A method for evaluating interface bonding strength based on first principles

Abstract

The invention relates to the field of surface and interface mechanical properties of composite materials and coatings, and discloses a method for evaluating interface bonding strength based on first principles. The method comprises the following steps: step 1, obtaining the structure of each material, establishing a surface model of each material, and establishing an initial interface model; step 2, performing a vacuum layer thickness test, a layer number convergence test, and an interface distance test on the initial interface model to obtain an interface test model; step 3, using a first principles calculation method to relax the surface model and the interface test model structure, calculate the surface energy of the surface, calculate the interface energy and adhesion work of the interface test model, analyze the change of the electronic structure during interface bonding through state density and differential charge density results, and evaluate the interface bonding strength of each material; step 4, performing simulated stretching on the interface test model to obtain the ultimate stress and strain of each material, and calculate the change of the differential charge density, population value and bond length of each material during the strain process.

Description

Technical Field

[0001] The present invention relates to the field of surface and interface mechanical properties of composite materials and coatings, and in particular to a theoretical calculation method for evaluating surface and interface bonding strength based on first principles. Background Art

[0002] Different materials have varying physical properties, service lives, and performance, all of which are closely related to the strength of the material interface. Interface strength refers to the ability of the matrix and reinforcement phase to resist separation under external forces and is divided into interface tensile strength and interface shear strength. In recent years, due to the continuous development of materials and processes, performance has become more diverse and interface structures have become increasingly complex. Therefore, it is crucial to develop simple, non-destructive, online, and quantitatively accurate methods for characterizing interface strength.

[0003] Numerous methods have been developed to characterize interfacial bond strength. These methods can be categorized into static and dynamic loading methods based on the loading mechanism. Static methods include tensile testing, peeling, scratching, indentation, bubbling, and bending. Dynamic methods include reciprocating scratching, impact testing, cyclic indentation, and fatigue testing. However, each method has its own specific application scope and cannot be applied to all interfaces. For example, the tensile method is intuitive and simple, but it does not allow for shear during loading and cannot affect material properties during bonding or welding. The indentation method, while simple to operate, cannot determine the critical load at which the film will detach, making it limited to qualitative characterization of interfacial bond strength. Overall, while static loading methods are well-established and widely used, they are susceptible to various external factors during the experimental process, resulting in large errors in the measured interfacial bond strength. Dynamic loading methods, due to their specific loading mechanisms, provide more realistic and instructive results. However, each method still has its limitations, and to date, no single method can characterize the bond strength of any interface. Summary of the Invention

[0004] The present invention provides a method for evaluating interface bonding strength based on first principles. The method is applicable to any interface formed by a precipitated phase and a matrix and has a wide range of applications.

[0005] A method for evaluating interface bonding strength based on first principles comprises the following steps:

[0006] Step 1: Obtain the structure of each material, establish a surface model of each material, match the surfaces of each material, and establish an initial interface model;

[0007] Step 2: Perform vacuum layer thickness test, layer number convergence test, and interface distance test on the initial interface model to obtain an interface test model; in this way, the initial interface model is optimized to ensure the rationality of the interface test model and the accuracy of subsequent calculation results;

[0008] Step 3: Using first-principles calculation methods, the surface model and the interface test model structures are relaxed respectively. Based on the relaxed surface model, the surface energy is calculated. Based on the relaxed interface test model, the interface energy and adhesion work of the interface test model are calculated. The changes in the electronic structure during interface bonding are analyzed through the state density and differential charge density results to evaluate the interface bonding strength of each material.

[0009] Step 4: simulate stretching of the interface test model to obtain the ultimate stress and strain of each material, and calculate the changes in the differential charge density, population value and bond length of each material during the strain process.

[0010] A preferred embodiment of the present invention is that the step 1 comprises:

[0011] Step 1.1: After obtaining the structure of each material, perform full relaxation on each material. Full relaxation is based on the exchange-correlation function calculation of the generalized gradient approximation. The plane wave cutoff energy converges to 300-400 eV and the energy converges to 1×10 -6 ~5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, the force convergence reaches 0.01-0.02GPa;

[0012] Step 1.2: Based on the two principles of low-index surface stability and low-surface-energy surface stability, sections are cut from each material after relaxation. Since different materials have different lattice constants, there is lattice mismatch after sectioning. Therefore, the mismatch is reduced by cell expansion and lattice vector change.

[0013] A preferred embodiment of the present invention is that the step 2 comprises:

[0014] Step 2.1: The vacuum layer can be used to isolate the interactions between atoms close to each other. A too thick vacuum layer will increase the calculation time, while a too thin vacuum layer will not be enough to isolate the interactions between atoms. Therefore, the thickness of the vacuum layer needs to be tested. The static energy is calculated using the interface test model with different vacuum layer thicknesses. In the vacuum layer thickness test, the static energy differs by 10 -3 Convergence is achieved below eV, and the vacuum layer thickness is

[0015] Step 2.2: The number of layers in the interface test model should reach a thickness that can mimic the bulk properties. Therefore, the thickness of the Fe surface and the V6C5 surface must be tested before building the interface test model. In the layer number convergence test, different surface layer numbers are optimized. After optimization, convergence is achieved when the interlayer spacing changes by 0% to 1%.

[0016] In step 2.3, after determining the number of layers and the thickness of the vacuum layer, the interface is made to have different interface distances, and the energy minimum point is found. The interface distance corresponding to this point is the optimal interface distance.

[0017] A preferred embodiment of the present invention is that step 3 comprises:

[0018] Step 3.1: Calculate the surface energy of the surface based on the surface model after relaxation. Use the first-principles calculation method of density functional theory and MS software to perform atomic relaxation and self-consistent calculation. The energy convergence criterion is set to 5×10 -4 ~1×10 -6 eV, the convergence criterion for atomic forces is set to The lower the surface energy, the more stable the surface;

[0019] Step 3.2: Calculate the interfacial energy and adhesion work of the interface test model based on the relaxed interface test model. The calculation formula for adhesion work is: Among them, W ad is the adhesion work, E int represents the static energy of the interface model, E salb1 , E slab2 represents the static energy of the two surfaces constituting the interface, A represents the interface area, and the first-principles calculation method of density functional theory is used to perform atomic relaxation and self-consistent calculation. The energy convergence standard is set to 1×10 -3 ~1×10 - 6 eV, the convergence criterion for atomic forces is set to

[0020] Step 3.3, calculate the interfacial energy, the calculation formula is Among them, N c 、N v 、N Fe Represent the number of C atoms, V atoms, and Fe atoms in the interface, μ C , μ V , μ Fe Represent the chemical potentials of C atoms, V atoms, and Fe atoms in the interface, σ Fe , σ V6C5 represent the surface energies of Fe surface and V6C5 surface, respectively;

[0021] Step 3.4 Density of states and differential charge density results analyze the changes in electronic structure during interface binding.

[0022] A preferred embodiment of the present invention is that the step 4 includes: each time performing atomic relaxation on the basis of the previous stretching, the relaxation is calculated based on the exchange correlation function of the generalized gradient approximation, the plane wave cutoff energy converges to 300-350 eV, and the energy converges to 1×10 -5 ~1×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 ~1×10 -6 eV / atom, the force converges to 0.2-0.02GPa, after which strain is applied and the atoms relax until the material breaks.

[0023] The advantages of the method for evaluating interface bonding strength based on first principles of the present invention are:

[0024] (1) All methods related to interface bonding strength have their own advantages and disadvantages, and are limited in use and are only applicable to certain materials or certain situations. However, the method for evaluating interface bonding strength based on first principles proposed in the present invention is applicable to any interface formed by a precipitate phase and a matrix, has a wide range of applications, and saves research resources.

[0025] (2) Through multiple parameters (surface index, mismatch, number of model layers, vacuum layer thickness, interface distance), multiple convergence tests (layer number convergence test, vacuum layer thickness test, interface distance test), multiple calculation parameter limits (energy convergence standard is set to 1×10 -3 ~1×10 -6 eV, the convergence criterion for atomic forces is set to Self-consistently converges to 1×10 -5 ~5×10 -6 eV) to determine the interface test model to ensure the rationality of the interface test model and the rationality of the calculation results.

[0026] (3) The evaluation indicators are comprehensive and the results such as surface energy and interface energy calculated by a method based on first principles to evaluate interface bonding strength are accurate.

[0027] (4) Compared with other research methods, the tensile test conducted does not require the destruction of the actual experimental specimens to conduct the test, saving resources and allowing batch stretching, thus saving the test cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Attachment Figure 1 This is a flow chart of the method for evaluating interface bonding strength based on first principles of the present invention;

[0029] Attachment Figure 2 Interface diagrams for different interface types;

[0030] Attachment Figure 3is the surface energy of V6C5(001) and the carbon chemical potential (μ C ) relationship diagram;

[0031] Attachment Figure 4 The interface energy between Fe(001) and V6C5(001) changes with the carbon chemical potential (μ C )’s change graph;

[0032] Attachment Figure 5 The stress-strain curves of the V end of the Fe(001) and V6C5(001)MT stacking models;

[0033] Attachment Figure 6 The stress-strain curves of the C-end of the Fe(001) and V6C5(001)MT stacking models;

[0034] Attachment Figure 7 The adhesion work diagram of different stacking methods for comparison example.

[0035] Attachment Figure 8 The charge density analysis diagram of the MT stacking interface at the V terminal;

[0036] Attachment Figure 9 Layout analysis results. DETAILED DESCRIPTION

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Example 1:

[0039] This embodiment is described using Fe and V6C5 as examples.

[0040] The method for evaluating interface bonding strength based on first principles is as follows:

[0041] Step 1: Based on the currently available databases, including Materials Project, OQMD, SpringerMaterials, ICSD and NIST, as well as relevant literature reports, the crystal structures of Fe and V6C5 were obtained, and the first-principles calculation method based on density functional theory was used to perform full structural relaxation of Fe and V6C5 by MS or VASP. The full relaxation was based on the exchange-correlation function calculation of the generalized gradient approximation, with the plane wave cutoff energy converged to 300 eV and the energy converged to 5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, and the force convergence reaches 0.02GPa.

[0042] Through the factors of surface index, surface energy and mismatch, Fe(001) and V6C5(001) sections are selected and matched to generate the initial interface model. Specifically, based on the two principles of low index surface stability and low surface energy surface stability, the mismatch is reduced by expanding the cell and changing the lattice vector. VESTA or MS software sections are selected to build a two-dimensional material and the interface lattice constant is selected from the lattice constant of the matrix Fe. Figure 2 That is, the schematic diagram of the initial interface model established in this embodiment, Figure 2 They are: (a) Fe-V6C5-C-OT interface, (b) Fe-V6C5-C-MT interface, (c) Fe-V6C5-C-HCP interface, (d) Fe-V6C5-V-OT interface, (e) Fe-V6C5-V-MT interface, and (f) Fe-V6C5-V-HCP interface.

[0043] Step 2: Use the initial interface model to conduct a series of parameter convergence tests, including vacuum layer thickness test, layer number convergence test, and interface distance test to obtain an interface test model to make the interface more reasonable and closer to reality.

[0044] Step 2.1, vacuum layer thickness convergence test, using different vacuum layer thickness interface test models using density functional first principle method, using MS software to calculate static energy, in the vacuum layer thickness test, the energy difference of 10 -3 Convergence is achieved below eV, and the vacuum layer thickness is Specifically, according to Table 1, in this embodiment, the vacuum layer thickness exceeds That is, convergence is achieved. Table 1 shows the static energy of the interface as the thickness of the interface vacuum layer changes. The thickness of the vacuum layer ranges from arrive

[0045] Table 1

[0046]

[0047]

[0048] Step 2.2, layer number convergence test, select different numbers of layers for Fe surface, V6C5-V surface and V6C5-C respectively, and calculate the percentage change of interlayer spacing before and after optimization. Specifically, it refers to the percentage change of interlayer spacing of each layer after interface optimization compared with the interlayer spacing before optimization. Convergence is reached when the change is less than 1%. According to the calculation results, the interlayer spacing changes of V6C5-V and V6C5-C surfaces are less than 1% when the interlayer spacing is 9 layers or more, and the interlayer spacing changes of Fe surface are less than 1% when the interlayer spacing is more than 7 layers.

[0049] Step 2.3, perform the interface distance test. Use the Movement key to make the interface have different interface distances. Set the convergence conditions as follows: the plane wave cutoff energy converges to 300 eV, the energy converges to 5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, the convergence of force reaches 0.02GPa. Calculate the static energy separately. After determining the number of layers and the thickness of the vacuum layer, extract the final energy from the result file after optimization, draw the curve of energy vs. interface distance and the curve of stress vs. interface distance, and the interface distance corresponding to the minimum energy is the optimal interface distance. It can be seen that the optimal interface distance of the V terminal in the Fe(001) / V6C5(001) interface is The optimal interface distance of C terminal is about about.

[0050] Step 3: Use the first principle calculation method to relax the surface model and the interface test model structure respectively, and calculate the surface energy of the surface based on the relaxed surface model, where the surface refers to the Fe surface and the V6C5 surface. Where ρ represents the surface energy, N represents the total number of atoms on the surface, and E bulk represents the static energy of the bulk material, A represents the interface area, and after calculation, the surface energy of the Fe surface is 2.80 J / m 2 , which is consistent with the values ​​in other literature and experimental values, but the surface of V6C5 does not conform to the stoichiometric ratio, so the chemical potential is introduced for calculation. Among them, E slab Represents the energy of the surface after optimization, E bulk Represents the optimized energy of each unit cell of the bulk material, A represents the surface area, represents the chemical potential of the V6C5 surface, represents the chemical potential of C in the bulk material, It represents the chemical potential of C on the V6C5 surface, Nv and Nc refer to the number of V atoms and C atoms in the surface model. It is calculated that the surface energy changes with the change of C chemical potential and is within a range. Figure 3 That is, the surface energy of V6C5 (001) calculated in this embodiment is 4.5 to 9.01 J / m 2 Table 2 shows the surface energy σ of Fe(001) and V6C5(001)-C, V6C5(001)-V surfaces.

[0051] Table 2

[0052]

[0053] According to the interface test model after relaxation, the interface energy and adhesion work of the interface test model are calculated, and the changes in the electronic structure during interface bonding are analyzed through the state density and differential charge density results to evaluate the interface bonding strength of each material. In this embodiment, an interface test model with two layers plus a vacuum layer is used to calculate the adhesion work of the interface. The two layers + vacuum layer represent an arrangement of Fe layer (representing the first layer), V6C5 layer (representing the second layer), and vacuum layer (representing the third layer). The number of layers described in the aforementioned step 2.2 refers to the number of Fe layers and the number of V6C5 layers, which is the specific number of layers.

[0054] The calculation formula for adhesion work is: Among them, W ad is the adhesion work, E int represents the static energy of the interface model, E salb1 , E slab2 represents the static energy of the two surfaces constituting the interface, and A represents the interface area. The first-principles calculation method of density functional theory was used to perform atomic relaxation and self-consistent calculations, and the energy convergence standard was set to 1×10 -3 ~1×10 -6 eV, the convergence criterion for atomic forces is set to

[0055] If the calculation of interfacial energy does not conform to the stoichiometric ratio, it is also necessary to introduce chemical potential like calculating surface energy, balance the chemical potential and calculate the interfacial energy. The calculation formula is Among them, N c 、N v 、N Fe Represent the number of C atoms, V atoms, and Fe atoms in the interface, μ C , μ V , μ Fe Represent the chemical potentials of C atoms, V atoms, and Fe atoms in the interface, σ Fe , σ V6C5 Represent the surface energies of Fe and V6C5 respectively. The interfacial energy calculated by this method is consistent with that calculated by other methods, and the interfacial energy changes with the change of C chemical potential and is within a range. Figure 5 and Figure 6 That is, the interface energy of Fe(001) and V6C5(001) in this embodiment changes with the carbon chemical potential (μ C ) changes, indicating that the interface energy of the interface in this study is between 0 and 12 J / m 2 between.

[0056] Check the Density of state and Electron difference options in the MS software properties to perform density of state, differential charge density, and population analysis. The self-consistent field convergence is set to 2.0×10 -6 During the optimization process, the total energy convergence value was set to 2.0×10 -2 meV, the force per atom is set to The adhesion work calculation results show that the V-MT stacking mode has the highest adhesion work at the Fe(001) and V6C5(001) interface.

[0057] Step 4: This example uses a first-principles method to evaluate interfacial bonding strength. During the tensile simulation, engineering strain is applied quasi-statically to the interface. This is done using a two-layer plus vacuum interface test model. The Optimize Cell option is unchecked; this model is only suitable for tensile deformation, not shear deformation. Before relaxation, the interface distance is set to the optimal distance for the test.

[0058] Specifically, it includes step 4.1, performing atomic relaxation on the interface test model, releasing stress, and calculating the exchange-correlation function based on the generalized gradient approximation. The plane wave cutoff energy converges to 300 eV and the energy converges to 5×10 -5 eV / atom, and the self-consistent convergence standard reaches 1×10 -5 eV / atom, and the force convergence reaches 0.2GPa.

[0059] In step 4.2, strain is applied to the interface test model. The strain step is 2% of the lattice constant c. The method is to directly change the lattice constant c of the interface and fix the lattice constants a and b. The stress is calculated and the calculation parameters are set the same as in step 4.1.

[0060] In step 4.3, each time the atoms are relaxed based on the previous stretching, this ensures the continuity of the interface stretching. During the stretching, the fractional coordinates of some bulk atoms are fixed, which does not affect the accuracy of the results and can reduce the amount of calculation. This operation is continued until the interface breaks. Figure 5 That is the stress-strain curve of the V-end and C-end of the Fe(001) / V6C5(001)MT stacking model in this embodiment. It can be seen that the maximum interface strain and stress of the V-end are 23% and 17.4GPa, respectively, and the maximum interface strain and stress of the C-end are 32% and 19.3GPa, respectively.

[0061] During stretching, the differential charge density and population analysis are calculated together to further analyze the inherent fracture mechanism of the material. The population analysis only needs to analyze the interface atoms, which can better reflect the changes in the atomic bonds at the interface. Figure 8As shown in the figure, it is a charge density analysis diagram of the V-terminal MT stacking interface, where I represents CC bond, II represents CV bond, III represents VV bond, IV represents V-Fe bond, and V represents Fe-Fe bond; as shown in the attached figure, Figure 9 The results of the layout analysis show the change of the bond length of the V-terminal MT stacking interface with strain. The calculation results show that the bonding mode of the Fe(001) / V6C5(001) interface is metallic bond, covalent bond, and ionic bond.

[0062] The above-mentioned case study method can overcome the shortcomings of the traditional "trial and error" method, batch calculate the properties of the interface, save resources and time, and establish the most reasonable and practical interface test model based on high-throughput first-principles through multiple convergence tests. It can further calculate the surface energy, interfacial energy, adhesion work, density of states, differential charge density and population analysis of the material, find the interface with good interfacial bonding strength, and then proceed to the next stretching to obtain stress-strain curves, revealing the changes in the material during the stretching process and the intrinsic mechanism of interfacial bonding. This calculation method has more evaluation indicators and a more comprehensive evaluation. Compared with experiments, it can save research time and resources, improve research efficiency, play a guiding role, and avoid blindness.

[0063] Example 2

[0064] A method for evaluating interface bonding strength based on first principles, the steps are as follows:

[0065] Step 1: Based on the currently available databases (Materials Project, OQMD, Springer Materials, ICSD, and NIST) and relevant literature reports, the structures of Fe and V6C5 were obtained, and the first-principles calculation method based on density functional theory was used to perform full structural relaxation through MS or VASP. The full relaxation was based on the exchange-correlation function calculation of the generalized gradient approximation, and the plane wave cutoff energy converged to 300 eV and the energy converged to 5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, and the force convergence reaches 0.02GPa.

[0066] Step 2: Based on the reports in other literature, the size of the surface energy, the size of the mismatch, and other factors, the Fe(001) and V6C5(001) sections are selected and matched to generate the initial interface model. When cutting, VESTA or MS software is used. When matching, build layers structure as surface is selected to build a two-dimensional material, and the interface lattice constant is the lattice constant of the matrix Fe, which is more consistent with the actual experiment.

[0067] Step 3: Use the initial interface model to conduct a series of parameter convergence tests to make the interface more reasonable and closer to reality.

[0068] Step 3.1, layer number convergence test, select different numbers of layers for Fe surface and V6C5 surface respectively, calculate the percentage change before and after the optimization of the interlayer spacing, when the change is small, less than 1%, it can be considered that convergence has been achieved.

[0069] Step 3.2: After determining the number of layers, the surface energy can be calculated. After calculation, the surface energy of Fe surface is 2.80 J / m 2 , which is consistent with the values ​​in other literature and experimental values, while the surface of V6C5 does not conform to the stoichiometric ratio. The chemical potential is introduced for calculation, and it is calculated that the surface energy changes with the change of C chemical potential and is within a range.

[0070] Step 3.3, vacuum layer thickness convergence test, with the same number of interface layers and different thicknesses of vacuum layers, the static energy is directly calculated. If the static energy changes slightly and reaches below 0.001 eV, it can be considered to have reached convergence.

[0071] Step 3.4, interface distance test, after determining the number of layers and the thickness of the vacuum layer, make the interface have different interface distances. After optimization, draw the curves of energy and interface distance and stress and interface distance. The interface distance corresponding to the minimum energy value is the optimal interface distance.

[0072] Step 4: After determining a series of interface parameters, the interface test model of two layers plus vacuum layer is used to calculate the adhesion work, interface energy, state density, differential charge density and population analysis of the interface. The self-consistent field convergence is set to 2.0×10 -6 During the optimization process, the total energy convergence value was set to 2.0×10 -2 meV, the force per atom is set to

[0073] Step 4.1: If the calculation of interfacial energy does not conform to the stoichiometric ratio, it is also necessary to introduce chemical potential and balance the chemical potential for calculation, just like calculating surface energy.

[0074] In step 4.2, the interfacial energy calculated using this method is of the same order of magnitude as that calculated by other methods, and the interfacial energy varies with the change of the C chemical potential and is within a certain range.

[0075] Step 5, a method for evaluating the interface bonding strength based on first principles, in which the engineering strain is applied to the interface in a quasi-static manner during the tensile simulation.

[0076] Step 5.1 is performed using a two-layer model without a vacuum layer. This model can be used for both tensile and shear deformations. Before relaxation, the interface distance does not need to be changed.

[0077] Step 5.2, fully relax the model, check the optimize cell option, release the stress, and relax the interface distance to the most appropriate value. Relaxation is based on the exchange-correlation function calculation of the generalized gradient approximation, and the plane wave cutoff energy converges to 350 eV and the energy converges to 3×10 -6 eV / atom, and the self-consistent convergence standard reached 3×10 -6 eV / atom, and the force convergence reaches 0.02GPa.

[0078] In step 5.3, strain is then applied to the interface test model with a strain step of 2% of the lattice constant c. The method is to directly change the lattice constant c of the interface and fix the lattice constants a, b, and c. Only atomic relaxation is performed and stress is calculated. The calculation parameter settings are the same as in step 5.2.

[0079] In step 5.4, each applied strain is applied based on the deformation of the previous optimization to ensure the continuity of the interface stretching. During stretching, the fractional coordinates of some bulk atoms are fixed. This does not affect the accuracy of the results and can reduce the computational effort. This operation is continued until the interface breaks.

[0080] Step 6: Calculate the differential charge density and population analysis during stretching to further analyze the inherent fracture mechanism of the material. Population analysis only requires analysis of interface atoms and can better reflect the changes in atomic bonds at the interface.

[0081] Compared with Example 1, the fatigue test interface test model established in Example 2 has a wider range of applications, releases profits more thoroughly during modeling optimization, and can be used not only for stretching but also for simulating shear, with better results and more in line with reality.

[0082] Comparative Example

[0083] The difference between this comparative example and the above one is that the model construction method is different, but the calculation method and formula are the same. The specific differences are:

[0084] Step 1: Based on the currently available databases (Materials Project, OQMD, Springer Materials, ICSD and NIST) and relevant literature reports, the structures of Fe and V6C5 were obtained, and the first-principles calculation method based on density functional theory was used to perform full structural relaxation through MS or VASP. The full relaxation was based on the exchange-correlation function calculation of the generalized gradient approximation, and the plane wave cutoff energy was converged to 450 eV and the energy was converged to 5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, and the force convergence reaches 0.02GPa.

[0085] Step 2: Select the cross-sections Fe(001) and V6C5(001) and match them based on the reports in other literature, the size of the surface energy, the size of the mismatch, and other factors to generate the initial interface model. When matching, select "build layers structure as surface" to build a two-dimensional material and the interface lattice constant is the average value of the Fe surface and the V6C5 surface.

[0086] In step 3, the layer number convergence test, vacuum layer convergence test, and interface distance convergence test were not performed.

[0087] In step 3.1, the number of layers selected is 3 layers on the Fe surface and 5 layers on the V6C5 surface.

[0088] Step 3.2, vacuum layer removal The theoretical basis is that other literature mentions that the vacuum layer is generally That's it.

[0089] Step 3.3: The interface distance is not tested, so the default value provided when MS built the interface is used directly. about.

[0090] Step 4: After the interface is built, the interface test model of two layers plus vacuum layer is used to calculate the adhesion work of the interface. Figure 7 As shown in the figure, the adhesion work diagram, interface energy, state density, differential charge density and population analysis of different stacking methods in this comparative example are shown. The plane wave cutoff energy converges to 450 eV, and the energy on each atom converges to 5×10 -6 eV, the maximum displacement converges to

[0091] In step 4.1, the calculation of surface energy and interfacial energy did not consider whether the surface and interface conformed to the stoichiometric ratio, and no chemical potential was introduced.

[0092] Step 4.2, calculate the adhesion work of the interface, the fracture work of the interface, and the differential charge density.

[0093] This implementation did not conduct a series of tests when constructing the interface test model, relying solely on empirical values ​​from other literature. This model is therefore illogical and inaccurate. The calculations, taking into account the stoichiometric ratios of the interface test model, did not balance the chemical potential, resulting in inaccurate results. This resulted in significant discrepancies between the calculated interface results and experimental values ​​from other literature, making them ineffective for future research.

[0094] The above describes the embodiments of the method of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any parameter changes or calculation simplifications made according to the principles of the technical solution of the present invention, as long as they meet the purpose of the invention and do not deviate from the principles and concepts of the present invention as a method for evaluating interface bonding strength based on first principles, fall within the scope of protection of the present invention.

Claims

1. A method for evaluating interface bonding strength based on first principles, characterized in that: The following steps are involved: Step 1: Obtain the structure of each material, establish a surface model of each material, match the surfaces of each material, and establish an initial interface model; Step 2: Perform vacuum layer thickness test, layer number convergence test, and interface distance test on the initial interface model to obtain an interface test model; The step 2 includes: step 2.1, in the vacuum layer thickness test, the static energy difference is 10 -3eV The convergence is reached below, so the vacuum layer thickness is Convergence has been reached; Step 2.2, in the layer number convergence test, different surface layer numbers are used for optimization. After optimization, convergence is achieved when the interlayer spacing changes by 0% to 1%. Step 2.3: After determining the number of layers and the thickness of the vacuum layer, the interface is made to have different interface distances, and the energy minimum point is found. The interface distance corresponding to this point is the optimal interface distance. Step 3: Using first-principles calculation methods, the surface model and the interface test model structures are relaxed respectively. Based on the relaxed surface model, the surface energy is calculated. Based on the relaxed interface test model, the interface energy and adhesion work of the interface test model are calculated. The changes in the electronic structure during interface bonding are analyzed through the state density and differential charge density results to evaluate the interface bonding strength of each material. Step 4: simulate stretching of the interface test model to obtain the ultimate stress and strain of each material, and calculate the changes in the differential charge density, population value and bond length of each material during the strain process.

2. The method for evaluating interface bonding strength based on first principles according to claim 1, characterized in that: The step 1 comprises: Step 1.1: After obtaining the structure of each material, perform full relaxation on each material. Full relaxation is based on the exchange-correlation function calculation of the generalized gradient approximation. The plane wave cutoff energy converges to 300-400 eV and the energy converges to 1×10 -6 ~5×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 eV / atom, the force convergence reaches 0.01-0.02GPa; In step 1.2, based on the two principles of low-index surface stability and low-surface-energy surface stability, cut the surface of each material after relaxation, and use the two methods of cell expansion and lattice vector change to reduce the mismatch.

3. The method for evaluating interface bonding strength based on first principles according to claim 1, characterized in that: The step 3 includes: step 3.1, calculating the surface energy of the surface based on the surface model after relaxation, using the first principle calculation method of density functional theory, using MS software to perform atomic relaxation and self-consistent calculation, and setting the energy convergence standard to 5×10 -4 ~1×10 -6eV , The convergence criterion for atomic forces is set to The lower the surface energy, the more stable the surface; Step 3.2: Calculate the interfacial energy and adhesion work of the interface test model based on the relaxed interface test model. The calculation formula for adhesion work is: Among them, W ad is the adhesion work, E int represents the static energy of the interface model, E salb1 , E slab2 represents the static energy of the two surfaces constituting the interface, A represents the interface area, and the first-principles calculation method of density functional theory is used to perform atomic relaxation and self-consistent calculation. The energy convergence standard is set to 1×10 -3 ~1×10 -6 eV, the convergence criterion for atomic forces is set to Step 3.3, calculate the interfacial energy, the calculation formula is Among them, N c 、N v 、N Fe Represent the number of C atoms, V atoms, and Fe atoms in the interface, μ C , μ V , μ Fe Represent the chemical potentials of C atoms, V atoms, and Fe atoms in the interface, σ Fe , σ V6C5 represent the surface energies of Fe surface and V6C5 surface, respectively; Step 3.4 uses density of states and differential charge density to analyze the changes in electronic structure during interface binding.

4. The method for evaluating interface bonding strength based on first principles according to claim 1, characterized in that: The step 4 includes: each time performing atomic relaxation based on the previous stretching, the relaxation is based on the exchange correlation function calculation of the generalized gradient approximation, the plane wave cutoff energy converges to 300-350eV, and the energy converges to 1×10 -5 ~1×10 -6 eV / atom, and the self-consistent convergence standard reaches 1×10 -4 ~1×10 -6 eV / atom, the force converges to 0.2-0.02GPa, after which strain is applied and the atoms relax until the material breaks.

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