First-principles study on structural, mechanical, electrical, optical and thermal properties of lithium- and calcium-based catalysts

This work presents a systematic first-principles study of the crystal structure, mechanical, electrical, optical, and thermodynamic properties of lithium- and calcium-based catalysts (Li3N, Ca3N2, Li3BN2, and Ca3B2N4) for the production of cubic boron nitride. The mechanical findings indicate that Ca3N2 is identified as a ductile material, with a higher B/G (20.04) and Poisson’s ratio (0.48). The other three materials are recognized as brittle materials, with B/G less than 1.75 and Poisson ratio less than 1/3. The electrical discoveries show that Li3BN2 has the widest band gap among the four catalyst materials, and the band gap of ternary catalyst materials (Li3BN2 and Ca3B2N4) is larger than that of corresponding binary catalyst materials (Li3N and Ca3N2). The optical results reveal that Li3N, Ca3N2, Li3BN2, and Ca3B2N4 have sufficient energy to prevent charge carriers from being scattered or captured by material defects. The absorption peaks of Ca-based materials (Ca3N2 and Ca3B2N4) are significantly higher than those of Li-based materials (Li3N and Li3BN2). In this frequency range, the light is the most difficult to pass through in Ca3N2 and the easiest to propagate in Ca3B2N4. The connection between Li3N and Ca3N2 bands is greater, while the Li3BN2 and Ca3B2N4 bands interact rather weakly. The thermodynamic conclusions demonstrate that the thermal stability of the four structures is as follows: Li3N< Ca3N2< Li3BN2< Ca3B2N4. The heat capacities of Li3N, Ca3N2, Li3BN2, and Ca3B2N4 tend to approach 23.74, 52.05, 70.73, and 311.48 J·mol−1·K−1, respectively.


Introduction
Cubic boron nitride (c-BN) has a high hardness, good high-temperature chemical stability, corrosion resistance, and oxidation resistance [1][2][3][4][5][6][7].It does not react with metals such as iron, cobalt, and nickel at high temperatures, making it the preferred material for processing ferrous metals [1][2][3][4].In addition, c-BN, as a third-generation semiconductor material, has excellent electrical and optical properties such as an ultra-wideband gap, high thermal conductivity, and a low dielectric constant [5][6][7].It has broad application prospects in fields such as high-power electronics, deep ultraviolet optoelectronics, and quantum communication.However, due to the limitations of high-quality materials, the research on the photoelectric performance of c-BN is still in the laboratory stage.The urgent demand for mass production of large-particle c-BN single crystals has prompted researchers to explore effective methods for preparing large-size c-BN single crystals.
The static high-temperature and pressure catalyst method is the main method for the industrial synthesis of c-BN.The raw material utilized in the synthesis process of c-BN is hexagonal boron nitride, and the catalysts available are diverse.A hexagonal top press is used to create c-BN after hexagonal boron nitride and catalyst are formed into sheets and put inside the synthesis chamber.The temperature and pressure of c-BN synthesis can be considerably decreased by using an acceptable catalyst.The selection of different catalysts not only has a tremendous influence on the synthesis process, but also on the growth rate conversion, crystal type, particle size, strength, purity, and so on.At present, the catalysts used in industrial synthesis are mainly nitrides or nitride borides of alkali metals and alkaline earth metals.Many scholars have shown that alkali earth metal nitrides will produce corresponding boron nitrides at high temperatures and pressures [8][9][10].For example, in the synthetic system where Li 3 N and Ca 3 N 2 are catalysts, the corresponding metal boron nitrides Li 3 BN 2 and Ca 3 B 2 N will be generated.Many studies have shown that the real catalyst for c-BN synthesis in an alkali metal or alkaline earth metal system at high temperature and pressure is ternary alkali metal or alkaline earth metal boron nitride [8,9].E. Tadashi of the National Institute of Inorganic Materials in Japan proposed that high purity ternary compound catalysts must be used to synthesize high-grade c-BN.Researchers have carried out a series of studies on ternary compound catalysts [11][12][13][14][15][16].E. Tadashi et al synthesized c-BN using Ca 3 B 2 N 4 and found that c-BN was generated in the melt of Ca 3 B 2 N 4 , but not by the melting or decomposition of Ca 3 B 2 N 4 , which is the same as in the Li-B-N system [11].In recent years, O. Fukunaga et al used Li 3 BN 2 as a catalyst to construct a temperaturepressure diagram for the synthesis of c-BN [12,13].The study showed that the minimum temperature limit for the formation of c-BN is determined by the stability of Li 3 BN 2 .This also applies to Ca-B-N systems.The further study of composite catalysts provides a new idea for the synthesis of high-quality c-BN.
Due to the limitations of preparation conditions and technology, the further study of c-BN single crystal synthesis by composite catalyst and its application in various fields are hindered.The design of composite catalyst components is closely related to material properties.At present, the physicochemical properties of metal boron nitrides such as Li 3 BN 2 and Ca 3 B 2 N 4 are rarely reported.With the development of theoretical research, the physical properties of materials such as structural, mechanics, electricity, optics, and thermodynamics can be effectively obtained by using the first principles method [17][18][19][20][21][22][23].R. Kurchania et al [17] used density functional theory to systematically analyze the mechanical and thermal stability of lithium-based half-Heusler compounds LiAlSi and LiAlGe.H. Wang et al [18] have made a detailed analysis of the structural, mechanics, dynamics, and electronic properties of Cr-doped ZrO 2 by using the first-principles method.In this paper, the crystal structural, mechanical, electrical, optical, and thermodynamic properties of Li 3 N and Ca 3 N 2 catalysts and corresponding ternary catalysts Li 3 BN 2 and Ca 3 B 2 N 4 are systematically studied by the method of first principles, which provides theoretical support for the subsequent research of new catalysts.

Calculation method
Based on density functional theory, the calculations in this article were performed using the Vienna Ab Initial Simulation Package (VASP) software.The Perdew-Burke-Ernzerhof (PBE) in generalized gradient approximation (GGA) is selected to calculate the exchange correlation energy.The thermal properties are obtained by using the PHONOPY code.The lattice constants of the four catalyst structures, hexagonal Li 3 N (space group P6/mmm), hexagonal Ca 3 N 2 (space group P63/mmc), tetragonal The selection of appropriate cutoff energies and K-points for each catalyst structure, determined by a reasonable convergence test, significantly reduces computational resources while maintaining computation accuracy.The cutoff energies of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 are determined to be 770 eV, 880 eV, 770 eV, and 880 eV, respectively.Based on the symmetry of each crystal structure, the Brillouin-zone sampling k-points are 5 × 5 × 4, 4 × 4 × 1, 5 × 5 × 5, and 1 × 5 × 1 Monkhorst-Pack grid, respectively.The energy and force convergence criteria for geometric optimization and physical property calculation are set at 10 −5 eV/atom and 0.02 eV Å.The performance calculation in this paper is based on the optimized geometric structures of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 .The crystal structural, mechanical, electrical, optical, and thermodynamic properties of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 were calculated, respectively.The difference values were 0% and 0.25%; 0.25%, 0.98%; 0.64%, 0.19%; and 1.6%, 2.7%, and 1.45%, respectively.The difference between theoretical calculation results and previous experimental results of the lattice constants of the four catalysts [24][25][26][27] is small, which has a good agreement and also verifies the rationality of the selected calculation parameters.The mechanical, electrical, optical, and thermodynamic properties are calculated on the basis of the four optimized structures.

Mechanical properties
For the four catalytic structures, Li 3 N and Ca 3 N 2 belong to the hexagonal system, Li 3 BN 2 to the tetragonal system, and Ca 3 B 2 N 4 to the orthorhombic system.Based on the Voigt-Reuss-Hill averaging scheme [28,29], the mechanical parameters can be obtained including Bulk modulus (B), Shear modulus (G), Young's modulus (E)), and Poisson's ratio (ν).The bulk modulus B H and shear modulus G H of the four structures are expressed as:    = + - 15 The formula for calculating Young's modulus E and Poisson's ratio is as follows: The elastic constant can be used to judge the mechanical stability of crystals with a certain spatial structure [30,31].According to the Born stability criterion, for hexagonal crystal systems: ´-´> According to the above criterion, it is found that the crystal structure of Li 3 N meets the criterion conditions and can be judged to have mechanical stability, while the Ca 3 N 2 structure does not meet the Born stability criterion of the criterion conditions, so its structure is unstable at room temperature and atmospheric pressure.
The Born stability criterion of tetragonal system is: The tetragonal Li 3 BN 2 satisfies the criterion conditions, and its crystal structure can also be judged to have mechanical stability.
The orthorhombic Ca 3 B 2 N 4 satisfies the above criteria, so it is determined that its crystal structure has mechanical stability.
The relationship between Vickers hardness (H V ) and B and G is [32]: Table 1 shows the calculated parameters for the elastic properties of the four catalytic structures.The calculated Vickers hardness of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 are 10.14 GPa, 0.10 GPa, 13.67 GPa, and 9.71 GPa, respectively.This shows that Li 3 N, Li 3 BN 2 , and Ca 3 B 2 N 4 are all hard, while Ca 3 N 2 is soft.The brittleness of the material can be determined by the values of B/G and the Poisson's ratio.When B/G>1.75 or Poisson ratio ν > 1/3, it is usually considered ductile material; otherwise, it is brittle material.By comparing four different materials, it is found that the B/G of Ca 3 N 2 is 20.04, much higher than 1.75, and the Poisson ratio ν is 0.48, so Ca 3 N 2 is identified as a ductile material.According to P. Meena et al 's research, cubic Ca 3 N 2 has a Poisson ratio of 0.275 [33], indicating that it is a ductile material as well.The B/G of other materials is less than 1.75, and the Poisson ratio ν is less than 1/3, so Li 3 N, Li 3 BN 2 , and Ca 3 B 2 N 4 are brittle materials.Li 3 N and Ca 3 N 2 with h-BN under pressure and temperature convey Li 3 BN 2 and Ca 3 B 2 N 4 , respectively.While N atoms typically prefer a typically octahedral metal co-ordination (N-Li and N-Ca), which is frequently replaced by a tetragonal bipyramidal co-ordination (N-B-Li and N-B-Ca), B atoms tend to adopt a triangular prismatic metal coordination (B-Li and B-Ca) or a tetrahedral surrounding B-Li and B-Ca, depending on the formation of the boron-metal and nitrogen-metal bond structures [34].The B-N covalent bond and boron-metal bond are stronger than those of the nitrogen-metal bond structures.The ternary catalysts have a greater packing density than the comparable binary catalysts.As a result, the ternary catalyst has a higher B/G value, shear modulus, and a lower Poisson's ratio than the corresponding binary catalyst.The crystal structures of Li 3 N and Ca 3 N 2 are both hexagonal, however, the interlayer spacing (c-value) of Ca 3 N 2 is significantly higher than that of Li 3 N.As a result, interlayer sliding is more likely to occur in response to external forces.The synergistic effect of these above factors results in Ca 3 N 2 having lower hardness, better ductility and higher shear modulus and Poisson's ratio values.
Hexagonal boron nitride and the catalyst are combined and pressed into sheets to produce c-BN.Low hardness and high ductility minimize production complexity and cost during sample processing.It was discovered by characterizing the synthetic samples that single crystals of c-BN were situated in between the catalyst and hexagonal boron nitride.Rapid nucleation and large-particle c-BN single crystal growth are advantageous when raw materials are ground, and catalyst and hexagonal boron nitride are well mixed.Water and oxygen are known to react with the catalyst during the production process as main impurities, which can have an impact on the catalytic activity.The Ca 3 N 2 material has a higher specific surface area, porosity, and superior adsorption capacity because of its high ductility and low mechanical strength.This is advantageous for the temperature-pressure reaction of Ca 3 N 2 with the raw material, but it can also lead to unintended reactions between Ca 3 N 2 and impurities, which would increase the number of defects in the final c-BN single crystal that is synthesized.1.37 eV for Ca 3 N 2 [25], and 2.2 eV for Ca 3 B 2 N 4 [35], which are in good agreement with previous research results [36], further demonstrating the accuracy of the calculated results in this work.Therefore, it can be seen that the band gap of the ternary catalyst structure (Li 3 BN 2 and Ca 3 B 2 N 4 ) is higher than that of the binary catalyst structure (Li 3 N and Ca 3 N 2 ).This is mainly due to the stronger polarity of the valence bonds contained in the ternary catalyst structure.

Electrical properties
Figures 3(a   The E F is located between peaks and valleys and can qualitatively indicate the stability and conductivity of the material.At E F , the total DOS of the four catalyst structures is not zero, which indicates that the bonding types of the four catalyst structures are mainly covalent bonds and some ionic bonds, so they have certain metallic characteristics.The sharpness of DOS peak reflects the strength of the interaction in this region.According to the sharpness of the peak, it can be divided into Ca 3 B 2 N 4 > Ca 3 N 2 > Li 3 BN 2 > Li 3 N.Therefore, the interaction between electrons of ternary catalysts is stronger than that of binary catalysts, and the interaction between electrons of Ca-based catalysts is stronger than that of Li-based catalysts.By comparing the orbitals of the different atoms, we can find that the widening of the energy gap of the ternary catalysts is mainly due to the extra B-2p orbitals at the top of the valence band and at the lower part of the conduction band compared to the corresponding binary catalysts.The B-2p and N-2p orbitals of the ternary catalysts overlap in different energy regions, especially in the top region of the valence band, suggesting that the B and N atoms are able to form strong covalent bonding connections.Ternary catalysts undergo structural changes due to the incorporation of B atoms, which results in tensile stress and lattice expansion, thus altering their electrical properties.The introduction of B atoms can isolate the metal ions and produce specific surface metal sites, which is beneficial for promoting the catalytic reaction.In addition, due to the difference in electronegativity between the different atoms, the charge is redistributed, thus also affecting the electronic structure of the ternary catalyst.The stronger the electronegativity of an element, the greater the ability of its atoms to attract electrons in a compound.In the process of c-BN synthesis, hexagonal boron nitride transforms B and N atoms from the sp 2 hybrid state to the sp 3 hybrid state during the transformation process.Compared to calcium-based catalysts, because lithium atoms are more reactive and less electronegative, they are more likely to lose electrons, which helps lithium atoms realize the transfer of charged electrons between B and N atoms.With their stronger ability to transfer charges, this can explain the higher nucleation rate of c-BN single crystal systems synthesized from lithiumbased catalysts.

Optical properties
By studying the optical properties of materials, potential photoelectric applications can be found [37][38][39][40][41].The calculation of complex dielectric functions is one of the best methods to study the optical properties of materials.The complex dielectric function ε(ω) = ε 1 (ω) + ε 2 (ω), which is often used to describe the optical properties, where the real part is ε 1 (ω) and the imaginary part is ε 2 (ω). Figure 4 shows the relationship between the real part ε 1 (ω) and the imaginary part ε 2 (ω) of complex dielectric functions of different catalyst structures with incident light energy E in .
The difference in dielectric constants of the four catalyst structures stems from the fact that they have complex structures with different symmetries, giving rise to differences in polarization effects.As shown in figure 4, when the incident light energy Ein = 0 at 0 GPa, the real parts of the dielectric constants ε(0) of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 in the x-direction are 6.31, 6.41, 4.31, and 4.39, respectively, corresponding to the real parts of the dielectric constant ε(0) in the z-direction are 5.97, 7.18, 3.74, and 4.23, respectively.The results indicate that Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 have good energy to prevent charge carriers from being scattered or captured by material defects; Ca-based materials (Ca 3 N 2 and Ca 3 B 2 N 4 ) have higher dielectric functions compared to Li-based materials (Li 3 N and Li 3 BN 2 ); and binary catalysts (Li 3 N and Ca 3 N 2 ) have better dielectric shielding effects than ternary catalysts (Li 3 BN 2 and Ca 3 B 2 N 4 ).The real part of the dielectric constant of Ca 3 N 2 is the largest, and the maximum intensity peak value is the largest, which indicates that the maximum polarization state of Ca 3 N 2 is the largest among the four catalyst structures.The highest dielectric constant of Ca 3 N 2 is due to the weaker metallicity of Ca, the higher electronegativity of N atoms, and the soft vibration mode [33].Meena et al reported that the ε(0) of Ca 3 N 2 is 8.87 in their recent study [33], which is slightly lower than that obtained from the calculation in this work, and this is relevant to computational modeling as well as the accuracy of the calculation software and method.
The imaginary part of the dielectric constant of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 in the x-direction ε 2 (ω) has significant peaks at 8.23, 5.60, 4.20, and 4.58 eV, respectively.The imaginary part of the dielectric constant of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 in the z-direction ε 2 (ω) has peaks of (0) at 3.53, 5.16, 3.68, and 4.55 eV, respectively.Combined with the density of states in figure 3, the main reason for the peak appearance is the electronic transitions of N-2p, Ca-3d, and B-2p.Materials with high dielectric constants can be candidates for high-end storage containers, and photoelectric devices with a long carrier migration distance, a long carrier lifetime, and high carrier mobility.Although no outcomes have been reported from the experimental studies on the photovoltaic properties of Ca 3 N 2 for application, J. Ding et al prepared Ca 3 B 2 N 4 self-activated yellow luminescent phosphor with long-lasting glow characteristics [35].The imaginary part of the dielectric constant of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 in the low energy region ε(ω) starts to rise at 0.13, 1.82, 0.01, and 2.13 eV in the x direction and starts to rise at 0.01, 2.16, 0.01, and 0.88 eV in the z direction.This corresponds to the absorption boundaries of Li 3 N, Ca 3 N 2 , Li 3 BN 2 and Ca 3 B 2 N 4 shown in figure 5, respectively.This also indicates that Li 3 N, Ca 3 N 2 , Li 3 BN 2 and Ca 3 B 2 N 4 all have certain conductivity, consistent with the above electronic structure analysis.From figure 5, it can be seen that the absorption peaks of Ca-based materials (Ca 3 N 2 and Ca 3 B 2 N 4 ) are significantly higher than those of Li-based materials (Li 3 N and Li 3 BN 2 ).This occurs because it is easier to achieve the electronic transition between the dense N-2p and Ca-3d shells.The reflectivity of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 is shown in figure 6.The different reflectivity of the same structure in the x and z directions indicates significant anisotropy between the two components in the x and z polarization directions, with the reflectivity of the x component being higher than that of the z component.At the same time, the response performance of different materials varies greatly under different frequencies of incident light.In fact, all four catalytic materials have relatively low reflectivity, and among them, Ca 3 N 2 is the highest, followed by Li 3 N and Li 3 BN 2 , and lastly Ca 3 B 2 N 4 .The maximum reflection peaks of four catalytic materials are observed in the ultraviolet region.
Figure 7 shows the energy loss of photoelectrons passing through Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 .We can see that there is no energy loss in the infrared region for all four catalytic materials, and there is a significant energy loss peak in the ultraviolet region.Compared to Li 3 BN 2 and Ca 3 B 2 N 4 , the energy loss peaks of Li 3 N and Ca 3 N 2 are sharper and larger, which corresponds to the results of reflectivity in figure 6.The Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 materials have maximum energy loss peaks at 14.84 eV, 12.52 eV, 19.02 eV, and 31.40 eV, respectively.The maximum energy loss of the material is consistent with the plasma frequency, so we can determine the plasma frequency of each of the four catalytic materials using the four peaks mentioned above.The plasma frequency is important because light waves below the plasma frequency are perfectly reflected by the substance [33,41].Therefore, we can infer that the four catalytic materials have good reflective ability for light in the infrared and visible wavelengths.Due to its lowest reflectivity in the infrared and visible light regions, Ca 3 B 2 N 4 deserves further investigation for applications in infrared detectors.

Thermodynamic properties
As shown in figure 8, we calculated the thermodynamic properties (vibrational free energy, entropy, heat capacity, and enthalpy) of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 in the temperature range of 0 ∼ 3000 K. From figure 8(a), it can be seen that the vibration-free energy of all four catalyst structures decreases with increasing temperature.The reduction in vibration-free energy of binary catalyst structures Li 3 N and Ca 3 N 2 is smaller than that of ternary catalyst structures Li 3 BN 2 and Ca 3 B 2 N 4 .Among them, the trend of free energy changes in Ca 3 N 2 and Li 3 BN 2 is relatively similar, while the decrease in free energy of Ca 3 B 2 N 4 is significantly higher than that of the other three catalyst materials.The free energy of vibration can be used as a standard to measure the thermal stability of materials.Generally speaking, the lower the free energy of vibration, the better the thermal stability [22,42].It can be seen that the thermal stability of the four structures is as follows: Li 3 N< Ca 3 N 2 < Li 3 BN 2 < Ca 3 B 2 N 4 .The thermal stability of Ca 3 B 2 N 4 is significantly superior to the other three catalyst structures.Compared to Li 3 N, Ca 3 N 2 has better thermal stability, mainly due to the difference in electronegativity and activity of the two metal atoms, Li and Ca, resulting in Ca possessing a stronger ability to bind electrons.Because of the addition of the B atom, the crystal structure of the ternary catalyst produces a B-N covalent bond with greater bond energy and stronger atomic vibration, resulting in greater thermal stability of the ternary catalyst when compared to the binary catalyst.Ca 3 B 2 N 4 can be dissolved into Ca 2+ and B 2 N 4 6-, while Li 3 BN 2 can be dissociated into Li + and BN 2 3-.N-B-N in BN 2 3-is connected in a chain form, with the shortest distance between B-N being 1.347, and N-B-N in B 2 N 4 6-is connected in a tetrahedral bi-pyramidal form, with the shortest distance between B-N being 1.339.Therefore, in terms of atomic structure and bond length, the bonding between the B atom and its adjacent N atom is greater in the Ca 3 B 2 N 4 structure, as is the atomic vibration and thermal stability.
The degree of disorder in a physical system can be reflected by entropy.Vibration entropy may be used to study the fluctuation of vibration-free energies regarding temperature [22,43].As shown in figure 8(b), the four catalyst materials investigated in this paper are primarily composed of three covalent bonds: Metal (Li or Ca)-B, Metal (Li or Ca)-N, and B-N.The number of resonances between nearby atoms increases as the temperature rises, resulting in an increase in amplitude and entropy [22,43].Ca 3 B 2 N 4 has a more complex structure, the highest entropy, the most disorder, and more microscopic states or degrees of freedom at high temperatures, making it more thermally stable when the temperature changes.The lower limit of synthesis temperature in the c-BN synthesis process is connected to the catalytic melting point.Ca 3 B 2 N 4 has higher thermal stability as well as a higher melting point; therefore, the synthesis temperature required for c-BN synthesis is higher.The lowest synthesis temperature of Li 3 BN 2 , for example, is 1050 °C [12,13], while the synthesis temperature range of Ca 3 B 2 N 4 is 1200 °C [11,13].Ca 3 B 2 N 4 , as a catalyst, has a higher nucleation rate at a higher temperature of 1500 °C [11,13].Enthalpy is an essential quantity in the thermodynamic theory that describes the energy of the material's systems.As shown in figure 8(c), the enthalpy values of the four catalyst structures increase with increasing temperature.From figure 8(d), it can be seen that the heat capacity of the four catalyst materials grows fast at a lower temperature and corresponds to T 3 .At low temperatures, it obeys Debye's rule of specific heat [44,45].According to the Dulong-Petit rule of classical thermodynamics, when the temperature climbs above the Debye temperature, the heat capacity values of the four catalysts increase and become closer to the Duron-Petty limit values [46].The heat capacities of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 tend to approach 23.74, 52.05, 70.73, and 311.48 J•mol −1 •K −1 , respectively.
With their superior mechanical, electrical, optical, and thermodynamic properties, the four materials computed in this work not only have a wide variety of applications in the field of catalysts, but also have extensive application possibilities in the fields of energy and photovoltaics [47][48][49][50][51][52].Because of their inexpensive cost, Li 3 N and Ca 3 N 2 are more extensively utilized in the industry as catalysts, and the synthesis process of c-BN crystals is characterized by a higher nucleation rate but a slow growth rate.Because the reaction between metal nitride and h-BN is reduced at high temperature and pressure in Li 3 BN 2 and Ca 3 B 2 N 4 , the temperature and pressure required for synthesizing c-BN are lower, and the synthesized c-BN has a higher growth rate, allowing it to form c-BN grains with larger particles.Due to the semiconducting properties of Li-based catalyst materials and the fact that the metal Li is very reactive, it is able to have better electrical conductivity after being de-embedded from Li 3 N and Li 3 BN 2 , and therefore has a better prospect for application in the field of lithium-ion batteries.S. Emani reported the application of Li 3 BN 2 as a high-capacity cathode [47].M. Shigeno studied glassy Li 3 BN 2 is a potential electrolyte for all-solid-state batteries, because of its high conductivity, excellent mechanical qualities, and electrochemical stability [48].In recent years, due to the demand for sustainable green energy in the field of photovoltaics, Ca-based catalysts have become excellent candidates for photovoltaic applications due to their semiconducting properties as well as their excellent mechanical and optical properties [49][50][51].J. Ding reported the application of Ca 3 B 2 N 4 as light-emitting phosphors with a long afterglow property [35].The calculations on the four catalyst materials in this paper are comprehensive and novel, which can offer theoretical assistance for the development of new catalyst materials and the enhancement of substitute optoelectronic materials for unique solar applications.

Conclusion
The following conclusions may be drawn from a comparison of the structural, mechanical, electrical, optical, and thermodynamic characteristics of the catalyst materials Li The sharpness of DOS peaks for the four types of catalyst structures varies from large to small: Ca 3 B 2 N 4 >Ca 3 N 2 >Li 3 BN 2 >Li 3 N.Therefore, the electron-to-electron interaction of ternary catalysts is stronger than that of binary catalysts, and the electron-to-electron interaction of Ca-based catalysts is stronger than that of Li-based catalysts.
Optical performance analysis found that suitable optoelectronic materials with long carrier migration distance, long carrier lifetime, and high carrier mobility are as follows: Ca 3 N 2 , Li 3 N, Ca 3 B 2 N 4 , and Li 3 BN 2 .
Thermodynamic performance analysis found that the thermal stability of the four structures is as follows: Li 3 N< Ca 3 N 2 < Li 3 BN 2 < Ca 3 B 2 N 4 .The thermal stability of Ca 3 B 2 N 4 is significantly superior to the other three catalyst structures.

Figure 1 .
Figure 1.Crystal structures of different catalysts (a) Li 3 N; (b) Li 3 BN 2 ; (c) Ca 3 N 2 ; (d) Ca 3 B 2 N 4 .The purple ball is the Li atom, the green ball is the Ca atom, the pink ball is the B atom, and the blue ball is the N atom.
Figures 2(a)-(d) shows the band structures of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 , respectively.It can be seen from figure 2 that among the four catalyst materials, Li 3 BN 2 has the widest band gap (3.448 eV).The band gap of the other three catalyst structures, in order of magnitude, is: Ca 3 B 2 N 4 (2.269 eV), Ca 3 N 2 (1.349 eV), and Li 3 N (1.048 eV).For a brief comparison, the values of the band gap are 0.98 eV for Li 3 N [24], 3.45 eV for Li 3 BN 2 [26], )-(d) shows the state densities and partial wave state densities of Li 3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 , respectively.The DOS in Li 3 N is mainly divided into four parts: −45.38 ∼ −43.12 eV at the bottom of the valence band, mainly from the Li-s orbital.The upper valence bands of −12.34 ∼ −10.48 eV and −3.23 ∼ 0.009 eV are mainly derived from the N-2p orbital.The 0.02 ∼ 13.06 eV of the conduction band is mainly derived from the Li-s and N-2p orbits.DOS analysis of Li 3 N shows that the proportion of 2s orbitals in the valence band is larger than that of 2p orbitals, and the proportion of 2p orbitals in the conduction band is slightly larger than that of 2s orbitals.The comparison of the PDOS of Li and N atoms shows that the N atom plays a greater role in the valence band of Li 3 N than the Li atom because the electronegativity of N is higher than that of the Li atom.As shown in figure3(b), the DOS of Li 3 BN 2 can also be divided into four parts: −45.32 ∼ −42.64 eV with the valence band bottom, which comes from the Li-s orbit.The upper valence bands of −15.01 ∼ −12.38 eV and −5.40 ∼ 0.57 eV are mainly derived from B-2p and N-2p orbitals.Li-s, B-2p, and N-2p all contribute to 2.95 ∼ 16.35 eV of the conduction band.The DOS analysis of Li 3 BN 2 shows that the proportion of 2p orbitals in the valence band is obviously larger than that of 2s orbitals, and the proportion of 2s orbitals in the conduction band is slightly larger than that of 2p orbitals.The comparison of the PDOS of Li, B, and N atoms shows that the B and N atoms play a greater role in the valence band of Li 3 BN 2 than the Li atoms, because the electronegativity of B and N is higher than that of Li.It can be seen from figure 3(c) that the valence band of Ca 3 N 2 is mainly contributed by the Ca-4s and N-2p orbitals, while the conduction band is partially contributed by the N-p and Ca-3d orbitals.As shown in figure 3(d), the valence band of Ca 3 B 2 N 4 is mainly contributed by B-2p and N-2p orbitals, and the conduction band is mainly contributed by Ca-3d orbitals.
3 N, Ca 3 N 2 , Li 3 BN 2 , and Ca 3 B 2 N 4 for the synthesis of c-BN: Mechanical property analysis shows that Ca 3 N 2 is a ductile material.Li 3 N, Li 3 BN 2 , and Ca 3 B 2 N 4 are brittle materials.The energy band gaps of the four types of catalyst materials are arranged in order of size: Li 3 BN 2 (3.448 eV) > Ca 3 B 2 N 4 (2.269 eV) > Ca 3 N 2 (1.349 eV) >Li 3 N (1.048 eV).