CN107796836B - Method for correcting Euler angle of plate texture - Google Patents
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Abstract
The inventor provides a method for correcting Euler angles of plate textures, which comprises the following steps: (1) counting the Euler angles of the centers of the peaks of the Euler angles in the Euler space; (2) matching the Euler angles obtained in the step (1) pairwise, and calculating a phase difference matrix X between the two Euler angles; (3) solving the rotation matrix M according to the symmetric phase difference matrix X'; (4) rotating all Euler angles in the Euler space by using the rotation matrix M; according to the technical scheme provided by the invention, the automatic correction of the possible existing deviation of the Euler angle is realized by calculation by utilizing the symmetry of the plate, so that the error caused by manual adjustment is avoided, the correction precision is greatly improved, and the difficult problem of adjustment of data such as large angle and the like which are difficult to adjust is solved; the efficiency is greatly improved.
Description
Technical Field
The invention relates to orientation of a plate texture, in particular to a method for correcting an Euler angle of the plate texture.
Background
Studying the texture of the sheet often requires cutting the sample and electron diffraction using an electron microscope (SEM). Under a scanning electron microscope, an electron beam acts on a sample surface area with a large-angle tendency, and diffraction is generated in the interaction of primary back-scattered electrons and a point front surface to form a Julian-chi pattern. Analyzing the information of crystal structure, orientation and the like of the obtained crystal grains of the Julian flower, wherein the orientation information is generally Euler angle
A description is given. Due to the fact that a sample is irregular, a certain angle deviation exists between the sample and a sample table when the sample is placed in an electron microscope, and the like, a sample coordinate system is difficult to determine accurately, errors are brought to EBSD data accuracy, a certain deviation exists between a polar diagram and an inverse polar diagram, an ODF diagram is unknown, and finally orientation is causedThe statistical result is not accurate. At present, the error brought by the sample coordinate system is generally reduced by manually rotating the euler angle data, but the following defects exist in the manual rotation:
the precision is low, and whether the rotation is in a reasonable state is generally determined by visual inspection;
when a plurality of Euler angles have deviation at the same time, the rotation to a more ideal position needs to be tried for many times;
when the deviation angle is too large, for example, the deviation angle is greater than 45 °, the sample is easily rotated to the direction perpendicular to the sample, and data errors are caused.
Disclosure of Invention
Aiming at the defects of the prior art, the applicant designs a method for correcting the Euler angle of the plate texture, which can automatically correct the deviation of the Euler angle, thereby greatly reducing the error and complexity; the difficult problem of adjusting data with large angle and the like which are difficult to adjust is solved; and all Euler angles in the Euler space are uniformly adjusted, so that the efficiency is greatly improved.
The invention aims to be realized by the following technical scheme:
the inventor provides a method for correcting Euler angles of plate textures, which comprises the following steps:
(1) counting the Euler angles of the centers of the peaks of the Euler angles in the Euler space;
(2) matching the Euler angles obtained in the step (1) pairwise, and calculating a phase difference matrix X between the two Euler angles;
(3) solving the rotation matrix M according to the symmetric phase difference matrix X';
(4) rotating all Euler angles in the Euler space using the rotation matrix M.
Preferably, the peak in step (1) is an euler space coordinate with a higher orientation distribution density.
Preferably, the number of the peaks is 4 or more.
Preferably, the method for calculating the phase difference matrix X in step (2) is as follows:
X＝A1 -1 *A2
wherein: a. the1、A2And (2) respectively representing matrixes corresponding to the Euler angles counted in the step (1).
Preferably, the symmetric phase difference matrix X' in step (3) is obtained by screening all the phase difference matrices X obtained in step (2).
Preferably, the screening comprises:
checking whether the phase difference matrix is a symmetric matrix;
checking whether the phase difference matrix is similar to the matrix lambda
Wherein:
preferably, the matrix checking in the first step and the second step allows an error, and the phase difference matrix X with the minimum error is selected as the symmetric phase difference matrix X'.
Preferably, the specific method for solving the rotation matrix M in step (3) is as follows:
setting the rotation matrix
The Euler angle corresponding to M is
② according to the formula
Calculating w, l and t;
solving a second angle phi of the Euler angle corresponding to the rotation matrix M according to a formula phi (arccos) (l) and l;
fourthly, according to the formula
w, t and phi are used for solving the first angle of the Euler angle corresponding to the rotation matrix M
Fifthly, all the Euler angles in the step (1) are adjusted according to
Rotating;
sixthly, screening a group of mirror symmetric matrixes P and Q from the matrixes corresponding to the Euler angles after the rotation in the fifth step;
the above-mentioned
And
the following conditions must be satisfied:
p13＝q23、
p23＝q13、
p33＝q33and
(p32+q32)/(p31+q31)＝-(p31-q31)/(p32-q32)＝(p21+q22)/(p11+q21)＝-(p11-p21)/(p12-q22)＝(p22+q12)/(p21+q11)＝-(p22-q12)/(p21-q11)；
according to the formula
Determining a third angle of the rotation matrix
Wherein: p is a radical of11、p12、p13、p21、p22、p23、p31、p32、p33、q11、q12、q13、q21、q22、q23、q31、q32And q is33The method comprises the following steps of (1) knowing;
according to the Euler angle
And the three angles
Phi and
is given by u, v, r, s, h and k in the rotation matrix M.
Preferably, in the step (c):
said p is13＝q23The allowable error of (a) is 0.001-0.01;
said p is23＝q13The allowable error of (a) is 0.001-0.01;
said p is33＝q33The allowable error of (2) is 0.001 to 0.01.
Preferably, the specific operations of the fifth step are as follows:
corresponding a matrix of Euler angles to be rotated to the Euler angles
Multiplying corresponding matrixes; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
Preferably, the specific operation of rotating in the step (4) is as follows:
multiplying a matrix corresponding to the Euler angle to be rotated by the rotation matrix M; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
Preferably, the steps (1) to (4) are incorporated in a computer program.
Compared with the closest prior art, the invention has the beneficial effects that:
1. according to the technical scheme provided by the invention, the symmetry of the plate is utilized, the automatic correction of the possible existing deviation of the Euler angle is realized through calculation, the error caused by manual adjustment is avoided, the correction precision is greatly improved, and the correction can be controlled at 0.1 degrees; the difficult problem of adjusting data with large angle and the like which are difficult to adjust is solved; and all Euler angles in the Euler space are uniformly adjusted, so that the efficiency is greatly improved.
Drawings
The invention will be further described with reference to the accompanying drawings in which:
FIG. 1: a flow chart of a method provided by the present invention;
Detailed Description
The technical solutions in the embodiments of the present application are clearly and completely described below with reference to the drawings in the embodiments of the present application.
As shown in fig. 1, the present inventors provide a method for correcting euler angles of plate texture, the method comprising the following steps:
(1) counting the Euler angles of the centers of the peaks of the Euler angles in the Euler space;
(2) matching the Euler angles obtained in the step (1) pairwise, and calculating a phase difference matrix X between the two Euler angles;
(3) solving the rotation matrix M according to the symmetric phase difference matrix X';
(4) rotating all Euler angles in the Euler space using the rotation matrix M.
The peak value in the step (1) is an Euler space coordinate with larger orientation distribution density.
The number of the peaks is 4 or more.
The method for calculating the phase difference matrix X in the step (2) comprises the following steps:
X＝A1 -1*A2
wherein: a. the1、A2And (2) respectively representing matrixes corresponding to the Euler angles counted in the step (1).
And (3) screening the symmetric phase difference matrix X' obtained in the step (2) from all the phase difference matrices X obtained in the step (2).
The screening comprises the following steps:
checking whether the phase difference matrix is a symmetric matrix;
checking whether the phase difference matrix is similar to the matrix lambda or not;
wherein
And (4) checking the matrix in the first step and the second step to allow errors, and selecting the phase difference matrix X with the minimum error as a symmetrical phase difference matrix X'.
The specific method for solving the rotation matrix M in the step (3) is as follows:
setting the rotation matrix
The Euler angle corresponding to M is
② according to the formula
Calculating w, l and t;
solving a second angle phi of the Euler angle corresponding to the rotation matrix M according to a formula phi (arccos) (l) and l;
fourthly, according to the formula
w, t and phi are used for solving the first angle of the Euler angle corresponding to the rotation matrix M
Fifthly, all the Euler angles in the step (1) are adjusted according to
Rotating;
sixthly, screening a group of mirror symmetric matrixes P and Q from the matrixes corresponding to the Euler angles after the rotation in the fifth step;
the above-mentioned
And
the following conditions must be satisfied:
p13＝q23、
p23＝q13、
p33＝q33and
(p32+q32)/(p31+q31)＝-(p31-q31)/(p32-q32)＝(p21+q22)/(p11+q21)＝-(p11-p21)/(p12-q22)＝(p22+q12)/(p21+q11)＝-(p22-q12)/(p21-q11)；
according to the formula
Determining a third angle of the rotation matrix
Wherein: p is a radical of11、p12、p13、p21、p22、p23、p31、p32、p33、q11、q12、q13、q21、q22、q23、q31、q32And q is33The method comprises the following steps of (1) knowing;
according to the Euler angle
And the three angles
Phi and
is given by u, v, r, s, h and k in the rotation matrix M.
In the step (c):
said p is13＝q23The allowable error of (a) is 0.001-0.01;
said p is23＝q13The allowable error of (a) is 0.001-0.01;
said p is33＝q33The allowable error of (2) is 0.001 to 0.01.
Preferably, the specific operations of the fifth step are as follows:
corresponding a matrix of Euler angles to be rotated to the Euler angles
Multiplying corresponding matrixes; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
The specific operation of rotating in the step (4) is as follows:
multiplying a matrix corresponding to the Euler angle to be rotated by the rotation matrix M; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
The steps (1) to (4) are incorporated in a computer program.
Finally, it should be noted that: the embodiments described are only a part of the embodiments of the present application, and not all embodiments, and all other embodiments obtained by those skilled in the art without making creative efforts based on the embodiments in the present application belong to the protection scope of the present application.
Claims (8)
1. A method of modifying the euler angles of a textured sheet material, the method comprising the steps of:
(1) counting the Euler angles of the centers of the peaks of the Euler angles in the Euler space;
(2) matching the Euler angles obtained in the step (1) pairwise, and calculating a phase difference matrix X between the two Euler angles;
(3) solving a rotation matrix M by the symmetric phase difference matrix X';
(4) rotating all Euler angles in the Euler space by using the rotation matrix M;
the method for calculating the phase difference matrix X in the step (2) comprises the following steps:
X＝A1 -1*A2
wherein: a. the1、A2Respectively are matrixes corresponding to the Euler angles counted in the step (1);
the symmetric phase difference matrix X' in the step (3) is obtained by screening all the phase difference matrices X obtained in the step (2);
the screening comprises the following steps:
checking whether the phase difference matrix is a symmetric matrix;
checking whether the phase difference matrix is similar to the matrix lambda or not;
wherein:
and (4) checking the matrix in the first step and the second step to allow errors, and selecting the phase difference matrix X with the minimum error as a symmetrical phase difference matrix X'.
2. The method for modifying the euler angle of the plate texture according to claim 1, wherein the peak value in the step (1) is the euler space coordinate with higher orientation distribution density.
3. The method for modifying the euler angle of the texture of the plate as claimed in claim 2, wherein the number of the peaks is 4 or more.
4. The method for modifying the euler angle of the plate texture according to claim 1, wherein the specific method for solving the rotation matrix M in the step (3) is as follows:
setting the rotation matrix
The Euler angle corresponding to M is
② according to the formula
Calculating w, l and t;
solving a second angle phi of the Euler angle corresponding to the rotation matrix M according to a formula phi (arccos) (l) and l;
fourthly, according to the formula
w, t and phi are used for solving the first angle of the Euler angle corresponding to the rotation matrix M
Fifthly, all the Euler angles in the step (1) are adjusted according to
Rotating;
sixthly, screening a group of mirror symmetric matrixes P and Q from the matrixes corresponding to the Euler angles after the rotation in the fifth step;
the above-mentioned
And
the following conditions must be satisfied:
p13＝q23、
p23＝q13、
p33＝q33and
according to the formula
Determining a third angle of the rotation matrix
Wherein: p is a radical of11、p12、p13、p21、p22、p23、p31、p32、p33、q11、q12、q13、q21、q22、q23、q31、q32And q is33The method comprises the following steps of (1) knowing;
according to the Euler angle
And the three angles
Phi and
is given by u, v, r, s, h and k in the rotation matrix M.
5. The method for correcting the euler angle of the plate texture according to claim 4, wherein the step (c) is as follows:
said p is13＝q23The allowable error of (a) is 0.001-0.01;
said p is23＝q13The allowable error of (a) is 0.001-0.01;
said p is33＝q33The allowable error of (2) is 0.001 to 0.01.
6. The method for correcting the euler angle of the plate texture according to claim 4, wherein the specific operations of the fifth step are as follows:
corresponding a matrix of Euler angles to be rotated to the Euler angles
Multiplying corresponding matrixes; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
7. The method for modifying the euler angle of the plate texture according to claim 1, wherein the specific operation of rotating in the step (4) is as follows:
multiplying a matrix corresponding to the Euler angle to be rotated by the rotation matrix M; and the Euler angle corresponding to the obtained matrix is the Euler angle after rotation.
8. The method for modifying the Euler angle of the plate texture according to any one of claims 1 to 7, wherein the steps (1) to (4) are programmed into a computer.
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| CN101733848A (en) * | 2009-12-29 | 2010-06-16 | 西北工业大学 | Convenient method for directionally cutting any crystal face of crystal |
| CN103278517A (en) * | 2013-05-29 | 2013-09-04 | 钢铁研究总院 | Method for measuring orientation differences of orientation silicon steel crystal particles |
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| US6784840B2 (en) * | 2002-12-23 | 2004-08-31 | Itt Manufacturing Enterprises, Inc. | Method for determining azimuth and elevation angles using a single axis direction finding system |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101733848A (en) * | 2009-12-29 | 2010-06-16 | 西北工业大学 | Convenient method for directionally cutting any crystal face of crystal |
| CN103278517A (en) * | 2013-05-29 | 2013-09-04 | 钢铁研究总院 | Method for measuring orientation differences of orientation silicon steel crystal particles |
Non-Patent Citations (3)
| Title |
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| Al-Cu-Li系合金热轧板材组织、性能;杨守杰等;《航空材料学报》;20010930;第21卷(第3期);全文 * |
| 关于机器人姿态偏差描述方法的讨论;冯振成;《河北机电学院学报》;19901231;第7卷(第1期);全文 * |
| 显微织构取向分布函数的电子背散射衍射测定;刘静等;《电子显微学报》;19990831;第18卷(第4期);全文 * |
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Effective date of registration: 20230110 Address after: 102209 South District of Future Science City, Beiqijia Town, Changping District, Beijing Patentee after: CHINALCO MATERIALS APPLICATION RESEARCH INSTITUTE Co.,Ltd. Patentee after: CHINALCO INSTITUTE OF SCIENCE AND TECHNOLOGY Co.,Ltd. Address before: 102209 building 10, Chinalco science and Technology Research Institute, South District, future science and Technology City, Beiqijia Town, Changping District, Beijing Patentee before: CHINALCO MATERIALS APPLICATION RESEARCH INSTITUTE Co.,Ltd. |