Band-Gap Engineering in High-Temperature Boron-Rich

Article

Cite This: J. Phys. Chem. C 2019, 123, 12505−12513 pubs.acs.org/JPCC

Band-Gap Engineering in High-Temperature Boron-Rich Icosahedral Compounds Hongwei Wang and Qi An* Department of Chemical and Materials Engineering, University of Nevada-Reno, Reno, Nevada 89557, United States

*S Supporting Information

ABSTRACT: Band-gap engineering is essential for boron-rich icosahedral compounds for high-temperature applications such as β-voltaic devices and thermoelectrics, and the extreme complex chemical bonding in these icosahedral compounds leads to intriguing electronic properties. Here, we first employed quantum mechanics simulations to determine the electronic states that control the valence band maximum and conduction band minimum of these icosahedral compounds, as well as the detailed band structures. Then, we examined the band-gap modulation by applying twin boundary, chemical substitution, structure arrangement, and hydrostatic pressure, with which the band gaps of these icosahedral compounds can be engineered wider or narrower to a large extent. Particularly, we find that some icosahedral compounds show an increased band gap with the applied hydrostatic pressure, an unusual phenomenon compared to the conventional inorganic semiconductors. Our study provides a fundamental understanding of the electronic properties of icosahedral solids and an effective way to tune their band gaps for designing promising optical, thermoelectric, and β-voltaic devices at extremely high temperature and radiation conditions.

1. INTRODUCTION conductors and perform band-gap engineering to optimize Icosahedral boron and boron-rich compounds are mainly their engineering performance. The boron-rich compounds α boron (α-B ), boron carbide composed of 12-atom boron clusters in which boron atoms 12 (B C), boron suboxide (B O ), and boron subphosphide occupy the 12 vertices of icosahedra,1 displaying promising 4 12 2 (B P ) have similar crystal structures in which the doped properties such as super hardness, high melting temperature, 12 2 2 elements C, O, and P form the multiatomic chains linked to and radioresistance. The ability of icosahedral boron-rich adjacent icosahedra. The different types of bonding inter- compounds to survive in extreme environments makes them actions between the chain and icosahedral atoms in these 3 − useful for various advanced device applications. One primary boron-rich systems result in unusual electronic properties.8 10 Downloaded via UNIV OF NEVADA RENO on July 26, 2019 at 02:46:57 (UTC). β use is -voltaic cells, which utilize energy from a radioactive Boron carbides, which have attracted more attention in β 2,3 β source of particles to generate electricity and heat. The - contrast to other boron-rich compounds, possess a wide voltaic devices made with conventional semiconductors tend See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. range of energy gaps between 0.48 and 2.5 eV reported to undergo very serious radiation damage, which can be experimentally.9,11,12 Moreover, boron carbide is also found to circumvented by replacing them with icosahedral boron-rich display a pressure-dependent energy gap,13 which is opaque at semiconductors. The long-life and low-power characteristics of the ambient condition but becomes transparent at high these icosahedral compounds are particularly well suited for pressure. The abundant electronic behaviors in boron carbides military and spacecraft applications. Another important are due to their complex structure configurations and various application of icosahedral boron-rich compounds is in stoichiometries. Ektarawong et al. found that one B atom of 4 thermoelectric energy conversion, generating electrical the icosahedron in B4C boron carbide tends to be substituted power from solar heat or recycling waste thermal energy.5 by one C atom able to be randomly distributed over all polar Some boron-rich semiconductors have been found to possess sites of the icosahedron.14 In addition, the complex large Seebeck coefficients,6 high electrical conductivities, and intericosahedral arrangements such as CBC, CBB, and B□B very low thermal conductivities.7 These are essential (□ represents a vacancy) may coexist in the actual boron prerequisites to achieve high-efficiency thermoelectric energy carbide structures,15,16 which has been investigated by Werheit conversion.5 Since the energy conversion through radiation and thermoelectricity highly depends on the systematic Received: March 10, 2019 electronic structures, it is essential to examine the band Revised: April 15, 2019 structures and band gaps of icosahedral boron-rich semi- Published: April 24, 2019

α Figure 1. Atomic structures, band structures, and partial charge density isosurfaces of (a) -B12, (b) B12O2, (c) B12P2, and (d) B4C. The blue and yellow isosurfaces represent the VBM and CBM electronic states.

α α Figure 2. (a) Schematic view of the B12 icosahedral unit in -B12. (b) Three-center intericosahedral bonds formed by equatorial B atoms in -B12. α (c) Two-center intericosahedral bonds formed by polar B atoms in -B12. (d, e) Schematic illustration of the B12 icosahedral unit and intericosahedral chain in B12P2. (f, g) Schematic view of the B12 icosahedral unit and intericosahedral chain in polar B4C. and his co-workers. The mixture of ∼10% B□B arrangements, transport through interface heterojunction,22,23 introducing a − − ∼ 19,24,25 <2% C B B chains, and 90% CBC chains with 100% B11C gap state with composition substitution, and band-edge icosahedron13,15 is responsible for the experimentally observed modulation by mechanical-strain-induced structure distor- 18,26 B4.3C structural formula, the carbon-rich limit composition of tion, have been utilized to tailor electronic properties in boron carbide compounds.16 The electron transition levels the traditional semiconductors and novelly discovered two- introduced by the above configurational disorder and chain- dimensional materials.27 Within these methods, their electronic related defects in B4.3C compound, accounting for the wide- conductivities, light-emitting properties, and visible-light- range band gap, have been systematically studied by Werheit induced photocatalytic efficiencies have gained significant with theoretical analysis recently.11 Furthermore, Hushur et al. improvements.28 However, the research on how to tune proposed that the optical transition in B4.3C compounds results electronic properties in boron-rich icosahedral compounds has from the reduced structural defects by high pressure,13 which not been considered so far because of the intriguing structure enable the stabilization of the defect-free B4C boron carbide and bonding characteristics in these materials. Hence, it is with a wide energy gap. necessary to explore the band-gap engineering in these boron- Although the electronic performances of the boron-rich rich systems to design more advanced devices, in combination compounds have been investigated both theoretically and with exciting electrical, thermal, and mechanical performances. experimentally before, the intrinsic electronic properties of In this study, we focus on the electronic structures of α 1,291,29 30 semiconductors are usually not attractable for practical icosahedral boron-rich compounds -B12, B12O2, 31,32 9,33 9 applications. For example, their band gaps need to be reduced B12P2, B4C, and B14C1, which are investigated by to raise the usage efficiency of sunlight for the photo- means of the first-principles method. The effects of twin − catalysis17 20 or increased for short-wavelength optical boundary (TB), high pressure, chemical substitution, and applications, ultraviolet photodetectors, and resisting radiation structure rearrangement on electronic properties are consid- damages.21 Several effective approaches, such as carrier ered in this work. As for the boron carbide, we consider only

12506 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article

a Table 1. Lattice Parameters, Volume, Structure Symmetry, and Band Gaps of the Boron-Rich Icosahedral Compounds

a (Å) b (Å) c (Å) volume (Å3) space group band gap (eV) ̅ indirect B12 5.026 85.744 R3m 2.18 5.064Expt. 87.834Expt. τ indirect -B12 4.870 8.798 16.019 686.376 Cmcm 2.21 ̅ indirect p-B12 4.853 76.872 R3m 1.58 ̅ direct B12O2 5.124 101.625 R3m 2.89 5.146Expt. 102.484Expt. τ indirect -B12O2 5.359 8.732 8.684 406.400 Cmcm 2.89 ̅ direct p-B12O2 4.928 91.551 R3m 3.22 ̅ indirect B12S2 5.324 123.325 R3m 2.15 ̅ indirect B12P2 5.221 120.800 R3m 3.40 5.256Expt. 123.222Expt. τ indirect -B12P2 5.965 8.583 18.899 967.497 Cmcm 3.80 indirect polar-B11C-CBC 5.182 5.182 5.031 107.381 Cm 3.84 ̅ direct chain-B12-CCC 5.160 109.681 R3m 2.53 5.163Expt. 109.419Expt. indirect equatorial-B11C-CBC 5.178 5.178 5.145 107.781 Cm 3.51 indirect kink-B14C1 5.062 5.111 5.184 108.945 P1 2.01 indirect p-kink-B14C1 4.829 4.917 4.920 95.938 P1 2.46 indirect linear-B14C1 5.103 107.785 R3m 1.59 indirect p-linear-B14C1 4.893 95.960 R3m 2.08 aτ and p represent the twinned and high-pressure structures, and the superscript index Expt. stands for the experimental results. the major constituent (B11C)CBC in B4.3C compounds, and two-atom or three-atom intericosahedral chain, which links the chain-related defects are not considered in our work. We with three neighboring icosahedra through the equatorial select three reprehensive structures of the (B11C)CBC system atoms. The more detailed structural information is shown in 14 fi studied by Ektarawong to investigate the con guration Figure 2. The 2-atom or 3-atom chains in both B12P2 and B4C ff fi fi disorder e ect on electronic structures. The rst one is the will transfer electrons to the 2-electron-de cient B12 or 1- fi fi lowest energy con guration with the substituted C atom at the electron-de cient B11C icosahedral units, forming 13 intra- polar site in the icosahedron, the second one is the high energy icosahedral bonds and satisfying Wade’s rule.34,37 However, in fi con guration with the substituted C atom at the equatorial site B12O2, the O atom attracts electrons from the B12 icosahedron in the icosahedron, and the third one is the configuration with because of its larger electronegativity than B, leading to fi 38 a chain containing three C atoms. We believe that the electron de ciency in the B12 icosahedron. mechanism of the modulated band gap by configuration Since the icosahedral boron-rich compounds can be disorder in these three structures is similar to that in other classified into the special molecular solids, named inverted structure configurations. We find that the valence band molecular solids, the bonding character has a significant effect maximum (VBM) and conduction band minimum (CBM) on the band structures of these compounds. To clarify this electronic states in these icosahedral boron-rich compounds effect, we examined the band structures of these compounds display the localized character, which are distributed over the using the Heyd−Scuseria−Ernzerhof (HSE06) hybrid ex- intraicosahedral and chain chemical bonds, respectively, and change functional,39 which has been proven to be capable of are capable of being tuned with the external physical or obtaining more accurate band gaps than the Perdew−Burke− chemical conditions. As a result, the VBM and CBM electronic Ernzerhof functional.40 The simulation details can be found in states correlated with these chemical bonds are readily tailored the Supporting Information (SI). The calculated band gaps of to a large extent as well. Based on the mechanisms, the design the B-rich compounds are in the range of 2.0−3.5 eV, as listed principles are established for the band-gap control in boron- in Table 1, indicating that all of these systems are rich icosahedral compounds. semiconductors. In particular, the predicted band gaps for α- B12 and B12P2 are 2.18 and 3.40 eV, respectively, which agree 2. STRUCTURAL AND ELECTRONIC PROPERTIES very well with experimental measurements of 2.00 and 3.35 FROM FIRST-PRINCIPLES CALCULATIONS eV,41,42 indicating the reliability of the HSE06 functional. Figure 1a−d shows the schematic crystal structures of four The calculated band structures and charge density isosur- α − typical boron-rich compounds -B12,B12O2,B12P2, and B4C. faces of four selected compounds are displayed in Figure 1a d. Here, we considered the ground-state structure polar (B11Cp)- The VBM is marked with blue color, and the CBM is marked 34 α CBC for B4C. The B12 icosahedral units in -B12 are with yellow color. The charge density analyses indicate that the interlinked via six strong two-center−two-electron (2c−2e) VBM electronic states originate from the intraicosahedral α and six weak three-center−two-electron (3c−2e) bonds (see bonding within the B12 units for -B12,B12O2, and B12P2, Figure 2). This results in 13 intraicosahedral bonds within the whereas they stem from the intericosahedral bonding between ’ 35,36 B12 icosahedron, satisfying Wade s rule. The icosahedral neighboring icosahedra in B4C. The CBM electronic states are − α atoms connected by 2c−2e and 3c−2e are called polar and determined by the intericosahedral 3c 2e bonding in -B12, equatorial atoms, respectively (see Figure 2), which locate at antibonding interactions between two chain P atoms in B12P2, the polar and equatorial sites in the icosahedron. For element- and antibonding interactions between the chain-carbon and doped systems B12O2,B12P2, and B4C, the doped atoms form a chain-boron atoms in B4C. However, in B12O2, the CBM

12507 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article

τ Figure 3. (a) Atomic structure of -B12P2. (b) Projected crystal orbital Hamilton population (pCOHP) analysis for the bond interactions associated τ with the CBM electronic states in B12P2 and -B12P2. (c) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM τ electronic states of B12P2 and -B12P2. The bond length is in the unit of angstrom. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals, respectively.

Figure 4. Hybridization function (%) of the chemical bonds belonging to the intericosahedral chains for (a) B12P2, (b) B6O, (c) polar B4C, (d) chain B4C, and (e) equatorial B4C. electronic state is also determined by the intraicosahedral To understand the different electronic behaviors, we utilized multicenter bonding. The unique CBM electronic state in the crystal orbital Hamilton population (pCOHP) approach to fi B12O2 arises from the electron de ciency in B12 icosahedra analyze the chemical bonds correlating with the VBM and because the chain O atom attracts electrons from the B12 CBM states for both perfect and twinned boron-rich icosahedron.38 compounds. The pCOHP approach provides a straightforward view of orbital-pair interactions, capable of a quantitative 3. BAND-GAP MODULATION BY CHEMICAL AND measure of bonding strength. The negative and positive parts MECHANICAL CONDITIONS of pCOHP represent bonding and antibonding contributions 43 Understanding band structures of boron-rich compounds is to the chemical-bond strength. Obviously, the band gaps are essential for band-gap engineering for wide engineering determined by the lower limit of the CBM bonding pCOHP applications. Here, we apply four realistic approaches to above the Fermi level and the upper limit of VBM-bonding investigate the band-gap engineering in B-rich compounds: (1) pCOHP below the Fermi level (see Figure S4 in SI). The τ twin boundary engineering, (2) composition modulation, (3) pCOHPs of B12P2 and -B12P2 shown in Figure 3b indicate that structure arrangement, and (4) pressure engineering. the lower limit of the antibonding-state edge responsible for 3.1. Twin Boundary. Twin boundaries (TBs) with low CBM is higher than that in B12P2, which accounts for the wider τ interfacial energy generally exist in crystalline materials, which band gap of -B12P2. Meanwhile, the upper limits of the have been extensively observed in B-rich compounds.30,33 bonding-state edge responsible for VBM are almost the same τ Therefore, it is necessary to investigate the dependence of in B12P2 and -B12P2 (see Figure S1 in SI). Since the CBM τ − band structures on TBs for boron-rich compounds. Here, we electronic states of B12P2 and -B12P2 both reside in the P P focus on three twinned structures of boron-rich compounds τ- chain bonds (see charge density in Figure 3c), the band-gap τ τ ff τ B12, -B12O2, and -B12P2 (Figure 3a). The computed band di erence between B12P2 and -B12P2 originates from the chain structures of these boron-rich compounds are shown in Figures bonding interactions. The length of P−P bonds remains the τ − S1−S3 of SI, and the band gaps are given in Table 1. The band same in both B12P2 and -B12P2, but one B P bond connecting α ff gaps of -B12 and B12O2 are almost una ected by TBs, whereas the intericosahedral chain and B12 icosahedron is shortened by τ τ − -B12P2 has a band-gap increment of 0.4 eV compared to that 0.02 Å for -B12P2. The contracted B P bond would enhance of the perfect B12P2 crystal. the bonding interaction between the chain and icosahedron,

12508 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article

Figure 5. (a) pCOHP analysis for the bond interactions associated with CBM electronic states in B12O2 and B12S2. (b) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM electronic states of B12O2 and B12S2. (c) pCOHP analysis for the bond interactions responsible for CBM electronic states in B4C and B14C1. (d) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM electronic states of B4C and B14C1. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals, respectively. fi − which increases the antibonding level as well as the band gap. de cient (B12O2)orthechainicosahedral interaction fi α It is noteworthy that each P atom with ve valence electrons depends weakly on the twinned structure ( -B12). donates one electron to the B12 icosahedron and the remaining 3.2. Composition Substitution. Composition modula- four electrons form the sp3-hybridization with the surrounding tion has been proved to be an effective approach to tailor the three equatorial B atoms and one chain P atom.44 This band edges in semiconductors21,28 and even for the continuous 22 accounts for the chain P−P bonding interaction affected by the tuning of the band gap. Hence, we calculated the electronic B−P bond. To verify this, the P−P chemical bonding orbitals structure for B12S2, which can be regarded as the S-substituted ff were obtained with a method of solid-state adaptive natural B12O2. Although the band gap of B12O2 is not a ected by TB, it density partitioning45 (SSAdNDP). As shown in Figure 3c, the undergoes a decrease of 0.74 eV after the S substitution (Table shape of CBM charge densities is quite similar compared to the 1). Figure 5a shows the CBM bonding pCOHPs and charge − τ density isosurfaces of the CBM electronic state for B O and P P antibonding orbitals for both B12P2 and -B12P2. The 12 2 relevant orbital compositions analyzed by the natural bond B12S2. The lower limit of antibonding-state edge above the orbital (NBO) method46 are shown in Figure 4. The P−P Fermi level in B12S2 has a large downward shift in contrast to antibonding orbital consists of about 25% s orbital and 75% p B12O2, and the upper limits of VBM-bonding pCOHPs below 3 the Fermi level are equal by coincidence (see Figure S6 in SI). orbital, indicating the character of sp -hybridization. Moreover, fi the wavefunction of the CBM electronic state was plotted for Therefore, the band-gap modi cation by composition 47 modulation in B O should originate from chemical bonding B P , as shown in Figure S5 of SI. The peaks of the wave 12 2 12 2 associated with the CBM electronic state. As mentioned above, function are concentrated at both equatorial B and chain P the CBM electronic orbital of B O locates at the center of the sites and exhibit the antibonding character, which is consistent 12 2 B icosahedron instead of the intericosahedral chain. The with the above charge density and orbital analyses. Since the 12 ff − reason can be attributed to the fact that O atoms with higher B12 icosahedron is sti er than the intericosahedral P P 10,48 electronegativity tend to attract electrons from their surround- chain, the VBM orbital distributed over intraicosahedral 38,44 fl ing equatorial B atoms, which leave the positive holes bonds is less sensitive to the external in uence, which accounts dispersed over the adjacent B atoms. The valence charges of for less varied energy edge of the VBM electronic state in τ- the oxygen and polar and equatorial boron atoms in B12O2 B12P2. obtained through the Bader analysis49 are about 8.0e, 3.0e, and α As for -B12, its VBM electronic orbitals reside in the B12 2.3e, respectively. This suggests that the O atoms have icosahedrons, whereas the CBM electronic orbitals are related attracted electrons from the equatorial B atoms to form the − − to 3c 2e bonds (see Figure 2). However, the 3c 2e bond closed-shell electronic configuration. The holes caused by B− α τ length is pretty similar in both -B12 (2.00 Å) and -B12 (2.00 O bonding interactions create unfilled orbitals at the equatorial ff α Å), leading to the smaller band-gap di erence between -B12 B atoms, which correspond to the CBM electronic states. As τ and -B12. Both the CBM and VBM electronic orbitals of shown in Figure 5b, the CBM charge density of B O lies in τ 12 2 B12O2 and -B12O2 sit inside the B12 icosahedron because of the plane of equatorial B atoms with vertexes toward the six fi 38 the electron de ciency in B12 icosahedron. Therefore, the B−O bonds, corresponding to the six-center B-bonding orbital τ band gap of -B12O2 is exactly the same as that of B12O2. Our situated in the B−O plane. The analysis of charge density and results suggest that nanotwin is not an effective way to perform SSAdNDP bonding orbital shows a good agreement with the band-gap engineering when the B12 icosahedron is electron above discussion for the origin of CBM electronic states in

12509 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article

Figure 6. (a) Atomic structures, partial charge densities (yellow isosurfaces), and chemical bonding orbitals for CBM electronic states of B4C. (b) pCOHP analysis for the bonding interactions associated with the CBM electronic states in B4C. (c) Atomic structures of B14C1, partial charge densities (yellow isosurfaces), and chemical bonding orbitals for CBM electronic states of B14C1. (d) pCOHP analysis for the bonding interactions ff fi associated with the CBM electronic states in B14C1. Polar, chain, and equatorial mean three di erent structural con gurations of B4C. Kink and ff fi linear represent two di erent structural con gurations of B14C1. The bond length is in the unit of angstrom. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals, respectively. − B12O2. The CBM electronic orbital of B12S2 has the character 3c 2e bonding character. In addition, the VBM electronic similar to that of B12O2. However, the lower electronegativity states of polar B11C-CBC and kink-B14C1 both originate from of S results in the weaker strength of the B−S bond. This leads the bonding orbitals of the two-center intericosahedral B−B to the lower hole densities around the equatorial B atoms bonds (see Figure S7 in SI), expecting to possess the closed (Figure 5b) as well as to the decreased CBM energy edge. VBM electronic state edges. Since the weak 3c−2e bond − − 3.3. Composition Concentration. Besides the composi- between the C B B chain and B12 icosahedron in B14C1 leads ff tion substitution, the e ect of the composition concentration to a lower CBM energy edge, the band gap of polar B11C-CBC − on electronic properties is also investigated for B4C determined by the intericosahedral B B bonding state and the − compounds. B4C exhibits a wide range of carbon solid chain C B antibonding state should be larger than that of solubilities ranging from 8 to 20%. Therefore, it is important kink-B14C1. The lower limit of CBM bonding pCOHPs above ff to investigate how the C concentration a ects the band gaps the Fermi level in kink-B14C1 is much smaller than that in polar and band structures. The polar B11C-CBC composed of one C- B11C-CBC (Figure 5c), showing a good agreement with the − atom-substituted B12 icosahedron at the polar site and one C above discussions. B−C chain is the ground-state structure configuration of 3.4. Structure Rearrangement. Molecular crystals with 9,50 B4C, which possesses a wide band gap of 3.84 eV. The kink- the same structural formula may possess numerous structural − − fi 9,52 B14C1 with a lower C concentration and a kinked B B C con gurations. Particularly, B4C possesses three possible fi chain has a largely reduced band gap of 2.01 eV in contrast to con gurations: (1) (B11Cp)-CBC, (2) equatorial (B11Ce)- 52,53 (B11C)p-CBC, indicating that stoichiometry plays an important CBC, and (3) (B12)-CCC. Although (B11Cp)-CBC is the ff role in the electronic structure of B4C. The B11C1 icosahedron ground-state structure, it is important to explore the e ect of fi in the polar B11C-CBC compound becomes one-electron various con gurations on the electronic property since these deficient, owing to the C-atom substitution at the polar site, configurations may exist in experimental samples. In the chain and it accepts one electron from the B atom in the CBC chain. B12-CCC, each chain-center C atom with four valence 3 The two C atoms in the CBC chain form the sp -hybridization electrons donates two electrons to the B12 icosahedron and with the surrounding three equatorial B atoms and one chain B the chain-end C atoms form the sp3-hybridization with the atom,44 and the one B atom in the CBC chain forms the sp- surrounding three equatorial B atoms and one chain-center C hybridization with the two C atoms. All bonding orbitals are atom with two valence electrons left. Similarly, the one chain- fi 3 completely lled in (B11Cp)-CBC, making it a rather stable end C atom in the equatorial B11C-CBC forms the sp - compound. This chain bonding information for B11C-CBC was hybridization with the surrounding two equatorial B atoms, also confirmed by the NBO analysis shown in Figure 4. As for one C atom at the equatorial site, and one chain-center B − − 3 the kink-B14C1, the two B atoms in the C B B chain form a atom, whereas the other chain-end C atom forms the sp - − 3c 2e bond with the connected B12 icosahedron, satisfying hybridization with the adjacent three equatorial B atoms and Wade’s rule.51 The bonding pCOHPs, charge densities, and one chain-center B atom. The above details for the orbital SSAdNDP orbitals of CBM for polar B11C-CBC and kink- hybridization of chain atoms in chain B12-CCC and equatorial B14C1 are shown in Figure 5c,d. As shown in Figure 5d, the (B11Ce)-CBC are also well consistent with the NBO analysis in CBM electronic state of the polar B11C-CBC stems from the Figure 4. The band gaps of equatorial B11C-CBC and chain − − fi antibonding interaction between C and B atoms in the C B B12-CCC have signi cantly changed compared to that of polar C chain. Similarly, the CBM electronic orbital of the kink- B11C-CBC (Table 1). Especially for the chain B12-CCC, the − B14C1 also resides in the chain B B bonds and exhibits the band gap is reduced by 1.31 eV in contrast to polar B11C-CBC.

12510 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article

α Figure 7. Pressure-dependent pCOHPs for (a) -B12, (b) kink-B14C1, (c) B12O2, and (d) linear-B14C1. The yellow isosurfaces stand for the partial charge densities for CBM electronic states. The bond length is in the unit of angstrom.

The atomic structures, CBM bonding pCOHPs, charge density smaller band gap (Figure 6d). Moreover, the chemical bonds isosurfaces, and SSAdNDP bonding orbitals of the CBM responsible for the VBM energy edge all lie on the B12 fi electronic state for these three structural con gurations are icosahedron in the above B4C and B14C1 compounds, which shown in Figure 6a,b. The SSAdNDP and charge density are less important to the band-gap modulations (see more analysis indicates that the CBM electronic state of the chain details in Figures S8 and S9 in SI). B12-CCC stems from the antibonding interaction between the 3.5. External Pressure. It is well known that the chain-center and chain-end C atoms. For equatorial B11C- mechanical loading conditions such as external pressure and CBC, the CBM electronic state originates from the epitaxial strain can have a large impact on electronic, optical, antibonding interaction between the chain-center B and magnetic properties through contracting or stretching − chain-end C atoms. The lower limit of CBM bonding interatomic distances in solid-state materials.54 56 Mechanical pCOHP above the Fermi level for the chain B12-CCC has an strain has been widely applied to tune the electronic structures evident low-energy shift in contrast to the polar B11C-CBC in some novel semiconductors, in which many existing (Figure 6b), which is attributed to the weaker C−C bond and phenomena like direct and indirect band-gap transitions, results in the smaller band gap in the chain B12-CCC. With enhanced electronic motilities, and largely modulated band-gap 26,27 ffi fi regard to the equatorial B11C-CBC, the chain-end C atom widths have been discovered. However, it is di cult to nd neighboring the C atom at the equatorial site forms a bit longer the proper substrates to impose a wide range of strains on the − chain C B bond compared to polar B11C-CBC (Figure 6a). complex boron-rich compounds because of their strong Therefore, the strength of the chain C−B bond in equatorial covalent bonds. Thus, we utilized the hydrostatic pressure to α B11C-CBC should be weaker than that in polar B11C-CBC, tune the band gaps in this work. The band gaps of -B12, leading to the slightly lower edge of the CBM bonding B12O2, kink B14C1, and linear B14C1 under the hydrostatic pCOHP and smaller band gap for equatorial B11C-CBC pressure of 30 GPa are listed in Table 1, which are 1.58, 3.22, (Figure 6b). 2.46, and 2.08 eV, respectively, exhibiting a significant change We also analyzed the electronic property of another compared to those of equilibrium states. Here, we focus on the fi structure con guration of B14C1, linear B14C1 in which the CBM state analysis because VBM electronic orbitals of these atoms of the intericosahedral C−B−B chain form a straight discussed boron-rich compounds sitting on the intraicosahe- − line (Figure 6c). The band gap of linear B14C1 is 0.42 eV dral B B bonds or the intericosahedral bonds linked to polar B smaller than that of kink B14C1, which is given in Table 1.As atoms are also less sensitive to pressure due to their less shown in Figure 6c, the CBM charge densities of kink and compressibility shown in Figures S10−S13 of SI. The CBM linear B14C1 structures reveal a bonding character of the CBM bonding pCOHPs and charge density isosurfaces of the CBM ff α electronic state, which is di erent from that of B4C and B12P2. electronic state for -B12,B12O2, kink B14C1, and linear B14C1 α − The SSAdNDP bonding orbitals indicate that the CBM are shown in Figure 7. For -B12, the intericosahedral 3c 2e electronic states of kink and linear B14C1 compounds both bonds accountable for the CBM electronic state undergo an stem from the 3c−2e bonding interactions. Moreover, the B−B evident compression with external pressure, and the charge bond responsible for the CBM electronic state possesses a density in the midst of these 3c−2e bonds is also increased, longer length in kink B14C1, which results in a relatively weaker indicating the pressure-enhanced bonding interactions for the bonding strength of the chain B−B bond. The strong bonding CBM electronic state. As a result, the CBM energy edge of α- interaction can lower the bonding state and lift the antibonding B12 will move toward to the Fermi energy as the pressure − state. Hence, the stronger chain B B bond in linear B14C1 increases, which accounts for the pressure-induced band-gap causes the lower bonding CBM energy edge as well as the reduction (Figure 7a). As mentioned above, the CBM

12511 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513 The Journal of Physical Chemistry C Article − electronic state of kink B14C1 arises from the B B bonding ■ AUTHOR INFORMATION − interactions, but it transfers to another B B bond after the Corresponding Author pressure is applied (Figure 7b) due to the complex chain * structure. The B−B bonds responsible for the CBM electronic E-mail: [email protected]. state are stretched by 0.1 Å after the pressure is applied. ORCID Therefore, the pressure-weakened CBM bonding interactions Qi An: 0000-0003-4838-6232 lead to an upper shift of the CBM energy edge and an Notes increased tendency for band gaps. Similarly, the CBM The authors declare no competing ﬁnancial interest. electronic state of linear B14C1 transforms the bonding state of a shorter B−B bond (1.56 Å) to that of an adjacent longer B−B bond (2.00 Å) under external pressure (Figure 7c). As a ■ ACKNOWLEDGMENTS result, the weaker bonding interaction of the CBM electronic This work was supported by the National Science Foundation state causes an increased band gap for linear B14C1 as well. (CMMI-1727428) and Ralph E. Powe Junior Faculty However, the CBM electronic state of B12O2 exhibits the Enhancement Awards from Oak Ridge Associated Universities antibonding character (Figure 7d); thus, the pressure- (ORAU). shortened B−O bonds make the CBM energy edge move far away from the Fermi energy, resulting in the increased band ■ REFERENCES gap with pressure (Figure 7d). (1) Emin, D. Icosahedral Boron-Rich Solids. Phys. Today 1987, 40, 55−62. 4. CONCLUSIONS (2) Emin, D. Unusual Properties of Icosahedral Boron-Rich Solids. J. We have investigated the band-gap modulation by twin Solid State Chem. 2006, 179, 2791−2798. boundary, composition modulation, structure arrangement, (3) Emin, D.; Aselage, T. L. 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12513 DOI: 10.1021/acs.jpcc.9b02254 J. Phys. Chem. C 2019, 123, 12505−12513