Effects of Doped Elements (Si, Cr, W and Nb) on the Stability, Mechanical Properties and Electronic Structures of MoAlB Phase by the First-Principles Calculation

First-principles calculations based on density functional theory (DFT) have been performed to explore the effects of Si, Cr, W, and Nb elements on the stability, mechanical properties, and electronic structures of MoAlB ternary boride. The five crystals, with the formulas of Mo4Al4B4, Mo4Al3SiB4, Mo3CrAl4B4, Mo3WAl4B4, and Mo3NbAl4B4, have been respectively established. All the calculated crystals are thermodynamically stable, according to the negative cohesive energy and formation enthalpy. By the calculation of elastic constants, the mechanical moduli and ductility evolutions of MoAlB with elemental doping can be further estimated, with the aid of B/G and Poisson’s ratios. Si and W doping cannot only enhance the Young’s modulus of MoAlB, but also improve the ductility to some degree. Simultaneously, the elastic moduli of MoAlB are supposed to become more isotropic after Si and W addition. However, Cr and Nb doping plays a negative role in ameliorating the mechanical properties. Through the analysis of electronic structures and chemical bonding, the evolutions of chemical bondings can be disclosed with the addition of dopant. The enhancement of B-B, Al/Si-B, and Al/Si-Mo bondings takes place after Si substitution, and W addition apparently intensifies the bonding with B and Al. In this case, the strengthening of chemical bonding after Si and W doping exactly accounts for the improvement of mechanical properties of MoAlB. Additionally, Si doping can also improve the Debye temperature and melting point of the MoAlB crystal. Overall, Si element is predicted to be the optimized dopant to ameliorate the mechanical properties of MoAlB.


Introduction
Binary transition metal borides are regarded as the superior candidates for high-temperature structural ceramics, due to their outstanding properties, such as high melting temperature, high hardness, and thermodynamic stability [1][2][3]. However, the inherent brittleness, poor oxidation resistance, as well as low damage tolerance have impeded the application of binary borides. To address these limitations, the researchers have tried to introduce an Al atomic layer into transition metal borides to form so-called MAB phases [4,5]. In MAB phases, single or double Al atomic layers are interleaved into a transition metal boride sublattice. The structures of MAB phases are analogous to the previous MAX phases, which show significant advantages for both metal and ceramics with good heat and electricity conduction, and considerable ductility and damage tolerance [6][7][8][9][10]. In this case, MAB phases are also expected to possess the excellent properties of both metals and borides.

Methodology
In this work, the calculations were performed by using density functional theory (DFT) implemented in the Cambridge Serial Total Energy Package (CASTEP) code [39,40]. The exchange correlation energy was treated according to the generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) [41,42]. Ultrasoft pseudopotentials were employed to describe the interactions between the ionic core and valence electrons in the reciprocal space [43]. The plane wave energy cutoff was fixed at 600 eV. Brillouin zone sampling was conducted by Monkhorst-Pack method, with the special k-point mesh of 10 × 10 × 10. The crystal was fully optimized by modifying the lattice parameters and internal atomic positions using the Broyden-Fletcher-Goldfarb-Shannon (BFGS) minimization scheme [44]. The total energy of the lattice structure was minimized to converge to 5 × 10 −6 eV/atom, along with the ionic Hellmann-Feynman force components, ionic displacements, and stress tensor components being converged to within 0.01 eV/Å, 5 × 10 −4 Å, and 0.02 GPa, respectively. Figure 1a illustrates the crystal cell of initial MoAlB, with an orthorhombic lattice structure. Mo, Al, and B atoms occupy the 4c Wyckoff positions of the Cmcm space group [11]. In this research, the crystal model of Si doped MoAlB was established by replacing one Al atom by Si, considering the similar atomic radius, as shown in Figure 1b. However, given the similarity among Cr, W, Nb, and Mo, the crystal structure of X (X representing Cr, W, or Nb) doped MoAlB was obtained with one X atom occupying the initial Mo position [45]. The crystal structure of X doped MoAlB is shown in Figure 1c. In this case, five crystals with the formulas of Mo 4 Al 4 B 4 , Mo 4 Al 3 SiB 4 , Mo 3 CrAl 4 B 4 , Mo 3 WAl 4 B 4 , and Mo 3 NbAl 4 B 4 were investigated in this work, involving the stability, mechanical properties, electronic structures, and thermal properties.
Materials 2020, 13, x FOR PEER REVIEW 3 of 18 components, ionic displacements, and stress tensor components being converged to within 0.01 eV/Å , 5 × 10 −4 Å , and 0.02 GPa, respectively. Figure 1a illustrates the crystal cell of initial MoAlB, with an orthorhombic lattice structure. Mo, Al, and B atoms occupy the 4c Wyckoff positions of the Cmcm space group [11]. In this research, the crystal model of Si doped MoAlB was established by replacing one Al atom by Si, considering the similar atomic radius, as shown in Figure 1b. However, given the similarity among Cr, W, Nb, and Mo, the crystal structure of X (X representing Cr, W, or Nb) doped MoAlB was obtained with one X atom occupying the initial Mo position [45]. The crystal structure of X doped MoAlB is shown in Figure 1c. In this case, five crystals with the formulas of Mo4Al4B4, Mo4Al3SiB4, Mo3CrAl4B4, Mo3WAl4B4, and Mo3NbAl4B4 were investigated in this work, involving the stability, mechanical properties, electronic structures, and thermal properties. (c) X doped MoAlB.

Equilibrium Structure and Stability
After full optimization, the calculated lattice parameters of the five crystal structures are shown in Table 1. Compared with experimental results, the theoretical results of MoAlB in this work show great agreement, with the deviations less than 0.56% [5,46]. In addition, the results in this work are highly consistent with the reported theoretical results calculated with the same method [47]. Thus, the calculating method and parameters implemented in this work are supposed to be suitable, which ensures highly accurate predictions of other doped crystals. From Table 1, it can be found that the volume of crystal cell shrunk after adding Si and Cr, while it tended to swell with the addition of W and Nb. This phenomenon can be easily understood considering the deviations between the doped atom and the initial one. In addition, Cr doped MoAlB crystal shows the lowest density, which decreases by 5.7% compared with the non-doping MoAlB. On the contrary, W doping dramatically increases the density of MoAlB by about 16.4%.
Thermostability of the crystal is an important parameter in evaluating the possibility of the doping reaction, and can be estimated by the parameters of cohesive energy (Ecoh) and formation

Equilibrium Structure and Stability
After full optimization, the calculated lattice parameters of the five crystal structures are shown in Table 1. Compared with experimental results, the theoretical results of MoAlB in this work show great agreement, with the deviations less than 0.56% [5,46]. In addition, the results in this work are highly consistent with the reported theoretical results calculated with the same method [47]. Thus, the calculating method and parameters implemented in this work are supposed to be suitable, which ensures highly accurate predictions of other doped crystals. From Table 1, it can be found that the volume of crystal cell shrunk after adding Si and Cr, while it tended to swell with the addition of W and Nb. This phenomenon can be easily understood considering the deviations between the doped atom and the initial one. In addition, Cr doped MoAlB crystal shows the lowest density, which decreases by 5.7% compared with the non-doping MoAlB. On the contrary, W doping dramatically increases the density of MoAlB by about 16.4%. Thermostability of the crystal is an important parameter in evaluating the possibility of the doping reaction, and can be estimated by the parameters of cohesive energy (E coh ) and formation enthalpy (∆H r ). In general, negative values of E coh and ∆H r indicate the crystal structure to be thermodynamically stable. The E coh and ∆H r of a compound can be calculated according to Equations (1) and (2) [48][49][50][51]: where E tol represents for total energy; E iso and E bulk represent the energy of an isolated atom and a single atom in bulk state, respectively. From

Elastic Properties
The mechanical properties can be investigated by calculating the elastic constants of the crystals. In this work, the elastic constants have been evaluated by the stress-strain method, where the stress-strain curve was described by generalized Hooker's law, as shown in Equation (3): where σ ij represents for the stress tensor; εij and Cijkl represent the Lagrangian strain tensor and elastic constant tensor, respectively. The elastic constants (C ij ) of all the five crystals have been calculated and listed in Table 2. The second order elastic constants of MoAlB show pretty good agreement with the reported results [37,47], indicating the reliability of our calculation. The mechanical stability of compounds can be justified according to Boron-Huang's criteria [52][53][54]. For the MoAlB crystals with orthorhombic lattice, the general criteria can be expressed as Equation (4): According to the constants in Table 2, all five crystal structures are mechanically stable, as they fully satisfy the above stability criterion. Like the MAX phases, the C 11 , C 22 , and C 33 of MoAlB crystal, representing elastic stiffness against principal strain, are much higher than those against shear strains (C 44 , C 55 and C 66 ). In other words, MoAlB crystal is considerably incompressible along a, b, and c crystal axis, but shows relatively weaker resistance to the shear deformation on the (1 0 0), (0 1 0) and (0 0 1) planes. Furthermore, it can be observed that C 11 and C 33 are higher than C 22 for all five crystals, indicating that MoAlB is more incompressible along the a and c axes [38]. The weaker incompressibility along the b axis may be attributed to the double-layer Al. C 33 is the largest among all the elastic constants, which signifies the strongest covalent bonding along the c axis. Compared with initial MoAlB, Si and W doping are beneficial to improving the incompressibility along the a and c axes, with the increase of C 11 and C 33 . On the other hand, it is apparent that the resistance to shear on the (0 1 0) plane is the weakest considering the smallest C 55 value. However, the (1 0 0) plane is expected to show the strongest resistance to shear. Intrinsically, the elastic properties are mainly responding to the chemical bonding in the crystal, which will be deeply discussed thereinafter.
The ductility and brittleness of a compound can be verified by the value of Cauchy pressure on some extent [38]. If the Cauchy pressure is negative, the compound is expected to be brittle in nature. According to Table 2, Cauchy pressure of each calculated crystal can be calculated by the equation of (C 12 -C 44 ). It can be deduced from the negative Cauchy pressures that the calculated MoAlB crystals are intrinsically brittle. Furthermore, the ductility relation is The bulk modulus (B), shear modulus(G), and Young's modulus(E) can be estimated based on the elastic constants (C ij ), according to the Voigt-Reuss-Hill (VRH) scheme [55]. The VRH approximation means the average of Voigt and Reuss approximations. Herein, Voigt approximation, based on the assumption of uniform strain, decides the upper bounds of the elastic modulus, as expressed by Equations (5) and (6): And Reuss approximation, based on the assumption of uniform stress, decides the lower bounds. It can be defined as the elastic compliances (S ij ) which are the inverse matrix of C ij , as expressed by Equations (7) and (8): Finally, the B, G, and E can be obtained following Equations (9)- (11), and Poisson's ratio (ν) can be calculated according to Equation (12). Table 3 lists the calculated bulk moduli (B), shear moduli (G), and Young's moduli (E) of all five calculated crystals. Additionally, the moduli data at 300K, measured by high-temperature resonant ultrasound spectroscopy (RUS) by Kota et al., have been provided as a comparison [56]. As shown, the calculated E of MoAlB is a little underestimated in this work compared with the experimental result. The calculated bulk modulus, shear modulus, and Young's modulus have been plotted in Figure 2a. First, it can be found that Young's moduli of MoAlB are considerably higher, with the values larger than 350 GPa indicating the strong chemical bonding inside the crystal. From Figure 2a, it can be visibly observed that the bulk modulus (B) is substantially larger than the shear modulus (G). Intriguingly, Si and W doped MoAlB exhibits a relatively higher elastic moduli compared to the others. This implies Si and W doping can help enhance the bonding interactions among the atoms. However, Cr and Nb doping seem to be detrimental to the elastic moduli. On the other hand, Pugh's ratio can be obtained by calculating the ratio of B/G. B/G ratio is usually used to judge the ductile and brittle character of a solid [57]. A higher B/G value indicates a higher ductility, with a critical value of 1.75. Thus, the five calculated MoAlB crystals can be classified as brittle materials, with a B/G value less than 1.75, which is totally consistent with the prediction from Cauchy pressure. However, according to the previously reported experimental results [5,14,17,22], MoAlB exhibits considerable toughness and damage tolerance. In this case, the predication about the toughness of MoAlB may not be so dependent as other compounds on the value the of B/G ratio. This phenomenon agrees well with the literature's reports that Pugh's ratio may not necessarily be a strong indication of ductility, for the ternary layered compounds, such as MAB and MAX phases [36,58,59], because the effects of the layered structure, and significantly weak bonds of Al, on ductility, are underestimated during the calculation.

Elastic Anisotropy
The anisotropy of mechanical properties is a key factor that affects the material's properties. Microcracks usually appear, originating from the mechanical anisotropy of materials. In MoAlB crystal, the elastic modulus along different principal axes are expected to differ from each other, considering the difference in the elastic constants in Table 2. To reveal the anisotropic features, the universal anisotropic index (A U ), percent anisotropies (A B and A G ), and shear anisotropic indexes (A1, A2 and A3) have been calculated in this work according to Equations (13)-(18): Poisson's ratio is also one of the important parameters in assessing the solid's ductility and brittleness. With the critical value of 0.26, the material with a Poisson's ratio lower than this usually behaves in a brittle manner, otherwise the material is expected to be ductile. In this context, the five calculated MoAlB crystals are all classified as brittle materials. This shows great consistency with the results of Cauchy's pressure and B/G ratio. Moreover, the variation of Poisson's ratio is also in good agreement with the B/G ratio. In summary, Si and W doping can enhance the elastic moduli and improve the ductility of MoAlB, which is expected to be an effective method to optimize the mechanical properties.

Elastic Anisotropy
The anisotropy of mechanical properties is a key factor that affects the material's properties. Microcracks usually appear, originating from the mechanical anisotropy of materials. In MoAlB crystal, the elastic modulus along different principal axes are expected to differ from each other, considering the difference in the elastic constants in Table 2. To reveal the anisotropic features, the universal anisotropic index (A U ), percent anisotropies (A B and A G ), and shear anisotropic indexes (A 1 , A 2 and A 3 ) have been calculated in this work according to Equations (13)-(18): Table 4 lists the calculated anisotropic indexes of MoAlB crystals, with and without elemental doping. First, it can be found that Mo 4 Al 3 SiB 4 and Mo 3 WAl 4 B 4 have relatively smaller A U , compared with the initial MoAlB, implying that the crystals tend to be more isotropic after Si and W doping. In addition, the A B and A G show the same varying trend with Si and W addition. Generally, directional covalent bonding plays a significant role in affecting the crystal's anisotropy, while the metallic bonding contributes to improving the isotropy. Thus, it can be hypothesized that Si and W doping can help ameliorate the metallic character of MoAlB, which is beneficial to the crystal's ductility. This results is in good agreement with the Pugh's and Poisson's ratios discussed above. Then, A 1 , A 2 , and A 3 reveal the anisotropies of shear moduli on the (1 0 0  Young's modulus is an important parameter to evaluate the mechanical properties of a material. Thus, the anisotropic features of Young's modulus are worthwhile to be clearly elucidated. The spatial surface contours are practical and visible, giving insight to the anisotropies of Young's modulus [37]. In this case, the spatial surface contours of Young's moduli, as a function of direction, have been depicted according to Equation (19): = l 1 4 S 11 + l 2 4 S 22 + l 3 4 S 33 + 2l 1 2 l 2 2 S 12 + 2l 1 2 l 3 2 S 13 + 2l 2 2 l 3 2 S 23 + l 2 2 l 3 2 S 44 + l 1 2 l 3 2 S 55 + l 1 2 l 2 2 S 66 (19) where l 1 , l 2 , and l 3 are the directional cosines; S ij represents the elastic compliance constant. In spherical coordinates: l 1 = sin θ cos ψ, l 2 = sinθ sin ψ and l 3 = cos θ, respectively. Figure 3 exhibits the three-dimensional surface contours of Young's modulus of the five calculated crystals. As seen, the Young's modulus of MoAlB shows great anisotropy, because the isotropic crystal usually has a spherical contour shape. The Young's modulus of the five calculated crystals is the largest along the [1 1 1] crystal direction. On the contrary, the Young's modulus seems to be the smallest along the [0 1 0] crystal direction. Overall, the contour shapes of the five crystals have considerable similarity, which may be attributed to the small difference in their lattice structures. To clarify the differences on different feature crystallographic planes, the planar projections on the (1 0 0), (0 1 0), (0 0 1), and (1 1 0) planes have been depicted in Figure 4. It can be noticed that the Young's moduli on the (1 0 0) and (0 1 0) planes are obviously more anisotropic than those on the other two planes. higher than 400GPa, indicating the superior stiffness. As for the three principal axes, the relationship of Young's modulus is E[0 0 1] > E[1 0 0] > E[0 1 0], which is consistent with the spatial contours in Figure 3.

Electronic Structures
To further put insight into the bonding character of MoAlB, as well as the elementally doped crystals, the electronic structures were explored, including the density of states (DOS) and electron density distribution. Figure 5 illustrates the total density of states (TDOS) and the partial density of states (PDOS) of the five calculated crystals. For all five crystals, the values of the DOS, at Fermi energy level (E f ), are larger than zero, implying the metallic character of MoAlB. In addition, it is noticed that the E f exactly locates in the valley position of the TDOS, which is a portent of decent stability. By analyzing the PDOS of different atoms, it can be found that the DOS at E f is mainly contributed to by the d states of Mo or the corresponding metal atoms. In other words, Mo, or the doped transition metal atoms, play the dominant role in the electronic conduction of MoAlB. density distribution. Figure 5 illustrates the total density of states (TDOS) and the partial density of states (PDOS) of the five calculated crystals. For all five crystals, the values of the DOS, at Fermi energy level (Ef), are larger than zero, implying the metallic character of MoAlB. In addition, it is noticed that the Ef exactly locates in the valley position of the TDOS, which is a portent of decent stability. By analyzing the PDOS of different atoms, it can be found that the DOS at Ef is mainly contributed to by the d states of Mo or the corresponding metal atoms. In other words, Mo, or the doped transition metal atoms, play the dominant role in the electronic conduction of MoAlB.  Figure 5b, which is possibly to facilitate the formation of Si-B bonds. In addition, the valence bands from −7.0 to −3.0 eV mainly originate from B-p, Al-p, Si-p, and Mo-d states, indicating the formation of covalent bonds between Mo, Al, B, and Si atoms, except for the initial Mo-B and Al-B bonds. Thus, the elastic properties of MoAlB are supposed to be improved due to the enhancement of internal bonding. However, after the doping of transition metal atoms of Cr, W, or Nb, the main differences in the states hybridization can be found to appear from −7.0 eV to Ef, originating from the contribution of their d states, as shown in Figure 5c to e. Herein, W is found to show the strongest hybridization with Mo, Al, and B, at around −4.0 eV, where the DOS peak is located, as shown in Figure 5d. In this case, the chemical bondings of W with Mo, Al, and B are hypothesized to be consequently intensified. Nevertheless, Cr and Nb mainly participate in the hybridization with Mo and Al at around −1.2 eV, which is deemed to affect the bonds of Mo (Cr or Nb)-Al.
To clearly elucidate the type of chemical bonding as well as the corresponding evolution of the bonding strength with elemental doping, the bond lengths and overlapped populations have been analyzed and listed in Table 5. Simultaneously, the electron density distributions on the (1 0 0) and (1 0 1) crystal planes have been depicted as shown in Figure 6. From Table 5, it can be visibly found that the B-B bond has the shortest bond length and largest population (much larger than 1), indicating the strongest B-B covalent bonding. This conclusion can be confirmed from Figure 6a, in which a significantly high electron density can be observed between B-B atoms. The bonding between B-B shows apparently directional characters. In addition, Al-B and Mo-B bonds have overlapped populations much smaller than one, indicating mixed ionic and covalent bondings. However, the populations of Al-Al and Al-Mo bonds are extremely close to one, implying a significant tendency to covalent bonding. Herein, a negative value of overlapped population appears, basically for the bonds with a long distance. Generally, the negative population implies the antibonding or nonbonding between the two atoms.  After the introduction of Si, Cr, W, and Nb atoms, the B-B bond changes little, maintaining to show strong B-B covalent bonding, as listed in Table 5. However, it is worth noting that Si addition contributes to intensifying the Al/Si-B and Al/Si-Mo bonds, by increasing the bond population but decreasing the bond length. As shown in Figure 6b and c, it can be visible that the electron densities between Si-B and Si-Mo are much higher compared with the initial MoAlB crystal. Additionally, the bond length of Si-Al is observed to be shortened due to the smaller radius of Si. Consequently, as a sacrifice, the Mo-B bonds adjacent to the doped Si atom seem to be weaken, as shown in Figure 6c, which can also be confirmed from the decreased population. From Figure 6d, it can be found that the Al-Al bonds can be enhanced to some degree, while the other bonds change little after Cr doping. Intriguingly, W-B and W-Al bonds can be apparently intensified with a higher electron density, as displayed in Figure 6e, which is also consistent with the results of bond population in Table 5. Thus, the improvement of the elastic properties of MoAlB after W doping can be explained from the perspective of bonding characters. For Mo3NbAl4B4, nearly all bonds can be extended due to the larger atomic radius, so that the bonding strength around Nb can be weakened somewhat. The worst mechanical performances of Mo3NbAl4B4 are reasonable from the discussion above.

Debye Temperature
Debye temperature (θD) is an important fundamental parameter in evaluating the physical properties of solids, for instance, the melting temperature, thermal expansion, and specific heat. It can be estimated by the average sound velocity (vm), according to Equation (20) [49,50,60,61]: After the introduction of Si, Cr, W, and Nb atoms, the B-B bond changes little, maintaining to show strong B-B covalent bonding, as listed in Table 5. However, it is worth noting that Si addition contributes to intensifying the Al/Si-B and Al/Si-Mo bonds, by increasing the bond population but decreasing the bond length. As shown in Figure 6b and c, it can be visible that the electron densities between Si-B and Si-Mo are much higher compared with the initial MoAlB crystal. Additionally, the bond length of Si-Al is observed to be shortened due to the smaller radius of Si. Consequently, as a sacrifice, the Mo-B bonds adjacent to the doped Si atom seem to be weaken, as shown in Figure 6c, which can also be confirmed from the decreased population. From Figure 6d, it can be found that the Al-Al bonds can be enhanced to some degree, while the other bonds change little after Cr doping. Intriguingly, W-B and W-Al bonds can be apparently intensified with a higher electron density, as displayed in Figure 6e, which is also consistent with the results of bond population in Table 5. Thus, the improvement of the elastic properties of MoAlB after W doping can be explained from the perspective of bonding characters. For Mo 3 NbAl 4 B 4 , nearly all bonds can be extended due to the larger atomic radius, so that the bonding strength around Nb can be weakened somewhat. The worst mechanical performances of Mo 3 NbAl 4 B 4 are reasonable from the discussion above.

Debye Temperature
Debye temperature (θ D ) is an important fundamental parameter in evaluating the physical properties of solids, for instance, the melting temperature, thermal expansion, and specific heat. It can be estimated by the average sound velocity (v m ), according to Equation (20) [49,50,60,61]: where k B , h, and N A are the Boltzmann, Planck, and Avogadro constants, respectively; n is the number of atoms in each formula; ρ is the density; and M is the molecular weight. Herein, the average sound velocity (v m ) can be calculated by Equation (21) [49,50,60]: where v t and v l are the transversal and longitudinal sound velocities, respectively. The v t and v l can be obtained by the elastic moduli B and G, according to Navier's equation [49,50,60], as shown below: The calculated sound velocities and Debye temperatures (θ D ) of the five calculated crystals have been summarized in Table 6. The Debye temperature of MoAlB is considerably high, indicating its correspondingly good thermal conductivity and strong average chemical bonding. After the introduction of Si, Cr, W, and Mo atoms, V t and V l change little, except that the V l of Mo 3 WAl 4 B 4 decreases dramatically. Not surprisingly, the average sound velocity shows a remarkable decrease, accounting for the lowest θ D of Mo 3 WAl 4 B 4 , as shown in Figure 7. In this case, W doping is supposed to weaken the average atomic bonding of MoAlB. By comparison, Si and Cr doping can trigger the increase of θ D of MoAlB. On the other hand, the melting temperature (T m ) can be empirically obtained with the aid of calculated elastic constants by Equation (24) [62]: where C 11 and C 33 are the elastic constants in Table 2, respectively. As the structural material applied in the high-temperature fields, the melting point is a fairly important parameter that affects MoAlB's application potential. From Figure 7, it can be visibly found that Mo 4 Al 3 SiB 4 and Mo 3 WAl 4 B 4 possess higher T m than the initial MoAlB. Gene.rally, the melting temperature is tightly associated with the strong covalent bonding in the solid. Thus, the considerable T m can provide some evidence of the enhancement of covalent bonding after Si and W doping. In conclusion, we can conclude that Si is supposed to be the best doping element to ameliorate the mechanical and physical performance of MoAlB, which will be verified through experimental research in the future.