A transition metal diboride compression-shear instability prediction method
By applying normal compressive stress and shear strain, calculating the local coordination mismatch amplification factor, and combining it with structural collapse information, the problem of evaluating the instability of transition metal diborides under combined loads, which is difficult in the prior art, is solved, and accurate instability prediction and stability comparison of materials under compressive-shear combined loads are realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2026-06-26
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies are insufficient to accurately assess the instability risk of transition metal diborides under compressive-shear combined loads. Traditional indicators are inadequate to reflect the structural evolution and instability tendency of materials under combined loads, especially since changes in the non-equivalent transition metal-boron coordination environment and bond state of layered or quasi-layered structures have a significant impact.
By applying normal compressive stress and performing structural relaxation, the bond lengths of inequivalent transition metals and boron are calculated, a local coordination mismatch amplification factor is constructed, and instability prediction and verification are performed by combining shear stress-shear strain response and structural collapse information.
It can more accurately predict the instability risk of transition metal diborides under combined loads, provide quantitative data to characterize the degree of local coordination imbalance, and realize the comparison of the relative shear stability of materials under compression-shear combined loads.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of computational materials, and more specifically to a method for predicting the compression-shear instability of transition metal diborides. Background Technology
[0002] Transition metal diborides possess significant application potential in hard coatings, wear-resistant materials, and materials for extreme service environments due to their high hardness, high melting point, good chemical stability, and high elastic modulus. Existing performance evaluation methods for transition metal diborides primarily focus on crystal structure stability, formation enthalpy, elastic constant, bulk modulus, shear modulus, empirical hardness, and ideal strength under zero-pressure conditions.
[0003] However, during indentation, scratching, friction wear, and coating contact service, the near-surface region of hard materials is often not under a single state of tension, compression, or shear, but rather subjected to a combined load of normal compression and tangential shear. Traditional indicators such as elastic constants, empirical hardness, and zero-compression shear strength are insufficient to fully reflect the structural evolution and instability tendency of materials under compression-shear coupling conditions.
[0004] For transition metal diborides with layered or quasi-layered structural characteristics, the local structural response can vary significantly under different shear paths. In particular, normal compression alters the transition metal-boron coordination environment, the undulation state of the boron layers, and the relative interactions of boron-boron bonds and transition metal-boron bonds, thus affecting the structural stability during subsequent shear deformation. Therefore, relying solely on equilibrium mechanical parameters is insufficient to accurately assess the instability risk of candidate materials under combined compressive-shear loading. Summary of the Invention
[0005] This invention provides a method for predicting compression-shear instability of transition metal diborides, addressing the problems existing in the prior art.
[0006] The technical solution adopted in this invention is: a method for predicting the compression-shear instability of transition metal diborides, comprising the following steps: Step 1: Obtain the crystal structure model of the transition metal diboride, apply normal compressive stress to the crystal structure model, and perform structural relaxation under the normal compressive stress to obtain the compressed crystal structure model; the transition metal diboride contains coordination of non-equivalent transition metals and boron; Step 2: Obtain the non-equivalent transition metal-boron bond lengths based on the compressed crystal structure model; Step 3: Calculate the local coordination mismatch amplification factor based on the inequivalent transition metal-boron bond lengths. :
[0007] In the formula: and These represent the bond lengths of two types of inequivalent transition metals-boron. The difference in the length of the inequivalent transition metal-boron bond under zero normal compressive stress; Normal compressive stress; Step 4: Instability prediction based on the value of the local coordination mismatch amplification factor.
[0008] Furthermore, the normal compressive stress in step 1 is applied along the
[0001] direction of the transition metal diboride crystal.
[0009] Furthermore, it also includes the following steps: Shear strain is applied to the compressed crystal structure model along the selected shear path while maintaining the normal compressive stress. The instability prediction results in step 4 are verified by the shear results under compression.
[0010] Furthermore, the shear path lies within the (0001) basal plane of the transition metal diboride crystal.
[0011] Furthermore, the cutting path is at least two of the following: the [1-100](0001) direction, the [11-20](0001) direction, the intermediate direction between the [1-100](0001) direction and the [11-20](0001) direction.
[0012] Furthermore, in step 1, the transition metal diboride crystal structure model is subjected to first-principles structural relaxation.
[0013] Furthermore, the transition metal is one or more of TcB2, WB2, and ReB2.
[0014] Furthermore, shear stress-shear strain response and structural collapse information are obtained from shear simulation calculations under compression. The instability prediction results are verified by determining whether the material has collapsed based on the shear stress-shear strain response and structural collapse information.
[0015] Furthermore, the structural collapse information includes a sudden drop in shear stress, a sudden change in the bond length of the transition metal-boron bond, a sudden change in the boron-boron bond length, and the inability of crystal structure optimization to converge to a continuous local equilibrium configuration.
[0016] The beneficial effects of this invention are: This invention introduces normal compressive stress, which can more closely approximate the composite stress state under contact load conditions; by constructing a local coordination mismatch amplification factor through inequivalent transition metal-boron bond lengths, the cumulative degree of local coordination imbalance under normal compression can be intuitively characterized by quantitative data.
[0017] This invention uses a local coordination mismatch amplification factor to predict the instability of transition metal diborides, and verifies it using shear stress response and structural collapse information. The combination of these three methods can be used to compare the relative shear stability of different transition metal diborides under compression-shear combined loads. Attached Figure Description
[0018] Figure 1 This is a schematic diagram of the method flow of the present invention.
[0019] Figure 2 The diagram shows the structure, coordination units, and local structural evolution of the ReB2 type crystal under different normal compressive stresses in Embodiment 1 of the present invention. I represents the structure of the ReB2 type crystal, while II, III, and IV represent the changing trends of crystal parameters with normal stress.
[0020] Figure 3 The figures show the representative shear path and shear stress-strain curves under normal stress of the ReB2 type crystal in the (0001) basal plane in Embodiment 1 of the present invention. I is the representative shear path of the ReB2 type crystal in the (0001) basal plane, and II, III, and IV are the shear stress-strain curves under normal stress under the three shear paths.
[0021] Figure 4 The figures show the representative structural configurations of the WB2 type crystal under different shear paths, the collapse normal compressive stress of different candidate transition metal diborides, and the results of the local coordination mismatch amplification factor as a function of normal compressive stress in Embodiment 1 of the present invention. I, II, and III are the microstructures of the WB2 type crystal after shear slip in three directions, respectively. IV is the normal stress corresponding to the collapse of the three different TMB2 type crystals in the three shear directions. V is the local coordination mismatch amplification factor calculated for the three different TMB2 type crystals.
[0022] Figure 5 The results of Hamiltonian population analysis of the projected crystal orbits of the WB2 type crystal under different normal compressive stresses in Embodiment 1 of the present invention are shown.
[0023] Figure 6 The results of Hamiltonian population analysis of the projected crystal orbitals of the ReB2 type crystal under different normal compressive stresses in Embodiment 1 of the present invention are shown.
[0024] Figure 7 The results of Hamiltonian population analysis of the projected crystal orbitals of the TcB2 type crystal under different normal compressive stresses in Embodiment 1 of the present invention are shown. Detailed Implementation
[0025] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0026] A method for predicting compressive-shear instability of transition metal diborides, such as Figure 1 As shown, it includes the following steps: Step 1: Obtain the crystal structure model of the transition metal diboride (using the Materials Project crystal database). Apply normal compressive stress to the crystal structure model and perform structural relaxation under the normal compressive stress to obtain the compressed crystal structure model. The transition metal diboride contains coordination of inequivalent transition metals and boron. The normal compressive stress is applied along the
[0001] direction of the transition metal diboride crystal. Optimize the lattice parameters and atomic positions of the transition metal diboride crystal structure model to obtain the equilibrium crystal structure model under zero-pressure conditions. The structural optimization, i.e., the relaxation process, is completed using first-principles calculations. The transition metal is one or more of TcB2, WB2, and ReB2.
[0027] Step 2: Obtain the non-equivalent transition metal-boron bond lengths based on the compressed crystal structure model; Step 3: Calculate the local coordination mismatch amplification factor based on the inequivalent transition metal-boron bond lengths. :
[0028] In the formula: and These represent the bond lengths of two types of inequivalent transition metals-boron. The difference in the length of the inequivalent transition metal-boron bond under zero normal compressive stress; Normal compressive stress; Step 4: Instability prediction based on the value of the local mismatch amplification factor. Instability prediction is performed based on the magnitude of this local mismatch amplification factor; a larger value indicates greater instability. In practical applications, specific thresholds can be set as needed to select materials that meet the requirements.
[0029] Shear strain is applied to the compressed crystal structure model along a selected shear path while maintaining normal compressive stress. The instability prediction results in step 4 are verified by the shear results under compression. The shear path is located within the (0001) basal plane of the transition metal diboride crystal. The shear path is at least two of the following: [1-100](0001), [11-20](0001), and intermediate directions between [1-100](0001) and [11-20](0001).
[0030] Based on the shear simulation calculation under compression (the simulation calculation is performed using existing calculation methods), the shear stress-shear strain response and structural collapse information are obtained; The instability prediction results are verified by determining whether the material has collapsed based on the shear stress-shear strain response and structural collapse information.
[0031] Structural collapse information includes a sudden drop in shear stress, a sudden change in the bond length of transition metal-boron bonds, a sudden change in the boron-boron bond length, and the inability of crystal structure optimization to converge to a continuous local equilibrium configuration. The simultaneous presence of the above information is considered a collapse.
[0032] Example 1 A method for predicting compressive-shear instability of transition metal diborides includes the following steps: Step 1: Obtain the crystal structure model of the transition metal diboride, apply normal compressive stress to the crystal structure model, and perform structural relaxation under normal compressive stress to obtain the compressed crystal structure model.
[0033] The initial crystal structure file of the candidate transition metal diboride TMB2 was obtained (using the Materials Project crystal database). TMB2 was selected from TcB2, WB2, ReB2, or other transition metal diborides with similar or identical structural characteristics. Then, the crystal structure file was optimized using first-principles calculations (i.e., a relaxation process, described in detail below). First-principles calculations refer to a computational method based on fundamental principles of quantum mechanics and density functional theory, which obtains the electron density, total energy, atomic forces, and stress tensors of the crystal system by solving the Kohn-Sham equations, and iteratively optimizes the lattice parameters and atomic positions based on the atomic forces and stress tensors (implemented using the VASP simulation software package based on plane wave density functional theory). This includes: ion-electron interactions can be described using the projected dissociative wave method, and exchange correlation energies can be described using the Perdew-Burke-Ernzerhof functional under the generalized gradient approximation. The lattice parameters and atomic positions were optimized through first-principles calculations until the preset energy and force convergence criteria were met.
[0034] Apply normal compressive stress along the
[0001] direction to the crystal structure model. The normal compressive stress is set to several different values; Use 0 GPa, 20 GPa, 40 GPa, 60 GPa, 80 GPa, and 100 GPa. For each target... First, the crystal structure is relaxed to reach a state near the target normal compressive stress, resulting in a compressed crystal structure model under the corresponding normal compressive stress. Each stress setting requires structural optimization, i.e., relaxation. During structural relaxation, the crystal structure is brought to a local equilibrium state near the target normal compressive stress. Based on this equilibrium state, the changes in lattice parameters, boron layer undulation height, and inequivalent transition metal-boron bond lengths under normal compressive stress can be obtained.
[0035] The specific process of crystal structure optimization, or relaxation, is as follows: Different diboride crystal structure files were obtained using the Materials Project crystal database. All structures provided in the database are stable ground-state compound crystal structures. After obtaining the crystal structure files, the target normal compressive stress was then applied. Under external stress boundary conditions (zero pressure) (With a compressive stress of 0 GPa, i.e., no compressive stress applied), the conjugate gradient algorithm is used to iteratively optimize the atomic positions and permissible lattice degrees of freedom in the crystal structure. The convergence criterion for the electronic self-consistent calculation is set to 1×10⁻⁶. -4 eV / cell, structural relaxation continues until the maximum residual atomic force is less than 1 meV / Å, and the deviation between the actual normal stress and the target normal compressive stress is no greater than 0.2 GPa. After satisfying the above convergence conditions (by iterating through the set compressive stress values to obtain the corresponding compressive configuration under the compressive stress according to the convergence conditions, and this compressive stress value can be selected according to the actual situation), the corresponding target normal compressive stress is obtained. The compression configuration is then used as the initial structure for subsequent local structural parameter extraction and shear loading under constant normal compressive stress.
[0036] The normal compressive stress is defined by the
[0001] direction of the crystal as the normal compressive direction, and the applied normal compressive stress is denoted as... Among them,
[0001] , [1-100] and [11-20] all adopt the four-index notation method of hexagonal crystal orientation, and (0001) represents the corresponding basal plane.
[0037] Step 2: Obtain the inequivalent transition metal-boron bond lengths based on the compressed crystal structure model; for the two types of inequivalent transition metal-boron atom pairs (see... Figure 2 (I) W-B1 and W-B2), the interatomic distances were measured using VESTA software, and the obtained distances were used as the bond lengths of the two types of inequivalent transition metal-boron bonds.
[0038] Step 3: Calculate the local coordination mismatch amplification factor based on the inequivalent transition metal-boron bond lengths. :
[0039] In the formula: and These represent the bond lengths of two types of inequivalent transition metals-boron. The difference in the length of the inequivalent transition metal-boron bond under zero normal compressive stress; Normal compressive stress; when When the value is greater than 1, it indicates that the normal compressive stress amplifies the bond length mismatch between the inequivalent transition metal and the boron bond relative to the zero-pressure state. The larger the value, the more significant the accumulation of local coordination mismatch under normal compression. Therefore, instability can be predicted based on the magnitude of this value.
[0040] Step 4: Instability prediction based on the value of the local coordination mismatch amplification factor (determine which type of material is more prone to instability based on the calculated local coordination mismatch amplification factor). The smaller the value, the more stable the material. When screening multiple materials, their calculated local coordination mismatch amplification factors can be compared, and materials with smaller values can be selected as candidate materials.
[0041] The instability prediction result can also be verified, as follows: Based on the optimized crystal structure model, including WB2, TcB2, and ReB2 type crystals, a 2×2×2 supercell was constructed for shear calculations, while maintaining the target normal compressive stress. Under the condition of [1-100](0001), shear strain is gradually applied to the compressed crystal structure model along a representative shear path in the (0001) basal plane. The representative shear path includes at least two of the following: the [1-100](0001) direction, the [11-20](0001) direction, and an intermediate direction located between the [1-100](0001) direction and the [11-20](0001) direction.
[0042] After each shear strain step, the current shear strain is fixed, and the atomic positions and lattice degrees of freedom in the non-loaded directions are optimized while maintaining the target normal compressive stress to obtain the stable configuration and shear stress under that shear strain step. This process is repeated to obtain the shear stress-shear strain response.
[0001] , [1-100], and [11-20] all use the four-index notation method of hexagonal crystal orientation, where (0001) represents the corresponding basal plane. [1-100](0001) represents the [1-100] direction of the (0001) plane, and [11-20](0001) represents the [11-20] direction of the (0001) plane.
[0043] Based on the stable configurations under different shear strains, structural collapse information can be obtained, which includes a sudden drop in shear stress; abrupt changes in the transition metal-boron bond length or boron-boron bond length; or the inability of structural optimization to converge to a continuous local equilibrium configuration.
[0044] The instability prediction can be verified based on the information about the structural collapse. Smaller materials exhibit later structural collapse, can withstand higher normal compressive stress and maintain continuous shear response, and have relatively high shear stability. Larger materials tend to collapse earlier or experience premature shear instability, exhibiting a relatively high tendency for shear instability.
[0045] The schematic diagram of how the configuration and parameters of the ReB2 type crystal change with normal stress in this embodiment is shown below. Figure 2 As shown in the figure, it can be seen that the crystal structure after applying normal stress compression can yield the corresponding crystal parameters (where...). a、c All are lattice constants. a Let be the lattice size of the hexagonal crystal within the (0001) basal plane, i.e., the period length along the basal plane direction. c The lattice size of the crystal along the
[0001] direction is the period length along the normal direction. Figure 2 Figure I shows a top view of the ReB2-type TMB2 compound, including its unit cell, a 2×2×2 supercell used for compression-shear calculations, representative local coordination units, and crystal structure. This view clarifies the computational object and structural model used in this application and illustrates two types of inequivalent transition metal-boron coordination bonds, boron atomic layers, and wrinkle height. h Location and meaning of local structural parameters. Ⅱ represents the relationship between normal compressive stress σ and other parameters. zz Increase, lattice parameters a and c Interlayer spacing between transition metal layer and boron layer L (i.e., the vertical height between the metal layer and the B1 atom, where B1 is the B atom at site 1) and the height of the boron layer wrinkles. h The change in the height of B atoms at sites 1 and 2 in the folded B layer (i.e., the vertical height of B atoms at sites 1 and 2) is used to show that normal compression not only causes changes in lattice size, but also changes the local geometry of the boron layer. The figure shows the curves showing the relationship between lattice parameters and normal compressive stress. Figure 2 Figure III shows the variations of two types of inequivalent transition metal-boron bonds and a representative boron-boron bond with normal compressive stress. This illustrates the different responses of the two types of inequivalent transition metal-boron bonds to normal compression and provides a basis for subsequent extraction... and Calculate the local coordination mismatch amplification factor Provides the data foundation, where (Tc-B1 is the bond length between Tc and B1 atoms, Tc-B2 is the bond length between Tc and B2 atoms, and B1-B2 is the bond length between B1 and B2 atoms). Figure 2 Figure IV represents the variation of bond angles with normal compressive stress, used to further illustrate how the crystal adapts to normal compressive loads through the coordinated adjustment of bond lengths and bond angles. The figure shows the curves of three representative bond angles ∠1, ∠2, and ∠3 as a function of normal compressive stress; where ∠1 is the angle between B1 and B2 atoms, ∠2 is the angle between WB1 and B2 atoms, and ∠3 is the angle between WB2 and B1 atoms.
[0046] In this embodiment, the shear stress-strain curve of the WB2 type crystal under normal stress during the shearing process is as follows: Figure 3As shown in the figure, it can be seen from the figure which direction is more likely to cause collapse in the shear calculation under normal stress (i.e., the position corresponding to "×" in the figure; whether collapse occurs is determined based on a comprehensive assessment of collapse information). The figure shows the representative shear directions of the TMB2 compound in the (0001) basal plane and the corresponding shear stress-strain curves of WB2. Among them, I is a schematic diagram of the [1-100], [11-20] and intermediate shear directions. II, III, and IV are the normal compressive stresses. The shear stress-strain curves along the above shear directions are shown below, and II is... Direction (i.e., [1-100](0001) direction), Ⅲ is The direction (i.e., the [11-20](0001) direction), Ⅳ is the intermediate direction between the two directions. The cross indicates the last locally stable configuration before the structure collapses under a fixed normal compressive stress condition. By comparing different shear paths and different σ zz By analyzing the shear strain location, peak shear stress, and curve changes corresponding to the lower cross number, the final stable shear strain, structural collapse behavior, and relative stability under different shear paths of the candidate material can be determined.
[0047] The results of shear slip on WB2 type crystals and the magnitude of the normal stress corresponding to structural collapse in three directions for three types of TMB2 type crystals, as well as the calculated local coordination mismatch amplification factor, are as follows: Figure 4 As shown. Figure 4 In the middle, I, II, and III represent WB2 along the [1-100] direction, =60 GPa, [11-20] direction, =40 GPa, and the middle direction, Representative structural configurations near the instability region at 60 GPa (i.e., the three directions given). These configurations are used to compare local structural evolution under different shear paths, rather than representing critical states determined based on the same instability criterion. Figure 4 In the middle, Ⅳ represents the collapse normal stress of TcB2, WB2, and ReB2 along different shear directions. Figure 4 V represents the amplification factor for inequivalent TM-B bond mismatch. Follow The changes. This indicates that no structural collapse was observed within the range of normal stresses examined.
[0048] from Figure 4 As can be seen from sections I, II, and III, the bond length changes in the WB2 type crystal are different in the three shear phases. From... Figure 4 As can be seen from section IV, WB2 requires a higher normal stress to collapse, while TcB2 requires the lowest. From... Figure 4As shown in Figure V, the local coordination mismatch amplification factor is lowest for WB2, while TcB2 and ReB2 are both very high. This indicates a correlation between the local coordination mismatch amplification factor and the normal stress required for collapse. Therefore, predicting material instability based on this calculated value is accurate and reliable.
[0049] Electronic structure analysis can also be introduced to help determine the local coordination changes under compressive-shear combined loads. The density of states of candidate transition metal diborides before and after normal compressive stress can be analyzed to obtain the total density of states and partial density of states, which can be used to determine the electronic state distribution near the Fermi level and the hybridization characteristics of transition metal d orbitals and boron p orbitals.
[0050] Projected crystal orbital Hamiltonian population (POHH) and integral crystal orbital Hamiltonian population (ICHH) analyses were performed on the candidate transition metal diborides to obtain changes in the bonding contributions of transition metal-boron bonds and boron-boron bonds. By comparing the ICHHHH values before and after normal compressive stress, it can be determined whether the bonding contributions have redistributed from the boron-boron network to the transition metal-boron coordination. Figure 5 , Figure 6 and Figure 7 The results show the Hamiltonian layout analysis of projected crystal orbitals for three different crystals under different normal compressive stresses; among them Figure 5 It is a WB2 crystal. Figure 6 It is a ReB2 crystal. Figure 7 It is a TcB2 crystal; as can be seen from the figure, the BB bond is weakened and the metal-B bond is strengthened in all three materials. Figure 5 , Figure 6 and Figure 7 Representative TM-B1, TM-B2, and B1-B2 bonds are in =0 GPa and 100 GPa ICHP value. The larger the ICOHP value, the stronger the bonding contribution of the corresponding atom pair.
[0051] When the normal compressive stress increases from 0 GPa to 100 GPa, the TM-B1 and TM-B2 bonds in the three materials... The overall ICOHP increases, while the B1-B2 bonds... The decrease in ICOHP values indicates that normal compression enhances the bonding contribution of transition metal-boron coordination while weakening the relative bonding contribution of boron-boron bonds. The different magnitudes of change in the two types of inequivalent TM-B bonds in different materials suggest that normal compression also alters the bonding asymmetry in the local coordination environment.
[0052] Figure 5 , Figure 6 and Figure 7It is used to explain the local coordination changes caused by normal compression from the perspective of electronic bonding, to provide electronic structural basis for the evolution of inequivalent TM-B bond length mismatch, and to help explain why different candidate transition metal diborides exhibit different instability tendencies under compression-shear combined loading.
[0053] Electronic locality function analysis was performed on the candidate transition metal diborides to obtain the changes in electronic locality in the boron-boron bond region and the transition metal-boron bond region before and after compression. If the electronic locality of the boron-boron bond center decreases while the electronic locality of the transition metal-boron coordination region increases, it indicates that normal compression may promote local bond redistribution.
[0054] The electronic structure analysis results can further verify The correlation with material instability can be further seen through... Using the value of for instability prediction is accurate and reliable.
[0055] Instability prediction methods can be used to quickly screen various materials. Multiple candidate TMB2 crystal structure models are constructed, and normal compression and shear loading calculations are performed according to the above method to obtain the results under different normal compressive stresses. By comparison, the relative shear stability of different candidate materials under compression-shear combined load can be obtained.
[0056] For example, when the first candidate material has a smaller [value] under the same normal compressive stress... The second candidate material exhibits greater strength under the same normal compressive stress. Therefore, it can be considered that the first candidate material has a lower tendency for shear instability compared to the second candidate material.
[0057] The above methods can be used to predict the instability tendency and compare the relative shear stability of different transition metal diborides under compression-shear combined loads, providing a basis for the screening and evaluation of hard boride materials under contact load-related conditions.
[0058] This invention introduces normal compressive stress, which more closely approximates the combined stress state under contact load conditions. By constructing a local coordination mismatch amplification factor through inequivalent transition metal-boron bond lengths, the cumulative degree of local coordination imbalance under normal compression can be intuitively characterized through quantitative data. The local coordination mismatch amplification factor is used to predict the instability of transition metal diborides, and shear stress response and structural collapse information are used for verification. The combination of these three methods can be used to compare the relative shear stability of different transition metal diborides under compressive-shear combined loads.
Claims
1. A method for predicting compressive-shear instability of transition metal diborides, characterized in that, Includes the following steps: Step 1: Obtain the crystal structure model of the transition metal diboride, apply normal compressive stress to the crystal structure model, and perform structural relaxation under the normal compressive stress to obtain the compressed crystal structure model; the transition metal diboride contains coordination of non-equivalent transition metals and boron; Step 2: Obtain the non-equivalent transition metal-boron bond lengths based on the compressed crystal structure model; Step 3: Calculate the local coordination mismatch amplification factor based on the inequivalent transition metal-boron bond lengths. : In the formula: and These represent the bond lengths of two types of inequivalent transition metals-boron. The difference in the length of the inequivalent transition metal-boron bond under zero normal compressive stress; Normal compressive stress; Step 4: Instability prediction based on the value of the local coordination mismatch amplification factor.
2. The method for predicting compression-shear instability of transition metal diborides according to claim 1, characterized in that, The normal compressive stress in step 1 is applied along the [0001] direction of the transition metal diboride crystal.
3. The method for predicting compression-shear instability of transition metal diborides according to claim 1, characterized in that, It also includes the following steps: Shear strain is applied to the compressed crystal structure model along the selected shear path while maintaining the normal compressive stress. The instability prediction results in step 4 are verified by the shear results under compression.
4. The method for predicting compression-shear instability of transition metal diborides according to claim 3, characterized in that, The shear path lies within the (0001) basal plane of the transition metal diboride crystal.
5. The method for predicting compression-shear instability of transition metal diborides according to claim 4, characterized in that, The shearing path is at least two of the following: the [1-100](0001) direction, the [11-20](0001) direction, the intermediate direction between the [1-100](0001) direction and the [11-20](0001) direction.
6. The method for predicting compression-shear instability of transition metal diborides according to claim 1, characterized in that, In step 1, the transition metal diboride crystal structure model is subjected to first-principles structural relaxation.
7. The method for predicting compression-shear instability of transition metal diborides according to claim 1, characterized in that, The transition metal is one or more of TcB2, WB2, and ReB2.
8. The method for predicting compression-shear instability of transition metal diborides according to claim 3, characterized in that, Shear stress-shear strain response and structural collapse information are obtained from shear simulation calculations under compression. The instability prediction results are verified by determining whether the material has collapsed based on the shear stress-shear strain response and structural collapse information.
9. The method for predicting compression-shear instability of transition metal diborides according to claim 8, characterized in that, The structural collapse information includes a sudden drop in shear stress, a sudden change in the bond length of transition metal-boron bonds, a sudden change in the boron-boron bond length, and the inability of crystal structure optimization to converge to a continuous local equilibrium configuration.