Three-dimensional neutron diffraction data processing method and system of single crystal material

Abstract

The invention provides a three-dimensional neutron diffraction data processing method and system for a single crystal material, and the method comprises the steps: carrying out the rough scanning of a single crystal sample through a pole figure mode, and determining the rotation center of a single crystal sample signal; performing fine scanning at the rotation center to obtain a three-dimensional neutron diffraction signal; decomposing the three-dimensional neutron diffraction signal to obtain a diffraction peak curve and a rocking curve plane; correcting the coordinates of the rocking curve plane; decomposing the corrected rocking curve plane to obtain a rocking curve; and according to the diffraction peak curve and the rocking curve, quantitatively analyzing interplanar spacing and orientation distribution information in the three-position diffraction signal. The method can realize nondestructive characterization of the internal microstructure of the single crystal material, provides accurate data support for research of lattice strain distribution and orientation characteristics, and can realize synchronous characterization analysis of lattice spacing and orientation distribution information.

Description

Technical Field

[0001] The present invention relates to the technical field of diffraction data processing, and in particular, to a method and system for processing three-dimensional neutron diffraction data of a single crystal material. Background Art

[0002] As a non-destructive characterization technique, neutron diffraction is widely used in the research of single crystal materials. Existing neutron diffraction experiments mainly collect and analyze single diffraction data using a two-dimensional area detector by fixing Euler angles.

[0003] The document "In-s itu neutron diffraction during stress relaxation of a singlecrystal nickel-base superalloy[J].Scripta Materialia,2017,131:103-107.CollinsD M,D’souza N,Panwisawas C." analyzed the lattice plane spacing of a nickel-based single crystal superalloy by processing two-dimensional diffraction data. However, this method can only process signals in a single orientation direction and does not consider the influence of multiple orientation directions on the overall crystal structure.

[0004] The document "A neutron diffraction study of lattice distortion,mi smatch andmi sorientation in a single-crystal superalloy after different heattreatments.Acta materialia.2013;61(7):2308-19.Wu E,Sun G,Chen B,Pirling T,Hughes DJ,Wang S,et al." obtained orientation-related information of a single crystal material by analyzing two-dimensional detector signals. However, due to the limitations of the two-dimensional area detector, it can only capture orientation information in a single direction and cannot comprehensively analyze the complete orientation distribution of the crystal. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method and system for processing three-dimensional neutron diffraction data of a single crystal material.

[0006] According to a method for processing three-dimensional neutron diffraction data of a single crystal material provided by the present invention, it includes:

[0007] Step S1: Roughly scan the single crystal sample in the form of a pole figure to determine the rotation center of the single crystal sample signal;

[0008] Step S2: Perform a fine scan at the rotation center to obtain three-dimensional neutron diffraction signals;

[0009] Step S3: Decompose the three-dimensional neutron diffraction signals to obtain a diffraction peak curve and a rocking curve plane;

[0010] Step S4: Correct the coordinates of the rocking curve plane;

[0011] Step S5: Decompose the corrected rocking curve plane to obtain a rocking curve;

[0012] Step S6: Based on the diffraction peak curve and the rocking curve, quantitatively analyze the interplanar spacing and orientation distribution information in the three-dimensional diffraction signals.

[0013] Preferably, after a rough scan of the pole figure, at the rotation position with diffraction signals, the rotation angle χ can be adjusted so that the diffraction signals are located at the center of the two-dimensional area detector, and the coordinates of this center are used as the rotation center position of the single-crystal sample signals.

[0014] Preferably, for a specific rotation angle χ, the three-dimensional neutron diffraction signals are expressed as follows:

[0015]

[0016] where θ represents the angle between the line connecting a single pixel point in the detector and the optical center and the incident neutrons / X-rays, and η represents the angle between the line connecting the single pixel point and the center of the detector and the positive direction of the z-axis.

[0017] Preferably, decomposing the three-dimensional neutron diffraction signals into a diffraction peak curve and a rocking curve plane, which respectively contain lattice constant and lattice orientation information, includes the following steps:

[0018] Step S3.1: Obtaining the diffraction peak curve, with the formula as follows:

[0019]

[0020] Step S3.2: Obtaining the rocking curve plane, with the formula as follows:

[0021]

[0022] Preferably, the said Step S4 includes:

[0023] Step S4.1: Calculate the direction coordinates N of the crystal plane after rotation on the Euler ring according to the reflection principle L , with the formula as follows:

[0024] Then

[0025] Among them, e x represents the unit vector of the x-axis;

[0026] Step S4.2: Calculate the direction coordinates N of the crystal plane before rotation according to the rotation angle as follows:

[0027]

[0028] Step S4.3: According to the definition of Euler angles, solve the following equations:

[0029]

[0030] Preferably, the said step S5 includes the following steps:

[0031] Step S5.1: Obtain the rocking curve I(η), and the formula is as follows:

[0032]

[0033] Step S5.2: Obtain the rocking curve I(ω), and the formula is as follows:

[0034]

[0035] Preferably, the said step S6 includes:

[0036] Step S6.1: Use the Gaussian function to perform fitting analysis on the diffraction peak curve, define the peak position as θ hkl , according to Bragg's law:

[0037] 2d hkl sinθ hkl = λ

[0038] where λ is the incident neutron wavelength, and the lattice plane spacing in the sub-grain can be solved;

[0039] Step S6.2: Calculate the full width at half maximum of the rocking curve I(η) and the rocking curve I(ω) respectively to quantify the orientation distribution.

[0040] According to a three-dimensional neutron diffraction data processing system for single crystal materials provided by the present invention, it includes:

[0041] Module M1: Roughly scan the single crystal sample in the form of a pole figure to determine the rotation center of the single crystal sample signal;

[0042] Module M2: Perform a fine scan at the rotation center to obtain a three-dimensional neutron diffraction signal;

[0043] Module M3: Decompose the three-dimensional neutron diffraction signal to obtain a diffraction peak curve and a rocking curve plane;

[0044] Module M4: Correct the coordinates of the rocking curve plane;

[0045] Module M5: Decompose the corrected rocking curve plane to obtain the rocking curve;

[0046] Module M6: Quantitatively analyze the lattice plane spacing and orientation distribution information in the three-dimensional diffraction signal based on the diffraction peak curve and the rocking curve.

[0047] Preferably, after the rough scan of the pole figure, at the rotation position with diffraction signals, the rotation angle χ can be adjusted so that the diffraction signal is located at the center of the two-dimensional area detector, and the coordinates of this center are used as the rotation center position of the single crystal sample signal.

[0048] Preferably, for a specific rotation angle χ, the three-dimensional neutron diffraction signal is expressed as follows:

[0049]

[0050] where θ represents the angle between the line connecting a single pixel point in the detector and the optical center and the incident neutron / X-ray, and η represents the angle between the line connecting the single pixel point and the center of the detector and the positive direction of the z-axis.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. Based on the rough scan of the pole figure to determine the single crystal diffraction signal, by fixing the Euler ring rotation angle χ and continuously rotating the rotation angle and effectively superimposing the data collected by the single two-dimensional area detector each time, the present invention realizes the problem of testing and collecting the three-dimensional neutron diffraction signal of a single crystal sample, and obtains a complete three-dimensional diffraction signal.

[0053] 2. By decomposing the three-dimensional neutron diffraction signal into the diffraction peak curve and the rocking curve plane, and after correcting the coordinates of the rocking curve plane according to the definition of the Euler angles, the rocking curve plane is decomposed into rocking curves in two perpendicular directions, thereby solving the synchronous testing and extraction of the lattice spacing and two-dimensional orientation distribution of a single crystal sample.

[0054] 3. The present invention can non-destructively characterize the internal microstructure of single crystal materials, provide accurate data support for studying the lattice strain distribution and orientation characteristics, and further enable synchronous characterization and analysis of the lattice plane spacing and orientation distribution information. Description of the Drawings

[0055] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objects and advantages of the present invention will become more apparent:

[0056] Figure 1Schematic diagram of a three-dimensional neutron diffraction experiment;

[0057] Figure 2 Schematic diagram of the working method flow of the present invention;

[0058] Figure 3 Three-dimensional neutron diffraction data and its decomposition results, where (a) is the three-dimensional neutron diffraction signal, (b) is the diffraction peak curve, and (c) is the rocking curve plane

[0059] Figure 4 Effect diagrams before and after coordinate transformation of the rocking curve plane, where (a) is before transformation and (b) is after transformation. Detailed implementation manners

[0060] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0061] The present invention realizes high-precision acquisition of three-dimensional diffraction signals of single crystal samples by fixing the Euler ring rotation angle χ and continuously rotating the rotation angle φ. The obtained three-dimensional diffraction signals are decomposed into diffraction peak curves and rocking curve planes, and the coordinates of the rocking curve planes are corrected based on the neutron diffraction geometric model. Finally, through comprehensive analysis of the diffraction peak curves and rocking curve planes, the lattice spacing and lattice orientation distribution information of single crystal materials are quantitatively extracted to accurately characterize the internal microstructural characteristics of single crystal materials.

[0062] The laboratory coordinate system and the rotation coordinate system defined in the present invention are (x, y, z) and The two-dimensional neutron diffraction signal coordinates are represented by two N 1 ×N 2 matrices, denoted as Θ and Η. Specifically, the origin of the laboratory coordinate system is the optical center of the experiment, the positive direction of the x-axis coincides with the direction of the incident neutrons / X-rays, the z-axis direction is vertically upward, and the y-axis direction is determined according to the right-hand rule. In the way of defining Euler angles, the rotation coordinate system is specified Thus, the three-dimensional rotation coordinates of the Euler ring in space are defined. The single diffraction signal is collected by a two-dimensional area detector, and the two-dimensional area detector has N 1 ×N 2Pixel points. According to the neutron diffraction geometry, the orientation information (θ, η) of each pixel point in the two-dimensional area detector is calculated, that is, the angle θ between the line connecting a single pixel point in the detector and the optical center and the incident neutron / X-ray, and the angle η between the line connecting a single pixel point and the center of the detector and the positive direction of the z-axis, where the clockwise direction is defined as the positive direction. Then the two-dimensional neutron diffraction signal coordinates, that is, the two-dimensional orientation information, can be represented by two N 1 ×N 2 matrices, denoted as Θ and Η.

[0063] Example 1

[0064] A three-dimensional neutron diffraction data processing method for single crystal materials provided by the present invention, as shown in Figure 1 and Figure 2 includes:

[0065] Step S1: Roughly scan the single crystal sample in the form of a pole figure to determine the rotation center of the single crystal sample signal. The neutron diffraction signal of the single crystal sample is spot-like in space, so it is necessary to rotate the Euler ring to search for the specific rotation angle corresponding to the spot. The rotation angle X increases step by step from 0° to 90° in steps of 10°. For each step of the rotation angle X, the rotation angle increases step by step from 0° to 360° in steps of 5°. After the rough scan of the pole figure, at the rotation position with the diffraction signal, the rotation angle X can be adjusted so that the diffraction signal is located at the center of the two-dimensional area detector, and this coordinate is used as the rotation center position of the single crystal sample signal

[0066] Step S2: Perform a fine scan at the rotation center to obtain the three-dimensional neutron diffraction signal. Perform a fine scan at the rotation center position , fix the rotation angle χ, and perform a fine scan within the range of ±5° of the rotation angle in steps of , where the step size is determined within the range of 0.1° to 0.25° according to the sample and specific experimental requirements, and it is stipulated that the set of all rotation angles is φ. Then for a specific rotation angle X, the three-dimensional neutron diffraction signal, that is, the signal intensity of each pixel point on the two-dimensional area detector, can be expressed as:

[0067]

[0068] Step S3: Decompose the three-dimensional neutron diffraction signal to obtain the diffraction peak curve and the rocking curve plane. Decompose the three-dimensional neutron diffraction signal into a diffraction peak curve and a rocking curve plane, which respectively contain the lattice constant and lattice orientation information. As shown in Figure 3 (a), the step S3 includes the following steps:

[0069] Step S3.1: Obtain the diffraction peak curve, with the formula as follows:

[0070]

[0071] Step S3.2: Obtain the rocking curve plane, with the formula as follows:

[0072]

[0073] Step S4: Correct the coordinates of the rocking curve plane. According to the definition of Euler angles, the rotation angle X is not perpendicular to Therefore, it is necessary to transform the rocking curve plane into I(η,ω), where the set φ is transformed into Ω. The effect diagrams before and after the transformation are as Figure 4 shown. The step S4 includes the following steps:

[0074] Step S4.1: Calculate the direction coordinates N of the crystal plane after rotation in the Euler ring according to the reflection principle L , assuming e x is the unit vector of the x-axis, then

[0075] Step S4.2: Calculate the direction coordinates N of the crystal plane before rotation according to the rotation angle as follows:

[0076]

[0077] Step S4.3: According to the definition of Euler angles, solve the following equations:

[0078]

[0079] Step S5: Decompose the corrected rocking curve plane to obtain the rocking curve. As Figure 3 (c) shown, decompose the transformed rocking curve plane I(η,ω) into two perpendicular rocking curves I(η) and I(ω). The step S5 includes the following steps:

[0080] Step S5.1: Obtain the rocking curve I(η), with the formula as follows:

[0081]

[0082] Step S5.2: Obtain the rocking curve I(ω), with the formula as follows:

[0083]

[0084] Step S6: According to the diffraction peak curve and the rocking curve, quantitatively analyze the crystal plane spacing and orientation distribution information in the three-dimensional diffraction signal. The step S6 includes the following steps:

[0085] Step S6.1: Calculate the interplanar spacing. Use the Gaussian function to perform fitting analysis on the diffraction peak curve. As shown in Figure 3 (b), define the peak position as θ hkl , and according to Bragg's law 2d hkl sinθ hkl = λ, where λ is the incident neutron wavelength, and then the interplanar spacing in the sub-grain can be solved.

[0086] Step S6.2: Calculate the orientation distribution information. Calculate the full width at half maximum of I(η) and I(ω) respectively to quantify the orientation distribution.

[0087] The object of the present invention is to achieve high-precision synchronous measurement of the lattice spacing and lattice orientation distribution of single crystal materials, and apply it to the neutron three-dimensional diffraction experiment of single crystal materials and subsequent data analysis. Based on the high-precision three-dimensional rotation of the Euler ring, the present invention collects three-dimensional neutron diffraction data of a single crystal sample at multiple angles to obtain a complete three-dimensional diffraction signal, and then decomposes the collected three-dimensional diffraction signal into the diffraction peak curve and the rocking curve plane, and decomposes the crystal structure information into lattice spacing information and orientation information, effectively realizing the microscopic characterization of the internal structure of single crystal materials, and providing accurate data support for studying the lattice strain distribution and orientation characteristics.

[0088] Example 2

[0089] The present invention also provides a three-dimensional neutron diffraction data processing system for single crystal materials. The three-dimensional neutron diffraction data processing system for single crystal materials can be realized by executing the process steps of the three-dimensional neutron diffraction data processing method for single crystal materials, that is, those skilled in the art can understand the three-dimensional neutron diffraction data processing method for single crystal materials as the preferred implementation manner of the three-dimensional neutron diffraction data processing system for single crystal materials.

[0090] According to a three-dimensional neutron diffraction data processing system for single crystal materials provided by the present invention, it includes:

[0091] Module M1: Roughly scan the single crystal sample in the form of a pole figure to determine the rotation center of the single crystal sample signal. The rotation center is at the rotation position with diffraction signals after rough scanning of the pole figure. The rotation angle χ can be adjusted so that the diffraction signal is located at the center of the two-dimensional area detector, and the coordinates of this center are used as the rotation center position of the single crystal sample signal

[0092] Module M2: Perform fine scanning at the rotation center to obtain a three-dimensional neutron diffraction signal. For a specific rotation angle χ, the three-dimensional neutron diffraction signal is expressed as follows: Among them, θ represents the angle between the line connecting a single pixel point in the detector and the optical center and the incident neutron / X-ray, and η represents the angle between the line connecting a single pixel point and the center of the detector and the positive direction of the z-axis.

[0093] Module M3: Decompose the three-dimensional neutron diffraction signal to obtain the diffraction peak curve and the rocking curve plane. Decompose the three-dimensional neutron diffraction signal into a diffraction peak curve and a rocking curve plane, which respectively contain lattice constant and lattice orientation information, including the following modules: Module M3.1: Obtain the diffraction peak curve, and the formula is as follows: Module M3.2: Obtain the rocking curve plane, and the formula is as follows:

[0094] Module M4: Correct the coordinates of the rocking curve plane. The module M4 includes: Module M4.1: Calculate the direction coordinate N of the crystal plane after rotation in the Euler ring according to the reflection principle L , and the formula is as follows: Then where e x represents the unit vector of the x-axis. Module M4.2: Calculate the direction coordinate N of the crystal plane before rotation according to the rotation angle , as shown below: Module M4.3: According to the definition of Euler angles, solve the following equations:

[0095] Module M5: Decompose the corrected rocking curve plane to obtain the rocking curve. The module M5 includes the following modules: Module M5.1: Obtain the rocking curve I(η), and the formula is as follows: I(η) = ∑ ω∈Ω I(η, ω) Module M5.2: Obtain the rocking curve I(ω), and the formula is as follows: I(ω) = ∑ η∈H I(η, ω).

[0096] Module M6: According to the diffraction peak curve and the rocking curve, quantitatively analyze the interplanar spacing and orientation distribution information in the three-dimensional diffraction signal. The module M6 includes: Module M6.1: Use the Gaussian function to perform fitting analysis on the diffraction peak curve, define the peak position as θ hkl , according to Bragg's law: 2d hkl sinθ hkl = λ, where λ is the wavelength of the incident neutron, and the interplanar spacing in the sub-grain can be solved. Module M6.2: Calculate the full width at half maximum of the rocking curve I(η) and the rocking curve I(ω) respectively to quantify the orientation distribution.

[0097] Those skilled in the art know that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0098] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A three-dimensional neutron diffraction data processing method for single crystal materials, characterized in that: include: Step S1: roughly scanning the single crystal sample by pole figure method to determine the rotation center of the single crystal sample signal; Step S2: performing a fine scan at the rotation center to obtain a three-dimensional neutron diffraction signal; Step S3: decomposing the three-dimensional neutron diffraction signal to obtain a diffraction peak curve and a rocking curve plane; Step S4: Correcting the coordinates of the rocking curve plane; Step S5: decomposing the corrected rocking curve plane to obtain the rocking curve; Step S6: quantitatively analyzing the interplanar spacing and orientation distribution information in the three-dimensional diffraction signal according to the diffraction peak curve and the rocking curve.

2. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: The rotation center is at the rotation position with the diffraction signal after the pole figure is roughly scanned. The rotation angle x can be adjusted so that the diffraction signal is located in the center of the two-dimensional surface detector. The coordinates of this center are used as the rotation center position of the single crystal sample signal.

3. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: For a specific rotation angle χ, the three-dimensional neutron diffraction signal is expressed as follows: Among them, θ represents the angle between the line connecting a single pixel point and the optical center in the detector and the incident neutron / X-ray, and η represents the angle between the line connecting a single pixel point and the center of the detector and the positive direction of the z-axis.

4. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: Decomposing the three-dimensional neutron diffraction signal into a diffraction peak curve and a rocking curve plane, which respectively contain lattice constant and lattice orientation information, comprises the following steps: Step S3.1: Obtain the diffraction peak curve, the formula is as follows: Step S3.2: Obtain the rocking curve plane, the formula is as follows:

5. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: The step S4 comprises: Step S4.1: Calculate the direction coordinate N of the crystal plane after the Euler ring is rotated according to the reflection principle L , the formula is as follows: Among them, e x represents the unit vector of the x-axis; Step S4.2: According to the rotation angle Calculate the orientation coordinate N of the crystal plane before rotation as follows: Step S4.3: According to the definition of Euler angle, solve the following equation:

6. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: The step S5 comprises the following steps: Step S5.1: Obtain the rocking curve I(η), the formula is as follows: I(η)=∑ ω∈Ω I(h,w); Step S5.2: Obtain the rocking curve I(ω), the formula is as follows: I(ω)=∑ η∈H I(η,ω).

7. The three-dimensional neutron diffraction data processing method of single crystal material according to claim 1, characterized in that: The step S6 comprises: Step S6.1: Use Gaussian function to fit the diffraction peak curve and define the peak position as θ hkl , according to Bragg's law: 2d hkl sinth hkl =λ Where λ is the wavelength of the incident neutron, and the interplanar spacing in the subgrains can be solved; Step S6.2: Calculate the half-widths of the rocking curve I(η) and the rocking curve I(ω) respectively to quantify the orientation distribution.

8. A three-dimensional neutron diffraction data processing system for single crystal materials, characterized in that: include: Module M1: Roughly scan the single crystal sample by pole figure method to determine the rotation center of the single crystal sample signal; Module M2: performing fine scanning at the rotation center to obtain a three-dimensional neutron diffraction signal; Module M3: decomposing the three-dimensional neutron diffraction signal to obtain a diffraction peak curve and a rocking curve plane; Module M4: Correcting the coordinates of the rocking curve plane; Module M5: decomposing the corrected rocking curve plane to obtain the rocking curve; Module M6: quantitatively analyzing the interplanar spacing and orientation distribution information in the three-dimensional diffraction signal according to the diffraction peak curve and the rocking curve.

9. The three-dimensional neutron diffraction data processing system for single crystal materials according to claim 8, characterized in that: The rotation center is at the rotation position with the diffraction signal after the pole figure is roughly scanned. The rotation angle x can be adjusted so that the diffraction signal is located in the center of the two-dimensional surface detector. The coordinates of this center are used as the rotation center position of the single crystal sample signal.

10. The three-dimensional neutron diffraction data processing system for single crystal materials according to claim 8, characterized in that: For a specific rotation angle χ, the three-dimensional neutron diffraction signal is expressed as follows: Among them, θ represents the angle between the line connecting a single pixel point and the optical center in the detector and the incident neutron / X-ray, and η represents the angle between the line connecting a single pixel point and the center of the detector and the positive direction of the z-axis.

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