay more attention to the experimental synthesis of the dense BC2N crystal. The calculated band structures and density of states (DOS) spectra of c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N are indicated in the Supporting Information S1 and Figure 2, respectively. The w-BC2N and cp-BC2N are wide gap semiconductors with an indirect band gap of 3.1 and 4.0 eV, much wider than the indirect band gap (1.7 eV) of c-BC2N. The band gap of cp-BC2N is close to the calculated value of diamond (4.04 eV) and less than that of c-BN (4.46 eV). It is noted that the band structures of z-BC2N and t-BC2N show direct gaps of 2.5 and 3.5 eV. As direct band gap semiconductors, the lightemitting coefficient should be better than that of indirect band gap materials and lead to more potential applications in the ultraviolet field. Due to the underestimation of the density functional method, the exact band gap of the five phases should be in fact wider. It can be seen from Figure 2 that for all five phases the deep valence bands below -15 eV originate from the major contribution of the s states of C and N atoms, and the valence bands between -15 and 0 eV are dominantly from the contributions of the p states of B, C, and N atoms. Meanwhile, we find that the p orbitals of B, C, and N atoms have strong hybridization near the Fermi energy level. For the conduction bands, the contributions of the p states of B, C, and N atoms are dominant, while the s states of B, C, and N atoms have little contribution. There are also many differences among the five structures. The conduction band of cp-BC2N extends from the Fermi level to about 15 eV, much narrower than those of the c-BC2N and w-BC2N, while z-BC2N and t-BC2N display a much wider energy range of conduction bands (about 0-35 eV). The difference in conduction bands means different activity of electrons. As mentioned above, the nonidentical atoms form more kinds of chemical bonds, which mean weaker location of electrons and lead to wider electron bands as in the cases of z-BC2N and t-BC2N, whereas the cp-BC2N has the opposite case. Besides, for cp-BC2N, a splitting in the valence bands has
been found, and it is due to the weaker hybridization action of the s and p orbitals. It is evidence that cp-BC2N seems to be an unstable structure compared to the other four phases. 3.2. Optical Properties. The optical properties are determined by the dielectric function ε(ω) ) ε1(ω) + iε2(ω), which is mainly contributed from the electronic structures. The imaginary part ε2(ω) of the dielectric function, a pandect of the optical properties, could be obtained from the momentum matrix elements between the occupied and unoccupied wave functions, and the real part ε1(ω) can be evaluated from ε2(ω) using the Kramer-Kronig relations.31
ε2(ω) )
2π2e2 Ωε0 i∈c · f∈V
∑ ∑ |〈Ψck|µˆ · r|ΨVk〉|2δ[Eck - EVk - pω] k
ε1(ω) ) 1 +
(
2 π
ω′2ε (ω′)
) ∫0∞ dω′ ω′2 -2 ω2
Arising from ε1(ω) and ε2(ω), all the other optical properties, such as reflectivity R(ω), absorption coefficient R(ω), refractive index n(ω), and energy-loss spectrum L(ω) can be calculated32,33
R(ω) )
|
|
√ε1(ω) + jε2(ω) - 1 2 √ε1(ω) + jε2(ω) + 1
R(ω) ) √2ω[√ε21(ω) + ε22(ω) - ε1(ω)]1/2 n(ω) ) [√ε21(ω) + ε22(ω) + ε1(ω)]1/2 / √2 L(ω) ) ε2(ω)/[ε21(ω) + ε22(ω)] The variation of the imaginary part of the frequencydependent dielectric function ε2(ω) for the c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N is shown in Figure 3. There is a sharp peak at 10.6 eV for c-BC2N, mainly arising from the electron transition from the hybridization p orbitals to the hybridization orbitals of s and p. The line shapes of ε2(ω) for
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Figure 3. Imaginary part of dielectric functions of BC2N polymorphs.
Figure 4. Real part of the dielectric function ε1(ω), reflectivity R(ω), and absorption coefficient R(ω), real part of the refractive index n(ω), imaginary part of the refractive index k(ω), and electron energy-loss functions L(ω) for BC2N.
w-BC2N, z-BC2N, and t-BC2N are similar to that of c-BC2N, and the strong peaks have the same origin of electron transition as c-BC2N. A few blue shifts could be observed. Much different from the other four phases, the plot of cp-BC2N shows a broad peak at around 8.38 eV as well as a shoulder at 11.5 eV. Combined with the analysis of DOS, we can get that the electronic transition from the hybridization p orbitals to the hybridization orbitals of B 2p, C sp, and N sp leads to the peaks of 8.38 eV, while the shoulder at 11.5 eV arises from the electronic transition from the hybridization p orbitals to the hybridization orbitals of B sp, C sp, and N 2p. The different line shape and the different electron transition form indicate that the cp-BC2N phase may exhibit some interesting optical characters. The real part of the dielectric function ε1(ω), reflectivity R(ω), and absorption coefficient R(ω), the real part of the refractive index n(ω), the imaginary part of the refractive index k(ω), and the energy-loss spectrum L(ω) of BC2N are plotted in Figure 4. The ε1(ω) of the c-BC2N, z-BC2N, and t-BC2N phases are quite similar, having smooth peaks at 8.48 and 9.58 eV, respectively, while an obvious peak of them could be found below zero at 14.4 eV, at which the material behaves like a metallic property. The ε1(ω) of w-BC2N reaches nearly the same minimization at nearly the same position, showing a similar metallic nature. Quite different from the former three phases, the ε1(ω) of cp-BC2N has an obvious peak at 5.34 eV with a
Li et al. large red shift and a smooth peak with metallic nature at 15.5 eV, showing different dielectric property. The static dielectric constants for c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N are 5.88, 5.49, 6.49, 5.52, and 5.55, respectively. Note that the calculations are carried out for a perfect static crystal at 0 K, and no zero-point vibration is considered. So, the experimental data, which are obtained at room temperature considering the effect of vibration, will be larger than the calculated value. The reflectivity spectra of the BC2N polymorphs indicate the same reflective ranges from 0 to 50 eV, and those of z-BC2N and t-BC2N exhibit much difference between 30 and 40 eV, which will be reflected in the electron energy-loss function L(ω). The five phases have no absorption when the energy is below 3 eV, meaning that they are transparent when the wavelength is longer than 414 nm. The absorptions of all the five structures are decreased with the photon energy in the high-energy range, where the electron is hard to respond. In the dispersion curve of the refractive index, all five phases lie in the regime of normal dispersion in the range from 0 to 10 eV and anomalous dispersion from 10 to 25 eV. The cp-BC2N still exhibits different features from the others in the low-energy region. Besides, the electron energy-loss function L(ω) is also an important optical parameter describing the energy loss of a fast electron traversing in a certain material, and the peaks in the L(ω) spectra represent the characteristic associated with the plasma resonance. In addition, the positions of peaks in L(ω) spectra, which correspond to the so-called plasma frequency, point out the transition from the metallic property [ε1(ω) < 0] to the dielectric property [ε1(ω) > 0] for a material. Moreover, the peaks of L(ω) correspond to the trailing edges in the reflection spectra; for instance, with regard to c-BC2N, w-BC2N, and cp-BC2N, the broad peaks of L(ω) are at 34.0, 32.8, and 32.3 eV, corresponding to the slow reduction of R(ω). For z-BC2N and t-BC2N phases, the sharper peaks at 36.3 eV just correspond to the abrupt descent of reflectivity. It is noted that all the optical properties of the z-BC2N and t-BC2N phases are almost the same, and this may be caused by the similar crystal structures and minor difference for the atomic position. Unfortunately, the related spectroscopic data, such as parallel electron energy loss spectroscopy,34 are insufficient at present. 3.3. Lattice Dynamics. Dynamical properties were obtained by the use of the linear response method, within density functional perturbation theory (DFPT).29,35 DFPT is not only one of the most robust methods for the calculation of dynamic properties but also a method that naturally enables the calculation of the second-order derivatives of the total energy with respect to atomic position, and thus the properties of phonon modes to be evaluated directly. The long-range behavior of the Coulomb interaction gives rise to macroscopic electric fields for longitudinal (LO) and transverse (TO) optical phonons, and the coupling between the phonon modes and the electric field leads to the LO-TO splitting at the G point.22,23 The Born effective tensor is a very important quantity, which determines the well-known phenomenon of LO-TO splitting.36 With knowledge of the normal modes and the Born effective tensor, the IR absorption spectrum can be calculated as
Im ∝
∑ | ∑ Z*κ,Rβem(κβ)|2 R
(1)
κ,β
where m is the mode of vibration; Z*κ,Rβ is the effective tensor in the direction Rβ for the ion κ; and em is the phonon eigenvector. LO-TO splitting affects only infrared active modes near the G point, raising the frequencies of LO modes above
First-Principles Study of BC2N those of TO modes. Since the region is rather small and thermodynamics samples the whole Brillouin zone, we can expect the influence of the LO-TO splitting on thermodynamic functions to be small. The calculated phonon dispersion relations along highsymmetry directions and the responding phonon density of states (PDOS) for c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N are illustrated in Figure 5. Since BC2N polymorphs have a mixed ionic-covalent nature of chemical binding, the macroscopic electric field splits the infrared active modes A1, B1, and B2 to transverse A1 (TO), B1 (TO), B2 (TO), and longitudinal A1 (LO), B1 (LO), and B2 (LO) components for c-BC2N, and the other four phases display analogous splitting action. There is a considerable energy overlap between some optic modes and the acoustic modes for BC2N polymorphs due to almost identical masses of B, C, and N atoms in the unit cell. It means that energy transfer between these modes is easy. With anharmonic effects, these low-frequency optic modes will strongly scatter the acoustic modes, which carry the beat flow and may lead to low lattice thermal conductivity. Meanwhile, the calculated phonon dispersion relations have no soft mode at any wave vectors, which indicates the stability of all five phases. The PDOS results well trace the main features of theoretical phonon dispersion relations. As expected, the contributions of B, C, and N movements are distributed in the whole energy regime from 0 to 40 eV, since B, C, and N have analogous atom masses and electronegativity. This phenomenon will be verified by the following vibration pattern analysis. It is well-known that the lattice vibration at the G point can be closely investigated by infrared (IR) and Raman spectra. So we present the calculated IR absorption spectra for c-BC2N, w-BC2N, cp-BC2N, z-BC2N, and t-BC2N as well as the theoretical positions of the Raman peaks in Figure 6. It appears that the five crystalline phases can easily be distinguished by both their Raman and IR vibration frequencies, which gives a strong support to the use of Raman scattering and IR absorption spectroscopy to identify the BC2N crystallites synthesized experimentally among the various polymorphs predicted theoretically. The calculated frequencies should also help to assign the measured peaks in terms of the underlying atomic bonding configuration. For c-BC2N, the group symmetry decomposition into irreducible representations of the Pmm2 point group at the G point yields a sum of A1 + B1 + B2 for three acoustic modes and 3A1 + 3B1 + 3B2 for the nine optical modes, which are simultaneously IR and Raman active, as listed in Table 2 in comparison with previous theoretical results.20 Due to the low symmetry of the orthorhombic structure, many peaks appear in the IR spectrum, and several peaks are so close to each other that they become one broad peak, as shown in Figure 6a. It can be found that there are five strong absorption modes at 771, 1046, 1189, 1207, and 1219 cm-1, two relatively weak absorption modes at 950 and 1150 cm-1, and one very weak absorption mode at 733 cm-1. The absorption mode at 710 cm-1 is too weak to be observed. To show a clear picture of the vibration patterns, we plot the atomic displacements of c-BC2N corresponding to the calculated infrared peaks in the Supporting Information S2. The lowest B1 mode, located at 771 cm-1, consists of the translational displacements of B, C2, and N atoms in the xz plane. There are two modes in the middle region (900-1150 cm-1), at 950 and 1046 cm-1, respectively. The relatively lower one is a B2 mode with the N and C2 atoms translational moving against C1 and B atoms in the xz plane, while the higher one is an A1 mode with the C2 atoms translational moving against C1, N, and B
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Figure 5. Phonon dispersion and corresponding density of phonon state curves for BC2N. (a) c-BC2N, (b) w-BC2N, (c) cp-BC2N, (d) z-BC2N, and (e) t-BC2N.
atoms along the y-axis. The middle region vibrations mainly come from the relative motions between C and N atoms, which are consistent with the contributions in the phonon density of states (Figure 5a). Similarly, we could bring the other four, at 1150, 1189, 1207, and 1230 cm-1, classified as high-frequency
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Figure 6. Infrared absorption spectra for BC2N. (a) c-BC2N, (b) w-BC2N, (c) cp-BC2N, (d) z-BC2N, and (e) t-BC2N, and the Raman frequencies (red vertical lines) are also indicated.
modes (1150-1300 cm-1). The A1 modes at 1150 and 1189 cm-1 all involve the serious translational motions of C1 and C2 atoms along the y-axis. The difference is that in the former C1 and C2 move against B atoms together, while in the latter C1 and C2 move against each other. The higher frequency B1 mode (1207 cm-1) involves the serious translational displacements in the xz plane with B and C1 atoms vibrating against each other. Though the highest mode (1230 cm-1) originates from the translational displacements of B, C1, C2, and N atoms in the xz plane, the relative motions of C1 and C2 are much more serious. So we can conclude that the high-frequency vibrations are dominant from the relative motions of B, C1, and C2, and the atomic displacements are much more serious than those in the low- and middle-frequency region. For w-BC2N, phonons at the G point can be classified according to the irreducible representations of the P3m1 point group as Γopt ) 3A1 + 3E for the nine optical modes, where the acoustic modes (A1 and E) have been omitted. The A1 and E modes are all IR and Raman active. Combined with the vibrational frequencies (listed in Table 2) and the infrared absorption spectra (Figure 6b), we plot the atomic displacement patterns corresponding to the five infrared peaks in Supporting
Information S3. The strongest IR peak (1012 cm-1) lies in the middle-frequency region, dominant by the relative translational movement of B and N atoms in the xy plane. Considering that other middle-frequency modes are contributed from the serious relative vibration of N and C atoms along the z-axis with the slight movement of B atoms for the mode at 965 cm-1 and the serious relative vibration of N and B atoms along the z-axis with the slight movement of C atoms for the mode at 1131 cm-1, we could assume that the translational movement of N atoms is the main contribution of the middle-frequency vibration. The two high-frequency modes, A1 mode at 1192 cm-1 and E mode at 1254 cm-1, are all from the serious relative motion between C1 and C2, which are along the z-axis for the A1 mode and in the xy plane for the E mode. The phenomenon that the relative motion between C1 and C2 is the main source of the highfrequency vibrations is the same as that of c-BC2N. For cp-BC2N, the lattice vibration spectrum consists of 24 vibration modes, and the 21 zone-center optical phonon modes decompose according to Γopt ) A1 + 2A2 + 3B1 + 3B2 + 6E, where the B2 and E modes are infrared active and the A1, B1, B2, and E modes are Raman active with A2 modes silent. The G point vibrational frequencies of cp-BC2N are also listed in Table 2, and the primitive cells are chosen to describe the atomic displacement patterns of calculated infrared peaks, as shown in Supporting Information S4. As discussed above, the atomic translational movements contribute to the main IR peaks for cand w-BC2N, whereas the case of cp-BC2N is more complicated. The low-frequency region (
