A method for calculating the crystallinity of hydroxyl aluminum oxide adjuvant based on the peak shape weight of XRD spectrum
By introducing a weighting function based on the full width at half maximum (FWHM) of diffraction peaks and an improved asymmetric least squares method to correct the baseline, the peak broadening problem in the calculation of crystallinity of alumina hydroxyacid adjuvant was solved, achieving rapid and accurate crystallinity assessment, which is suitable for high-throughput analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2026-04-16
- Publication Date
- 2026-06-30
Smart Images
Figure CN122306851A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of materials characterization and analysis technology, specifically relating to a quantitative analysis method for the microstructure of materials based on X-ray diffraction (XRD) technology. More specifically, this invention relates to a method for calculating the crystallinity of alumina hydroxya adjuvant by analyzing the peak shape characteristics of its XRD diffraction pattern and introducing a weighting function. Background Technology
[0002] Aluminum hydroxyaluminate (usually boehmite, γ-AlOOH) is a widely used inorganic adjuvant, commonly used in human and veterinary vaccines to enhance the immunogenicity of antigens. Its adjuvant efficacy is closely related to the physicochemical properties of the material, with crystallinity being a key parameter. Crystallinity affects the surface characteristics of adjuvant particles, their ability to adsorb antigens, and their degradation behavior in vivo, thus influencing the effectiveness of the immune response. Therefore, accurate and rapid assessment of the crystallinity of aluminum hydroxyaluminate adjuvants is of great significance for its quality control, process optimization, and efficacy studies.
[0003] X-ray diffraction (XRD) is a standard technique for analyzing the crystal structure of materials. The crystallinity of a material is generally related to the ratio of the intensity (or area) of sharp diffraction peaks in an XRD pattern to the intensity (or area) of a broad amorphous diffuse scattering background. Currently, common methods for calculating crystallinity based on XRD patterns include simple integration and peak height methods. These methods typically divide the diffraction pattern into crystalline peak regions and amorphous background regions, integrate the values separately, and then calculate the ratio.
[0004] However, directly applying these traditional methods to aluminosilicate adjuvants has significant limitations. Aluminosilicate, especially nanoscale adjuvant materials, often exhibits significant broadening of its XRD diffraction peaks. This broadening primarily stems from the small crystallite size and potential micro-strain. The traditional simple area integration method assigns equal weight to both sharp and broad peaks, leading to calculation biases: a slightly broadened crystalline peak may be treated as equal to a sharp, strong peak, thus misestimating crystallinity and failing to accurately reflect the actual contribution of the long-range ordered lattice structure in the material.
[0005] To address the issue of peak broadening, more sophisticated methods such as Rietveld full-spectrum fitting or analysis using crystal structure models have been employed for crystallinity analysis. These methods offer high accuracy but are computationally extremely complex, heavily reliant on the initial structural model and refinement techniques, demanding a high level of expertise from the operator, and are not suitable for high-throughput, rapid quality control scenarios.
[0006] Therefore, there is an urgent need in this field for a crystallinity calculation method suitable for rapid, batch analysis of alumina hydroxyacid adjuvants, which can take into account the diffraction peak broadening effect to improve accuracy, while also having strong operability and repeatability. Summary of the Invention
[0007] This invention aims to provide a method for calculating the crystallinity of alumina hydroxyl adjuvants based on XRD peak shape weighting analysis. The method introduces a weighting function related to the full width at half maximum (FWHM) of the diffraction peaks, dynamically weighting the integral area of each identified diffraction peak. This quantifies the contribution of peak shape to crystallinity, significantly improving the reliability of alumina hydroxyl adjuvant crystallinity calculations. It overcomes the crystallinity miscalculation errors caused by traditional XRD crystallinity calculation methods when analyzing materials with broadened diffraction peaks, such as alumina hydroxyl, due to the equal weighting of broadened peaks with sharp peaks. Simultaneously, it effectively avoids the complexity of methods such as Rietveld full-spectrum fitting, achieving an accurate calculation scheme suitable for rapid batch analysis, and providing a solution for high-throughput calculation of alumina hydroxyl crystallinity.
[0008] A method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis includes the following steps:
[0009] S1: XRD data loading and diffraction angle (2θ) range delineation, and baseline correction based on fitting algorithm within the delineated range to obtain background baseline and correction data after baseline subtraction; S2: Determine the actual peak position of each peak by finding the peak within the interval according to the standard diffraction card, and obtain the full width at half maximum (FWHM) based on the actual peak center by peak fitting. S3: Quantify the crystallinity contribution coefficient of the diffraction peaks according to the weighting function. When FWHM is less than the first threshold, the weight is 1.0; when FWHM is greater than the second threshold, the weight is 0.0; when FWHM is between the first and second thresholds, the weight value smoothly transitions between 1.0 and 0.0. S4: Calculate the integral area of each diffraction peak within a specific window as its original peak area, and weight it using the weights to obtain the weighted peak area; calculate the total integral area of the correction data throughout the entire analysis range; determine the final crystallinity based on the ratio of the sum of the weighted areas of all diffraction peaks to the total integral area.
[0010] Furthermore, step S1 includes: S11: Obtain raw XRD data of the aluminum hydroxyaluminate adjuvant, including diffraction angle (2θ) and intensity sequence; and define a preset diffraction angle analysis range, such as 10.0° to 75.0°; S12: An improved asymmetric least squares method is used to perform baseline correction on the original data within the defined range to accurately subtract the background signal and obtain clean, corrected intensity data suitable for peak analysis. The asymmetric least squares method is the IASLS algorithm, with parameters: asymmetric weight p satisfying 0-0.1, smoothing coefficient lam satisfying 1e5-1e7, and maximum iteration count max_iter greater than 20. A preferred setting is asymmetric weight p=0.04, smoothing coefficient lam=8e6, and maximum iteration count max_iter=25. The output is the baseline curve and the corrected intensity, i.e., the original intensity minus the baseline.
[0011] This invention provides a method for calculating the crystallinity of aluminum hydroxyacid adjuvant based on XRD peak shape weighting analysis. This method can define the range of diffraction angles of aluminum hydroxyacid adjuvant in XRD patterns that have analytical value, and effectively subtract the background baseline of the pattern through an improved asymmetric least squares method.
[0012] Furthermore, step S2 includes: S21: Based on the preset peak positions of the standard diffraction card γ-AlOOH (Boehmite, JCPDS 21-1307), search for the maximum intensity point of the correction data within a certain window. The window range can preferably be ±1.0°. The maximum intensity point of the i-th peak is determined as the actual peak center position, denoted as . ; S22: Based on the actual peak center position, fit a Gaussian model within a certain window, preferably ±3.0°, and extract the full width at half maximum (FWHM) value. .
[0013] This invention provides a method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting, which further improves the peak searching efficiency by optimizing the peak searching logic.
[0014] Furthermore, key step S3 includes: According to the Scherrer formula ,in, The subgrain size is perpendicular to the crystal plane. Half height and width, It is a shape constant. The wavelength of the radiation is usually a fixed value. The angle at which diffraction occurs is given; therefore, for a specific material, the diffraction peaks, i.e., the formula, can be simplified to: This indicates that the subgrain size of the material is inversely proportional to the full width at half maximum (FWHM), and the subgrain size reflects the degree of crystallinity to some extent, which serves as the theoretical basis for selecting the weighting function.
[0015] The key innovative step of this invention is to calculate the crystallinity contribution weighting coefficient of each diffraction peak based on its full width at half maximum (FWHM). For each diffraction peak identified in step S2, a peak shape weighting coefficient is calculated, and the FWHM of the i-th diffraction peak is obtained based on its FWHM value. The corresponding weight coefficient is calculated using a preset weight function. The weighting function is configured such that when the half-width ratio is... When the peak value is less than the first threshold, it indicates that the peak shape is sharp and the crystallization is complete, and the highest weighting coefficient is assigned. For example, the first threshold can be set to 0.5-2.0°, preferably 1.5°; when the half-width is... When the peak value exceeds the second threshold, it indicates extreme peak broadening and poor crystallinity, and the lowest weighting coefficient is assigned. For example, the second threshold can be set to 2.5-5.0°, preferably 3.0°; when the half-width is... When the weighting coefficient is between the first threshold and the second threshold, A smooth transition is achieved between 1.0 and 0.0. This smooth transition is implemented through a weighting function, which can take the following form: weighting function. ,in, Half height and width, This is the steepness coefficient. This serves as the transition center point. For example... The value can range from 1 to 10, with 6 being the preferred value. The value is taken between the first threshold and the second threshold, and is preferably 2.5°. This functional relationship reflects the basic principle that crystal size is inversely proportional to diffraction peak broadening (Scherrer formula). When the full width at half maximum (FWHM) is smaller, the contribution weight is higher, thus quantifying the degree of peak broadening as an effective contribution weight to crystallinity.
[0016] This invention provides a method for calculating the crystallinity of aluminum hydroxyacid adjuvants based on XRD peak shape weighting analysis. This method can handle the unique broadening effect of diffraction peaks of aluminum hydroxyacid adjuvants, accurately convert the full width at half maximum (FWHM) of the diffraction peaks into contribution weights to crystallinity, and improve the robustness of XRD pattern analysis of aluminum hydroxyacid adjuvants.
[0017] Furthermore, key step S4 includes: S41: Calculate the area of each identified diffraction peak within its specific integration window as the original peak area. The size of the integration window may be related to the full width at half maximum (FWHM) of the peak. The specific window is based on the peak position in step S2. and half height and width Take interval , The value should be between 0.7 and 1.2, and preferably 0.9. S42: Use the corresponding weighting coefficients obtained in step S3 ( The area of each original peak is weighted to obtain the weighted peak area. Simultaneously, the total integrated area of the corrected intensity data obtained in step S1 over the entire diffraction angle analysis range is calculated. Finally, the crystallinity of the aluminum hydroxyaluminate adjuvant ( It is calculated using the following formula: .in, Crystallinity Let be the original peak area of the i-th peak. Let be the weighting coefficient for the i-th peak. The total integral area is given. The physical meaning of this formula is that crystallinity is equal to the proportion of the effective crystalline signal area after peak shape integrity correction of all diffraction peaks to the total signal area.
[0018] Compared with the prior art, the method of the present invention has the following beneficial effects: By introducing a peak shape weighting function based on half-width at half-maximum (HWHM), this invention quantifies the negative impact of diffraction peak broadening on crystallinity assessment. It automatically assigns lower weights to severely broadened diffraction peaks, effectively avoiding the overestimation of crystallinity caused by traditional equal-weighted integral methods. This makes the calculation results more closely reflect the proportion of long-range ordered lattice structures in the material, thus significantly improving calculation accuracy. Furthermore, the design of the weighting function in this invention is directly derived from the intrinsic relationship between crystal size and diffraction peak broadening in materials science (Scherrer equation), giving the entire calculation method a solid physical foundation. This makes it particularly suitable for nano- or submicron-sized crystalline materials that are prone to diffraction peak broadening, such as alumina hydroxyaluminate adjuvants.
[0019] The method of this invention has a clear flow and standardized steps, making it easy to automate the analysis through programming. Without introducing complex crystal structure models and tedious refinement processes, it significantly improves the accuracy of traditional area methods, making it highly suitable for rapid, batch crystallinity assessment and quality control of large numbers of alumina hydroxyl adjuvant samples. All key parameters in the method have clearly defined values, minimizing interference from subjective human judgment and ensuring the comparability and repeatability of analytical results between different operators and batches. Attached Figure Description
[0020] Figure 1 This is a flowchart of a method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis.
[0021] Figure 2The image shows the result obtained after Sample A was processed using the aforementioned calculation method. The thin blue-purple solid line in the image represents the original XRD data curve, the green dashed line represents the background baseline obtained after processing with the improved asymmetric least squares method (IASLS algorithm), and the thick red solid line represents the corrected data obtained after subtracting the background baseline from the original data curve. The peak position, full width at half maximum (FWHM), and weight are marked with a purple dashed line or a thin red solid line at each diffraction peak. Detailed Implementation
[0022] The following non-limiting embodiments are intended to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.
[0023] Example 1 This embodiment uses the XRD test data of a batch of aluminum hydroxide (boehmite, γ-AlOOH) vaccine adjuvant powder sample (denoted as Sample A, the specific synthesis method is referred to: Zhao Jiashu. Study on the influence of aluminum source and precipitant on the physicochemical properties of aluminum adjuvant [D]. Liaoning: Dalian University of Technology, 2024. [2] Dalian University of Technology. In this embodiment, the aluminum source is aluminum chloride hexahydrate and the precipitant is sodium hydroxide) as an example to explain in detail the implementation steps of the method of the present invention.
[0024] Please refer to Figure 1 A method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis, the calculation method includes the following steps: S1: XRD data loading and 2θ range delineation, and baseline correction based on IASLS algorithm to obtain background baseline and corrected data after baseline subtraction; S2: Find the peak within the interval based on the standard diffraction card, and obtain the actual peak center and half-width at half-maximum; S3: Quantify the crystallinity contribution coefficient of the diffraction peak based on the weighting function; S4: Calculate the crystallinity of the alumina hydroxyacid adjuvant based on the peak area and crystallinity contribution coefficient.
[0025] The detailed steps are as follows: 1) Data Preparation and Input. Specifically, obtain the raw X-ray diffraction (XRD) data of Sample A in a text file containing two columns (e.g., SampleA.txt). The first column is the diffraction angle 2θ (in degrees), and the second column is the corresponding diffraction intensity (count). Save the data file in the specified directory. Simultaneously, prepare a standard diffraction peak position file for alumina hydroxya (boehmite, JCPDS21-1307) (e.g., standard_peaks.txt), which lists the main characteristic diffraction peak positions.
[0026] Table 1 shows the main diffraction peaks of the standard diffraction card γ-AlOOH (Boehmite, JCPDS 21-1307).
[0027]
[0028] 2) XRD Data Loading, Preprocessing, and Baseline Correction. Specifically, the SampleA.txt file is read, and the 2θ and intensity data are loaded. The analysis range is defined as 2θ between 10.0° and 75.0°, excluding irrelevant or noisy regions outside this range. For the original intensity data within the defined range, a modified asymmetric least squares method (IASLS algorithm) is used for baseline correction. The algorithm parameters are set as follows based on the correction effect: asymmetric weight p = 0.04, smoothing coefficient lam = 8e6, and maximum number of iterations max_iter = 25. Through iterative calculation, a smooth baseline curve is obtained. Then, the original intensity data is subtracted from this baseline to obtain the baseline-corrected diffraction intensity data I_corrected(2θ), as shown in the curve. Figure 2 As shown. This step effectively eliminates continuous background caused by air scattering, instrument background, etc.
[0029] 3) Identification of diffraction peaks and acquisition of full width at half maximum (FWHM). Specifically, each standard peak position P_std listed in standard_peaks.txt is traversed. For each P_std, based on the I_corrected(2θ) data from step 2), the maximum intensity point is searched within a window of [P_std - 1.0°, P_std + 1.0°]. The 2θ value corresponding to this maximum intensity point is recorded as the actual center position x of the diffraction peak. i With the actual center position x i Centered on [x], extract [x] i - 3.0°, x i The I_corrected(2θ) data within the [+3.0°] window. Using the lmfit library or a similar tool, a nonlinear least-squares fit was performed on this window of data using a Gaussian function model. The full width at half maximum (FWHM_i) of the diffraction peak was extracted from the successfully fitted Gaussian model parameters. The identified data are shown in Table 2.
[0030] 4) For each diffraction peak of FWHM_i successfully obtained in step 3), according to its FWHM_i (denoted as β) i Calculate the weighting coefficients k_i. Apply the preset weighting function: if β i If β < 1.5°, then k_i = 1.0. i If β > 5.0°, then k_i = 0.0. If 1.5° ≤ β iFor angles ≤ 5.0°, the weights are calculated using the following Sigmoid function: The steepness coefficient s = 6, and the transition center point W0 = 2.5°. This function reduces the contribution weight of broadened peaks (large FWHM).
[0031] Table 2 shows the actual diffraction peak positions and the full width at half maximum (FWHM) obtained from the fitting.
[0032]
[0033] 5) Calculate the weighted area of each peak. Specifically, for each diffraction peak, calculate the weighted area based on its center position. Centered on, with ±0.9 β i The boundary of integration is the interval [0, 1] The original peak area A_i is calculated using the trapezoidal integral method for the I_corrected(2θ) data. Then, the weighted area A_weighted_i = A_i is calculated. k_i. Within the complete analytical range (10.0° to 75.0°), the total integral area A_total is calculated using the trapezoidal integral method on the I_corrected(2θ) data. The crystallinity C is obtained by summing the weighted areas of all diffraction peaks and comparing them with the total area. The calculation formula is: The final processing result is as follows Figure 2 As shown, the crystallinity is 74.86%.
[0034] Using the traditional simple integration method, if all identified diffraction peaks are considered as crystallization peaks based on a full width at half maximum (FWHM) ≤ 2.0 and their weights are ignored, the crystallinity is 48.44%; if all identified diffraction peaks are considered as crystallization peaks based on a FWHM ≤ 2.5 and their weights are ignored, the crystallinity is 94.05%.
[0035] As can be seen from this embodiment, for Sample A, the traditional simple integration method yields a huge range of crystallinity due to different divisions of the full width at half maximum (FWHM) characteristics of the crystallization peaks. The crystallinity is 48.44% when β≤2.0 and 94.05% when β≤2.5, while the crystallinity obtained by the method of this invention is approximately 74.86%. There is a significant difference between the results of the two calculation methods. The method of this invention, by introducing peak shape weighting, reasonably calculates the contribution of diffraction peaks with varying degrees of broadening, thus calculating a crystallinity closer to reality. This more realistically reflects the actual situation in the sample where small grains or defects lead to broadening of many diffraction signals and decreased crystal integrity, avoiding the miscalculations that may be caused by the traditional method's equal-weighting of all peaks. Furthermore, this method can perform high-throughput sample processing. This embodiment demonstrates the beneficial effect of the method of this invention in improving the accuracy of crystallinity assessment of alumina hydroxyacid adjuvant.
[0036] For anyone skilled in the art, many possible variations and modifications can be made to the technical solutions of this invention based on the disclosed technical content, or equivalent embodiments can be modified accordingly, without departing from the scope of the technical solutions of this invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of this invention without departing from the content of the technical solutions of this invention should still fall within the protection scope of the technical solutions of this invention.
Claims
1. A method for calculating the crystallinity of a hydroxy alumina adjuvant based on the peak shape weight of the XRD pattern, characterized in that, Includes the following steps: S1: XRD data loading and 2θ range delineation, and baseline correction based on fitting algorithm within the delineated range to obtain background baseline and corrected data after baseline subtraction; S2: Find the peaks within the interval based on the standard diffraction card, and obtain the full width at half maximum (FWHM) based on the actual peak center through peak fitting. S3: The crystallinity contribution coefficient of the diffraction peak is quantified according to the weighting function. When FWHM is less than the first threshold, the weight is 1.0; when FWHM is greater than the second threshold, the weight is 0.0; when FWHM is between the first and second thresholds, the weight value smoothly transitions between 1.0 and 0.
0. S4: Calculate the integral area of each diffraction peak within a specific window as its original peak area, and weight it with the weights to obtain the weighted peak area; calculate the total integral area of the correction data throughout the entire analysis range; determine the final crystallinity based on the ratio of the sum of the weighted areas of all diffraction peaks to the total integral area.
2. The method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 1, characterized in that, Step S1 includes: S11: Obtain raw XRD data of aluminum hydroxyaluminate adjuvant, including diffraction angle (2θ) and intensity sequence; and define a preset diffraction angle analysis range; S12: Perform baseline correction on the original data within the defined range using the asymmetric least squares method. The parameters are asymmetric weight p satisfying 0-0.1, smoothing coefficient lam satisfying 1e5-1e7, maximum number of iterations max_iter greater than 20, and output the baseline curve and the corrected intensity, i.e. the original intensity minus the baseline.
3. The method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 2, characterized in that, The asymmetric least squares method is the IASLS algorithm.
4. The method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 1, characterized in that, Step S2 includes: S21: Based on the preset peak positions of the standard diffraction card γ-AlOOH (Boehmite, JCPDS 21-1307), search for the maximum intensity point of the correction data within a certain range window. The maximum intensity point of the i-th peak is determined as the actual peak center position, denoted as . ; S22: Based on the actual peak center position, fit a Gaussian model within a suitable window and extract the half-width at half-maximum (WHM) value.
5. The method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 1, characterized in that, Step S3 includes: For each diffraction peak identified in step S2, a peak shape weighting coefficient is calculated. Based on its half-width at half-maximum (WHM), the contribution weight of the peak is calculated using a preset weighting function. The first threshold of the weighting function is set to 0.5-2.0°, and the second threshold is set to 2.5-5.0°. The smooth transition segment is achieved by the weighting function.
6. A method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 1 or 5, characterized in that, The weighting function is: weight ,in, Half height and width, This is the steepness coefficient. It serves as the transition center point.
7. The method for calculating the crystallinity of alumina hydroxyaluminate adjuvant based on XRD peak shape weighting analysis according to claim 1, characterized in that, Step S4 includes: S41: Specific window takes a range based on half-height and width. , The value of 0.7-1.2 is satisfied; S42: The crystallinity of the aluminum hydroxide adjuvant is calculated by the following formula: Crystallinity ,in, Crystallinity Let be the original peak area of the i-th peak. Let be the weighting coefficient for the i-th peak. The total integral area is denoted as .