An interlayer centering method and device for 3D-EBSD continuous section data

Abstract

This invention relates to a method and apparatus for interlayer alignment of 3D-EBSD continuous cross-sectional data. The method includes the following steps: Step S1, obtaining grain boundaries with a ∑3 orientation relationship between grains on both sides in the reconstructed 3D-EBSD data, i.e., ∑3 grain boundaries; Step S2, performing three-dimensional spatial plane fitting on the ∑3 grain boundaries to obtain the optimal fitting plane; Step S3, selecting "potential coherent ∑3 grain boundaries"; Step S4, linearly translating the centroids of all triangular elements constituting the ∑3 grain boundaries in the 3D-EBSD microstructure to obtain the optimal translation distance, and calculating the M of the "potential coherent ∑3 grain boundaries". AB Value, where M AB The value is the weighted average of the minimum angle between the best-fit surface and the {111} / {111} crystal plane; Step S5, when M AB When the value is minimized, the grain boundaries of the "potential coherent ∑3 grain boundaries" are as parallel as possible to the {111} / {111} crystal planes of the grains on both sides, achieving interlayer alignment of 3D-EBSD continuous cross-sectional data. Compared with the prior art, this invention has the advantages of achieving alignment of multi-layer continuous 2D-EBSD cross-sections and improving accuracy.

Description

Technical Field

[0001] This invention relates to the field of interlayer alignment in microscopic characterization techniques, and in particular to an interlayer alignment method and apparatus for 3D-EBSD continuous cross-sectional data. Background Technology

[0002] Three-dimensional electron backscattered diffraction (3D-EBSD) is a tomographic characterization method that acquires and reconstructs three-dimensional EBSD cross-sectional data from multiple consecutive layers, obtaining the three-dimensional microstructure of materials containing crystallographic orientation information. To address the alignment problem between 2D-EBSD cross-sections, two common methods are used:

[0003] The first method involves marking the same location at each layer of the 2D-EBSD cross-section while acquiring continuous 2D-EBSD cross-sectional data to achieve interlayer alignment. Hardness indentation is a commonly used marker. Multiple indentations mark the same area, and then EBSD data is acquired in this area. This marking is helpful for the approximate location of the 2D-EBSD cross-section; however, indentation deformation and the instability of manual operation can lead to micrometer-level deviations in the cross-section's position.

[0004] The second method obtains the positional information of the 2D-EBSD cross-section from local crystallographic orientation differences, which is used to adjust the positional deviation between adjacent layers and reconstruct the microstructure of the grains in the material. This method calculates the orientation difference between voxels of adjacent layers, finds the corresponding position of the 2D-EBSD cross-section that minimizes the average value of this orientation difference, and then iteratively calculates to determine the relative position of each pair of adjacent layers. The translation distance of the 2D-EBSD cross-section is represented by the number of voxels. This alignment algorithm has been widely used in three-dimensional microstructure analysis software. However, because the algorithm itself only considers the relative position of adjacent 2D-EBSD cross-sections and is limited by the EBSD acquisition step size, there is an error between the relative position of adjacent 2D-EBSD cross-sections and the actual position within the material. The accumulation of this error layer by layer may lead to distortion of the orientation of three-dimensional grain boundaries. This method lacks a reference standard to confirm whether the orientation of grain boundaries is correct, so it can only reconstruct the topological structure of three-dimensional microstructures, but cannot accurately reconstruct the planar orientation of grain boundaries. Therefore, it is necessary to design new technical solutions to optimize the interlayer alignment between continuous 2D-EBSD cross-sections.

[0005] The orientation difference between the annealed twins and the parent crystal of a face-centered cubic (FCC) metal is <111> At 60°, grain boundaries are typically located on the {111} / {111} crystal plane. This is because in the FCC structure, the {111} plane is the closest-packed plane, providing the lowest interfacial energy and the highest atomic coordination degree; such grain boundaries are also called coherent ∑3 grain boundaries. The intersection line between the grain boundary and the 2D-EBSD section is called the grain boundary trace. The trace of a coherent ∑3 grain boundary is always parallel to the trace of the {111} crystal plane. A grain boundary whose trace is parallel to the trace of the {111} crystal plane is very likely a coherent ∑3 grain boundary. The coherent ∑3 grain boundary has a stable structure and can be initially identified based on its trace on the 2D-EBSD section, thus serving as a reference interface for centering. Other interfaces with fixed crystal planes in the material can also be used as reference interfaces. On the other hand, during the reconstruction of the three-dimensional grain boundary network using software such as DREAM.3D, grain boundaries are divided into a large number of triangular elements. Translating the centroid of the triangular elements of the grain boundary can achieve fine-tuning of the grain boundary orientation.

[0006] Grain boundaries are key microstructures affecting the mechanical properties and corrosion resistance of materials. Achieving interlayer alignment of continuous multilayer 2D-EBSD data to accurately characterize the orientation of intramaterial grain interfaces plays a crucial role in the structural characterization and performance analysis of metallic materials. This invention proposes a method for interlayer alignment of continuous multilayer 2D-EBSD data using coherent ∑3 grain boundaries as internal reference interfaces, specifically for 3D-EBSD data obtained by the continuous section method.

[0007] Achieving precise interlayer alignment between continuous 2D-EBSD sections has become a technical problem that needs to be solved. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art by providing a method and device for interlayer alignment of 3D-EBSD continuous cross-sectional data.

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] According to one aspect of the present invention, a method for interlayer alignment of 3D-EBSD continuous cross-sectional data is provided, the method being used for interlayer alignment of 3D-EBSD continuous cross-sectional data containing coherent ∑3 grain boundary materials, the method comprising the following steps:

[0011] Step S1: Obtain the grain boundaries with ∑3 orientation relationship between the grains on both sides in the reconstructed 3D-EBSD data, i.e., ∑3 grain boundaries;

[0012] Step S2: Perform three-dimensional space plane fitting on the ∑3 grain boundary to obtain the best fitting plane;

[0013] Step S3: Select “potential coherent ∑3 grain boundaries”;

[0014] Step S4: Linearly translate the centroids of all triangular elements constituting ∑3 grain boundaries in the 3D-EBSD microstructure to obtain the optimal translation distance, and calculate the M of the "potential coherent ∑3 grain boundary". AB Value, where M AB The value is the weighted average of the minimum angle between the best-fit plane and the {111} / {111} crystal planes of the grains on both sides of the grain boundary;

[0015] Step S5, when M AB When the value is at its minimum, the grain boundary of the "potential coherent ∑3 grain boundary" is as parallel as possible to the {111} / {111} crystal plane of the grains on both sides, achieving interlayer alignment of the 3D-EBSD continuous cross-sectional data.

[0016] Preferably, the grain boundary with a ∑3 orientation relationship between the grains on both sides is defined as the grains on both sides of the grain boundary circling a common orientation. <111> The crystal axis is rotated by 60°, specifically: the orientation difference rotation axis of the grain boundary is... <111> The crystal axis orientation deviation is within A°, and the orientation difference rotation angle is within 60°±B°.

[0017] Preferably, the process of obtaining the optimal fitting plane specifically involves defining the perpendicular distance from the centroid of all triangular elements constituting a certain ∑3 grain boundary, or the geometric point representing the position of the triangular element in three-dimensional space, to a certain fitting plane as dist. i When these dist i The best-fit plane is the one where the sum of the absolute values ​​of the values ​​is minimized.

[0018] Preferably, the process of selecting "potential coherent ∑3 grain boundaries" includes:

[0019] Step S11: Select ∑3 grain boundaries with 3D morphology close to a plane in the ∑3 grain boundary;

[0020] Step S12: Obtain the trace of the best-fit plane of the grain boundary close to the plane ∑3 intersecting with the cross section of a certain layer of 2D-EBSD.

[0021] Step S13: Calculate the angle between the trace and the {111} / {111} crystal plane trace of the grains on both sides of the grain boundary on the 2D-EBSD section. If the angle on both sides is less than C°, it is considered to be nearly parallel, and the grain boundary is defined as a "potential coherent ∑3 grain boundary".

[0022] More preferably, in step S11, selecting ∑3 grain boundaries with 3D morphology close to a plane specifically involves: calculating all dist corresponding to the ∑3 grain boundaries. i The normalized root mean square error of the value is defined as the ∑3 grain boundary with a normalized root mean square error less than D. The ∑3 grain boundary is defined as a near-planar ∑3 grain boundary.

[0023] Preferably, the calculation of M for "potential coherent ∑3 grain boundaries" AB Values ​​include:

[0024] Step S21: Calculate all the angles between the best-fit plane and the {111} crystal planes in the grains on both sides of a grain boundary on a certain 2D-EBSD section, and define the minimum values ​​of the angles in the grains on both sides as θ. A and θ B ;

[0025] Step S22, calculate M of the "potential coherent ∑3 grain boundary". AB Value, M AB The mathematical expression for the value is:

[0026]

[0027]

[0028]

[0029] Among them, A i Let A be the area of ​​the i-th grain boundary. T W is the sum of the areas of all potential coherent ∑3 grain boundaries, where n is the number of grain boundaries. θA and W θB θ represents all potential coherent ∑3 grain boundaries. A and θ B The weighted average, M AB For W θA and W θB The average value.

[0030] Preferably, in step S4, all the centroids of the triangular elements constituting the ∑3 grain boundary in the 3D-EBSD microstructure are linearly translated to obtain the optimal translation distance, and the M of the "potential coherent ∑3 grain boundary" is calculated. AB The values ​​include: the translation distances of the centroid of the topmost triangular element in the 3D-EBSD microstructure along the X-axis and Y-axis are defined as ΔX and ΔY, respectively, and the mathematical expressions for the new coordinates of each triangular element centroid after translation are:

[0031]

[0032] X i =x i +K i ·ΔX

[0033] Y i =y i +K i ·ΔY

[0034] Where Z represents the height of the 3D-EBSD microstructure, z i K represents the height of the centroid of the i-th triangular element relative to the bottom of the 3D-EBSD microstructure. i x is the scaling factor for the translation distance of the centroid of the i-th triangular element. i and y i These are the original coordinates of the i-th centroid on the X and Y axes, respectively. ΔX and ΔY are the translational distances of the centroid of the topmost triangular element in the 3D-EBSD microstructure along the X and Y axes, respectively. i and Y i This represents the new coordinates of the centroid of the i-th triangular element after translation.

[0035] More preferably, in step S4, all the centroids of the triangular elements constituting the ∑3 grain boundary in the 3D-EBSD microstructure are linearly translated to obtain the optimal translation distance, and the M of the "potential coherent ∑3 grain boundary" is calculated. AB The values ​​also include continuously varying the ΔX and ΔY values ​​within a range of n times the volume of the 3D-EBSD data along the X and Y directions, and calculating the corresponding M for the "potential coherent ∑3 grain boundary". AB value.

[0036] Preferably, the 3D-EBSD data is obtained by reconstructing a series of consecutive 2D-EBSD cross-sectional data.

[0037] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention selects a coherent ∑3 grain boundary located within the material and possessing a special fixed crystal plane as a reference interface. It obtains the best-fit plane and "potential coherent ∑3 grain boundaries," and linearly translates the centroid of the grain boundary triangular element. This overcomes the limitation in existing technologies where the translation distance of the 2D-EBSD section can only be an integer multiple of the EBSD image acquisition step size. This allows the weighted average value M of the minimum angle between the best-fit plane of the grain boundary and the {111} / {111} crystal plane to be obtained. AB At its minimum, the crystal interface of the "potential coherent ∑3 grain boundary" is as parallel as possible to the {111} / {111} crystal plane of the grain, thereby achieving the centering of multi-layer continuous 2D-EBSD cross sections, that is, the inter-layer centering of 3D-EBSD continuous cross section data. Therefore, compared with the existing centering methods between 2D-EBSD cross sections, the distortion of crystal interface orientation is greatly reduced and the accuracy is higher. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the inter-layer alignment method in this invention;

[0041] Figure 2(a) is a frontal view of the centroid of the grain boundary triangular element and the best-fit plane of the grain boundary in this invention.

[0042] Figure 2(b) is a side view of the centroid of the grain boundary triangular element and the best-fit plane of the grain boundary in this invention.

[0043] Figure 3 This is a schematic diagram comparing the positions of the centroids of the triangular elements of multiple grain boundaries before and after linear translation in this invention.

[0044] Figure 4(a) shows the ΔX and ΔY values ​​and M in Embodiment 2 of the present invention. AB A diagram illustrating the contour relationships between values;

[0045] Figure 4(b) shows the ΔX and ΔY values ​​and M in Embodiment 3 of the present invention. AB A schematic diagram showing the contour relationship between values. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0047] Example 1

[0048] This embodiment relates to an interlayer alignment method for 3D-EBSD continuous cross-sectional data. This method is used for 3D-EBSD data processing and analysis of various materials containing coherent ∑3 grain boundaries, such as... Figure 1 The method includes the following steps:

[0049] Step S1: In the reconstructed 3D-EBSD data, identify the grains on both sides with a ∑3 orientation relationship (i.e., <111> A grain boundary (twin boundary) with a 60° angle is a grain boundary on both sides of a common yoke. <111> The crystal axis is rotated by 60°; specifically, the orientation difference rotation axis of the grain boundary is... <111> The crystal axis deviation is within 8°, and the orientation difference rotation angle is within 60°±12°; that is, the tolerance values ​​of the grain boundary orientation difference axis and the orientation difference angle are set to 8° and 12°, respectively.

[0050] 3D-EBSD data is reconstructed from a series of continuous 2D-EBSD cross-sectional data.

[0051] Step S2: Perform three-dimensional planar fitting on the ∑3 grain boundaries selected in step S1:

[0052] In three-dimensional space, the perpendicular distance from the centroids of all triangular elements constituting a certain ∑3 grain boundary (or other geometric points that can represent the positions of the triangular elements in three-dimensional space) to a certain fitted plane is defined as dist. i When these dist i The best-fit plane is the one where the sum of the absolute values ​​of the values ​​is minimized.

[0053] Step S3: Select ∑3 grain boundaries with 3D morphology close to a plane within the grain boundaries. Calculate all dist corresponding to a given grain boundary according to equation (1). i Normalized Root Mean Square Error (NRMSE) of the values:

[0054]

[0055] In the expression, dist i The distance is the measured perpendicular distance between the centroid of each triangular element in a single grain boundary and the best-fit plane, where N is the number of centroids of the triangular elements in a single grain boundary, and dist is the distance between the centroids of each triangular element in a single grain boundary. max and dist min These represent the maximum and minimum vertical distances between the centroid of the triangular element and the best-fit plane, respectively.

[0056] Step S4: Define the ∑3 grain boundaries with an NRMSE value < 0.6 in step S2 as ∑3 grain boundaries that are close to a plane.

[0057] Step S5, select "potential coherent ∑3 grain boundaries", specifically:

[0058] Obtain the traces of the near-planar ∑3 grain boundary intersecting with a certain 2D-EBSD cross section from step S4, and calculate the angles between these traces and the {111} / {111} crystal plane traces of the grains on both sides of the grain boundary on the 2D-EBSD cross section. If the angles are all <15°, they are considered to be nearly parallel, and the grain boundary is defined as a "potential coherent ∑3 grain boundary".

[0059] Step S6: Calculate all the angles between the best-fit plane of the grain boundary obtained in step S2 and the {111} crystal planes in the grains on both sides of the grain boundary on a certain 2D-EBSD section indicated in step S3.

[0060] The minimum values ​​of these included angles are defined as θ in the two grains on either side. A and θ B Calculate the M of the "potential coherent ∑3 grain boundary" obtained in step S5. AB Value, M ABThe mathematical expression for the value is:

[0061]

[0062]

[0063]

[0064] Among them, A i Let A be the area of ​​the i-th grain boundary. T W is the sum of the areas of all potential coherent ∑3 grain boundaries, where n is the number of grain boundaries. θA and W θB θ represents all potential coherent ∑3 grain boundaries. A and θ B The weighted average, M AB It is W θA and W θB The average value, θ A and θ B These represent the minimum angles between the best-fit plane and the {111} crystal planes in the grains on either side. For each grain boundary, the minimum angle between the best-fit plane and the {111} crystal plane in one grain is selected, and the minimum angle between the best-fit plane and the {111} crystal plane in the other grain is also selected. For multiple grain boundaries, the minimum angles in the grains on both sides are weighted and averaged, and then the average of the two weighted averages is taken to obtain M. AB .

[0065] Step S7: Linearly translate the centroids of all triangular elements at all grain boundaries in the 3D-EBSD microstructure. Define the translation distances of the topmost triangular element centroid in the X-axis and Y-axis directions as ΔX and ΔY, respectively. The mathematical expressions for the new coordinates of each triangular element centroid after translation are:

[0066]

[0067] X i =x i +K i ·ΔX (6)

[0068] Y i =y i +K i ·ΔY (7)

[0069] Where Z represents the height of the 3D-EBSD microstructure, z i K represents the height of the centroid of the i-th triangular element relative to the bottom of the 3D-EBSD microstructure. i x is the scaling factor for the translation distance of the centroid of the i-th triangular element.i and y i Let X and Y be the original coordinates of the i-th centroid on the X and Y axes, respectively, and ΔX and ΔY be the translational distances of the centroid of the topmost triangular element in the 3D-EBSD microstructure along the X and Y axes, respectively. i and Y i This represents the new coordinates of the centroid of the i-th triangular element after translation.

[0070] Step S8: Obtain the optimal translation distance to achieve inter-layer centering of 3D-EBSD continuous cross-sectional data.

[0071] Within a range of X and Y lengths twice the volume of the 3D-EBSD data, the values ​​of ΔX and ΔY are continuously varied, and the corresponding M values ​​for the "potential coherent ∑3 grain boundaries" selected in step S5 are calculated. AB When M AB When the value is at its minimum, the crystal interface of the "potential coherent ∑3 grain boundary" in step S5 is as parallel as possible to the {111} / {111} crystal plane of the grain, thereby achieving interlayer alignment of the 3D-EBSD continuous cross-sectional data.

[0072] Currently, there is a lack of parameters to quantify whether the interlayer alignment of 3D-EBSD is sufficient. However, insufficient alignment will inevitably lead to distorted grain interface orientation. Therefore, this invention proposes an M-type alignment method based on the planar orientation of coherent ∑3 grain boundaries. AB .

[0073] Example 2

[0074] This embodiment also relates to a method for inter-layer alignment of 3D-EBSD continuous cross-sectional data, as detailed below:

[0075] a1) First, the 316L austenitic stainless steel to be tested is mechanically polished, and the area to be scanned by EBSD is initially located using a single Vickers hardness indentation.

[0076] a2) A CamScan Apollo 300 thermal field emission scanning electron microscope (FE-SEM) equipped with an Oxford Instrument / HKL-EBSD probe was used to collect the backscattered electron diffraction pattern (Kikuchi pattern) of each pixel in the scanning area, and the position and crystal information of each pixel were stored in the EBSD data. The method to control the polishing thinning amount was to control the rotation speed of the polishing machine, the polishing intensity, and the polishing time. A total of 101 continuous cross-sections were collected. The EBSD image acquisition step size was 2.5 μm, the scanning area was 600 μm × 600 μm, the preset step size in the Z-axis direction was 2.5 μm, and the actual average step size in the Z-axis direction was 2.55 μm.

[0077] a3) Import the acquired EBSD images into DREAM.3D software. Set the thickness of the 2D-EBSD cross-section to the average actual thickness of 2.55 μm. Then, process the 3D-EBSD data using the corresponding filters in the following steps: identify bad pixels, convert crystal orientation data, perform preliminary alignment processing, remove or repair some bad pixels, edge shearing, retrieve and reconstruct grains and grain boundaries, perform grain boundary triangular element mesh generation, and perform grain boundary smoothing. The preliminary alignment processing uses the filter "AlignSections (Misorientation)". After processing the 3D-EBSD data, visualize the data using Paraview software.

[0078] a4) Extract the three-dimensional spatial coordinates of the centroids of all triangular elements in the grain boundary, establish the best fitting plane for each grain boundary using plane fitting, and calculate the plane approximation value for each grain boundary.

[0079] a5) The selection criteria for the "potential coherent ∑3 grain boundary" in this example are: the orientation difference rotation axis of the grain boundary and... <111> The crystal axis deviation is within 2°, the orientation difference rotation angle is within 60°±2°, the NRMSE value ranges from 0 to 0.25, and the number of triangular elements constituting a single grain boundary is greater than 100; the angle between the grain boundary trace and the multiple {111} crystal plane traces on both sides is less than 3°. Based on the conditions in this step, a total of 71 "potential coherent ∑3 grain boundaries" that meet the conditions were selected.

[0080] a6) In this example, the translational distance of the centroid of the topmost triangular element in the three-dimensional microstructure does not exceed 200 μm on either the X or Y axis, meaning that the values ​​of ΔX and ΔY both range from -200 μm to 200 μm. Within this range, the M of the "potential coherent ∑3 grain boundary" at the optimal alignment position... AB The value is 5.24°, corresponding to a ΔX value of 3 μm and a ΔY value of -115 μm. Before implementing this invention, M... AB The value is 15.94°. M using the method of this invention... AB The value is much lower than before the execution, so the plane orientation accuracy of the ∑3 grain boundary is greatly improved, indicating that the interlayer alignment is more accurate.

[0081] As shown in Figures 2(a) and 2(b), it can be seen from the figures that for grain boundaries with a morphology close to a plane, the normal of the best-fit plane can represent the plane normal of the grain boundary, and thus can represent the plane orientation of the grain boundary in the grains on both sides, providing a calculation basis for the angle between the plane orientation of the "potential coherent ∑3 grain boundary" and the {111} crystal plane orientation.

[0082] Figure 3Comparison images of the positions of several example grain boundaries and local triangular element centroids before and after linear translation are provided. It can be seen that linear translation does not change the morphological characteristics of the grain boundaries, but only alters their planar orientation. This preserves the positional information of the 2D-EBSD data provided by the local crystallographic difference minimization method.

[0083] Figure 4(a) shows the relationship between ΔX and ΔY values ​​and M in this embodiment. AB The contour plot shows the relationship between the values. It can be seen that within a certain range of translation, M... AB The existence of a minimum value, which is significantly smaller than the original value, indicates that after implementing the alignment method of the present invention, the plane orientation of the coherent ∑3 grain boundaries in the three-dimensional microstructure is closer to the crystal plane orientation of {111} / {111}.

[0084] Example 3

[0085] This embodiment also relates to a method for inter-layer alignment of 3D-EBSD continuous cross-sectional data, as detailed below:

[0086] b1) First, the 316L austenitic stainless steel to be tested is mechanically polished, and the area to be scanned by EBSD is initially located using a single Vickers hardness indentation.

[0087] b2) In this example, a CamScan Apollo 300 thermal field emission scanning electron microscope (FE-SEM) equipped with an Oxford Instrument / HKL-EBSD probe was used to collect the backscattered electron diffraction pattern (Kikuchi pattern) of each pixel in the scanning area, and the position and crystal information of each pixel were stored in the EBSD data. The method for controlling the polishing thinning amount was to control the rotation speed of the polishing machine, the polishing intensity, and the polishing time. A total of 101 continuous cross-sections were collected. The EBSD image acquisition step size was 2.5 μm, the scanning area was 600 μm × 600 μm, the preset step size in the Z-axis direction was 2.5 μm, and the actual average step size in the Z-axis direction was 2.65 μm.

[0088] b3) Import the acquired EBSD images into DREAM.3D software. Set the thickness of the 2D-EBSD cross-section to the average actual thickness of 2.65 μm. Then, process the 3D-EBSD data using the corresponding filters in the following steps: identify bad pixels, convert crystal orientation data, perform preliminary alignment processing, remove or repair some bad pixels, edge shearing, retrieve and reconstruct grains and grain boundaries, perform grain boundary triangular element mesh generation, and perform grain boundary smoothing. The preliminary alignment processing uses the filter "AlignSections (Misorientation)". After processing the 3D-EBSD data, visualize the data using Paraview software.

[0089] b4) Extract the three-dimensional spatial coordinates of the centroids of all triangular elements in the grain boundary, establish the best fitting plane for each grain boundary using plane fitting, and calculate the plane approximation value for each grain boundary.

[0090] b5) The selection criterion for "potential coherent ∑3 grain boundaries" is: the orientation difference rotation axis of the grain boundary is parallel to... <111> The crystal axis deviation is within 2°, and the orientation difference rotation angle is within 60°±2°; the approximate value of the grain boundary plane ranges from 0 to 0.3, and the number of triangular elements constituting a single grain boundary is greater than 100; the angles between the grain boundary trace and the multiple {111} crystal plane traces on both sides are all less than 3°. Based on the conditions in this step, a total of 44 "potential coherent ∑3 grain boundaries" that meet the conditions were selected.

[0091] b6) In this example, the translational distance of the centroid of the topmost triangular element in the three-dimensional microstructure does not exceed 200 μm on either the X or Y axis, meaning that the values ​​of ΔX and ΔY both range from -200 μm to 200 μm. Within this range, the M of the "potential coherent ∑3 grain boundary" at the optimal alignment position... AB The value is 7.60°, corresponding to a ΔX value of 44 μm and a ΔY value of -62 μm. Before implementing this invention, M... AB The value is 12.11°.

[0092] Figure 4(b) shows the relationship between ΔX and ΔY values ​​and M in this embodiment. AB The contour plot shows the relationship between the values. It can be seen that within a certain range of translation, M... AB The existence of a minimum value, which is significantly smaller than the original value, indicates that after implementing the alignment method of the present invention, the plane orientation of the coherent ∑3 grain boundaries in the three-dimensional microstructure is closer to the crystal plane orientation of {111} / {111}.

[0093] Example 4

[0094] The electronic device of this invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0095] Multiple components in the device are connected to the I / O interface, including: input units such as keyboards and mice; output units such as various types of displays and speakers; storage units such as disks and optical discs; and communication units such as network interface cards (NICs), modems, and wireless transceivers. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0096] The processing unit executes the various methods and processes described above, such as methods S1 to S8. For example, in some embodiments, methods S1 to S8 may be implemented as computer software programs tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of methods S1 to S8 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S8 by any other suitable means (e.g., by means of firmware).

[0097] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0098] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0099] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0100] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for inter-layer alignment of 3D-EBSD continuous cross-sectional data, characterized in that, This method is used for interlayer pairs of 3D-EBSD continuous cross-sectional data containing coherent ∑3 grain boundary materials, and the method includes the following steps: Step S1: Obtain the grain boundaries with ∑3 orientation relationship between the grains on both sides in the reconstructed 3D-EBSD data, i.e., ∑3 grain boundaries; Step S2: Perform three-dimensional space plane fitting on the ∑3 grain boundary to obtain the best fitting plane; Step S3: Select "potential coherent ∑3 grain boundaries"; Step S4 involves linearly translating the centroids of all triangular elements constituting ∑3 grain boundaries in the 3D-EBSD microstructure to obtain the optimal translation distance, achieving interlayer alignment of the continuous 3D-EBSD cross-sectional data. Specifically, this includes calculating the "potential coherent ∑3 grain boundaries". Value, of which The value is the weighted average of the minimum angles between the best-fit plane and the {111} / {111} crystal planes of the grains on both sides of the grain boundary; when When the value is at its minimum, the grain boundary of the "potential coherent ∑3 grain boundary" is as parallel as possible to the {111} / {111} crystal plane of the grains on both sides; The grain boundary with a ∑3 orientation relationship between the grains on both sides is defined as the grains on both sides of the grain boundary oriented around a common... <111> The crystal axis is rotated by 60°, specifically: the orientation difference rotation axis of the grain boundary is... <111> The crystal axis orientation deviation is within 8°, and the orientation difference rotation angle is within 60°±12°. The process of obtaining the optimal fitting plane is as follows: Define the perpendicular distance from the centroid of all triangular elements constituting a certain ∑3 grain boundary, or the geometric point representing the position of the triangular element in three-dimensional space, to a certain fitting plane as... When these The fitting plane is the best-fitting plane when the sum of the absolute values ​​of the values ​​is the smallest. The process of selecting "potential coherent ∑3 grain boundaries" includes: Step S11: Select ∑3 grain boundaries with 3D morphology close to a plane in the ∑3 grain boundary; Step S12: Obtain the trace of the best-fit plane of the grain boundary close to the plane ∑3 intersecting with the cross section of a certain layer of 2D-EBSD. Step S13: Calculate the angle between the trace and the {111} / {111} crystal plane trace of the grains on both sides of the grain boundary on the 2D-EBSD section. If the angle on both sides is less than 15°, it is considered to be nearly parallel, and the grain boundary is defined as a "potential coherent ∑3 grain boundary". In step S11, selecting ∑3 grain boundaries with 3D morphology close to a plane specifically involves: calculating all ∑3 grain boundaries corresponding to... The normalized root mean square error of the value is used to define a ∑3 grain boundary with a normalized root mean square error less than 0.6 as a near-planar ∑3 grain boundary.

2. The method for inter-layer alignment of 3D-EBSD continuous cross-sectional data according to claim 1, characterized in that, The calculation of "potential coherent ∑3 grain boundaries" Values ​​include: Step S21: Calculate all the angles between the best-fit plane and the {111} crystal planes in the grains on both sides of a grain boundary on a certain 2D-EBSD section, and define the minimum values ​​of the angles in the grains on both sides as follows: and ; Step S22, calculate the "potential coherent ∑3 grain boundaries". value, The mathematical expression for the value is: in, For the first i The area of ​​each grain boundary The sum of the areas of all potential coherent ∑3 grain boundaries. n The number of grain boundaries. and These represent all potential coherent ∑3 grain boundaries. and The weighted average, for and The average value.

3. The method for inter-layer alignment of 3D-EBSD continuous cross-sectional data according to claim 1, characterized in that, In step S4, all the centroids of the triangular elements constituting the ∑3 grain boundaries in the 3D-EBSD microstructure are linearly translated to obtain the optimal translation distance, and the "potential coherent ∑3 grain boundaries" are calculated. The values ​​include: the translational distances of the centroid of the topmost triangular element in the 3D-EBSD microstructure along the X-axis and Y-axis, respectively defined as... and The mathematical expression for the new coordinates of the centroids of each triangular element after translation is: in, The height of 3D-EBSD microstructure, For the first i The height of the centroid of each triangular element relative to the bottom of the 3D-EBSD microstructure. For the first i The proportionality coefficient of the translation distance of the centroid of each triangular element, and They are the first i The original coordinates of the centroid on the X and Y axes and These represent the translational distances along the X-axis and Y-axis of the centroid of the topmost triangular element in the 3D-EBSD microstructure. and Indicates the translation of the first... i The new coordinates of the centroid of the triangular element.

4. The method for inter-layer alignment of 3D-EBSD continuous cross-sectional data according to claim 3, characterized in that, In step S4, the "potential coherent ∑3 grain boundaries" are calculated. The values ​​specifically include: n Within a range of X and Y lengths equal to or greater than the volume of 3D-EBSD data, continuously change ΔX and ΔY Values, and calculate the corresponding values ​​for "potential coherent ∑3 grain boundaries". value.

5. The method for inter-layer alignment of 3D-EBSD continuous cross-sectional data according to claim 1, characterized in that, The 3D-EBSD data was obtained by reconstructing a series of consecutive 2D-EBSD cross-sectional data.

6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 5.

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