First-Principles Study on Graphene/Mg 2 Si Interface of Selective Laser Melting Graphene/Aluminum Matrix Composites

: The bonding strength of a Gr/Mg 2 Si interface was calculated by ﬁrst principles. Graphene can form a stable, completely coherent interface with Mg 2 Si. When the (0001) Gr /(001) Mg 2 Si crystal plane is combined, the mismatch degree is 5.394%, which conforms to the two-dimensional lattice mismatch theory. At the interface between Gr/Mg 2 Si, chemical bonds were not formed, there was only a strong van der Waals force; the interfaces composed of three low index surfaces (001), (011) and (111) of Mg 2 Si and Gr (0001) have smaller interfacial adhesion work and larger interfacial energy, the interfacial energy of Gr/Mg 2 Si is much larger than that of α -Al/Al melt and Gr/Al interfacial (0.15 J/m 2 , 0.16 J/m 2 ), and the interface distance of a stable interface is larger than the bond length of a chemical bond. The interface charge density difference diagram and density of states curve show that there is only strong van der Waals force in a Gr/Mg 2 Si interface. Therefore, when the Gr/AlSi10Mg composite is stressed and deformed, the Gr/Mg 2 Si interface in the composite is easy to separate and become the crack propagation source. The Gr/Mg 2 Si interface should be avoided in the preparation of Gr/AlSi10Mg composite. atoms, the results show that the partial-wave state density curves of interface mg and Si atoms are very close. Compared with inner Mg atoms, the s and p orbitals of interface Mg atoms are smoother and the number of peaks is less. There is only one large peak between 5 e~0 V for interface Si atoms, while there are two adjacent large peaks between 5 e~0 V for inner Si atoms, which indicates the location of interface Si atoms and inner Si atoms. However, there is no overlap or hybridization in the partial-wave state density curves of the two Si-termination interface structures, so no chemical bond is formed at the interface.


Introduction
As a common metal matrix composite, aluminum matrix composite has been widely used in many fields. AlSi10Mg belongs to cast Al-Si alloy, which is a kind of highperformance aluminum alloy with good casting performance and wear resistance. It is mainly used for manufacturing parts bearing a medium load [1]. With the development of science and technology, and the continuous exploration of human civilization, the existing metal materials have been unable to meet the application requirements of some high-end fields.
Researchers usually add rare earth elements into metal matrixes to strengthen materials. For example, Zhao et al. found that the plate like Mg Sn La compound can be refined, spheroidized and uniformly distributed in the Mg-3Sn-1Mn alloy with the increase of rolling reduction, and the spherical Mg Sn La compound can pin the dislocation and increase the driving force of dynamic recrystallization [2]. However, the appearance of graphene provides a new direction for the research and development of various metal matrix composites. Graphene has unique electrical, mechanical and thermal properties. It is an ideal reinforcing material for preparing light, high-strength and high-performance metal matrix composites [3]. In recent years, graphene and its derivatives have been added to the matrix materials in the form of short fibers and nanoparticles, which can improve the properties of the matrix materials.
In order to develop new aluminum matrix composites, graphene as a reinforcement phase has become a hot topic to improve the properties of aluminum-based materials [4,5].

Calculation
The convergence test and structural stability calculation of the surface model and interface model were completed by the CASTEP module of Materials Studio software. In this module, the self-consistent field method (SCF) is used to solve the Kohn-Sham equation of the multiparticle system, and the ground state energy of the multiparticle system is obtained [17]. The convergence threshold of the self-consistent field calculation in simulation calculation is set to 5.0 × 10 −7 eV/atom. In the CASTEP module, the BFGS (Broyden Fletcher Goldfarb Shanno) algorithm is used to optimize the total energy of the multi particle system, and then the stable model with the lowest energy is obtained [18]. The Generalized Gradient Approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) potential function is used in the simulation, the cutoff energy of Gr/Mg 2 Si interface is 620 eV, the vacuum layer with thickness of 10 Å is used to establish the model and the k-point grid is selected (9 × 9 × 1).

Results and Discussion
Gr/AlSi10Mg composites containing 0.15 wt% GR were fabricated by SLM. It can be seen from the XRD patterns of AlSi10Mg material Al and Gr/AlSi10Mg composite in Figure 1 that there are Al, Si and Mg 2 Si in AlSi10Mg formed by SLM, and these three phases exist in the same sample of Gr/AlSi10Mg composite. Zhao et al. used SLM technology to form Gr/AlSi10Mg composites containing 0.15 wt% Gr. SEM analysis showed that graphene did not agglomerate in the composites and dispersed evenly. The first principles calculation showed that there was a mixture of covalent bonds and ionic bonds on the Gr (0001)/Al 4 C 3 (0001) interface, and it was found that the carbon end was easier to alloy the interface between GR and Al 4 C 3 [19]. The Mg 2 Si/Gr interface is formed in the composite material due to the random distribution of graphene in the composite material. The stability of this interface has a certain influence on the performance of the composite material, so it is necessary to calculate the interface bonding strength.
selected to establish heterogeneous interfaces with Gr (0001), respectively. The interfacial bonding strength, interfacial electron distribution and bonding of the three interfaces were calculated. The calculated interfacial energy was compared with that of α-Al/Al melt, and its effect on crack propagation was analyzed.

Calculation
The convergence test and structural stability calculation of the surface model and interface model were completed by the CASTEP module of Materials Studio software. In this module, the self-consistent field method (SCF) is used to solve the Kohn-Sham equation of the multiparticle system, and the ground state energy of the multiparticle system is obtained [17]. The convergence threshold of the self-consistent field calculation in simulation calculation is set to 5.0 × 10 −7 eV/atom. In the CASTEP module, the BFGS (Broyden Fletcher Goldfarb Shanno) algorithm is used to optimize the total energy of the multi particle system, and then the stable model with the lowest energy is obtained [18]. The Generalized Gradient Approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) potential function is used in the simulation, the cutoff energy of Gr/Mg2Si interface is 620 eV, the vacuum layer with thickness of 10 Å is used to establish the model and the k-point grid is selected (9 × 9 × 1).

Results and Discussion
Gr/AlSi10Mg composites containing 0.15wt% GR were fabricated by SLM. It can be seen from the XRD patterns of AlSi10Mg material Al and Gr/AlSi10Mg composite in Figure 1 that there are Al, Si and Mg2Si in AlSi10Mg formed by SLM, and these three phases exist in the same sample of Gr/AlSi10Mg composite. Zhao et al. used SLM technology to form Gr/AlSi10Mg composites containing 0.15wt% Gr. SEM analysis showed that graphene did not agglomerate in the composites and dispersed evenly. The first principles calculation showed that there was a mixture of covalent bonds and ionic bonds on the Gr (0001)/Al4C3 (0001) interface, and it was found that the carbon end was easier to alloy the interface between GR and Al4C3 [19]. The Mg2Si/Gr interface is formed in the composite material due to the random distribution of graphene in the composite material. The stability of this interface has a certain influence on the performance of the composite material, so it is necessary to calculate the interface bonding strength.     The Bramfitt two-dimensional lattice mismatch model is used to calculate the lattice mismatch of Gr/Mg2Si interface. The formula of the Bramfitt two-dimensional lattice mismatch model is [20]: According to the two-dimensional lattice mismatch theory, a core with δ less than 6% is an effective nucleation core, which can realize one-to-one correspondence between atoms on both sides of the interface. This kind of interface is called a fully coherent interface; a core with δ = 6%~15% is a medium effective nucleation core, which may form semi coherent interface; when δ is more than 15%, the interface type belongs to noncoherent interface, which cannot be used as a heterogeneous nucleation substrate of nucleating material. Table 1 shows the specific facet index, orientation index, offset angle and calculated lattice mismatch under the three matching methods in Figure 2. When the (0001) plane of graphene is combined with the (001) plane of Mg2Si, the lattice mismatch is 5.394%, which indicates that the atoms on both sides of the interface are one-to-one corresponding, forming a fully coherent interface with low interface energy. For (0001) Gr/(111) Mg2Si orientation, the lattice mismatch degree belongs to the range of medium effective nucleation and can form a semi-coherent interface. For (0001) Gr/(011) Mg2Si orientation, the lattice mismatch degree between the two materials reaches 15.340%, and the interface bonding mode is incoherent interface. In conclusion, a stable interface structure can be formed between graphene and Mg2Si under the specific matching orientation. The formula of the Bramfitt two-dimensional lattice mismatch model is [20]:

Gr/Mg2Si Interface Mismatch Degree
where (hkl) s is the low index crystal plane of Gr substrate; [uvw] s is the low index crystal direction on the (hkl) s crystal plane; (hkl) n is the low index crystal plane of Mg 2 Si substrate; [uvw] n is the low index crystal direction on the (hkl) n crystal plane; d [uvw]  According to the two-dimensional lattice mismatch theory, a core with δ less than 6% is an effective nucleation core, which can realize one-to-one correspondence between atoms on both sides of the interface. This kind of interface is called a fully coherent interface; a core with δ = 6~15% is a medium effective nucleation core, which may form semi coherent interface; when δ is more than 15%, the interface type belongs to non-coherent interface, which cannot be used as a heterogeneous nucleation substrate of nucleating material. Table 1 shows the specific facet index, orientation index, offset angle and calculated lattice mismatch under the three matching methods in Figure 2. When the (0001) plane of graphene is combined with the (001) plane of Mg 2 Si, the lattice mismatch is 5.394%, which indicates that the atoms on both sides of the interface are one-to-one corresponding, forming a fully coherent interface with low interface energy. For (0001) Gr /(111) Mg 2 Si orientation, the lattice mismatch degree belongs to the range of medium effective nucleation and can form a semi-coherent interface. For (0001) Gr /(011) Mg 2 Si orientation, the lattice mismatch degree between the two materials reaches 15.340%, and the interface bonding mode is incoherent interface. In conclusion, a stable interface structure can be formed between graphene and Mg 2 Si under the specific matching orientation.

Gr/Mg 2 Si Interfacial Bonding Strength
Three Mg 2 Si/Gr interface models, Mg 2 Si (001)/Gr (0001), Mg 2 Si (011)/Gr (0001) and Mg 2 Si (111)/Gr (0001), were established. The interfacial adhesion work, interfacial energy and interfacial charge distribution of these three interface structures were calculated and analyzed, and the stability of the Mg 2 Si/Gr interface was discussed.
The interfacial adhesion work of the Mg 2 Si/Gr interface is calculated as follows [21,22]: where E Gr total , E Mg 2 Si total and E Gr/Mg 2 Si total are the total energy of the surface model and the interface model; A is the area of the interface model.
The interface energy of Mg 2 Si/Gr interface structure can be calculated by the following formula [23,24]: where E Mg 2 Si is the total energy of the Mg 2 Si/Gr interface model; N Mg and N Si are the number of magnesium and silicon atoms in Mg 2 Si surface model; N c is the number of carbon atoms in graphene surface model; µ bulk C is the chemical potential of a single carbon atom in the graphene surface model; δ Mg 2 Si and δ Gr are the surface energies of Mg 2 Si and Gr surface models respectively.

Mg 2 Si (001)/Gr (0001) Interfacial Bonding Strength
According to the convergence test of the Mg 2 Si (001) surface model, there are two kinds of Mg 2 Si (001) surface models used to establish the interface structure, which are seven-layer Mg-termination surface and nine-layer Si-termination surface. Because there are two different atomic arrangements in the first layer of the nine-layer Si-termination surface, three Mg 2 Si (001)/Gr (0001) interface models in Figure 3, Mg-termination, Sitermination center-sited and Si-termination top-sited, are established according to the relative positions of the interface atoms. After structural relaxation, the interface model is in the lowest energy state, and the interfacial adhesion work of the interface structure is shown in Table 2. The data in Table  2 show that the interfacial adhesion work of the Si-termination-top-sited interface is the largest, which is 1.187 J/m 2 , while that of the other two interface models is relatively small. After structural relaxation, the interface model is in the lowest energy state, and the interfacial adhesion work of the interface structure is shown in Table 2. The data in Table 2 show that the interfacial adhesion work of the Si-termination-top-sited interface is the largest, which is 1.187 J/m 2 , while that of the other two interface models is relatively small. From the optimized interface spacing in the table, it is found that the interface spacing of the three interface models is still large after structure optimization, which indicates that the stability of the Mg 2 Si (001)/Gr (0001) interface model is poor. The distance of the chemical bond is usually less than 2.6 Å, the distance of the hydrogen bond is in the range of 2.6~3.1 Å and the distance of the strong van der Waals interaction is 3.1~5.0 Å [25]. According to the data in Table 2, the stable interface spacing of the three interface models is relatively large, and the stable interface spacing of Mg-termination interface is 4.31 Å, which reaches the distance of strong van der Waals action. According to the bond length, the strong van der Waals bond is formed at the interface of Mg 2 Si (001)/Gr (0001) three models. The interface energy of the Mg 2 Si (001)/Gr (0001) interface model can be calculated by Equation (3). The calculated interface energy results are shown in Table 2. The interface energy of the Si-termination interface is larger than that of Mg-termination interface, and the combination of magnesium atoms and graphene at the interface is more conducive to the formation of a stable interface structure. At the same time, it is found that the interface energy of the three kinds of interface is relatively large, the maximum value is 5.495 J/m 2 , which is much larger than that of α-Al/Al melt and Gr/Al interfacial (0.15 J/m 2 , −0.16 J/m 2 ) [14,26]. The higher the interfacial energy is, the worse the stability of the interface structure is. Therefore, when the binding orientation between Mg 2 Si and graphene is Mg 2 Si (001)/Gr (0001), the stability of the interface structure is poor. Figure 4 shows the charge differential density diagram of three Mg 2 Si (001)/Gr (0001) interfaces. In the three interface models, there is a strong interaction between the carbon atoms of graphene, and there are directional charge accumulation regions around each carbon atom. The existence of these charge accumulation regions makes the regular hexagonal carbon atom grid of graphene very stable. It can be seen from Figure 4 that there are wide gap regions at the three interfaces, and there is no chemical bond between the atoms on the Mg 2 Si (001) surface and the carbon atoms on the Gr (0001) surface. There are directional charge regions around the interface atoms of the Mg 2 Si (001) surface in the three interface models. The charge around the interface Mg atom in Figure 4a tends to transfer to graphene. This phenomenon can also be observed in Figure 4b,c. It shows that there are weak interaction forces between the Mg 2 Si (001) surface and the Gr (0001) surface in the three models, and these forces can improve the interfacial bonding strength of Mg 2 Si (001)/Gr (0001) to a certain extent. Figure 5 shows the partial-wave state density curves of three Mg 2 Si (001)/Gr (0001) interfaces. Figure 5a shows the partial-wave state density curve of the Mg-termination interface structure. The charge orbit of the nearest Mg atom from graphene changes greatly compared with that of the inner Mg atom. A new peak appears on the P orbit of the 1st Mg atom near the Fermi level; there is no peak value of carbon atoms in graphene near the same charge level, which indicates that there is no hybridization between the charge orbitals of carbon atoms and magnesium atoms, only mutual attraction, which is consistent with the analysis results of the charge differential density diagram. Figure 5b,c are the partial-wave state density curves of Si-termination interface structures of two different end atoms, the results show that the partial-wave state density curves of interface mg and Si atoms are very close. Compared with inner Mg atoms, the s and p orbitals of interface Mg atoms are smoother and the number of peaks is less. There is only one large peak between 5 e~0 V for interface Si atoms, while there are two adjacent large peaks between 5 e~0 V for inner Si atoms, which indicates the location of interface Si atoms and inner Si atoms. However, there is no overlap or hybridization in the partial-wave state density curves of the two Si-termination interface structures, so no chemical bond is formed at the interface.
Metals 2021, 11, x FOR PEER REVIEW 7 of 1 carbon atom. The existence of these charge accumulation regions makes the regula hexagonal carbon atom grid of graphene very stable. It can be seen from Figure 4 tha there are wide gap regions at the three interfaces, and there is no chemical bond betwee the atoms on the Mg2Si (001) surface and the carbon atoms on the Gr (0001) surface. Ther are directional charge regions around the interface atoms of the Mg2Si (001) surface in th three interface models. The charge around the interface Mg atom in Figure 4a tends t transfer to graphene. This phenomenon can also be observed in Figure 4b and Figure 4c It shows that there are weak interaction forces between the Mg2Si (001) surface and the G (0001) surface in the three models, and these forces can improve the interfacial bondin strength of Mg2Si (001)/Gr (0001) to a certain extent.  Figure 5 shows the partial-wave state density curves of three Mg2Si (001)/Gr (0001 interfaces. Figure 5a shows the partial-wave state density curve of the Mg-terminatio interface structure. The charge orbit of the nearest Mg atom from graphene change greatly compared with that of the inner Mg atom. A new peak appears on the P orbit o the 1st Mg atom near the Fermi level; there is no peak value of carbon atoms in graphen near the same charge level, which indicates that there is no hybridization between th charge orbitals of carbon atoms and magnesium atoms, only mutual attraction, which i consistent with the analysis results of the charge differential density diagram. Figure 5 and Figure 5c are the partial-wave state density curves of Si-termination interfac structures of two different end atoms, the results show that the partial-wave state densit curves of interface mg and Si atoms are very close. Compared with inner Mg atoms, the and p orbitals of interface Mg atoms are smoother and the number of peaks is less. Ther is only one large peak between 5 e~0 V for interface Si atoms, while there are two adjacen large peaks between 5 e~0 V for inner Si atoms, which indicates the location of interfac Si atoms and inner Si atoms. However, there is no overlap or hybridization in the partia wave state density curves of the two Si-termination interface structures, so no chemica bond is formed at the interface. After structural relaxation, the calculated stable interfacial spacing and interfacial adhesion work of the Mg 2 Si (011)/Gr (0001) interface are shown in Table 3. The results show that the interface spacing of the two models are 4.010 Å and 3.873 Å, respectively. The interface spacing is large, and there is van der Waals force at the interface. Moreover, the interfacial adhesion work of the two models is negative. It is concluded that the stability of the Mg 2 Si (011)/Gr (0001) interface is poor.  The interface energy of the Mg 2 Si (011)/Gr (0001) interface model is calculated by Equation (3). The results are shown in Table 3. The interface energy of the two interfaces is much larger than that of the α-Al/Al melt and Gr/Al interfacial (0.15 J/m 2 , −0.16 J/m 2 ), which indicates that when the Mg 2 Si (011) surface is combined with the Gr (0001) surface, the interface stability is poor, the bonding strength is low and the interface separation occurs easily. The difference in interface energy between the two interfaces is small, which indicates that the type of end atoms on the Mg 2 Si (011) surface has little effect on the interface structure in the Mg 2 Si (011)/Gr (0001) interface. As shown in Figure 7, there is obvious interaction between carbon atoms in graphene in the two Mg 2 Si (011)/Gr (0001) interfaces, the charge distribution around carbon atoms has obvious directionality and there is a strong charge accumulation region between adjacent carbon atoms, which makes graphene structure have strong stability.  In Figure 7, there is also a gap between the graphene and the Mg 2 Si in the Mg 2 Si (011)/Gr (0001) interface model, but the width is reduced, which indicates that the interaction strength between the two surface models is enhanced. However, because there is no charge transfer phenomenon in the two interface models, no chemical bond is formed. It can be seen from Figure 7a that the charge distribution around the surface silicon atoms in the Si-center-sited interface has a certain directionality, and the charge transfer trend from silicon atoms to graphene is obvious. Because of the large interface spacing, there is no charge transfer between them. The two surface Mg atoms in the Mg-center-sited interface also forms a low charge region on the side close to the graphene, and the distance between the low charge region of graphene and Mg 2 Si in the Mg-center-sited interface is relatively close, which leads to the enhancement of the bonding strength between them. After structural relaxation, the calculated stable interfacial spacing and interfacial adhesion work of the Mg2Si (011)/Gr (0001) interface are shown in Table 3. The results show that the interface spacing of the two models are 4.010 Å and 3.873 Å, respectively. The interface spacing is large, and there is van der Waals force at the interface. Moreover, the interfacial adhesion work of the two models is negative. It is concluded that the stability of the Mg2Si (011)/Gr (0001) interface is poor. The interface energy of the Mg2Si (011)/Gr (0001) interface model is calculated by Equation (3). The results are shown in Table 3. The interface energy of the two interfaces is much larger than that of the α-Al/Al melt and Gr/Al interfacial (0.15 J/m 2 , −0.16 J/m 2 ), which indicates that when the Mg2Si (011) surface is combined with the Gr (0001) surface, the interface stability is poor, the bonding strength is low and the interface separation occurs easily. The difference in interface energy between the two interfaces is small, which indicates that the type of end atoms on the Mg2Si (011) surface has little effect on the interface structure in the Mg2Si (011)/Gr (0001) interface. As shown in Figure 7, there is obvious interaction between carbon atoms in graphene in the two Mg2Si (011)/Gr (0001) interfaces, the charge distribution around carbon atoms has obvious directionality and there is a strong charge accumulation region between adjacent carbon atoms, which makes graphene structure have strong stability.
In Figure 7, there is also a gap between the graphene and the Mg2Si in the Mg2Si (011)/Gr (0001) interface model, but the width is reduced, which indicates that the interaction strength between the two surface models is enhanced. However, because there is no charge transfer phenomenon in the two interface models, no chemical bond is formed. It can be seen from Figure 7a that the charge distribution around the surface silicon atoms in the Si-center-sited interface has a certain directionality, and the charge transfer trend from silicon atoms to graphene is obvious. Because of the large interface spacing, there is no charge transfer between them. The two surface Mg atoms in the Mg-   Figure 8 shows the partial-wave state density curves of two Mg2Si (011)/Gr (0001) interfaces. Figure 8a shows the partial-wave state density curve of the Si-center-sited interface structure. Compared with the charge orbit of the inner silicon atom, the charge orbit of the interface silicon atom changes obviously under the influence of graphene. The peaks of the S and P orbitals of the first carbon atom are greatly enhanced, and the number of peaks of P orbitals of the first carbon atom decreases near Fermi level, which indicates that the first carbon atom is different from graphite, and that there is a strong interaction between the carbon atoms in alkenes; however, because there is no orbital hybridization between them, no chemical bond is formed at the interface. Figure 8b shows the partialwave state density curve of the Mg-center-sited interface structure. Compared with the charge orbit of the inner Mg atom, the results show that there are some new and smaller peaks in the charge orbit of the first Mg atom between 5 ev~10 ev, and the peaks at other positions have also changed, which indicates that there is interaction force between the first magnesium atom and the carbon atom in graphene, but there is no obvious orbital resonance between them, therefore there is no chemical bond at the interface.  Figure 8 shows the partial-wave state density curves of two Mg 2 Si (011)/Gr (0001) interfaces. Figure 8a shows the partial-wave state density curve of the Si-center-sited interface structure. Compared with the charge orbit of the inner silicon atom, the charge orbit of the interface silicon atom changes obviously under the influence of graphene. The peaks of the S and P orbitals of the first carbon atom are greatly enhanced, and the number of peaks of P orbitals of the first carbon atom decreases near Fermi level, which indicates that the first carbon atom is different from graphite, and that there is a strong interaction between the carbon atoms in alkenes; however, because there is no orbital hybridization between them, no chemical bond is formed at the interface. Figure 8b shows the partial-wave state density curve of the Mg-center-sited interface structure. Compared with the charge orbit of the inner Mg atom, the results show that there are some new and smaller peaks in the charge orbit of the first Mg atom between 5 ev~10 ev, and the peaks at other positions have also changed, which indicates that there is interaction force between the first magnesium atom and the carbon atom in graphene, but there is no obvious orbital resonance between them, therefore there is no chemical bond at the interface.  Figure 8 shows the partial-wave state density curves of two Mg2Si (011)/G interfaces. Figure 8a shows the partial-wave state density curve of the Si-cen interface structure. Compared with the charge orbit of the inner silicon atom, th orbit of the interface silicon atom changes obviously under the influence of graph peaks of the S and P orbitals of the first carbon atom are greatly enhanced, and the of peaks of P orbitals of the first carbon atom decreases near Fermi level, which that the first carbon atom is different from graphite, and that there is a strong in between the carbon atoms in alkenes; however, because there is no orbital hybr between them, no chemical bond is formed at the interface. Figure 8b shows the wave state density curve of the Mg-center-sited interface structure. Compared charge orbit of the inner Mg atom, the results show that there are some new and peaks in the charge orbit of the first Mg atom between 5 ev~10 ev, and the peaks positions have also changed, which indicates that there is interaction force betw first magnesium atom and the carbon atom in graphene, but there is no obviou resonance between them, therefore there is no chemical bond at the interface.   Figure 9 shows the interface model and atomic stacking position of the Mg2Si (111)/Gr (0001) interface. According to the convergence test of the surface model, 8 layers of Mgtermination surface and 10 layers of Si-termination surface and Gr (0001) surface were selected to construct the Mg2Si (111)/Gr (0001) interface structure. The Gr (0001) surface model is above the Mg2Si (111) surface model. In this simulation, two kinds of interface models with different kinds of end atoms are constructed: Mg-termination and Sitermination. The data in Table 4 are the interfacial adhesion work of the two Mg2Si (111)/Gr (0001) interfaces after structural optimization. According to the bond length classification, it is judged that there is a strong van der Waals force at the Mg2Si (111)/Gr (0001) interface. Comparing the strength of the two interfaces, it is found that the Mg-termination interface has smaller stable interface spacing and larger interfacial adhesion work, and its stability is higher than that of the Si-termination interface.
According to Equation (3), the change of interface energy of two Mg2Si (111)/Gr (0001) interfaces in the range of ΔμMg is shown in Table 4. The interfacial energy of the Mg-termination interface is 4.32~6.68 J/m 2 , and that of Si-termination interface is 5.97~8.35 The data in Table 4 are the interfacial adhesion work of the two Mg 2 Si (111)/Gr (0001) interfaces after structural optimization. According to the bond length classification, it is judged that there is a strong van der Waals force at the Mg 2 Si (111)/Gr (0001) interface. Comparing the strength of the two interfaces, it is found that the Mg-termination interface has smaller stable interface spacing and larger interfacial adhesion work, and its stability is higher than that of the Si-termination interface.  According to Equation (3), the change of interface energy of two Mg 2 Si (111)/Gr (0001) interfaces in the range of ∆µ Mg is shown in Table 4. The interfacial energy of the Mg-termination interface is 4.32~6.68 J/m 2 , and that of Si-termination interface is 5.97~8.35 J/m 2 . The interfacial energy of both interfaces is relatively large, which is not conducive to the formation of stable interface structure. Figure 10a shows the charge differential density diagram of the Mg-termination interface. There is a strong charge accumulation region between carbon atoms in graphene, which indicates that the carbon atoms in graphene have charge transfer and form a strong covalent bond. The distance between the Mg layer and the graphene layer is large, and the charge distribution around the Mg atom is almost circular, which indicates that the graphene layer has little influence on the Mg atom at the interface, and the interaction between Mg 2 Si and graphene in the Mg-termination interface is small. Figure 10b shows the charge differential density diagram of the Si-termination interface. In Figure 10b, there is also a strong charge accumulation area between the carbon atoms in graphene. The difference is that the silicon atom layer combined with graphene has obvious regionalization characteristics, and the charge around silicon atom shows a trend of transferring to one side of the graphene, indicating that there is a force between the graphene and silicon atom layers. in graphene. The difference is that the silicon atom layer comb obvious regionalization characteristics, and the charge around sil of transferring to one side of the graphene, indicating that ther graphene and silicon atom layers.  Figure 11 shows the partial density of states of two Mg2Si (1 Figure 11a shows the partial-wave state density curve of graphen Mg-termination interface. Comparing the partial-wave state den atoms in different layers, the density of states curves of two laye near the interface have changed greatly. Due to the influence of states curve of the first Mg atom is obviously different from tha atoms. In the vicinity of −2 eV, a new peak appears in the P orb but there is no orbital hybridization between the electronic orbi only the peak increases, so there is no chemical bond between th above analysis, it is judged that there is a strong van der Waals for interface. Figure 11b shows the partial-wave state density curves of gr at the Si-termination interface. Compared with the inner silicon  Figure 11 shows the partial density of states of two Mg 2 Si (111)/Gr (0001) interfaces. Figure 11a shows the partial-wave state density curve of graphene and Mg 2 Si atoms in the Mg-termination interface. Comparing the partial-wave state density curve of magnesium atoms in different layers, the density of states curves of two layers of magnesium atoms near the interface have changed greatly. Due to the influence of graphene, the density of states curve of the first Mg atom is obviously different from that of fourth and fifth Mg atoms. In the vicinity of −2 eV, a new peak appears in the P orbital of the first Mg atom, but there is no orbital hybridization between the electronic orbitals of Mg and C atoms; only the peak increases, so there is no chemical bond between them. Combined with the above analysis, it is judged that there is a strong van der Waals force in the Mg-termination interface. Figure 11b shows the partial-wave state density curves of graphene and Mg 2 Si atoms at the Si-termination interface. Compared with the inner silicon atom, the partial density of states of the first silicon atom changes greatly. Besides, the peak value of the first silicon atom near −8 eV becomes higher. In addition, a high isolated peak is formed near −1 eV instead of a continuous peak such as the inner silicon atom. According to these phenomena, it is found that there is interaction between carbon atoms in graphene and silicon atoms in Mg 2 Si, and the peak values of the first silicon atoms are increased. This is because there is a strong interaction force between silicon atoms and carbon atoms, but there is no orbital hybridization between silicon atoms and carbon atoms. Therefore, there is no chemical bond between the surface of graphene and the surface of Mg 2 Si in a Si-termination interface, only van der Waals force exists. Combined with the above analysis, it can be concluded that the force in a mg-termination interface is stronger than that in a Si-termination interface.
phenomena, it is found that there is interaction between carbon atoms in graphene and silicon atoms in Mg2Si, and the peak values of the first silicon atoms are increased. This is because there is a strong interaction force between silicon atoms and carbon atoms, but there is no orbital hybridization between silicon atoms and carbon atoms. Therefore, there is no chemical bond between the surface of graphene and the surface of Mg2Si in a Sitermination interface, only van der Waals force exists. Combined with the above analysis, it can be concluded that the force in a mg-termination interface is stronger than that in a Si-termination interface.

Conclusions
(1). According to the calculation results of the Bramfitt two-dimensional lattice mismatch model, the Gr/Mg2Si matching model has a small lattice mismatch under the specific interface orientation, which can form a stable two-phase interface, indicating that graphene can form a stable interface with Mg2Si. (2). The results of the interface stability calculation of Mg2Si/Gr show that the three kinds of Mg2Si/Gr interface have smaller interfacial adhesion work, larger stable interface spacing and larger interface energy, which are not conducive to the formation of stable interface structure. The results of the charge differential density analysis show that there is no charge transfer between the interface atoms in the Mg2Si/Gr interface, and there is no chemical bond between the Mg2Si surface and the Gr surface. The partial-wave state density curve of the interface atom shows that the partial charge orbit of the interface atom has changed, indicating that, although there is no chemical

Conclusions
(1). According to the calculation results of the Bramfitt two-dimensional lattice mismatch model, the Gr/Mg 2 Si matching model has a small lattice mismatch under the specific interface orientation, which can form a stable two-phase interface, indicating that graphene can form a stable interface with Mg 2 Si. (2). The results of the interface stability calculation of Mg 2 Si/Gr show that the three kinds of Mg 2 Si/Gr interface have smaller interfacial adhesion work, larger stable interface spacing and larger interface energy, which are not conducive to the formation of stable interface structure. The results of the charge differential density analysis show that there is no charge transfer between the interface atoms in the Mg 2 Si/Gr interface, and there is no chemical bond between the Mg 2 Si surface and the Gr surface. The partial-wave state density curve of the interface atom shows that the partial charge orbit of the interface atom has changed, indicating that, although there is no chemical bond at the interface, there is still interaction force between the two surfaces. Judging from the bond length, there is a strong van der Waals force at the Mg 2 Si/Gr interface. (3). According to the analysis results of the Mg 2 Si/Gr interface stability, the interface energy of Mg 2 Si/Gr is much higher than that of α-Al/Al melt (0.15 J/m 2 ), no chemical bond is formed at the interface and the Mg 2 Si surface and Gr surface only rely on physical adsorption. When the Gr/AlSi10Mg composite is deformed by the applied load, the Mg 2 Si/Gr interface can easily separate and become a crack propagation source. Therefore, the interface between Mg 2 Si and Gr should be avoided as much as possible in the preparation of Gr/AlSi10Mg composite. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study has been presented in figures and tables in this article.

Conflicts of Interest:
The authors declare no conflict of interest.