Method and system for processing two-dimensional diffraction data of single crystal material

Abstract

The application provides a two-dimensional diffraction data processing method and system of a single crystal material, relates to the technical field of diffraction data processing, and comprises the following steps: analyzing two-dimensional face detector diffraction data of the single crystal material, realizing multi-directional compression from two-dimensional data to one-dimensional data, and quantifying anisotropy distribution of each subgrain in the single crystal material. The method integrates various diffraction two-dimensional data compression methods through a system, obtains one-dimensional overall diffraction curves, rocking curves and subgrain diffraction curves of each subgrain in the sample, realizes separation of diffraction peaks of each subgrain, and realizes quantitative characterization of crystal face orientation and spacing through fusion function fitting analysis. The application can more accurately and comprehensively quantitatively analyze two-dimensional diffraction data of a single crystal, and further researches crystal face spacing and orientation of subgrains in the single crystal material.

Description

Technical Field

[0001] This invention relates to the field of diffraction data processing technology, and more specifically, to a method and system for processing two-dimensional diffraction data of single-crystal materials. Background Technology

[0002] Currently, because existing software focuses more on the interplanar spacing and texture information of polycrystalline materials, two-dimensional diffraction data processing methods still rely on various data compression methods for analysis in isolation, which is not conducive to the simultaneous quantitative study of the grain orientation and interplanar spacing of subgrains in single-crystal samples.

[0003] In 2015, C. Prescher et al. proposed a two-dimensional X-ray diffraction data processing software called DIOPTAS (Prescher C, Prakapenka V B. DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration[J]. High Pressure Research, 2015, 35(3): 223-230.). The data simplification algorithm of this method makes it suitable for real-time data processing and batch image post-processing. However, this method cannot calculate the rocking curve of the diffraction image, thus lacking the ability to study grain orientation information.

[0004] In 2017, J. Filik et al. proposed a software called DAWN2 for processing two-dimensional X-ray powder diffraction and small-angle scattering data (

[61] Filik J, Ashton A, Chang P, et al. Processing two-dimensional X-ray diffraction and small-angle scattering data in DAWN 2[J]. Journal of applied crystallography, 2017, 50(3): 959-966.). This method has the ability to compress Debye rings into one-dimensional diffraction peaks and rocking curves, respectively. However, this method lacks the ability to make reasonable use of various two-dimensional compression methods, and therefore does not have the ability to separate and analyze diffraction peaks caused by subgrains. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for processing two-dimensional diffraction data of single-crystal materials.

[0006] According to the present invention, a method and system for processing two-dimensional diffraction data of single-crystal materials are provided, the scheme of which is as follows:

[0007] In a first aspect, a method for processing two-dimensional diffraction data of single-crystal materials is provided, the method comprising:

[0008] Step S1: Based on the experimental and instrument setup, and combined with diffraction geometry, define an orthogonal coordinate system (x, y, z) and form a diffraction experimental geometric model; where the origin of the orthogonal coordinate system is the optical center of the experiment, that is, the intersection of the rotation axes of the sample, the positive direction of the x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule.

[0009] Step S2: Based on the geometric model of the diffraction experiment, calculate the orientation information (θ, η) of each pixel in the two-dimensional surface detector, that is, the angle θ between the line connecting a single pixel in the detector to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction.

[0010] Step S3: Combining the geometric model and orientation information of the diffraction experiment, set three intensity calibration factors: solid angle factor, polarization factor, and absorption factor, to calibrate the original diffraction intensity and form a diffraction intensity matrix C(θ, η); where the solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation caused by the optical path difference between each pixel.

[0011] Step S4: Perform a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single crystal sample, i.e., the one-dimensional diffraction peak of a certain crystal plane or a specific diffraction angle of the single crystal sample; use a Gaussian function to fit and analyze the overall diffraction peak curve to obtain the overall diffraction peak information, including peak intensity a. overall Peak position θ overall Standard deviation u overall ;

[0012] Step S5: Using θ overall With a overall The parameters are analyzed by performing an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters, including the peak position η, are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M,

[0013] Step S6: Based on the rocking curve parameters, determine the main range of each subgrain diffraction peak, and perform M 2θ subgrain scans to obtain the diffraction curves of each subgrain in the single crystal sample; use a Gaussian function to fit and analyze the diffraction curves of each subgrain to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j ;

[0014] Step S7: Using the diffraction experiment geometric model, combined with the subgrain diffraction peak information and rocking curve parameters, obtain the orientation information of the diffraction peaks of each subgrain, and then calculate the crystal plane orientation and spacing information in each subgrain.

[0015] Preferably, in the geometric model of the diffraction experiment, the distance R from the sample to the detector is specified, and the angle 2θ between the center of the detector and the incident neutron beam is defined. center Detector size (W) det H det The detector pixel count (M, N) and detector pixel index (m, n) are also specified.

[0016] Calculating the orientation information (θ, η) of each pixel in a two-dimensional surface detector includes:

[0017] First, according to 2θ center , (W det H det (M, N) calculates the position information (X, Y, Z) of a specific pixel (m, n) in an orthogonal coordinate system;

[0018] Secondly, the position information (X, Y, Z) of a specific pixel (m, n) is used to represent the position information (X, Y, Z) in the orthogonal coordinate system. By solving the simultaneous equations, the position information (θ, η) of each pixel in the two-dimensional surface detector is calculated.

[0019] Preferably, step S4 includes:

[0020] Step S4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data;

[0021] Step S4.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i :

[0022]

[0023] Step S4.3: By analyzing set A iCalculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1);

[0024] Step S4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted;

[0025] Step S4.5: Define the objective function as mean squared error, i.e.

[0026] Step S4.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the overall diffraction peak information.

[0027] Preferably, step S5 includes:

[0028] Step S5.1: Using the overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data;

[0029] Step S5.2: Determine the range of azimuth angle η [η min η max ], and step size Δη1, define set B i :

[0030]

[0031] Step S5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve I. RC (θ1, η) i );

[0032] Step S5.4: Define the Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted;

[0033] Step S5.5: Define the objective function as mean squared error, i.e.

[0034] Step S5.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the parameters of the swing curve.

[0035] Preferably, step S6 includes:

[0036] Step S6.1: Determine the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data;

[0037] Step S6.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i :

[0038]

[0039] Step S6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve I. j (θ i η j );

[0040] Step S6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted;

[0041] Step S6.5: Define the objective function as mean squared error, i.e.

[0042] Step S6.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain diffraction peak information.

[0043] Preferably, step S7 includes:

[0044] Step S7.1: Combining the subgrain diffraction peak information and the rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j );

[0045] Step S7.2: Based on the geometric model of the diffraction experiment and the law of reflection, let the normal vector of the crystal plane in the subgrain be (X... j Z j Y j Solve by solving the following equations simultaneously:

[0046]

[0047] Step S7.3: Based on the incident wavelength and diffraction angle, use Bragg's law 2dsinθ=λ to solve for the interplanar spacing in the subgrains.

[0048] Secondly, a two-dimensional diffraction data processing system for single-crystal materials is provided, the system comprising:

[0049] Module M1: Based on the experimental and instrument setup, and combined with diffraction geometry, define an orthogonal coordinate system (x, y, z) and form a diffraction experimental geometric model; where the origin of the orthogonal coordinate system is the optical center of the experiment, that is, the intersection of the rotation axes of the sample, the positive direction of the x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule.

[0050] Module M2: Based on the geometric model of the diffraction experiment, calculate the orientation information (θ, η) of each pixel in the two-dimensional surface detector, that is, the angle θ between the line connecting a single pixel in the detector to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction.

[0051] Module M3: Combining the geometric model and orientation information of the diffraction experiment, three intensity calibration factors—solid angle factor, polarization factor, and absorption factor—are set to calibrate the original diffraction intensity, forming a diffraction intensity matrix C(θ, η). The solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation between pixels caused by the optical path difference.

[0052] Module M4: Performs a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single-crystal sample, i.e., the one-dimensional diffraction peak of a certain crystal plane or specific diffraction angle of the single-crystal sample; uses a Gaussian function to fit and analyze the overall diffraction peak curve to obtain overall diffraction peak information, including peak intensity 'a'. overall Peak position θ overall Standard deviation u overall ;

[0053] Module M5: Utilizing θ overall With a overall The parameters are analyzed by performing an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters, including the peak position η, are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M,

[0054] Module M6: Based on the rocking curve parameters, determine the main range of each subgrain diffraction peak, perform M 2θ subgrain scans respectively to obtain the diffraction curves of each subgrain in the single crystal sample; use a Gaussian function to fit and analyze the diffraction curves of each subgrain to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j ;

[0055] Module M7: Using the geometric model of the diffraction experiment, combined with the subgrain diffraction peak information and rocking curve parameters, the orientation information of the diffraction peaks of each subgrain is obtained, thereby calculating the crystal plane orientation and spacing information in each subgrain.

[0056] Preferably, in the geometric model of the diffraction experiment, the distance R from the sample to the detector is specified, and the angle 2θ between the center of the detector and the incident neutron beam is defined. center Detector size (W) det H det The detector pixel count (M, N) and detector index (m, n) are also specified.

[0057] Calculating the orientation information (θ, η) of each pixel in a two-dimensional surface detector includes:

[0058] First, according to 2θ center , (W det H det (M, N) calculates the position information (X, Y, Z) of a specific pixel (m, n) in an orthogonal coordinate system;

[0059] Secondly, the position information (X, Y, z) of a specific pixel (m, n) in the orthogonal coordinate system is represented by the orientation information (θ, η). By solving the equations simultaneously, the orientation information (θ, η) of each pixel in the two-dimensional surface detector is calculated.

[0060] Preferably, the module M4 includes:

[0061] Module M4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data;

[0062] Module M4.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i :

[0063]

[0064] Module M4.3: By analyzing set A iCalculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1);

[0065] Module M4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted;

[0066] Module M4.5: Defines the objective function as mean squared error, i.e.

[0067] Module M4.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining overall diffraction peak information.

[0068] Preferably, the module M5 includes:

[0069] Module M5.1: Utilizing overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data;

[0070] Module M5.2: By determining the range of azimuth angle η [η min η max ], and step size Δη1, define set B i :

[0071]

[0072] Module M5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve I. RC (θ1, η) i );

[0073] Module M5.4: Define Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted;

[0074] Module M5.5: Defines the objective function as mean squared error, i.e.

[0075] Module M5.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining the parameters of the swing curve;

[0076] Preferably, the module M6 includes:

[0077] Module M6.1: Determines the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data;

[0078] Module M6.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i :

[0079]

[0080] Module M6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve I. j (θ i η j );

[0081] Module M6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted;

[0082] Module M6.5: Defines the objective function as mean squared error, i.e.

[0083] Module M6.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining diffraction peak information;

[0084] Preferably, the module M7 includes:

[0085] Module M7.1: Combining subgrain diffraction peak information with rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j );

[0086] Module M7.2: Based on the geometric model of diffraction experiments and the law of reflection, let the normal vector of the crystal plane in the subgrain be (X...) in the orthogonal coordinate system. j Z j Y j Solve by solving the following equations simultaneously:

[0087]

[0088] Module M7.3: Based on the incident wavelength and diffraction angle, use Bragg's law 2dsinθ=λ to solve for the interplanar spacing in the subgrains.

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] 1. This invention integrates existing two-dimensional data compression methods and performs 2θ scanning, η scanning and 2θ subgrain scanning in sequence. The scanning analysis data is automatically transferred before and after the scan, which solves the problem that existing two-dimensional diffraction data processing methods cannot quickly analyze single crystal diffraction data.

[0091] 2. This invention solves the problem of separating subgrain diffraction peaks within a single crystal sample by fitting and analyzing the rocking curve after η scanning using a mixed Gaussian function model.

[0092] 3. This invention solves the problem of quantitative analysis of the interplanar spacing and orientation of each subgrain by using rocking curve parameters to determine the scanning range of each 2θ subgrain and combining it with Gaussian function fitting analysis.

[0093] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0094] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0095] Figure 1 This is an overall flowchart of the present invention;

[0096] Figure 2 This is the geometric model for the diffraction experiment;

[0097] Figure 3 This is diffraction data from a two-dimensional surface detector;

[0098] Figure 4 The overall diffraction curve;

[0099] Figure 5 It is a swaying curve;

[0100] Figure 6 The diffraction curve is for subgrain. Detailed Implementation

[0101] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0102] This invention provides a method for processing two-dimensional diffraction data of single-crystal materials, referring to... Figure 1 As shown, the method specifically includes:

[0103] Step S1: Based on the experimental and instrument setup, and combined with diffraction geometry, define an orthogonal coordinate system (x, y, z). The origin is the optical center of the experiment, i.e., the intersection of all rotation axes of the sample. The positive x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule. The distance R from the sample to the detector is defined, and the angle 2θ between the detector center and the incident neutron beam is specified. center Detector size (W) det H det The detector pixel count (M, N) and detector index (m, n) are used to form the geometric model of the diffraction experiment, referring to... Figure 2 As shown, where, Figure 2 In It is a two-dimensional surface detector.

[0104] Step S2: Refer to Figure 3 As shown, based on the geometric model of the diffraction experiment, the orientation information (θ, η) of each pixel in the two-dimensional surface detector is calculated. This includes the angle θ between the line connecting a single pixel to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction. First, based on 2θ... center , (W det H det First, the position information (X, Y, Z) of a specific pixel (m, n) in the orthogonal coordinate system is calculated. Second, the position information (X, Y, Z) of the specific pixel (m, n) in the orthogonal coordinate system is represented by the orientation information (θ, η). Then, the orientation information (θ, η) of each pixel in the two-dimensional surface detector is calculated by solving the simultaneous equations.

[0105] Step S3: Combining the geometric model and orientation information of the diffraction experiment, set three intensity calibration factors: solid angle factor, polarization factor, and absorption factor, to calibrate the original diffraction intensity and form a diffraction intensity matrix C(θ, η). The solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation caused by the optical path difference between each pixel.

[0106] Step S4: Perform a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single crystal sample, referring to... Figure 4As shown, this represents the one-dimensional diffraction peak of a single crystal sample at a specific crystal plane or diffraction angle. By fitting and analyzing the overall diffraction peak curve using a Gaussian function, the overall diffraction peak information, including peak intensity 'a', is obtained. overall Peak position θ overall Standard deviation u overall .

[0107] Step S4 specifically includes:

[0108] Step S4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data;

[0109] Step S4.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i :

[0110]

[0111] Step S4.3: By analyzing set A i Calculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1);

[0112] Step S4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted;

[0113] Step S4.5: Define the objective function as mean squared error, i.e.

[0114] Step S4.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the overall diffraction peak information.

[0115] Step S5: Using θ overall With a overall The parameters are used to perform an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). (Refer to...) Figure 5 As shown, including peak position η RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M,

[0116] Specifically, step S5 includes:

[0117] Step S5.1: Using the overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data;

[0118] Step S5.2: Determine the range of azimuth angle η [η min η max ], and step size Δη1, define set B i :

[0119]

[0120] Step S5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve I. RC (θ1, η) i );

[0121] Step S5.4: Define the Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted;

[0122] Step S5.5: Define the objective function as mean squared error, i.e.

[0123] Step S5.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the parameters of the swing curve.

[0124] Step S6: Based on the rocking curve parameters, determine the main range of the diffraction peaks of each subgrain, and perform M 2θ subgrain scans to obtain the diffraction curves of each subgrain in the single crystal sample, referring to... Figure 6 As shown; using the Gaussian function, the diffraction curves of each subgrain are fitted and analyzed to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j .

[0125] Step S6 specifically includes:

[0126] Step S6.1: Determine the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data;

[0127] Step S6.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i :

[0128]

[0129] Step S6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve.

[0130] Step S6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted;

[0131] Step S6.5: Define the objective function as mean squared error, i.e.

[0132] Step S6.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain diffraction peak information.

[0133] Step S7: Using the diffraction experiment geometric model, combined with the subgrain diffraction peak information and rocking curve parameters, obtain the orientation information of the diffraction peaks of each subgrain, and then calculate the crystal plane orientation and spacing information in each subgrain.

[0134] Step S7 specifically includes:

[0135] Step S7.1: Combining the subgrain diffraction peak information and the rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j );

[0136] Step S7.2: Based on the geometric model of the diffraction experiment and the law of reflection, assume that the normal vector of the crystal plane in the subgrain is (X... j Z j Y j The following equations can be solved by combining them:

[0137]

[0138] Step S7.3: Based on the incident wavelength and diffraction angle, the interplanar spacing in the subgrains can be calculated using Bragg's law 2dsinθ=λ.

[0139] This invention also provides a two-dimensional diffraction data processing system for single-crystal materials. This system can be implemented by executing the steps of a two-dimensional diffraction data processing method for single-crystal materials. That is, those skilled in the art can understand the two-dimensional diffraction data processing method for single-crystal materials as a preferred embodiment of the two-dimensional diffraction data processing system for single-crystal materials. Specifically, the system includes the following:

[0140] Module M1: Based on the experimental and instrument setup, and combined with diffraction geometry, an orthogonal coordinate system (x, y, z) is defined. The origin is the optical center of the experiment, i.e., the intersection of all rotation axes of the sample. The positive x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule. The distance R from the sample to the detector is specified, and the angle 2θ between the detector center and the incident neutron beam is defined. center Detector size (W) det H det The detector pixel array number (M, N) and detector array index (m, n) are used to form the geometric model of the diffraction experiment.

[0141] Module M2: Based on the geometric model of the diffraction experiment, calculate the orientation information (θ, η) of each pixel in the two-dimensional surface detector, i.e., the angle θ between the line connecting a single pixel to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction. First, based on 2θ... center , (W det H det First, the position information (X, Y, Z) of a specific pixel (m, n) in the orthogonal coordinate system is calculated. Second, the position information (X, Y, Z) of the specific pixel (m, n) in the orthogonal coordinate system is represented by the orientation information (θ, η). Then, the orientation information (θ, η) of each pixel in the two-dimensional surface detector is calculated by solving the simultaneous equations.

[0142] Module M3: Combining the geometric model and orientation information of the diffraction experiment, three intensity calibration factors—solid angle factor, polarization factor, and absorption factor—are set to calibrate the original diffraction intensity, forming a diffraction intensity matrix C(θ, η). The solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation caused by the optical path difference between each pixel.

[0143] Module M4: Performs a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single-crystal sample, i.e., the one-dimensional diffraction peak of a certain crystal plane or specific diffraction angle of the single-crystal sample; uses a Gaussian function to fit and analyze the overall diffraction peak curve to obtain overall diffraction peak information, including peak intensity 'a'. overallPeak position θ overall Standard deviation u overall .

[0144] The M4 module specifically includes:

[0145] Module M4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data;

[0146] Module M4.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i :

[0147]

[0148] Module M4.3: By analyzing set A i Calculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1);

[0149] Module M4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted;

[0150] Module M4.5: Defines the objective function as mean squared error, i.e.

[0151] Module M4.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining overall diffraction peak information.

[0152] Module M5: Utilizing θ overall With a overall The parameters are analyzed by performing an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters, including the peak position η, are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M,

[0153] Specifically, module M5 includes:

[0154] Module M5.1: Utilizing overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data;

[0155] Module M5.2: By determining the range of azimuth angle η [η min η max ], and step size Δη1, define set B i :

[0156]

[0157] Module M5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve I. RC (θ1, η) i );

[0158] Module M5.4: Define Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted;

[0159] Module M5.5: Defines the objective function as mean squared error, i.e.

[0160] Module M5.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining the parameters of the swing curve.

[0161] Module M6: Based on the rocking curve parameters, determine the main range of each subgrain diffraction peak, perform M 2θ subgrain scans respectively to obtain the diffraction curves of each subgrain in the single crystal sample; use a Gaussian function to fit and analyze the diffraction curves of each subgrain to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j .

[0162] The M6 ​​module specifically includes:

[0163] Module M6.1: Determines the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data;

[0164] Module M6.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i :

[0165]

[0166] Module M6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve I. j (θ i η j );

[0167] Module M6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted;

[0168] Module M6.5: Defines the objective function as mean squared error, i.e.

[0169] Module M6.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining diffraction peak information.

[0170] Module M7: Using the geometric model of the diffraction experiment, combined with the subgrain diffraction peak information and rocking curve parameters, the orientation information of the diffraction peaks of each subgrain is obtained, thereby calculating the crystal plane orientation and spacing information in each subgrain.

[0171] The M7 module specifically includes:

[0172] Module M7.1: Combining subgrain diffraction peak information with rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j );

[0173] Module M7.2: Based on the geometric model of diffraction experiments and the law of reflection, it is assumed that the normal vector of the crystal plane in the subgrain is (X... j Z j Y j The following equations can be solved by combining them:

[0174]

[0175] Module M7.3: Based on the incident wavelength and diffraction angle, the interplanar spacing in the subgrains can be calculated using Bragg's law 2dsinθ=λ.

[0176] This invention provides a method and system for processing two-dimensional diffraction data of single-crystal materials. It analyzes two-dimensional surface detector diffraction data of single-crystal materials, achieving multi-directional compression from two-dimensional to one-dimensional data, thereby quantifying the anisotropic distribution of subgrains in the single-crystal material. This method integrates various two-dimensional diffraction data compression methods to obtain the one-dimensional overall diffraction curve, rocking curve, and subgrain diffraction curve of each subgrain in the sample. By fusing function fitting analysis methods, it achieves the separation of diffraction peaks of each subgrain and the quantitative characterization of crystal plane orientation and spacing.

[0177] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0178] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, 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. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for processing two-dimensional diffraction data of a single-crystal material, characterized in that, include: Step S1: Based on the experimental and instrument setup, and combined with diffraction geometry, define an orthogonal coordinate system (x, y, z) and form a diffraction experimental geometric model; where the origin of the orthogonal coordinate system is the optical center of the experiment, that is, the intersection of the rotation axes of the sample, the positive direction of the x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule. Step S2: Based on the geometric model of the diffraction experiment, calculate the orientation information (θ, η) of each pixel in the two-dimensional surface detector, that is, the angle θ between the line connecting a single pixel in the detector to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction. Step S3: Combining the geometric model and orientation information of the diffraction experiment, set three intensity calibration factors: solid angle factor, polarization factor, and absorption factor, to calibrate the original diffraction intensity and form a diffraction intensity matrix C(θ, η); where the solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation caused by the optical path difference between each pixel. Step S4: Perform a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single crystal sample, i.e., the one-dimensional diffraction peak of a certain crystal plane or a specific diffraction angle of the single crystal sample; use a Gaussian function to fit and analyze the overall diffraction peak curve to obtain the overall diffraction peak information, including peak intensity a. overall Peak position θ overall Standard deviation u overall ; Step S5: Using θ overall With a overall The parameters are analyzed by performing an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters, including the peak position η, are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M, Step S6: Based on the rocking curve parameters, determine the main range of each subgrain diffraction peak, and perform M 2θ subgrain scans to obtain the diffraction curves of each subgrain in the single crystal sample; use a Gaussian function to fit and analyze the diffraction curves of each subgrain to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j ; Step S7: Using the diffraction experiment geometric model, combined with the subgrain diffraction peak information and rocking curve parameters, obtain the orientation information of the diffraction peaks of each subgrain, and then calculate the crystal plane orientation and spacing information in each subgrain.

2. The two-dimensional diffraction data processing method for single-crystal materials according to claim 1, characterized in that, In the geometric model of the diffraction experiment, the distance R from the sample to the detector is specified, and the angle 2θ between the center of the detector and the incident neutron beam is defined. center Detector size (W) det H det The detector pixel count (M, N) and detector pixel index (m, n) are also specified. Calculating the orientation information (θ, η) of each pixel in a two-dimensional surface detector includes: First, according to 2θ center , (W det H det (M, N) calculates the position information (X, Y, Z) of a specific pixel (m, n) in an orthogonal coordinate system; Secondly, the position information (X, Y, Z) of a specific pixel (m, n) is used to represent the position information (X, Y, Z) in the orthogonal coordinate system. By solving the simultaneous equations, the position information (θ, η) of each pixel in the two-dimensional surface detector is calculated.

3. The method for processing two-dimensional diffraction data of single-crystal materials according to claim 1, characterized in that, Step S4 includes: Step S4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data; Step S4.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i : Step S4.3: By analyzing set A i Calculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1); Step S4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted; Step S4.5: Define the objective function as mean squared error, i.e. Step S4.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the overall diffraction peak information.

4. The method for processing two-dimensional diffraction data of single-crystal materials according to claim 1, characterized in that, Step S5 includes: Step S5.1: Using the overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data; Step S5.2: Determine the range of azimuth angle η [η min η max ], and step size Δη1, define set B i : Step S5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve I. RC (θ1, η) i ); Step S5.4: Define the Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted; Step S5.5: Define the objective function as mean squared error, i.e. Step S5.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain the parameters of the swing curve.

5. The method for processing two-dimensional diffraction data of single-crystal materials according to claim 1, characterized in that, Step S6 includes: Step S6.1: Determine the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data; Step S6.2: Determine the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i : Step S6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve I. j (θ i η j ); Step S6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted; Step S6.5: Define the objective function as mean squared error, i.e. Step S6.6: Use the least squares algorithm to adjust the parameters to be fitted and reduce the objective function to obtain diffraction peak information.

6. The method for processing two-dimensional diffraction data of single-crystal materials according to claim 1, characterized in that, Step S7 includes: Step S7.1: Combining the subgrain diffraction peak information and the rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j ); Step S7.2: Based on the geometric model of the diffraction experiment and the law of reflection, let the normal vector of the crystal plane in the subgrain be (X... j Z j Y j Solve by solving the following equations simultaneously: Step S7.3: Based on the incident wavelength and diffraction angle, use Bragg's law 2dsinθ=λ to solve for the interplanar spacing in the subgrains.

7. A two-dimensional diffraction data processing system for single-crystal materials, characterized in that, include: Module M1: Based on the experimental and instrument setup, and combined with diffraction geometry, define an orthogonal coordinate system (x, y, z) and form a diffraction experimental geometric model; where the origin of the orthogonal coordinate system is the optical center of the experiment, that is, the intersection of the rotation axes of the sample, the positive direction of the x-axis coincides with the direction of the incident neutron beam, the z-axis is vertically upward, and the y-axis is determined according to the right-hand rule. Module M2: Based on the geometric model of the diffraction experiment, calculate the orientation information (θ, η) of each pixel in the two-dimensional surface detector, that is, the angle θ between the line connecting a single pixel in the detector to the optical center and the incident neutron beam, and the angle η between the line connecting a single pixel to the detector center and the positive z-axis direction, where clockwise is defined as the positive direction. Module M3: Combining the geometric model and orientation information of the diffraction experiment, three intensity calibration factors—solid angle factor, polarization factor, and absorption factor—are set to calibrate the original diffraction intensity, forming a diffraction intensity matrix C(θ, η). The solid angle factor is used to calibrate the deviation of the probability of receiving neutrons caused by the scattering cross-sectional area of ​​the pixel, the polarization factor is used to correct the signal deviation caused by the calibration of linear polarization, and the absorption factor is used to calibrate the signal deviation between pixels caused by the optical path difference. Module M4: Performs a 2θ scan on the diffraction intensity matrix to obtain the overall diffraction peak curve of the single-crystal sample, i.e., the one-dimensional diffraction peak of a certain crystal plane or specific diffraction angle of the single-crystal sample; uses a Gaussian function to fit and analyze the overall diffraction peak curve to obtain overall diffraction peak information, including peak intensity 'a'. overall Peak position θ overall Standard deviation u overall ; Module M5: Utilizing θ overall With a overall The parameters are analyzed by performing an η-scan to obtain the rocking curve of the single-crystal sample. By determining the number M of subgrains in the single-crystal sample, the rocking curve parameters, including the peak position η, are obtained through fitting analysis using a Gaussian mixture function (i.e., the linear superposition of multiple Gaussian functions). RC，j Standard deviation u RC，j Peak strength b RC，j Where 1≤j≤M, Module M6: Based on the rocking curve parameters, determine the main range of each subgrain diffraction peak, perform M 2θ subgrain scans respectively to obtain the diffraction curves of each subgrain in the single crystal sample; use a Gaussian function to fit and analyze the diffraction curves of each subgrain to obtain subgrain diffraction peak information, including peak position θ. j Standard deviation u j Peak strength a j ; Module M7: Using the geometric model of diffraction experiments, combined with the subgrain diffraction peak information and rocking curve parameters, the orientation information of the diffraction peaks of each subgrain is obtained, thereby calculating the crystal plane orientation and spacing information in each subgrain.

8. The two-dimensional diffraction data processing system for single-crystal materials according to claim 7, characterized in that, In the geometric model of the diffraction experiment, the distance R from the sample to the detector is specified, and the angle 2θ between the center of the detector and the incident neutron beam is defined. center Detector size (W) det H d酡 The detector pixel count (M, N) and detector pixel index (m, n) are also specified. Calculating the orientation information (θ, η) of each pixel in a two-dimensional surface detector includes: First, according to 2θ center , (W det H det (M, N) calculates the position information (X, Y, Z) of a specific pixel (m, n) in an orthogonal coordinate system; Secondly, the position information (X, Y, Z) of a specific pixel (m, n) is used to represent the position information (X, Y, Z) in the orthogonal coordinate system. By solving the simultaneous equations, the position information (θ, η) of each pixel in the two-dimensional surface detector is calculated.

9. The two-dimensional diffraction data processing system for single-crystal materials according to claim 7, characterized in that, The module M4 includes: Module M4.1: By determining the center azimuth angle η1 and the azimuth range δη1, the condition will be satisfied. C(θ, η) is used as the effective diffraction intensity data; Module M4.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A i : Module M4.3: By analyzing set A i Calculate the average value of the diffraction intensities to determine the overall diffraction peak curve I. overall (θ i ,η1); Module M4.4: Define the Gaussian function Let a be the fitting function, where a overall θ overall u overall b overall These are the parameters to be fitted; Module M4.5: Defines the objective function as mean squared error, i.e. Module M4.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining overall diffraction peak information.

10. The two-dimensional diffraction data processing system for single-crystal materials according to claim 7, characterized in that, The module M5 includes: Module M5.1: Utilizing overall diffraction peak information, determine the central diffraction angle θ1 and the diffraction angle range δθ1, satisfying... C(θ, η) is used as the effective diffraction intensity data; Module M5.2: By determining the range of azimuth angle η [η min η max ], and step size Δη1, define set B i : Module M5.3: By analyzing set B i Calculate the average value of the diffraction intensity to determine the rocking curve IR. C (θ1, η) i ); Module M5.4: Define Gaussian mixture function Let a be the fitting function, where a RC，j η RC，j u RC，j b RC，j These are the parameters to be fitted; Module M5.5: Defines the objective function as mean squared error, i.e. Module M5.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining the parameters of the swing curve; The module M6 includes: Module M6.1: Determines the center azimuth angle η j and the azimuth range δη j , will satisfy C(θ, η) is used as the effective diffraction intensity data; Module M6.2: By determining the range of diffraction angle θ [θ min θ max ], and step size Δθ1, define set A j，i : Module M6.3: By analyzing set A j，i Calculate the average value of the diffraction intensities to determine the subgrain diffraction peak curve I. j (θ i η j ); Module M6.4: Define the Gaussian function Let a be the fitting function, where a j θ j u j b j These are the parameters to be fitted; Module M6.5: Defines the objective function as mean squared error, i.e. Module M6.6: Utilizes the least squares algorithm to adjust the parameters to be fitted and reduce the objective function, thereby obtaining diffraction peak information; The module M7 includes: Module M7.1: Combining subgrain diffraction peak information with rocking curve parameters, determine the orientation information of each subgrain diffraction peak as (θ). j η RC，j ); Module M7.2: Based on the geometric model of diffraction experiments and the law of reflection, let the normal vector of the crystal plane in the subgrain be (X...) in the orthogonal coordinate system. j Z j Y j Solve by solving the following equations simultaneously: Module M7.3: Based on the incident wavelength and diffraction angle, use Bragg's law 2dsinθ=λ to solve for the interplanar spacing in the subgrains.

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