Method for predicting twinning transmission probability of different crystal systems

Abstract

The invention belongs to the technical field of material science foundation, and discloses a method for predicting twinning transmission probability of different crystal systems. Aiming at the characteristic that cross-crystal system twinning transfer needs to experience distinct reconstruction mechanism characteristics in an allotropical system interface, by introducing crystal symmetry and twinning system variant spatial orientation, the minimum orientation difference from rotation of matrix crystal grains to generation of a parallel twinning system is determined, and the alignment difficulty of twinning faces and twinning directions of two crystal systems at the interface is quantified. The method breaks through the limitation of homomorphic system symmetry hypothesis, can analyze the microscopic matching mechanism of heteromorphic system interface twinning activation, and clarifies the constraint effect of lattice parameter difference on twinning system preferential activation and transmission. The method is suitable for strength and toughness collaborative optimization design of complex multiphase systems such as heterojunction interfaces.

Description

Technical Field

[0001] This invention belongs to the field of basic materials science and relates to a method for predicting the twinning transmission probability of different crystal systems. Background Technology

[0002] In the inter-crystal interfaces of polycrystalline materials, the atomic arrangement at grain boundaries not only exhibits significant differences in lattice parameters but also suffers from non-uniform distribution of local coherence and mismatch due to abrupt symmetry changes. This structural complexity necessitates a complex reconstruction process during the trans-crystal interface twinning, and its twinning activation mechanism differs significantly from that of homo-crystal boundaries. Traditional twinning transmission models, largely based on the symmetry assumption of the same crystal system, struggle to adapt to the complexity of twinning activation at hetero-crystal boundaries, thus limiting their predictive ability for deformation coordination behavior at high-interface-energy grain boundaries. At grain boundaries with significant crystal system differences, deformation transmission between the two grains is extremely difficult, easily leading to local strain concentration at the interface and crack initiation. Therefore, establishing a model capable of characterizing the ease of trans-crystal boundary twinning transmission and analyzing the competition and activation mechanisms of twin systems at hetero-crystal interfaces has become a key technological bottleneck in overcoming the synergistic improvement of strength and plasticity in hetero-crystal polycrystalline materials. Summary of the Invention

[0003] To address the aforementioned technical issues, a method for predicting the twinning transmission probability in different crystal systems is proposed, the specific scheme of which is as follows:

[0004] A method for predicting the transmission probability of twins in different crystal systems includes the following steps:

[0005] The minimum angle required for a parallel twin system to be generated when the first grain rotates to a second grain of a different crystal system is calculated. Here, parallel means that the twin planes and twinning directions of the two grains are parallel. The parallel twin system includes any subset of all slip systems of the two crystal systems, which can be determined according to specific conditions. The minimum angle is defined as the twin orientation difference between the two crystal systems, and the smaller the value, the greater the twin propagation probability.

[0006] Step 1: Determine the crystal systems M and N to which the first grain g1 and the second grain g2 belong, respectively; determine the rotational symmetry operation matrix groups F1 and F2 of crystal systems M and N; and determine the crystal orientations G1 and G2 of the two grains g1 and g2.

[0007] Step 2: Determine the number of twin systems m and n in crystal systems M and N. Sort the twin systems in M ​​and N according to the same rule. The twin system numbers are from 1 to m and from 1 to n, respectively. Note that the common twin systems in M ​​and N are arranged before the different twin systems, and the common twin systems have the same number. Then determine the number of twin variants in each twin system.

[0008] Step 3: Based on the twin system indices in Step 2, determine the set of twin system indices K and L that need to be considered for the crystal systems where g1 and g2 grains in the parallel twin system are located;

[0009] Step 4: Construct the corresponding transformation matrix T from crystal orientation to twin orientation using the rotational symmetry operation matrix groups F1 and F2 from Step 1, the crystal orientations G1 and G2, and K and L from Step 3. K and T L ;

[0010] Step 5: Establish the expressions for parallel twin systems of different crystal systems, and solve for the rotation matrix R that generates a parallel twin system that meets the requirements when the g2 grain is rotated to the g1 grain;

[0011] Step 6: Calculate the twin orientation difference δ for different crystal systems based on the rotation matrix R;

[0012] Step 7: Determine the twin transmission probability based on the twin orientation difference δ. The smaller the δ value, the greater the twin transmission probability.

[0013] In a preferred embodiment of the method for predicting the transmission probability of twins in different crystal systems, in step 3, the twin system indices K and L have the following conditions:

[0014] In a single twin system, K=L and the number of elements in the two sets is k=l=1;

[0015] For two twin systems, K≠L and the number of sets k=l=1, or K=L and the number of sets k=l=2;

[0016] In the case of multiple twins, K and L, k and l may be the same or different, but k <m、l<n;

[0017] In the case of all twins, K and L, k and l may be the same or different, but k=m and l=n.

[0018] In a preferred embodiment of the method for predicting the transmission probability of twins in different crystal systems, in step 5, the parallel twin systems of different crystal systems are represented as follows:

[0019]

[0020] The rotation matrix R is obtained by the following formula:

[0021]

[0022] In a preferred embodiment of the method for predicting the twinning transmission probability of different crystal systems, in step 6, the twinning orientation difference δ is obtained by the following formula:

[0023]

[0024] The preferred embodiment of the method for predicting the probability of twin propagation in different crystal systems is as follows: in step 7, when the twin orientation difference δ is less than a specific value, it is determined that twin propagation is likely to occur; the specific value can be changed according to conditions, and is generally 12°.

[0025] Beneficial effects: This method uses orientation rotation angle to quantify the alignment degree of twin systems in heterocrystalline grains. Combined with crystal symmetry constraints, it constructs a quantitative model of the difficulty of cross-crystal twin transfer, breaking through the limitations of the traditional homocrystalline assumption. Its technical advantages are reflected in: (1) Through the calculation framework of minimum rotation angle, it is compatible with the combination system of typical crystal systems such as face-centered cubic, body-centered cubic, and hexagonal close-packed, realizing the universal characterization of the twin system matching degree at the heterocrystalline interface; (2) Based on the joint matching criterion of twin plane normal and twin direction, the difficulty gradient of twin activation between different crystal systems can be quantified; (3) The calculation can be completed by relying only on crystal system parameters and grain boundary orientation data, which has high operability and application efficiency. This method is applicable to complex systems such as heterocrystalline multiphase structures, heterocrystalline composite materials, and heterojunction interfaces, providing a theoretical basis for the prediction and optimization of material twin transfer behavior, and can assist in the design of metal materials with synergistic improvement of strength and plasticity. Attached Figure Description

[0026] Figure 1 This is a diagram showing the twin distribution of titanium alloys. Detailed Implementation

[0027] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings; the following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0028] Example 1

[0029] Twin phenomenon such as Figure 1 As shown, this manifests as the appearance of slender new grains within the grain, with the new grains and the parent grain satisfying a specific orientation relationship. Taking the twinning transmission between two grains in a close-packed hexagonal crystal system and a body-centered cubic crystal system as an example, the probability prediction method for twinning transmission between different crystal systems of this invention is used for calculation:

[0030] Step 1. Determine the crystal systems M and N of the two grains g1 and g2, where M is HCP and N is BCC. Determine the rotational symmetry operation matrix groups F1 and F2 of crystal systems M and N, as shown in Tables 1 and 2. Determine the crystal orientations G1 and G2 of the two grains g1 and g2 based on the Euler angles of each grain in Table 3.

[0031] Table 1. Rotational symmetry operation matrix group for hexagonal close-packed crystal systems

[0032]

[0033] Table 2. Rotational Symmetry Operation Matrix Group for Body-Centered Cubic Crystal System

[0034]

[0035] Table 3 Euler angles of each grain

[0036]

[0037] Step 2. Determine the number of twin systems in crystal systems M and N, m=4 and n=2 respectively. Sort the twin systems in M ​​and N according to the same rule, with the twin system numbers from 1 to m and from 1 to n respectively. Note that the common twin systems in M ​​and N are all arranged before the different twin systems, and the common twin systems have the same number. Then determine the number of twin variants in each twin system.

[0038] Step 3. Based on the twin system indices in Step 2, determine the set of twin system indices K and L that need to be considered for the crystal systems where g1 and g2 grains in the parallel twin system are located. In this example, all twin systems need to be considered. However, M and N do not have a common twin system in this example, so K=[1, 2, 3, 4] and L=[1, 2].

[0039] Step 4. Construct the corresponding transformation matrix T from crystal orientation to twin orientation using the rotational symmetry operation matrix groups F1 and F2 from Step 1, the crystal orientations G1 and G2, and K and L from Step 3. K and T L See Tables 4 and 5 for details;

[0040] Table 4 Orientation transformation matrix of hexagonal close-packed grain twins

[0041]

[0042] Table 5 Orientation transformation matrix of grain twins in body-centered cubic crystal systems

[0043]

[0044] Step 5: Establish the expressions for parallel twin systems of different crystal systems, and solve for the rotation matrix R that generates a parallel twin system that meets the requirements when the g2 grain is rotated to the g1 grain;

[0045] Parallel twin systems of different crystal systems are represented as follows:

[0046]

[0047] The rotation matrix R is obtained by the following formula:

[0048]

[0049] Step 6: Calculate the twin orientation difference δ for different crystal systems based on the rotation matrix R;

[0050] The twin orientation difference δ between different crystal systems is obtained by the following formula:

[0051]

[0052] Step 7: Determine the twin transmission probability based on the twin orientation difference δ.

[0053] Table 6 shows the twinning orientation differences of each group of grains in Table 3.

[0054]

[0055] Conclusion: Based on the orientation of each grain in Table 3, the twin orientation difference between each group of grains was calculated, and the results are shown in Table 6. Grains with a twin orientation difference of less than 12° are more likely to undergo twin propagation.

[0056] The above embodiments are only for illustrating the technical concept and specific calculation method of the present invention, and are not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, such as the selection of other alloy systems, should be included within the protection scope of the present invention.

Claims

1. A different crystal system twinning transmission prediction method characterized by, The method comprises the following steps: calculating the minimum angle of the rotation of the first grain to the second grain of a different crystal system to generate a parallel twin system; wherein the parallel refers to the parallel of the twin plane and the twin direction of the two grains; the parallel twin system includes any subset of all slip systems of the two crystal systems, which is determined according to specific conditions; the minimum angle is defined as the twin orientation difference of different crystal systems, and the smaller the value is, the greater the twin transmission probability is; the specific implementation comprises the following steps: Step 1: determining the crystal systems M and N to which the two grains g1 and g2 belong, obtaining the rotation symmetry operation matrix groups F1 and F2 of the crystal systems M and N, and the crystal orientations G1 and G2 of the two grains g1 and g2; Step 2: determining the number of twin systems m and n in the crystal systems M and N, sorting the twin systems in M and N according to the same rule, and the twin system serial numbers are from 1 to m and from 1 to n, noting that the common twin systems of M and N are arranged before different twin systems, and the serial numbers of the common twin systems are the same, and then determining the number of twin variants in each twin system; Step 3: determining the twin system serial number set K and L of the crystal system to which the grains g1 and g2 belong in the parallel twin system according to the twin system serial numbers in step 2; Step 4: Construct the respective transformation matrix T from crystal orientation to twinning system orientation from the rotation symmetry operation matrix group F1 and F2 in step 1, the crystal orientations G1 and G2 and K and L in step 3 K and T L ; Step 5: establishing the expression of the parallel twin system of different crystal systems, and solving the rotation matrix R of the rotation of the g2 grain to the g1 grain to generate the required parallel twin system; Step 6: calculating the twin orientation difference δ of different crystal systems based on the rotation matrix R; Step 7: judging the twin transmission probability according to the twin orientation difference δ, and the smaller the value of δ is, the greater the twin transmission probability is.

2. The method of claim 1, wherein the different crystal system twin transmission probability is predicted by the equation: ###0001### where a is the lattice parameter of the crystal system, and c is the lattice parameter of the crystal system. In step 3, the twin system serial number set K and L have the following situations: Single twin system, K=L and the number of elements in the two sets k=l=1; Two twin systems, K≠L and the number of sets k=l=1, or K=L and the number of sets k=l=2; Multiple twin systems, K and L, k and l may be the same or different but k<m, l<n; All twin systems, K and L, k and l may be the same or different but k=m, l=n.

3. The method of claim 1, wherein the different crystal system twin transmission probability is predicted by the following equation: ###0001### where, a is the lattice parameter of the crystal, c is the lattice parameter of the crystal, and d is the interplanar spacing of the crystal. In step 5, the parallel twin system of different crystal systems is expressed as: ​ The rotation matrix R is obtained by the following formula:

4. The method of claim 1, wherein the different crystal system twin transmission probability is predicted by the following equation: ###0001### where, a is the lattice parameter of the crystal, c is the lattice parameter of the crystal, and d is the interplanar spacing of the crystal. In step 6, the twin orientation difference δ is obtained by the following formula: ​ 5. The method of claim 1, wherein the different crystal system twin transmission probability is predicted by the following equation: ###0001### where, a is the lattice parameter of the crystal, c is the lattice parameter of the crystal, and d is the interplanar spacing of the crystal. In step 7, when the twin orientation difference δ is less than a specific value, it is judged that twin transmission is easy to occur; the specific value can be changed according to the conditions, and is generally 12°. ​

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