Two B-C-O Compounds: Structural, Mechanical Anisotropy and Electronic Properties under Pressure

The structural, stability, mechanical, elastic anisotropy and electronic properties of two ternary light element compounds, B2CO2 and B6C2O5, are systematically investigated. The elastic constants and phonon calculations reveal that B2CO2 and B6C2O5 are both mechanically and dynamically stable at ambient pressure, and they can stably exist to a pressure of 20 GPa. Additionally, it is found that B2CO2 and B6C2O5 are wide-gap semiconductor materials with indirect energy gaps of 5.66 and 5.24 eV, respectively. The hardness calculations using the Lyakhov-Oganov model show that B2CO2 is a potential superhard material. Furthermore, the hardness of B6C2O5 is 29.6 GPa, which is relatively softer and more easily machinable compared to the B2CO2 (41.7 GPa). The elastic anisotropy results show that B6C2O5 exhibits a greater anisotropy in the shear modulus, while B2CO2 exhibits a greater anisotropy in Young’s modulus at ambient pressure.

Using the developed particle swarm optimization (PSO) algorithm for crystal structure prediction, Wang et al. [4] explored the possible crystal structures of B-C systems that are mechanically and dynamically stable. They found that with the exception of B 4 C and BC 4 , all boron carbides have high shear moduli (more than 240 GPa), indicating their strong resistance to shape change at constant volume. Theoretical Vickers hardness calculations showed that these boron carbides are potential superhard materials because the predicted hardnesses exceed 40 GPa. Zhang et al. [20] designed different kinds of superhard materials using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) algorithm. They found superhard phases in binary B-N compounds (such as Pct-BN, Pbca, Z-BN, BC 8 -BN, and M-BN) and ternary B-C-N compounds (such as I-4m2 BCN, Imm2 BCN [21], and P3m1 BCN [22]). Pbca-BN with an orthorhombic structure was investigated by first-principles calculations by Fan et al. [23], who found that Pbca-BN has the shear modulus of 316 GPa, bulk modulus of 344 GPa, large Debye temperature of 1734 K, and hardness of 60.1 GPa. Ternary B-C-N compounds I-4m2 BCN, Imm2 BCN, and P3m1 BCN were investigated by first-principles calculations by Fan et al. [21,22] and were all found to be potential superhard materials. Electronic structure studies showed that BCN materials in the P3m1 and I-4m2 phases are indirect semiconductors

Theoretical Methods
The calculations were performed using density functional theory with the exchange-correlation functional treated using the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form [37] and the Perdew-Burke-Ernzerhof for solids (PBEsol) form [38], and with local density approximation (LDA) based on the data of Ceperley and Alder as parameterized by Perdew and Zunger (CA-PZ) [39,40]. The calculations in this work were performed using the Cambridge Serial Total Energy Package (CASTEP) code [41]. Structural optimizations were conducted using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm [42]. A high-density k-point [43] sampling with a grid spacing of less than 2π × 0.025 Å −1 (4 × 16 × 7 for B 2 CO 2 , 9 × 9 × 9 for B 2 CO 2 ) in the Brillouin zone was used. The self-consistent convergence criterion for the total energy was 5 × 10 −6 eV/atom, the maximum force on the atom was 0.01 eV/Å, the maximum ionic displacement was within 5 × 10 −4 Å and the maximum stress was within 0.02 GPa. The HSE06 hybrid functional [44] was used for the calculations of electronic structures of B 2 CO 2 and B 6 C 2 O 5 .

Structural Properties
The crystal structures of B 2 CO 2 and B 6 C 2 O 5 are shown in Figure 1a Table 1. The calculated lattice parameters of B 2 CO 2 and B 6 C 2 O 5 are in excellent agreement with the previous report [12], and the calculated lattice parameters of the other B-C-O compounds are also in excellent agreement with the previous report (see Table 1).  [12], and the calculated lattice parameters of the other B-C-O compounds are also in excellent agreement with the previous report (see Table 1).   The relationships among the calculated lattice parameter ratios X/X0 (a/a0, b/b0, c/c0) and lattice volume ratios V/V0 of B2CO2 and B6C2O5 and pressure are shown in Figure 2, where a0, b0, c0 and V0 are the zero temperature and zero pressure equilibrium lattice constants and lattice volume, respectively. For B2CO2, it can be easily seen that the compression of the b-axis is the most difficult, whereas that of the a-axis is the easiest. For B6C2O5, similar to B2CO2, the b-axis is the most difficult to compress, while the c-axis is the easiest to compress. When the pressure increases, the compression along the b-axis of B6C2O5 is much larger than that along the b-axis of B2CO2. In addition, it is found that the lattice constants b/b0, c/c0 compression of B6C2O5 is changed at 10 GPa. This is because the lengths of some bonds decrease strongly along the lattice vector b-axis or the lattice vector c-axis.

Materials
Source The relationships among the calculated lattice parameter ratios X/X 0 (a/a 0 , b/b 0 , c/c 0 ) and lattice volume ratios V/V 0 of B 2 CO 2 and B 6 C 2 O 5 and pressure are shown in Figure 2, where a 0 , b 0 , c 0 and V 0 are the zero temperature and zero pressure equilibrium lattice constants and lattice volume, respectively. For B 2 CO 2 , it can be easily seen that the compression of the b-axis is the most difficult, whereas that of the a-axis is the easiest. For B 6 C 2 O 5 , similar to B 2 CO 2 , the b-axis is the most difficult to compress, while the c-axis is the easiest to compress. When the pressure increases, the compression along the b-axis of B 6 C 2 O 5 is much larger than that along the b-axis of B 2 CO 2 . In addition, it is found that the lattice constants b/b 0 , c/c 0 compression of B 6 C 2 O 5 is changed at 10 GPa. This is because the lengths of some bonds decrease strongly along the lattice vector b-axis or the lattice vector c-axis. For example, there are three kinds of B-O bonds along the lattice vector c-axis; the bond lengths of B-O bonds are 1.571 Å (1.553 Å), 1.456 Å (1.459 Å) and 1.561 Å (1.543 Å) at 0 (5) GPa, respectively, and while the lengths of the first and the third bonds suddenly decreased to 1.516 Å and 1.508 Å under 10 GPa, the second bond length suddenly decreased to 1.489 Å under 10 GPa. Under 15 GPa, the first, second and third bond lengths dropped to 1.502 Å, 1.479 Å and 1.497 Å, respectively. From the above discussion, we can see that the abrupt change of the lattice constants c/c 0 compression of B 6 C 2 O 5 is due to the sudden decrease of the bond length of the B-O bonds along the lattice vector c-axis. The abrupt changes along the lattice vector b-axis is similar to that due to the abnormal change of the B-C bond length and the B-O bond. Their lattice constants changes show different trends with the pressure, which is related to the crystal structure and atomic composition. B 6 C 2 O 5 exists in the P1 space group, whereas B 2 CO 2 is found in the C2/m space group and the P1 space group has the lowest symmetry among the 230 space groups. In Figure 2b, for the lattice volume ratio, we predict that B 2 CO 2 has better compressive resistance than B 6 C 2 O 5 . The results of Figure 2b confirm our prediction. Here, we can also predict that the bulk modulus of B 2 CO 2 is greater than that of B 6 C 2 O 5 . while the lengths of the first and the third bonds suddenly decreased to 1.516 Å and 1.508 Å under 10 GPa, the second bond length suddenly decreased to 1.489 Å under 10 GPa. Under 15 GPa, the first, second and third bond lengths dropped to 1.502 Å, 1.479 Å and 1.497 Å, respectively. From the above discussion, we can see that the abrupt change of the lattice constants c/c0 compression of B6C2O5 is due to the sudden decrease of the bond length of the B-O bonds along the lattice vector c-axis. The abrupt changes along the lattice vector b-axis is similar to that due to the abnormal change of the B-C bond length and the B-O bond. Their lattice constants changes show different trends with the pressure, which is related to the crystal structure and atomic composition. B6C2O5 exists in the P1 space group, whereas B2CO2 is found in the C2/m space group and the P1 space group has the lowest symmetry among the 230 space groups. In Figure 2b, for the lattice volume ratio, we predict that B2CO2 has better compressive resistance than B6C2O5. The results of Figure 2b confirm our prediction.
Here, we can also predict that the bulk modulus of B2CO2 is greater than that of B6C2O5.

Stability
To demonstrate the dynamical stability of these compound, their phonon spectra are shown in Figure 3. At ambient pressure, there are no virtual frequencies in the entire Brillouin zone, proving that B2CO2 and B6C2O5 are both dynamically stable. When P = 20 GPa, there are still no virtual frequencies in the entire Brillouin zone; in other words, B2CO2 and B6C2O5 are still dynamically stable. The calculated elastic constants of B2CO2 and B6C2O5 under different pressures are listed in Table 2. The calculated elastic constants of B2CO2 and B6C2O5 at ambient pressure are in excellent agreement with the previously reported results [12]. There is no doubt that based on the data presented in Table  2, the elastic constants of B2CO2 and B6C2O5 satisfy the mechanical stability criteria [45], indicating that B2CO2 and B6C2O5 are mechanically stable. While dynamical and mechanical stabilities are verified by the phonon spectra and elastic constants, respectively, the formation enthalpy can be used to determine whether the new materials can be synthesized experimentally. Wang et al. have also described the possible synthetic routes of B2CO2 and B6C2O5 in Ref. [12]. With regard to elastic constants, compared to other B-C-O compounds, some elastic constants of B2CO2 and B6C2O5 are larger and some are smaller.

Stability
To demonstrate the dynamical stability of these compound, their phonon spectra are shown in Figure 3. At ambient pressure, there are no virtual frequencies in the entire Brillouin zone, proving that B 2 CO 2 and B 6 C 2 O 5 are both dynamically stable. When P = 20 GPa, there are still no virtual frequencies in the entire Brillouin zone; in other words, B 2 CO 2 and B 6 C 2 O 5 are still dynamically stable. The calculated elastic constants of B 2 CO 2 and B 6 C 2 O 5 under different pressures are listed in Table 2. The calculated elastic constants of B 2 CO 2 and B 6 C 2 O 5 at ambient pressure are in excellent agreement with the previously reported results [12]. There is no doubt that based on the data presented in Table 2, the elastic constants of B 2 CO 2 and B 6 C 2 O 5 satisfy the mechanical stability criteria [45], indicating that B 2 CO 2 and B 6 C 2 O 5 are mechanically stable. While dynamical and mechanical stabilities are verified by the phonon spectra and elastic constants, respectively, the formation enthalpy can be used to determine whether the new materials can be synthesized experimentally. Wang et al. have also described the possible synthetic routes of B 2 CO 2 and B 6 C 2 O 5 in Ref. [12]. With regard to elastic constants, compared to other B-C-O compounds, some elastic constants of B 2 CO 2 and B 6 C 2 O 5 are larger and some are smaller.

Mechanical Properties and Elastic Anisotropy
The primary elastic constants and elastic modulus values of B2CO2 and B6C2O5 as functions of pressure are shown in Figure 4, and the elastic modulus values for B2CO2, B6C2O5 and other B-C-O compounds are also listed in Table 2. Inspection of Figure 4 shows that almost all primary elastic constants and elastic moduli increase with increasing pressure. For B2CO2, the rate of increase of the elastic constants and elastic moduli remains almost constant, while for B6C2O5, the elastic constants and elastic moduli suddenly increase from 5 GPa to 10 GPa, and the rate of increase of elastic constants and elastic moduli remains almost constant under other pressures. As is well-known, the elastic constant represents the elastic properties of a material. Elastic constants provide a description of the relationship of stress and strain of different directions in an anisotropic medium. The elastic

Mechanical Properties and Elastic Anisotropy
The primary elastic constants and elastic modulus values of B 2 CO 2 and B 6 C 2 O 5 as functions of pressure are shown in Figure 4, and the elastic modulus values for B 2 CO 2 , B 6 C 2 O 5 and other B-C-O compounds are also listed in Table 2. Inspection of Figure 4 shows that almost all primary elastic constants and elastic moduli increase with increasing pressure. For B 2 CO 2 , the rate of increase of the elastic constants and elastic moduli remains almost constant, while for B 6 C 2 O 5 , the elastic constants and elastic moduli suddenly increase from 5 GPa to 10 GPa, and the rate of increase of elastic constants and elastic moduli remains almost constant under other pressures. As is well-known, the elastic constant represents the elastic properties of a material. Elastic constants provide a description of the relationship of stress and strain of different directions in an anisotropic medium. The elastic constants also obey Hooke's law, and strain is proportional to stress, as expressed by Hooke's law F = −kx, where k is a constant, called the stiffness coefficient. The stiffness coefficient is a complex physical quantity related to the material itself and the external conditions such as the temperature, so that the changes in the elastic constants for B 6 C 2 O 5 observed in Figure 4c are also understandable. The lattice constant changes show different trends with the pressure, which are related to the differences in the crystal structure and atomic composition. B 6 C 2 O 5 is found in the P1 space group, while B 2 CO 2 is found in the C2/m space group, and the P1 space group has the lowest symmetry among the 230 space groups. For the P1 space group, there are 21 independent elastic constants, while for the C2/m space group, there are only 13 independent elastic constants. The hardnesses of B 2 CO 2 and B 6 C 2 O 5 were calculated by Wang et al. [11] using the Chen-Niu model [47] and the Lyakhov-Oganov model [48]. The results show that B 2 CO 2 is a kind of superhard material. The Young's modulus E is calculated as: E = 9BG/(3B + G). The calculated results for Young's modulus for B 2 CO 2 and B 6 C 2 O 5 are also listed in Table 2. The Young's moduli of B 2 CO 2 and B 6 C 2 O 5 increase with pressure, and the increase for B 6 C 2 O 5 is greater than that for B 2 CO 2 . The increase for B 6 C 2 O 5 was 23.88%, almost two times larger than that of B 2 CO 2 (12.01%). constants also obey Hooke's law, and strain is proportional to stress, as expressed by Hooke's law F = −kx, where k is a constant, called the stiffness coefficient. The stiffness coefficient is a complex physical quantity related to the material itself and the external conditions such as the temperature, so that the changes in the elastic constants for B6C2O5 observed in Figure 4c are also understandable. The lattice constant changes show different trends with the pressure, which are related to the differences in the crystal structure and atomic composition. B6C2O5 is found in the P1 space group, while B2CO2 is found in the C2/m space group, and the P1 space group has the lowest symmetry among the 230 space groups. For the P1 space group, there are 21 independent elastic constants, while for the C2/m space group, there are only 13 independent elastic constants. The hardnesses of B2CO2 and B6C2O5 were calculated by Wang et al. [11] using the Chen-Niu model [47] and the Lyakhov-Oganov model [48]. The results show that B2CO2 is a kind of superhard material. The Young's modulus E is calculated as: E = 9BG/(3B + G). The calculated results for Young's modulus for B2CO2 and B6C2O5 are also listed in Table 2. The Young's moduli of B2CO2 and B6C2O5 increase with pressure, and the increase for B6C2O5 is greater than that for B2CO2. The increase for B6C2O5 was 23.88%, almost two times larger than that of B2CO2 (12.01%). To analyze the anisotropy of B2CO2 and B6C2O5 more systematically, the anisotropies of the shear moduli and Young's moduli of B2CO2 and B6C2O5 are investigated using the ELAM codes [22,45,49]. To better understand the mechanical and anisotropic properties of B2CO2 and B6C2O5, 3D surface figures of the shear moduli and Young's moduli for B2CO2 and B6C2O5 are shown in Figure 5. The 3D surface figures represent the geometric figure that consists of the maximum or minimum value of the shear modulus or Young's modulus in all directions of space. The magnitude of the shear modulus or Young's modulus in all directions can be studied by using plane cutting, and the magnitude of the shear modulus or Young's modulus in any plane can be represented by a two-dimensional graph. The 2D representations of the shear modulus and Young's modulus are shown in Figures 6 and 7, respectively. The 3D figure appears as a spherical shape for an isotropic material, while the deviation from the spherical shape is a measure of the degree of anisotropy [50]. It is clear that the shear and To analyze the anisotropy of B 2 CO 2 and B 6 C 2 O 5 more systematically, the anisotropies of the shear moduli and Young's moduli of B 2 CO 2 and B 6 C 2 O 5 are investigated using the ELAM codes [22,45,49]. To better understand the mechanical and anisotropic properties of B 2 CO 2 and B 6 C 2 O 5 , 3D surface figures of the shear moduli and Young's moduli for B 2 CO 2 and B 6 C 2 O 5 are shown in Figure 5. The 3D surface figures represent the geometric figure that consists of the maximum or minimum value of the shear modulus or Young's modulus in all directions of space. The magnitude of the shear modulus or Young's modulus in all directions can be studied by using plane cutting, and the magnitude of the shear modulus or Young's modulus in any plane can be represented by a two-dimensional graph.
The 2D representations of the shear modulus and Young's modulus are shown in Figures 6 and 7, respectively. The 3D figure appears as a spherical shape for an isotropic material, while the deviation from the spherical shape is a measure of the degree of anisotropy [50]. It is clear that the shear and Young's moduli of B 2 CO 2 and B 6 C 2 O 5 exhibit different degrees of anisotropy, and the anisotropies of the shear and Young's moduli of B 2 CO 2 and B 6 C 2 O 5 increase with as the pressure increases from 0 GPa to 20 GPa. For example, a depression appears on the minimum value surface (green surface) of the shear modulus of B 2 CO 2 at 20 GPa (see Figure 5b), but there is no dent under ambient pressure. In another example, at 20 GPa, a distinct dent appears on the three-dimensional Young's modulus surface for B 6 C 2 O 5 (see Figure 5h). Similarly, the indentation on the three-dimensional Young's modulus surface for B 6 C 2 O 5 is not so obvious at ambient pressure. Young's moduli of B2CO2 and B6C2O5 exhibit different degrees of anisotropy, and the anisotropies of the shear and Young's moduli of B2CO2 and B6C2O5 increase with as the pressure increases from 0 GPa to 20 GPa. For example, a depression appears on the minimum value surface (green surface) of the shear modulus of B2CO2 at 20 GPa (see Figure 5b), but there is no dent under ambient pressure.
In another example, at 20 GPa, a distinct dent appears on the three-dimensional Young's modulus surface for B6C2O5 (see Figure 5h). Similarly, the indentation on the three-dimensional Young's modulus surface for B6C2O5 is not so obvious at ambient pressure.  Young's moduli of B2CO2 and B6C2O5 exhibit different degrees of anisotropy, and the anisotropies of the shear and Young's moduli of B2CO2 and B6C2O5 increase with as the pressure increases from 0 GPa to 20 GPa. For example, a depression appears on the minimum value surface (green surface) of the shear modulus of B2CO2 at 20 GPa (see Figure 5b), but there is no dent under ambient pressure.
In another example, at 20 GPa, a distinct dent appears on the three-dimensional Young's modulus surface for B6C2O5 (see Figure 5h). Similarly, the indentation on the three-dimensional Young's modulus surface for B6C2O5 is not so obvious at ambient pressure.   Figure 6, the anisotropy of B2CO2 and B6C2O5 in the shear modulus increases with increasing pressure. Examination of Figure 6a shows that along the direction of the x-axis, the maximum values of shear modulus shrink inwards at 20 GPa, but the maximum values of the shear modulus remain constant in the direction of the x-axis at ambient pressure. According to the geometrical shape of the profile, the anisotropy of B6C2O5 in the shear modulus is larger than that of B2CO2 at ambient pressure, while under high pressure, the anisotropy of B6C2O5 is smaller than that of B2CO2. This can be proved by comparing the ratio of the maximum to the minimum of the shear modulus (Gmax/Gmin). The maximum and the minimum values of the shear modulus and Young's modulus for B2CO2 and B6C2O5 are listed in Table 3. The maximum value of shear modulus for B2CO2 increases with pressure, while the minimum value of the shear modulus for B2CO2 increases first and then decreases with pressure, so that the anisotropy of B2CO2 in the shear modulus becomes increasingly large. The anisotropy of B6C2O5 in the shear modulus decreases first and then increases.  Figure 6, the anisotropy of B 2 CO 2 and B 6 C 2 O 5 in the shear modulus increases with increasing pressure. Examination of Figure 6a shows that along the direction of the x-axis, the maximum values of shear modulus shrink inwards at 20 GPa, but the maximum values of the shear modulus remain constant in the direction of the x-axis at ambient pressure. According to the geometrical shape of the profile, the anisotropy of B 6 C 2 O 5 in the shear modulus is larger than that of B 2 CO 2 at ambient pressure, while under high pressure, the anisotropy of B 6 C 2 O 5 is smaller than that of B 2 CO 2 . This can be proved by comparing the ratio of the maximum to the minimum of the shear modulus (G max /G min ). The maximum and the minimum values of the shear modulus and Young's modulus for B 2 CO 2 and B 6 C 2 O 5 are listed in Table 3. The maximum value of shear modulus for B 2 CO 2 increases with pressure, while the minimum value of the shear modulus for B 2 CO 2 increases first and then decreases with pressure, so that the anisotropy of B 2 CO 2 in the shear modulus becomes increasingly large. The anisotropy of B 6 C 2 O 5 in the shear modulus decreases first and then increases.  The 2D representations of the Young's moduli of B2CO2 and B6C2O5 in the (001) plane (xy plane), (010) plane (xz plane), (100) plane (yz plane) and (111) plane are displayed in Figure 7a-h, respectively. The anisotropy of Young's modulus at each plane is also different, taking B2CO2 as an example. The Young's modulus in the (010) plane (Emax/Emin = 628 GPa/414 GPa = 1.52) of B2CO2 exhibits the largest anisotropy compared to the other planes, while the (100) plane (Emax/Emin = 734 GPa/571 GPa = 1.29) exhibits the smallest anisotropy. This result can also be demonstrated by the ratio of the maximum to the minimum of the Young's modulus at each plane. The maximum values of Young's modulus for B2CO2 appear in the (001) plane and (100) plane, while the minimum value of Young's modulus appears in the (010) plane. The maximum and minimum values appear in the same plane, whether at ambient pressure or at high pressure. Another interesting phenomenon is that  The 2D representations of the Young's moduli of B 2 CO 2 and B 6 C 2 O 5 in the (001) plane (xy plane), (010) plane (xz plane), (100) plane (yz plane) and (111) plane are displayed in Figure 7a-h, respectively. The anisotropy of Young's modulus at each plane is also different, taking B 2 CO 2 as an example. The Young's modulus in the (010) plane (E max /E min = 628 GPa/414 GPa = 1.52) of B 2 CO 2 exhibits the largest anisotropy compared to the other planes, while the (100) plane (E max /E min = 734 GPa/ 571 GPa = 1.29) exhibits the smallest anisotropy. This result can also be demonstrated by the ratio of the maximum to the minimum of the Young's modulus at each plane. The maximum values of Young's modulus for B 2 CO 2 appear in the (001) plane and (100) plane, while the minimum value of Young's modulus appears in the (010) plane. The maximum and minimum values appear in the same plane, whether at ambient pressure or at high pressure. Another interesting phenomenon is that the anisotropy of Young's modulus in the (001) plane decreases with increasing pressure, and that of the (010) plane increases with increasing pressure, while those of the (100) plane and (111) plane decrease first and then increase. For the whole material, the anisotropies of the Young's moduli of B 2 CO 2 and B 6 C 2 O 5 decrease first and then increase. In addition, although the maximum and minimum values appear in the same plane, whether at ambient pressure or at high pressure, the direction is changed. For B 6 C 2 O 5 , the maximum value appears at θ = 2.82, φ = 5.93 (the two angles are used to describe the unit vector, which is fully characterized by the angles θ (0, π), φ (0, 2π), as explained in more detail in Refs. [48,49]) at ambient pressure, where the angle is in radians. While the maximum value appears at θ = 1.59, φ = 2.90 at 10 GPa, for the pressure of 20 GPa, the maximum value appears at θ = 1.55, φ = 2.73. At these three pressures (0 GPa, 10 GPa, 20 GPa), the direction of the minimum appears to be different. However, for B 2 CO 2 , the maximum values all appear at θ = 1.57, φ = 4.73, whether at ambient pressure or at high pressure, but the direction of the minimum appears to have changed.

Electronic Properties
The electronic band structure is a significant physical property of a material that can be used to determine whether the material is a semiconductor, metal, or insulator. The electronic band structures of B 2 CO 2 and B 6 C 2 O 5 under different pressures are illustrated in Figure 8a-d, respectively. In Figure 8a [22]: the band gap of B 6 C 2 O 5 , diamond and c-BN all increase with increasing pressure, but the changes for the band gaps of diamond and c-BN are relatively smooth, and the band gap changes for B 6 C 2 O 5 are quite abrupt. Then, we investigated the origin of the pressure-driven abrupt increase of the band and the non-monotonic trend of first increase and then decrease of the band gap for B 6 C 2 O 5 and B 2 CO 2 , respectively. We analyzed the trend in the Fermi level and the conduction band minimum with the change of pressure. The relationships between the Fermi level and the conduction band minimum for B 2 CO 2 and B 6 C 2 O 5 and the pressure are shown in Figure 8f. For the Fermi level and the conduction band minimum of B 2 CO 2 and the conduction band minimum of B 6 C 2 O 5 , the changes are relatively smooth, but the energy at the CBM of B 6 C 2 O 5 increases abruptly from 0 GPa to 5 GPa and from 5 GPa to 10 GPa. Therefore, the band gaps of B 6 C 2 O 5 changes abruptly due to the sudden increase in the energy at the CBM leading to a sudden increase of the band gap from 5.309 eV under 5 GPa to 5.549 eV under 10 GPa.
To better understand why the band gap of B 6 C 2 O 5 becomes larger with increased pressure, we also analyze the density of states of B 6 C 2 O 5 . The densities of states of B 6 C 2 O 5 under different pressures are shown in Figure 9. Examination of Figure 9a shows that the valence band moves towards low energy, while the conduction band moves towards high energy in the 0-20 GPa range, so that the band gap of B 6 C 2 O 5 increases with increased pressure. However, as shown in Figure 8e, the Fermi level increases with increased pressure, so, why does the band gap of B 6 C 2 O 5 increase with the pressure in the 0-20 GPa range? According to Figure 9c, the density of states of the carbon atom almost does not vary with the pressure. Figure 9 b,d shows that, considering the density of states distribution of the oxygen atom, the peak value of the oxygen contribution to the conduction band increases with the increasing pressure, indicating that for the oxygen atoms under the action of external pressure, the local energy level is higher, resulting in reduced oxygen ions and leading to further changes of the band gap. Further consideration of the B atoms shows that the peak density of states increases with increasing pressure, decreasing the degree of localization of these atoms; however, the decrease in the density of states (from 1.07 state/eV/fu to 0.82 state/eV/fu when the pressure increases from 5 GPa to 10 GPa) is much smaller than the increase in the degree of the O atom localization (from 1.62 state/eV/fu to 3.24 state/eV/fu when the pressure increases from 5 GPa to 10 GPa), so that the results showed that the band gap of B 6 C 2 O 5 becomes larger. external pressure, the local energy level is higher, resulting in reduced oxygen ions and leading to further changes of the band gap. Further consideration of the B atoms shows that the peak density of states increases with increasing pressure, decreasing the degree of localization of these atoms; however, the decrease in the density of states (from 1.07 state/eV/fu to 0.82 state/eV/fu when the pressure increases from 5 GPa to 10 GPa) is much smaller than the increase in the degree of the O atom localization (from 1.62 state/eV/fu to 3.24 state/eV/fu when the pressure increases from 5 GPa to 10 GPa), so that the results showed that the band gap of B6C2O5 becomes larger.

Conclusions
Based on first-principles calculations, we have systematically investigated two ternary light element compounds, B6C2O5 and B2CO2. We find that such two sp 2 and sp 3 hybridized structures could be obtained by other compounds and elements and that these structures are dynamically stable through calculations of the phonon spectra for B6C2O5 and B2CO2. The electronic band structures are also calculated, showing that B2CO2 and B6C2O5 are wide-gap semiconductor materials with indirect energy gaps of approximately 5.66 and 5.24 eV, respectively. The elastic anisotropy of B2CO2 and B6C2O5 phase has been demonstrated by the Young's modulus and shear modulus along different crystal orientations. The elastic anisotropy results show that B6C2O5 exhibits a larger anisotropy in the shear modulus, while B2CO2 exhibits a larger anisotropy in Young's modulus at ambient pressure. Another interesting phenomenon is that the anisotropy of the shear modulus of B2CO2 increases with increasing pressure, while the anisotropy of Young's modulus of B2CO2, and the anisotropy of Young's modulus and the shear modulus of B6C2O5 all first decrease and then increase with increasing pressure. The changes of the physical properties of B2CO2 and B6C2O5 show different trends with the pressure, and are strongly related to the crystal structure and atomic composition. The origin of band gap increases with increased pressure is explained from the viewpoint of the density of states. In addition, hardness calculations using the Lyakhov-Oganov model show that B2CO2 is a potential superhard material.

Conclusions
Based on first-principles calculations, we have systematically investigated two ternary light element compounds, B 6 C 2 O 5 and B 2 CO 2 . We find that such two sp 2 and sp 3 hybridized structures could be obtained by other compounds and elements and that these structures are dynamically stable through calculations of the phonon spectra for B 6 C 2 O 5 and B 2 CO 2 . The electronic band structures are also calculated, showing that B 2 CO 2 and B 6 C 2 O 5 are wide-gap semiconductor materials with indirect energy gaps of approximately 5.66 and 5.24 eV, respectively. The elastic anisotropy of B 2 CO 2 and B 6 C 2 O 5 phase has been demonstrated by the Young's modulus and shear modulus along different crystal orientations. The elastic anisotropy results show that B 6 C 2 O 5 exhibits a larger anisotropy in the shear modulus, while B 2 CO 2 exhibits a larger anisotropy in Young's modulus at ambient pressure. Another interesting phenomenon is that the anisotropy of the shear modulus of B 2 CO 2 increases with increasing pressure, while the anisotropy of Young's modulus of B 2 CO 2 , and the anisotropy of Young's modulus and the shear modulus of B 6 C 2 O 5 all first decrease and then increase with increasing pressure. The changes of the physical properties of B 2 CO 2 and B 6 C 2 O 5 show different trends with the pressure, and are strongly related to the crystal structure and atomic composition. The origin of band gap increases with increased pressure is explained from the viewpoint of the density of states. In addition, hardness calculations using the Lyakhov-Oganov model show that B 2 CO 2 is a potential superhard material.