Analysis method of nano-particle size distribution and related product
By inverting the size distribution of nanoparticles using XRD patterns, constructing the total kernel matrix, and solving the particle size distribution vector, the problem of insufficient analytical precision in existing technologies is solved, and high-precision analysis of nanoparticle size distribution is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-15
- Publication Date
- 2026-04-03
AI Technical Summary
Existing methods for analyzing the size distribution of nanoparticles rely on dynamic light scattering techniques, which cannot accurately reflect the true size distribution of the original nanoparticles within the aggregates, resulting in poor analytical accuracy.
By obtaining the XRD patterns of nanoparticle samples, the target peak range is determined, the total kernel matrix is constructed, and the particle size distribution vector is solved using the nonlinear least squares method in combination with preset constraints and difference matrices, thus obtaining the distribution information of the original nanoparticles inside the agglomeration.
While ensuring analytical efficiency, the accuracy of nanoparticle size distribution analysis has been improved, enabling accurate acquisition of the distribution information of original nanoparticles within agglomerates.
Smart Images
Figure CN121784043A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of nanoparticle detection technology, and in particular to an analytical method for nanoparticle size distribution and related products. Background Technology
[0002] Nanoparticles refer to ultrafine particles with a size between 1 nanometer and 100 nanometers. They are widely used in many fields (such as catalysis, electrochemical energy storage, fuel cells, water electrolysis, and medicine), and their performance largely depends on the nanoparticle size and its distribution. Therefore, for nanoparticle systems with obvious aggregation behavior or a very small number of particles at the hundred-nanometer level, it is often necessary to understand their particle size distribution.
[0003] Existing nanoparticle size distribution analysis relies heavily on dynamic light scattering (DLS) technology. However, for powder samples with severe agglomeration, the scattering of light cannot obtain the scattering results of individual particles inside the agglomeration. Therefore, the analysis results often fail to reflect the true size distribution of the original nanoparticles inside the agglomeration, resulting in poor analytical accuracy.
[0004] Therefore, how to improve analytical accuracy while ensuring analytical efficiency is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0005] To address the aforementioned issues, this application provides a method and related products for analyzing the size distribution of nanoparticles. This method can invert the particle size distribution and obtain the distribution information of the original nanoparticles within the agglomerates using only X-ray diffraction (XRD) patterns, thereby improving analytical accuracy while ensuring analytical efficiency.
[0006] In a first aspect, embodiments of this application provide a method for analyzing the size distribution of nanoparticles, including: Obtain the XRD pattern corresponding to the nanoparticle sample to be tested; The target peak interval is determined based on the XRD pattern; the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern. A total kernel matrix is constructed based on a preset particle size grid and the target peak interval; The particle size distribution vector is determined based on the total kernel matrix and the preset difference matrix, taking into account preset constraints. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the particle size distribution vector.
[0007] Optionally, determining the target peak interval based on the XRD pattern includes: Determine the target diffraction peaks from the XRD pattern; Determine the lateral position of the target corresponding to the target diffraction peak; Based on the preset fluctuation range, the lateral position interval corresponding to the target diffraction peak is determined according to the target lateral position, and the lateral position interval is taken as the target peak interval.
[0008] Optionally, the method further includes: Determine the preset particle size range and preset particle size step size; Discretize the preset particle size range based on the preset particle size step size to obtain a preset particle size grid; The size broadening of the target diffraction peak and each particle size point in the preset particle size grid is determined based on the Scherrer-type relationship.
[0009] Optionally, the step of constructing the total kernel matrix based on the preset particle size grid and the target peak interval includes: Determine the peak shape parameters corresponding to each particle size point in the preset particle size grid; the peak shape parameters include peak width parameters and shape parameters; Based on the peak shape parameters and the target peak interval, determine the target peak shape function corresponding to each particle size point in the preset particle size grid and each target diffraction peak; Based on the target peak shape function, the target angle grid is determined according to the target peak interval and the actual step size; Determine the theoretical diffraction intensity value of each particle size point in the preset particle size grid corresponding to each angle point in the target angle grid; The theoretical intensity vector corresponding to each particle size point is determined based on the theoretical diffraction intensity value. The total kernel matrix is obtained by concatenating the theoretical intensity vectors.
[0010] Optionally, the method further includes: The data points to be deducted are determined based on the target peak interval; the data points to be deducted are located at both ends of the target peak interval; Based on a polynomial, background fitting is performed on the data points to be deducted, and the data points to be deducted are then deducted.
[0011] Optionally, determining the particle size distribution vector based on the total kernel matrix and the preset difference matrix, in conjunction with preset constraints, includes: Determine the regularization parameters; Based on the regularization parameter, the total kernel matrix, and the preset difference matrix, a set of regularized target augmented equations is constructed. Based on the preset constraints, the target augmented equations are solved using the non-negative least squares (NNLS) method, and the particle size distribution vector is obtained.
[0012] Optionally, determining the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector includes: The particle size distribution vector is segmented based on the number of target diffraction peaks to obtain the corresponding target sub-distribution; Normalize each target sub-distribution and obtain the corresponding target result value; Based on the target result value, maximum detection is performed to obtain the local peak set corresponding to each target sub-distribution; A target index set is constructed by combining the preset particle size grid and the local peak set; Determine the intra-peak component parameters corresponding to each local peak set; the intra-peak component parameters include component center particle size, component weight, and intra-peak proportion; By combining the target index set and the intra-peak component parameters, cross-peak global component normalization is performed to obtain the global relative proportion of each component. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the global relative proportion.
[0013] Secondly, embodiments of this application provide an analytical apparatus for the size distribution of nanoparticles, comprising: The acquisition module is used to acquire the XRD pattern corresponding to the nanoparticle sample to be tested; The first determining module is used to determine the target peak interval based on the XRD pattern; the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern; The construction module is used to construct the total kernel matrix based on the preset particle size grid and the target peak interval; The second determining module is used to determine the particle size distribution vector based on the total kernel matrix and the preset difference matrix, in conjunction with preset constraints. The third determining module is used to determine the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector.
[0014] Thirdly, embodiments of this application provide an analytical device for nanoparticle size distribution, including: a memory for storing computer programs; A processor is used to execute the computer program to implement the steps of the analytical method for nanoparticle size distribution as described above.
[0015] Fourthly, embodiments of this application provide a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for analyzing the size distribution of nanoparticles as described above.
[0016] As can be seen from the above technical solutions, compared with the prior art, this application has the following advantages: The present application provides a method for analyzing the size distribution of nanoparticles. First, the XRD pattern of the nanoparticle sample to be tested is obtained. Then, a target peak interval is determined based on the XRD pattern. The target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern. Next, a total kernel matrix is constructed based on a preset particle size grid and the target peak interval. Finally, combined with preset constraints, a particle size distribution vector is determined based on the total kernel matrix and a preset difference matrix, and a particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the particle size distribution vector. Thus, particle size distribution inversion can be completed with only the XRD pattern, and the distribution information of the original nanoparticles within the aggregates can be obtained, thereby improving analytical accuracy while ensuring analytical efficiency. Attached Figure Description
[0017] Figure 1 A flowchart illustrating a method for analyzing the size distribution of nanoparticles provided in this application embodiment; Figure 2 This application provides a schematic diagram of the overall grain size distribution and a locally magnified size distribution. Figure 3 This is a schematic diagram of the structure of an analytical device for analyzing the size distribution of nanoparticles provided in an embodiment of this application. Detailed Implementation
[0018] As mentioned earlier, existing methods for analyzing nanoparticle size distribution suffer from low analytical accuracy. Specifically, most current methods rely on DLS (Diffraction Linear Sequencing) technology, which uses the Brownian motion velocity of particles in a dispersion medium to infer the hydrated particle size. However, for powder samples with severe agglomeration, light scattering cannot capture the scattering results of individual particles within the agglomerates. Even with ultrasonic treatment and dispersants, only the scattering results of the agglomerates or large clusters are often obtained, thus only providing the equivalent particle size information of the agglomerates and failing to reflect the true size distribution of the original nanoparticles within the agglomerates. This results in the poor analytical accuracy of existing methods.
[0019] To address the aforementioned issues, this application provides a method for analyzing the size distribution of nanoparticles, comprising: first, acquiring the XRD pattern corresponding to the nanoparticle sample to be tested; then, determining the target peak interval based on the XRD pattern, wherein the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern; next, constructing a total kernel matrix based on a preset particle size grid and the target peak interval; finally, determining the particle size distribution vector based on the total kernel matrix and a preset difference matrix, and determining the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector, in conjunction with preset constraints.
[0020] Thus, particle size distribution can be inverted using only XRD patterns, and the distribution information of the original nanoparticles inside the agglomerates can be obtained, thereby improving analytical accuracy while ensuring analytical efficiency.
[0021] It should be noted that the method and related products for analyzing the size distribution of nanoparticles provided in this application can be applied to the field of nanoparticle detection technology. The above are merely examples and do not limit the application areas of the method and related products for analyzing the size distribution of nanoparticles provided in this application.
[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0023] Figure 1 This is a flowchart illustrating a method for analyzing the size distribution of nanoparticles, provided as an embodiment of this application. (In conjunction with...) Figure 1 As shown in the embodiments of this application, a method for analyzing the size distribution of nanoparticles may include: S101: Obtain the XRD pattern corresponding to the nanoparticle sample to be tested.
[0024] In practical applications, the embodiments of this application can complete the inversion of particle size distribution and obtain the distribution information of the original nanoparticles inside the agglomerates using only XRD patterns. Therefore, the first step is to obtain the standard data file (diffraction intensity – 2θ data), i.e., the XRD pattern, corresponding to the nanoparticle sample to be tested, using a powder XRD instrument. Taking a Pt / C catalyst powder sample as an example, the corresponding XRD instrument can be a laboratory powder XRD instrument with a Cu Kα target (λ≈0.15406 nm), with a scanning range of 10° to 90° and a step size of 0.02°. It is understood that this method is also applicable to other nanocrystalline systems such as oxides, metal alloys, and organic crystals. The Pt / C catalyst powder sample is only one example, not the only nanoparticle sample to be tested. Correspondingly, different nanoparticle samples require different XRD instruments, which can be adjusted according to the actual situation. The corresponding scanning step size and particle size grid accuracy can also be adjusted according to the actual testing requirements.
[0025] S102: Determine the target peak interval based on the XRD pattern; the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern.
[0026] In practical applications, to avoid the shift of the strongest diffraction peak caused by the height difference of the powder on the testing stage, this application also introduces the concept of a target peak interval. The small lateral position interval (2θ interval) at both ends of the target diffraction peak in the XRD pattern is used as the target peak interval for subsequent calculations. Any diffraction peak in the XRD pattern can be a target diffraction peak, and the target peak interval can include the 2θ interval corresponding to any one or more target diffraction peaks in the XRD pattern. For example, the target diffraction peak can be the strongest peak in the XRD pattern, or it can be a crystal plane such as (111), (200), or (220) of a nanocrystalline material.
[0027] Furthermore, since there are different ways to determine the target peak range, this application embodiment can describe one possible determination method.
[0028] In one case, S102: Determining the target peak interval based on the XRD pattern may specifically include: Determine the target diffraction peaks from the XRD pattern; Determine the lateral position of the target corresponding to the target diffraction peak; Based on the preset fluctuation range, the lateral position interval corresponding to the target diffraction peak is determined according to the target lateral position, and the lateral position interval is taken as the target peak interval.
[0029] In practical applications, target diffraction peaks can be selected from the XDR spectrum first, and then the corresponding lateral positions (i.e., 2θ) of the target diffraction peaks can be determined. For example, the 2θ corresponding to the three selected target diffraction peaks are 67.5°, 81.3°, and 85.7°, which correspond to Pt(220), (311), and (222). Furthermore, combined with a preset fluctuation range (e.g., ±1.5°), the lateral position intervals corresponding to the three target diffraction peaks can be obtained as (66°-69°), (79.8°-82.8°), and (84.2°-87.2°), and the obtained 2θ intervals can be used as the determined target peak intervals. It is understandable that the number of target diffraction peaks and 2θ can also be other values. Similarly, the preset fluctuation range can also be other values, which can be adjusted according to actual testing requirements. In addition, for each 2θ interval, it is also necessary to determine and record the X-ray wavelength selected by the testing instrument as the basic parameter for subsequent kernel matrix construction.
[0030] S103: Construct a total kernel matrix based on the preset particle size grid and the target peak interval.
[0031] In practical applications, the preset particle size grid discretizes the continuous size distribution, defining the coordinate system for solving the problem. The kernel matrix, on the other hand, is a dictionary of physical laws within this coordinate system, quantitatively answering the fundamental question of what the instrument would observe if all particles were of a certain size. Because the kernel matrix clearly defines the physical mapping relationship from "size distribution" to "measurement data," we use it as the basis for numerical solutions, formulating the inversion problem by first constructing the overall kernel matrix between the preset particle size grid and the target peak interval after determining the target peak interval.
[0032] Furthermore, since there are different ways to construct the particle size grid, this application embodiment can describe one possible construction method.
[0033] In one instance, the method further includes: Determine the preset particle size range and preset particle size step size; Discretize the preset particle size range based on the preset particle size step size to obtain a preset particle size grid; The size broadening of the target diffraction peak and each particle size point in the preset particle size grid is determined based on the Scherrer-type relationship.
[0034] In practical applications, the preset particle size range [D_min, D_max] and preset particle size step size ΔD are first determined. D_min is typically 0.1-1 nm, while ΔD is typically 0.05–0.5 nm, and can be adjusted according to actual needs. Then, within the preset particle size range [D_min, D_max], the particle size is discretized with the preset particle size step size ΔD, resulting in a set of particle size grids, i.e., the preset particle size grid D = { , Furthermore, for each particle size point D_j in the preset particle size grid D, the corresponding size expansion β(D_j) needs to be determined according to the Scherrer type relation or its equivalent expression. For each particle size point D_j, the corresponding size expansion expression is as follows: β(D_j) ∝ λ / (D_j×cos(θ)); In the formula, β(D_j) is the size broadening corresponding to the particle size point D_j, λ is the X-ray wavelength, D_j is the particle size, and θ is half of the diffraction angle (i.e., the Bragg angle).
[0035] Furthermore, since the methods for constructing the total kernel matrix are not entirely the same, this application embodiment can describe one possible construction method.
[0036] In one case, S103: Constructing a total kernel matrix based on a preset particle size grid and the target peak interval, which may specifically include: Determine the peak shape parameters corresponding to each particle size point in the preset particle size grid; the peak shape parameters include peak width parameters and shape parameters; Based on the peak shape parameters and the target peak interval, determine the target peak shape function corresponding to each particle size point in the preset particle size grid and each target diffraction peak; Based on the target peak shape function, the target angle grid is determined according to the target peak interval and the actual step size; Determine the theoretical diffraction intensity value of each particle size point in the preset particle size grid corresponding to each angle point in the target angle grid; The theoretical intensity vector corresponding to each particle size point is determined based on the theoretical diffraction intensity value. The total kernel matrix is obtained by concatenating the theoretical intensity vectors.
[0037] In practical applications, a parameterized peak shape function can be used as the diffraction peak line shape model. Correspondingly, it is first necessary to determine the peak shape parameters corresponding to each particle size point D_j in the preset particle size grid. The peak shape function can be Pearson VII, Gaussian, Lorentzian, Voigt, pseudo-Voigt, Split pseudo-Voigt, or a combination thereof. The peak shape parameters include the peak width parameter γ(D_j) and the shape parameter. Taking Pearson VII as an example, the peak shape parameters corresponding to each particle size point D_j in the preset particle size grid that need to be determined include the peak width parameter γ(D_j) and the shape parameter m(D_j), where m(D_j) varies linearly with D and its value is in the range of 0.5–5.0. If pseudo-Voigt is selected, the peak shape parameters corresponding to each particle size point D_j in the preset particle size grid that need to be determined include the peak width parameter γ(D_j) and the mixing coefficient η(D_j). Further, continuing with Pearson VII as an example, it is necessary to calculate the 2θ position corresponding to each target diffraction peak at Kα1 and Kα2 respectively. Then, according to the actual intensity ratio of the experimental equipment (e.g., 2:1), the two peak shape functions of Kα1 and Kα2 are superimposed to form the "double-peak superposition line shape basis function" corresponding to each particle size point D_j in the preset particle size grid and each target diffraction peak, i.e., the target peak shape function. Then, combined with the target peak shape function, within each 2θ interval, a discrete target angle grid {2θ_i}, i = 1…M, is generated according to the actual step size Δ2θ (the scanning step size of the XRD instrument used to obtain the XRD pattern, e.g., 0.02). The theoretical diffraction intensity value of each particle size point D_j at each angle point 2θ_i in the target angle grid is calculated to form a theoretical intensity vector of length M. The kernel matrix of the current target diffraction peak is obtained by concatenating the theoretical intensity vectors corresponding to all particle size points in the preset particle size grid column by column. The total kernel matrix P can be obtained by combining the kernel matrices of multiple target diffraction peaks by row concatenation or diagonal concatenation. Furthermore, the total kernel matrix P holds the following relationship: y ≈ P ·f; In the formula, y is the column vector obtained by stitching together the measured intensities of the target peak interval (after background subtraction), P is the total kernel matrix, and f is the unknown particle size-volume fraction distribution vector. In this way, by incorporating the line shapes corresponding to multiple Bragg peaks into the kernel matrix, multiple constraints on the same particle size distribution are formed, which is more conducive to distinguishing size broadening from other factors and improving the reliability of the inversion results.
[0038] Furthermore, since the methods of background subtraction are not entirely the same, this application embodiment can describe one possible subtraction method.
[0039] In one instance, the method further includes: The data points to be deducted are determined based on the target peak interval; the data points to be deducted are located at both ends of the target peak interval; Based on a polynomial, background fitting is performed on the data points to be deducted, and the data points to be deducted are then deducted.
[0040] In practical applications, an optimization loop for the target diffraction peak center 2θ can be introduced during the inversion solution process. By minimizing the residual ||Pf - y||, peak position offsets caused by instrument zero-point drift, lattice constant changes, or differences in powder sample stage height can be automatically corrected. For background subtraction, linear or polynomial fitting methods can be used. Specifically, taking polynomial fitting for background subtraction as an example, several points (data points to be subtracted) can be selected from the left and right edges of each target peak interval. Then, a (first- or second-order) polynomial is used to fit the background curve to subtract the data points to be subtracted. The measured intensities after background subtraction are then spliced together to obtain y, and normalized to the maximum value.
[0041] S104: Combine the preset constraints and determine the particle size distribution vector based on the total kernel matrix and the preset difference matrix.
[0042] In practical applications, a smoothing constraint can be applied to adjacent particle size points by constructing a (preset) difference matrix, and then a regularized augmented equation system can be constructed based on the total kernel matrix and the preset difference matrix. Under the preset constraint conditions, the corresponding particle size distribution vector can be obtained by using NNLS to solve it.
[0043] Furthermore, since there are different ways to determine the particle size distribution vector, this application embodiment can describe one possible determination method.
[0044] In one scenario, S104: Based on the total kernel matrix and the preset difference matrix, a particle size distribution vector is determined by combining preset constraints. Specifically, this may include: Determine the regularization parameters; Based on the regularization parameter, the total kernel matrix, and the preset difference matrix, a set of regularized target augmented equations is constructed. Based on the preset constraints, the target augmented equations are solved using NNLS to obtain the particle size distribution vector.
[0045] In practical applications, a pre-defined difference matrix L is first needed to constrain the smoothness of the particle size distribution vector's variation between adjacent particle size points. L can be a first-order difference matrix or a higher-order difference matrix. Taking a first-order and a second-order difference matrix as examples, their corresponding expressions are as follows: (Lf)k = f_{k+1} - f_k, k=1,…,N-1; (Lf)k=f_{k+2}-2f_{k+1}+f_k, k=1,…,N-2; Furthermore, select regularization parameters. And construct the objective function with Tikhonov regularization, the corresponding objective function expression is as follows: J(f) =‖P f - y‖ 2 2+ ‖L f‖ 2 2; in, This is a regularization parameter, which can be adjusted by the user based on the fitting residuals and smoothness, typically between 0.01 and 0.1. Then, given the peak center parameter... And the preset constraint f_j ≥ 0, In the case of j, a regularized augmented system of equations is constructed, and its expression is as follows: ; Then, under preset constraints, a numerical algorithm combining NNLS and regularization is used to solve the optimization problem, and the final particle size distribution vector is obtained. Thus, by using nonnegativity constraints to ensure the absence of "negative volume fractions," and by using first-order or second-order and higher-order difference regularization to suppress high-frequency oscillations, spurious oscillation peaks caused by ill-conditioned problems are avoided, thereby improving the interpretability of the results.
[0046] S105: Determine the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector.
[0047] In practical applications, the particle size distribution curve corresponding to the obtained continuous particle size distribution vector is discretized or fuzzified, and methods such as nearest peak assignment, Gaussian fitting, threshold segmentation, or cluster analysis are used to refine the calculated particle size distribution vector. Feature extraction is performed to obtain the volume fraction of each mode, which in turn determines the particle size distribution curve corresponding to the nanoparticle sample to be tested.
[0048] Furthermore, since there are different ways to determine the particle size distribution curve, the embodiments of this application can describe one possible determination method.
[0049] In one case, S105: determining the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector, specifically including: The particle size distribution vector is segmented based on the number of target diffraction peaks to obtain the corresponding target sub-distribution; Normalize each target sub-distribution and obtain the corresponding target result value; Based on the target result value, maximum detection is performed to obtain the local peak set corresponding to each target sub-distribution; A target index set is constructed by combining the preset particle size grid and the local peak set; Determine the intra-peak component parameters corresponding to each local peak set; the intra-peak component parameters include component center particle size, component weight, and intra-peak proportion; By combining the target index set and the intra-peak component parameters, cross-peak global component normalization is performed to obtain the global relative proportion of each component. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the global relative proportion.
[0050] In practical applications, the particle size distribution vector obtained above first needs to be processed. The target is segmented according to the number of diffraction peaks, resulting in K target sub-distributions. , where each target sub-distribution The particle size contribution distribution corresponds to a diffraction peak of a target. Then, for each target sub-distribution... Normalizing it by its maximum value yields the following normalization expression: ; In the formula, The normalized target result value, For primitive functions, This is the maximum value of the function. Then... Perform local maximum detection and obtain a set of local peaks. Local peak detection can be configured with a minimum peak height threshold (e.g., 0.001) and a minimum peak spacing, based on actual needs. Furthermore, a nearest-peak assignment method is used to assign each particle size point D_j on the preset particle size grid to the nearest local peak center, thereby dividing the entire particle size axis within the peak into several non-overlapping target index sets. The target index set satisfies "full coverage". Then, the parameters of the intra-peak components are calculated. For each intra-peak component, its component center particle size, component weight, and corresponding intra-peak proportion need to be determined, and the target index set corresponding to each component is recorded for subsequent decomposition, fitting of curves, or data export. Among these, the component center particle size... That is, the local peak position; component weight. Peak proportion Next, cross-peak global component normalization is performed to achieve a comparison of component intensities between different target derived peaks. Specifically, the component area of all components within all target diffraction peaks is first calculated, and the calculation expression is as follows:
[0051] In the formula Let the component area be the total area. Then, take the largest component area globally. As a 100% reference, each component is converted into a global relative proportion, thus obtaining the global relative proportion corresponding to each component. The corresponding expression for the global relative proportion is as follows:
[0052] In the formula This represents the global relative proportion. Figure 2 This is a schematic diagram illustrating the overall grain size distribution and a locally magnified size distribution, provided as an embodiment of this application. (Combined with...) Figure 2 As shown, assuming the target diffraction peaks include peak 1, peak 2, and peak 3, the corresponding XRD fitting curves are plotted by statistically analyzing the global relative proportions of each component (e.g., ...). Figure 2 a) The particle size distribution curves corresponding to the nanoparticle sample to be tested (e.g.) Figure 2 (b) in the above example is used to analyze the size distribution of the nanoparticle sample. Furthermore, the particle size distribution curve can be locally magnified to obtain the corresponding locally magnified size distribution results (e.g., ...). Figure 2 (c) Thus, starting from the diffraction line width of the crystal, the inversion retrieves the size distribution at the grain / nanoparticle level, rather than the equivalent size of the aggregate. Even if the sample is in a severely aggregated state, as long as the crystal still has clear diffraction peaks, the distribution information of the original nanoparticles inside the aggregate can be obtained. In addition, the embodiments of this application do not preset a specific distribution type at the numerical inversion level, but obtain a continuous particle size distribution through non-negative regularization inversion, and then automatically identify one or more peaks, thereby quantifying the central particle size and volume fraction of each peak, which is more suitable for the complex distribution characteristics of real industrial nanomaterials.
[0053] In summary, this application first obtains the XRD pattern corresponding to the nanoparticle sample to be tested. Then, the target peak interval is determined based on the XRD pattern. The target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern. Next, a total kernel matrix is constructed based on a preset particle size grid and the target peak interval. Finally, combined with preset constraints, the particle size distribution vector is determined based on the total kernel matrix and a preset difference matrix, and the particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the particle size distribution vector. Thus, particle size distribution inversion can be completed with only the XRD pattern, and the distribution information of the original nanoparticles within the aggregates can be obtained, thereby improving analytical accuracy while ensuring analytical efficiency.
[0054] Figure 3 This is a schematic diagram of a nanoparticle size distribution analysis device provided in an embodiment of this application. (Combined with...) Figure 3 As shown, the nanoparticle size distribution analysis device 300 includes: The acquisition module 301 is used to acquire the XRD pattern corresponding to the nanoparticle sample to be tested; The first determining module 302 is used to determine the target peak interval based on the XRD pattern; the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern; Construction module 303 is used to construct a total kernel matrix based on a preset particle size grid and the target peak interval; The second determining module 304 is used to determine the particle size distribution vector based on the total kernel matrix and the preset difference matrix, in conjunction with preset constraints. The third determining module 305 is used to determine the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector.
[0055] As one implementation method, regarding how to determine the target peak interval, the first determining module 302 is specifically used for: Determine the target diffraction peaks from the XRD pattern; Determine the lateral position of the target corresponding to the target diffraction peak; Based on the preset fluctuation range, the lateral position interval corresponding to the target diffraction peak is determined according to the target lateral position, and the lateral position interval is taken as the target peak interval.
[0056] As one implementation method, the above-mentioned nanoparticle size distribution analysis device 300 further includes a discrete module for obtaining a preset particle size grid; The discrete module is used to determine the preset particle size range and the preset particle size step size; Discretize the preset particle size range based on the preset particle size step size to obtain a preset particle size grid; The size broadening of the target diffraction peak and each particle size point in the preset particle size grid is determined based on the Scherrer-type relationship.
[0057] As one implementation method, regarding how to construct the total kernel matrix, the aforementioned construction module 303 is specifically used for: Determine the peak shape parameters corresponding to each particle size point in the preset particle size grid; the peak shape parameters include peak width parameters and shape parameters; Based on the peak shape parameters and the target peak interval, determine the target peak shape function corresponding to each particle size point in the preset particle size grid and each target diffraction peak; Based on the target peak shape function, the target angle grid is determined according to the target peak interval and the actual step size; Determine the theoretical diffraction intensity value of each particle size point in the preset particle size grid corresponding to each angle point in the target angle grid; The theoretical intensity vector corresponding to each particle size point is determined based on the theoretical diffraction intensity value. The total kernel matrix is obtained by concatenating the theoretical intensity vectors.
[0058] As one implementation method, the above-mentioned nanoparticle size distribution analysis device 300 further includes a subtraction module to achieve background subtraction; The deduction module is used to determine the data points to be deducted based on the target peak interval; the data points to be deducted are located at both ends of the target peak interval; Based on a polynomial, background fitting is performed on the data points to be deducted, and the data points to be deducted are then deducted.
[0059] As one implementation method, regarding how to determine the particle size distribution vector, the second determining module 404 is specifically used for: Determine the regularization parameters; Based on the regularization parameter, the total kernel matrix, and the preset difference matrix, a set of regularized target augmented equations is constructed. Based on the preset constraints, the target augmented equations are solved using NNLS to obtain the particle size distribution vector.
[0060] As one implementation method, regarding how to determine the particle size distribution curve, the aforementioned third determining module 305 is specifically used for: The particle size distribution vector is segmented based on the number of target diffraction peaks to obtain the corresponding target sub-distribution; Normalize each target sub-distribution and obtain the corresponding target result value; Based on the target result value, maximum detection is performed to obtain the local peak set corresponding to each target sub-distribution; A target index set is constructed by combining the preset particle size grid and the local peak set; Determine the intra-peak component parameters corresponding to each local peak set; the intra-peak component parameters include component center particle size, component weight, and intra-peak proportion; By combining the target index set and the intra-peak component parameters, cross-peak global component normalization is performed to obtain the global relative proportion of each component. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the global relative proportion.
[0061] In summary, this application first obtains the XRD pattern corresponding to the nanoparticle sample to be tested. Then, the target peak interval is determined based on the XRD pattern. The target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern. Next, a total kernel matrix is constructed based on a preset particle size grid and the target peak interval. Finally, combined with preset constraints, the particle size distribution vector is determined based on the total kernel matrix and a preset difference matrix, and the particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the particle size distribution vector. Thus, particle size distribution inversion can be completed with only the XRD pattern, and the distribution information of the original nanoparticles within the aggregates can be obtained, thereby improving analytical accuracy while ensuring analytical efficiency.
[0062] In addition, this application also provides an analysis system for nanoparticle size distribution, including: a data interface module, a computing core unit, and a user interface. The system runs on a general-purpose computer with at least a 4-core CPU and 8GB of memory, achieving second-level inversion without relying on a supercomputing center. The data interface module can be used to read XRD raw data files in .txt or .xy format. The computing core unit is built on a Python environment and integrates the NumPy and SciPy scientific computing libraries. This unit has a built-in pre-compiled JIT (Just-In-Time) acceleration module for quickly generating peak shape functions; and is configured with a multi-process pool for executing the nanoparticle size distribution analysis method described above.
[0063] In addition, this application also provides an analytical device for nanoparticle size distribution, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the analytical method for nanoparticle size distribution as described above.
[0064] In addition, this application also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the analysis method for nanoparticle size distribution as described above.
[0065] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for analyzing the size distribution of nanoparticles, characterized in that, The analytical method includes: Obtain the XRD pattern corresponding to the nanoparticle sample to be tested; The target peak interval is determined based on the XRD pattern; the target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern. A total kernel matrix is constructed based on a preset particle size grid and the target peak interval; The particle size distribution vector is determined based on the total kernel matrix and the preset difference matrix, taking into account preset constraints. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the particle size distribution vector.
2. The analytical method according to claim 1, characterized in that, Determining the target peak interval based on the XRD pattern includes: Determine the target diffraction peaks from the XRD pattern; Determine the lateral position of the target corresponding to the target diffraction peak; Based on the preset fluctuation range, the lateral position interval corresponding to the target diffraction peak is determined according to the target lateral position, and the lateral position interval is taken as the target peak interval.
3. The analytical method according to claim 1, characterized in that, The method further includes: Determine the preset particle size range and preset particle size step size; Discretize the preset particle size range based on the preset particle size step size to obtain a preset particle size grid; The size broadening of the target diffraction peak and each particle size point in the preset particle size grid is determined based on the Scherrer-type relationship.
4. The analytical method according to claim 1, characterized in that, The construction of the total kernel matrix based on the preset particle size grid and the target peak interval includes: Determine the peak shape parameters corresponding to each particle size point in the preset particle size grid; the peak shape parameters include peak width parameters and shape parameters; Based on the peak shape parameters and the target peak interval, determine the target peak shape function corresponding to each particle size point in the preset particle size grid and each target diffraction peak; Based on the target peak shape function, the target angle grid is determined according to the target peak interval and the actual step size; Determine the theoretical diffraction intensity value of each particle size point in the preset particle size grid corresponding to each angle point in the target angle grid; The theoretical intensity vector corresponding to each particle size point is determined based on the theoretical diffraction intensity value. The total kernel matrix is obtained by concatenating the theoretical intensity vectors.
5. The analytical method according to claim 1, characterized in that, The method further includes: The data points to be deducted are determined based on the target peak interval; the data points to be deducted are located at both ends of the target peak interval; Based on a polynomial, background fitting is performed on the data points to be deducted, and the data points to be deducted are then deducted.
6. The analytical method according to claim 1, characterized in that, The step of determining the particle size distribution vector based on the total kernel matrix and the preset difference matrix, in conjunction with preset constraints, includes: Determine the regularization parameters; Based on the regularization parameter, the total kernel matrix, and the preset difference matrix, a set of regularized target augmented equations is constructed. Based on the preset constraints, the target augmented equations are solved using NNLS to obtain the particle size distribution vector.
7. The analytical method according to claim 1, characterized in that, The step of determining the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector includes: The particle size distribution vector is segmented based on the number of target diffraction peaks to obtain the corresponding target sub-distribution; Normalize each target sub-distribution and obtain the corresponding target result value; Based on the target result value, maximum detection is performed to obtain the local peak set corresponding to each target sub-distribution; A target index set is constructed by combining the preset particle size grid and the local peak set; Determine the intra-peak component parameters corresponding to each local peak set; the intra-peak component parameters include component center particle size, component weight, and intra-peak proportion; By combining the target index set and the intra-peak component parameters, cross-peak global component normalization is performed to obtain the global relative proportion of each component. The particle size distribution curve corresponding to the nanoparticle sample to be tested is determined based on the global relative proportion.
8. An analytical device for the size distribution of nanoparticles, characterized in that, include: The acquisition module is used to acquire the XRD pattern corresponding to the nanoparticle sample to be tested; The first determining module is used to determine the target peak interval based on the XRD pattern; The target peak interval is the lateral position interval corresponding to at least one target diffraction peak in the XRD pattern; The construction module is used to construct the total kernel matrix based on the preset particle size grid and the target peak interval; The second determining module is used to determine the particle size distribution vector based on the total kernel matrix and the preset difference matrix, in conjunction with preset constraints. The third determining module is used to determine the particle size distribution curve corresponding to the nanoparticle sample to be tested based on the particle size distribution vector.
9. An analytical device for the size distribution of nanoparticles, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the steps of the method for analyzing the size distribution of nanoparticles as described in any one of claims 1 to 7.
10. A readable storage medium, characterized in that, The readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method for analyzing the size distribution of nanoparticles as described in any one of claims 1 to 7.