Method for predicting mechanical properties of graphene / aluminum composite material

By using molecular dynamics simulations to regulate the moiré stripe characteristic interface of graphene/aluminum composites, their mechanical properties can be predicted. This solves the problem of interface structure regulation in existing technologies, improves material properties, and reduces experimental costs.

CN116844678BActive Publication Date: 2025-12-05NORTHWEST INSTITUTE FOR NONFERROUS METAL RESEARCH
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Patent Information

Application Number
CN202310947815.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-31
Publication Date
2025-12-05
Estimated Expiration
2043-07-31

AI Technical Summary

Technical Problem

Existing technologies cannot effectively control the interfacial structural characteristics of graphene/aluminum composites, which limits the improvement of their mechanical properties and makes it difficult to quickly verify the strengthening design ideas due to high experimental costs.

Method used

An initial model of graphene/aluminum composite material was established through molecular dynamics simulation. The moiré fringe characteristic interface was controlled, and the influence of the moiré fringe characteristic interface on the mechanical behavior of graphene/aluminum composite material was predicted by uniaxial tensile stress test and stress-strain analysis.

Benefits of technology

This study improved the mechanical properties of graphene/aluminum composites, provided a new approach to joint reinforcement by interfaces and twins, reduced experimental costs, and rapidly verified the feasibility of the moiré stripe characteristic interface structure.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application discloses a kind of graphene / aluminum composite material mechanical property prediction method, the method comprises: one, determine the initial model of molecular dynamics composite material;Two, select characteristic molecular dynamics composite material model;Three, determine the structure of characteristic molecular dynamics composite material model;Four, stress analysis is carried out to the structure of characteristic molecular dynamics composite material model.The interface structure characteristics between graphene and aluminum are regulated in the application, the deformation mechanism of metal matrix is changed, the mechanical properties of graphene / aluminum metal composite material are improved, and a new way of interface and twin crystal co-strengthening mechanical properties is provided for graphene reinforced aluminum matrix composite material;Using the research method of molecular dynamics simulation, not only the cost and consumption caused by experiment can be effectively reduced, but also the deformation evolution process can be directly observed, whether the strengthening design idea of moire characteristic interface structure is feasible can be quickly verified, and the simulation result provides theoretical guidance for experiment.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical property optimization of graphene reinforced metal matrix composites, and particularly relates to a method for predicting the mechanical properties of graphene / aluminum composites. BACKGROUND

[0002] Most aluminum and its alloys have low intrinsic mechanical strength. By utilizing the superior in-plane mechanical properties of two-dimensional graphene, the combination of aluminum and graphene can have the characteristics of weight reduction, high specific strength, specific stiffness, etc., and is expected to obtain excellent comprehensive performance, so that graphene / aluminum composites become promising and competitive candidate materials in the fields of aerospace and automobile industry. Previous studies have shown that the mechanical strengthening mechanisms of graphene / metal composites include dislocation pile-up at the interface, interface load transfer, Orowan strengthening, and interface (modulus, geometry, thermal expansion rate) mismatch strengthening, indicating that the interface-related strengthening behavior of graphene / metal plays a crucial role in determining the overall mechanical properties.

[0003] Moire fringe (two materials are stacked in three-dimensional space to form periodic unit structures) is one of the important structural characteristics of the graphene / metal interface, and has been reported in a large number of graphene / transition metal systems (Batzill, M. (2012). Surface Science Reports 67(3-4): 83-115, Yang, M., et al. (2020). Progress in Materials Science 110: 100652). Moire fringe is closely related to the intrinsic physical functional properties of the interface, such as electricity and magnetism. However, so far, the key role of the intrinsic graphene / metal interface structure in controlling the mechanical behavior and performance of graphene / metal composite systems has been rarely reported. Research has found that in the field of graphene / metal interfaces, only in the impact experiment of Long et al. (Long, X.J., et al. (2016). Carbon 103: 457-463), it is shown that the interface dislocation nucleation in graphene / copper composites is controlled by the interface moire fringe characteristics. Therefore, the influence of the moire fringe characteristic interface on the initial plasticity and plastic deformation behavior of the composite material is worth attention.

[0004] In metal / metal or ceramic / metal systems, numerous studies have reported that the interfacial structure plays a crucial role in dislocation nucleation behavior, i.e., initial plasticity (Wang, J., et al. (2011). Current Opinion in Solid State and Materials Science 15(1):20-28). Some studies even report (Zuo, JD, et al. (2019). Acta Materials 174:279-288) that the Al / AlN heterogeneous interface promotes the formation of nanotwins in aluminum films, enabling twinning deformation in high-fault-energy aluminum, which is difficult to deform, and thus enhancing its strength. In recent years, twinning engineering has been considered an effective method to simultaneously achieve high strength and high plasticity, attracting considerable attention from researchers. Inspired by this, if, in graphene / aluminum systems, the initial plasticity is controlled by regulating the interface from the perspective of the graphene / aluminum heterogeneous interface, especially the graphene / aluminum moiré stripe characteristic interface, thereby introducing deformable twins into the aluminum matrix, it is hoped that the strengthening effect of the aluminum matrix can be fully utilized. By combining existing graphene / metal interface-related strengthening mechanisms with the positive contribution of the reinforcing phase graphene itself, the mechanical properties of graphene / aluminum composites can be further improved, which is expected to meet the development needs of high-performance lightweight metal matrix composites.

[0005] Based on initial experimental results (Zhang, S., et al. (2021). Materials and Design 201:109509), moiré fringe characteristic interfaces were observed in graphene / aluminum composites. Analysis revealed that moiré fringe interfaces can generate various structural morphologies by rotating the orientation angle. However, current experimental studies on the mechanical behavior of specific interfaces present challenges. Therefore, this invention uses molecular dynamics simulations to accurately construct initial molecular dynamics models of composite materials with multiple types of moiré fringe characteristic interfaces, and investigates the influence of moiré fringe characteristic interfaces on the mechanical behavior and properties of graphene / aluminum composites. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a method for predicting the mechanical properties of graphene / aluminum composite materials. By controlling the interfacial structural characteristics between graphene and aluminum, namely the moiré stripe feature, the deformation mechanism of the metal matrix is ​​transformed, thereby improving the mechanical properties of the graphene / aluminum composite material. Furthermore, this invention provides a new approach for strengthening the mechanical properties of graphene-reinforced aluminum-based composite materials through the joint enhancement of interface and twinning. The use of molecular dynamics simulation not only effectively reduces the cost and consumption associated with experiments but also allows for direct observation of the deformation evolution process, quickly verifying the feasibility of the moiré stripe feature interface structure strengthening design. The simulation results provide theoretical guidance for experiments.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for predicting the mechanical properties of graphene / aluminum composite materials, characterized in that: the method includes the following steps:

[0008] Step 1: Establish an initial molecular dynamics composite material model: Establish an initial molecular dynamics composite material model composed of multiple graphene and aluminum materials. The interface of each initial molecular dynamics composite material model is a (111) plane. The initial molecular dynamics composite material model includes multiple composite material units, which are stacked sequentially from bottom to top. Each composite material unit includes an aluminum layer and a graphene layer disposed below the aluminum layer. The initial spacing between the aluminum layer and the graphene layer is h = 0.858σ; where h is the initial spacing between the aluminum layer and the graphene layer, and σ is the distance between atoms when the interaction potential between graphene atoms and aluminum atoms is equal to 0.

[0009] Step 2: Select characteristic molecular dynamics composite material models: Change the relative orientation between graphene and aluminum in the multiple initial molecular dynamics composite material models in Step 1, and select the models in which twinning deformation and dislocation deformation dominate the deformation in different moiré fringe characteristic interfaces, respectively, as characteristic molecular dynamics composite material models.

[0010] Step 3: Determine the characteristic molecular dynamics composite material model structure: Set periodic boundary conditions for the characteristic molecular dynamics composite material model obtained in Step 3 to obtain a characteristic molecular dynamics composite material model structure with the same size;

[0011] Step 4: Perform stress analysis on the characteristic molecular dynamics composite material model structure, as follows:

[0012] Step 401: Perform a uniaxial tensile stress test on the characteristic molecular dynamics composite material model structure, and determine the strain range of uniaxial tension to obtain the stress and strain values ​​of the characteristic molecular dynamics composite material model structure within the strain range of uniaxial tension.

[0013] Step 402: Based on the data obtained in step 401, plot the stress-strain curve of the characteristic molecular dynamics composite material model structure. Analyze the stress-strain curve to find that the larger the period of the moiré stripes at the graphene / aluminum interface and the more the symmetry axis of the moiré stripe unit is tilted relative to the y-axis, the higher the model yield strength and the stronger the strain hardening ability of the characteristic molecular dynamics composite material model structure.

[0014] The above-mentioned method for predicting the mechanical properties of graphene / aluminum composite materials is characterized by: in step one, determining the initial orientation of the initial molecular dynamics composite material model: in the initial molecular dynamics composite material model of step one, the initial orientation of the aluminum in the aluminum layer is x-axis... Crystal orientation, y-axis is The crystal orientation is

[111] for the z-axis; the initial orientation of the graphene in the graphene layer is a zigzag orientation aligned with the x-axis and an armchair orientation aligned with the y-axis.

[0015] The above-mentioned method for predicting the mechanical properties of graphene / aluminum composite materials is characterized in that: the graphene layer is a single layer of graphene.

[0016] The above-mentioned method for predicting the mechanical properties of graphene / aluminum composite materials is characterized in that: in step three, changing the relative orientation between graphene and aluminum refers to rotating the direction of the graphene layer along the normal direction of the layer interface; wherein, the layer interface is the interface formed when the aluminum layer and the graphene layer are combined.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] 1. This invention modulates the interfacial structural characteristics, namely moiré stripe characteristics, between graphene and aluminum, thereby changing the deformation mechanism of the metal matrix and improving the mechanical properties of graphene / aluminum composite materials. It also provides a new approach for strengthening the mechanical properties of graphene-reinforced aluminum-based composite materials through the joint enhancement of interfacial and twinning properties.

[0019] 2. This invention employs molecular dynamics simulation, which not only effectively reduces the costs and consumption associated with experiments but also allows for direct observation of the deformation evolution process. It also enables rapid verification of the feasibility of the moiré fringe characteristic interface structure reinforcement design concept, and the simulation results provide theoretical guidance for experiments.

[0020] In summary, this invention modulates the interfacial structural features between graphene and aluminum, namely the moiré stripe feature, to alter the deformation mechanism of the metal matrix, thereby improving the mechanical properties of the graphene / aluminum composite material. Furthermore, it provides a novel approach for enhancing the mechanical properties of graphene-reinforced aluminum-based composites through the combined strengthening of the interface and twins. The use of molecular dynamics simulation not only effectively reduces the cost and consumption associated with experiments but also allows for direct observation of the deformation evolution process, rapidly verifying the feasibility of the moiré stripe feature interface structure strengthening design. The simulation results provide theoretical guidance for the experiments.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1This is a flowchart of the method of the present invention.

[0023] Figure 2 This is a schematic diagram of the structure of the graphene / aluminum composite material with different moiré stripe features.

[0024] Figure 3 This is a molecular dynamics model diagram of the different moiré stripe characteristic interfaces of the graphene / aluminum composite material of the present invention.

[0025] Figure 4 This is a microscopic deformation structure diagram of the interface with different moiré stripe characteristics of the graphene / aluminum composite material of the present invention.

[0026] Figure 5 This is a statistical diagram showing the dislocation density and twin volume content of different moiré stripe characteristic interfaces of the graphene / aluminum composite material of the present invention.

[0027] Figure 6 This is a stress-strain curve diagram of the graphene / aluminum composite material of the present invention with different moiré stripe characteristic interfaces.

[0028] Explanation of reference numerals in the attached figures:

[0029] 1—Graphene layer; 2—Aluminum layer; 3—Twin deformation;

[0030] 4—Dislocation deformation. Detailed Implementation

[0031] like Figures 1 to 6 The method shown is for predicting the mechanical properties of graphene / aluminum composite materials. The method includes the following steps:

[0032] Step 1: Establishing an initial molecular dynamics composite material model: Establishing multiple initial molecular dynamics composite material models composed of graphene and aluminum materials. The interface of each initial molecular dynamics composite material model is a (111) plane. The initial molecular dynamics composite material model includes multiple composite material units, which are stacked sequentially from bottom to top. Each composite material unit includes an aluminum layer 2 and a graphene layer 1 disposed below the aluminum layer 2. The initial spacing between the aluminum layer 2 and the graphene layer 1 is h = 0.858σ; where h is the initial spacing between the aluminum layer 2 and the graphene layer 1, and σ is the distance between atoms when the interaction potential between graphene atoms and aluminum atoms is equal to 0.

[0033] Step 2: Select a characteristic molecular dynamics composite material model: Change the relative orientation between graphene and aluminum in the initial molecular dynamics composite material models of Step 1, and select the models in which twin deformation 3 and dislocation deformation 4 are the dominant deformations in different moiré fringe characteristic interfaces, respectively, as the characteristic molecular dynamics composite material models.

[0034] Step 3: Determine the characteristic molecular dynamics composite material model structure: Set periodic boundary conditions for the characteristic molecular dynamics composite material model obtained in Step 3 to obtain a characteristic molecular dynamics composite material model structure with the same size;

[0035] Step 4: Perform stress analysis on the characteristic molecular dynamics composite material model structure, as follows:

[0036] Step 401: Perform a uniaxial tensile stress test on the characteristic molecular dynamics composite material model structure, and determine the strain range of uniaxial tension to obtain the stress and strain values ​​of the characteristic molecular dynamics composite material model structure within the strain range of uniaxial tension.

[0037] Step 402: Based on the data obtained in step 401, plot the stress-strain curve of the characteristic molecular dynamics composite material model structure. Analyze the stress-strain curve to find that the larger the period of the moiré stripes at the graphene / aluminum interface and the more the symmetry axis of the moiré stripe unit is tilted relative to the y-axis, the higher the model yield strength and the stronger the strain hardening ability of the characteristic molecular dynamics composite material model structure.

[0038] This invention modulates the interface structural characteristics, namely moiré stripe characteristics, between graphene and aluminum, thereby altering the deformation mechanism of the metal matrix and improving the mechanical properties of graphene / aluminum composite materials. It also provides a new approach for enhancing the mechanical properties of graphene-reinforced aluminum-based composite materials through the combined strengthening of the interface and twins.

[0039] This invention employs molecular dynamics simulation, which not only effectively reduces the costs and expenses associated with experiments but also allows for direct observation of the deformation evolution process. It also enables rapid verification of the feasibility of the moiré fringe characteristic interface structure reinforcement design concept, and the simulation results provide theoretical guidance for experiments.

[0040] It should be noted that the x, y, and z directions in the initial model of the molecular dynamics composite material are all periodic boundaries to provide a perfect uniaxial tensile model and avoid affecting the initial plastic behavior due to imperfect boundary conditions.

[0041] In step one, the interface of each initial model of the molecular dynamics composite material is a (111) plane, where the (111) plane represents a crystal plane.

[0042] In step two, the characteristic period of the moiré stripes, which varies with the relative orientation angle, is calculated based on the mathematical model proposed by Zeller et al. Graphene / aluminum interface structures with characteristic periods of 1.15 nm, 1.74 nm, 3.08 nm, 5.20 nm, 8.90 nm, and 17.49 nm are selected for modeling. The graphene / aluminum interfaces with different moiré stripe characteristics are shown below. Figure 2 As shown, there are a total of 6 models. Among them, the symmetry of the graphene / aluminum moiré stripe units about the y-axis changes, as shown... Figure 2 The white lines in the diagram indicate that the two models with moiré fringe periods of 1.74 nm and 17.49 nm have moiré fringe units that are symmetrical about the y-axis, while the symmetry axis of the moiré fringe units in the other models is tilted relative to the y-axis.

[0043] A Lammps modeling program was developed to create graphene / aluminum multilayer molecular dynamics models with different moiré fringe interface features. The z-axis single-layer metal layer thickness of 5.38 nm sufficiently accommodates defects such as dislocations. A three-layer graphene / aluminum multilayer model with alternating graphene / aluminum layers was used for uniaxial tensile mechanical calculations, such as... Figure 3 As shown in the figure, the dark color represents the graphene layer and the light color represents the aluminum layer.

[0044] A uniaxial stretching in-file was written and calculated using Lammps software. Specifically, the initial simulation parameters were set in the in-file program, using a 3D simulation mode, selecting metal format as the unit of measurement, importing the graphene / aluminum multilayer molecular dynamics model established in step two, setting the atomic masses of graphene and aluminum, and setting the three axes as periodic boundary conditions. The step size was set to 1 fs. The interatomic interaction forces were defined. Initial velocities were assigned to the model. Energy minimization and relaxation were performed under isothermal and isobaric ensembles for structural optimization. Then, uniaxial stretching was performed along the x-axis until the total strain reached 0.105. During uniaxial stretching, the x and y directions remained periodic boundaries, the z-axis was a free boundary condition, and the pressure in the y-direction was set to 0 GPa. A series of cfg files were output for visual analysis of the deformation process.

[0045] Uniaxial tensile calculations were performed on the above six models to measure the mechanical behavior of the graphene / aluminum system. The cfg files of the deformation process were analyzed using the Ovito open-source visualization software to determine the plastic deformation behavior, obtaining the microstructure and deformation mechanism of the models under different moiré fringe characteristics, such as... Figure 4 As shown, color coding is used to display the deformation patterns; the figure illustrates dislocation deformation mode 4 and twinning deformation mode 3. This demonstrates that the initial plastic mechanical behavior of the graphene / aluminum composite material is controlled by changing the moiré fringe characteristic interface. Furthermore, the content of each deformation carrier is quantified to clarify the dominant deformation mechanism, such as... Figure 5As shown, when the moiré fringe interface period is 8.90 nm, the deformation mode is mainly twinning deformation 3, and when the moiré fringe period is 1.74 nm, the deformation mode of the model is mainly dislocation deformation 4.

[0046] In step two, "dominant" means that the model consists almost entirely of dislocation deformation or twinning deformation. For example... Figure 4 As shown, in the two selected characteristic models, the 1.74nm model has a very high dislocation density and a very low twinning integral number; the 8.9nm model only exhibits twinning deformation with a very high twinning integral number. The dislocation density and twinning integral number are moderate in the remaining models. Whether twinning or dislocations dominate is a relative value. When dislocation deformation, twinning deformation, and other deformation carriers jointly undertake the plastic deformation of the material, the part with the larger proportion of deformation can be considered the dominant deformation; when the proportions of each deformation mode are roughly the same, it is generally considered that several deformations jointly dominate the plastic deformation.

[0047] In step three, based on the 1.74nm model with dislocation as the dominant deformation mechanism and the 8.90nm model with twinning as the dominant deformation mechanism obtained in step two, graphene / aluminum multilayer molecular dynamics models with two deformation mechanisms are created using the Lammps modeling program. Periodic boundary conditions are set to ensure that the model size is the same or similar to eliminate the influence of model size on mechanical properties, which is used to compare the mechanical properties of models with different deformation mechanisms.

[0048] In step four, a uniaxial tension .ini file is created and calculated using Lammps software. Uniaxial tension is applied until the total strain reaches 0.2, resulting in a stress-strain data .txt file. This data is then imported into Origin software to plot the stress-strain curve under uniaxial tension, as shown below. Figure 6 As shown. The first stress peak is selected as the yield strength, and the slope of the stress-strain curve after yielding is compared to measure the strain hardening capacity. Figure 6 As shown in the stress-strain curves, the 8.90 nm model exhibits higher yield strength and enhanced strain hardening ability compared to the 1.74 nm model. This indicates that the mechanical properties of graphene / aluminum composites can be improved by controlling the moiré stripe characteristic interface. When testing the mechanical properties of the aforementioned characteristic molecular dynamics composite model structure using Lammps, the potential function for the graphene / aluminum composite system was chosen as the hybrid interaction potential. The aluminum-aluminum interaction was described using the embedded atom method potential EAM given by Mishin et al. The carbon atom interaction was described using the adaptive intermolecular reaction empirical bond order potential AIREBO, and the carbon-aluminum interaction was described using Lennard-Jones LJ type van der Waals interaction. The potential well depth ε and the interatomic distance σ when the interaction potential is equal to 0 were 0.035078 V and 0.035078 V, respectively.

[0049] In this embodiment, in step one, the initial orientation of the molecular dynamics composite material initial model is determined: In the molecular dynamics composite material initial model of step one, the initial orientation of the aluminum in the aluminum layer 2 is such that the x-axis is... Crystal orientation, y-axis is The crystal orientation is

[111] for the z-axis; the initial orientation of the graphene in the graphene layer 1 is a zigzag orientation aligned with the x-axis and an armchair orientation aligned with the y-axis.

[0050] In actual use, in step one, the initial spacing between the aluminum layer 2 and the graphene layer 1 is set to 0.259 nm.

[0051] In this embodiment, the graphene layer 1 is a single layer of graphene.

[0052] In this embodiment, in step three, changing the relative orientation between graphene and aluminum refers to rotating the direction of graphene layer 1 along the normal direction of the layer interface; wherein, the layer interface is the interface formed when aluminum layer 2 and graphene layer 1 are combined.

[0053] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method of predicting mechanical properties of graphene / aluminum composites, characterized by, The method comprises the following steps: Step one, establishing a molecular dynamics composite material initial model: a plurality of graphene and aluminum material molecular dynamics composite material initial models are established, the interface of each molecular dynamics composite material initial model is a 111 surface, the molecular dynamics composite material initial model comprises a plurality of composite material units, the plurality of composite material units are stacked in order from bottom to top, the composite material unit comprises an aluminum layer (2) and a graphene layer (1) arranged below the aluminum layer (2), and the initial spacing h between the aluminum layer (2) and the graphene layer (1) is 0.858σ; wherein h is the initial spacing between the aluminum layer (2) and the graphene layer (1), and σ is the distance between atoms when the interaction potential between graphene atoms and aluminum atoms is equal to 0; Step two, selecting a characteristic molecular dynamics composite material model: changing the relative orientation between graphene and aluminum in the plurality of molecular dynamics composite material initial models of step one, and selecting the model in which the twin deformation (3) and dislocation deformation (4) are dominant in the different moire characteristic interface as the characteristic molecular dynamics composite material model; Step three, determining the structure of the characteristic molecular dynamics composite material model: setting a periodic boundary condition for the characteristic molecular dynamics composite material model obtained in step three to obtain a characteristic molecular dynamics composite material model structure with the same size; Step four, stress analysis of the characteristic molecular dynamics composite material model structure, the process is as follows: Step 401, uniaxial tensile stress test is performed on the characteristic molecular dynamics composite material model structure, and the strain range of uniaxial tension is determined to obtain the stress value and strain value of the characteristic molecular dynamics composite material model structure in the strain range of uniaxial tension; Step 402, according to the data obtained in step 401, a stress-strain curve diagram of the characteristic molecular dynamics composite material model structure is drawn, and the stress-strain curve diagram is analyzed to obtain that the larger the moire stripe period of the graphene / aluminum interface is, and the more the symmetry axis of the moire stripe unit is inclined relative to the y axis, the higher the model yield strength of the characteristic molecular dynamics composite material model structure is, and the stronger the strain hardening ability is.

2. The method of claim 1, wherein the method is characterized by: In step one, the initial orientation of the initial model of the molecular dynamics composite material is determined: in the initial model of the molecular dynamics composite material of step one, the initial orientation of the aluminum in the aluminum layer (2) is x-axis as crystal direction, y-axis as crystal direction, and z-axis as [111] crystal direction; the initial orientation of the graphene in the graphene layer (1) is that the zigzag orientation is aligned with the x-axis, and the armchair orientation is aligned with the y-axis.

3. The method of claim 1, wherein the method is characterized by: The graphene layer (1) is single-layer graphene.

4. The method of claim 1, wherein the method is characterized by: In step three, changing the relative orientation between graphene and aluminum refers to rotating the direction of the graphene layer (1) along the layer interface normal direction; wherein the layer interface is the interface formed when the aluminum layer (2) and the graphene layer (1) are combined.