Helium bubble size and density analysis method based on slow positron beam chromatography
By combining slow positron beam measurements with first-principles calculations, a depth distribution mapping of helium bubble size and density is established, solving the problem of difficulty in distinguishing helium bubble size and density in existing technologies. This enables high-precision helium bubble analysis, applicable to the evaluation of various materials.
Patent Information
- Application Number
- CN202511752494.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-26
- Publication Date
- 2026-03-06
AI Technical Summary
Existing technologies struggle to achieve depth-resolved analysis of helium bubble size and density in materials. The laboratory conditions of slow positron beams limit their application in helium bubble identification and multi-parameter spectrum coupling correlation analysis, resulting in a lack of depth-resolved mapping relationships between helium bubble size and density.
By combining slow positron beam measurements with first-principles calculations, and through joint analysis of Doppler broadened spectrum, coincidence Doppler spectrum, and lifetime spectrum, a depth distribution mapping of helium bubble size and density is established. Using multi-parameter spectral coupling and deconvolution fitting, combined with a trapping model, the helium bubble density is calculated.
A high-precision depth distribution analysis of helium bubble size and density based on slow positron beams was achieved, simplifying the measurement steps, improving the accuracy of the analysis results, and applicable to helium bubble evaluation of various material systems.
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Figure CN121612907A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of non-destructive quantitative and depth-resolved characterization technology of helium bubble microstructure in materials, and relates to an analytical method that combines slow positron beam spectroscopy with first-principles simulation calculations, and particularly to a method for analyzing the size and density of helium bubbles based on slow positron beam tomography. Background Technology
[0002] Helium in materials can nucleate and grow into nanoscale helium bubbles at vacancy clusters, dislocations, etc., significantly affecting strength, ductility, creep and swelling behavior; the size and density of helium bubbles that vary with depth are key quantities for safety assessment and lifetime prediction.
[0003] Existing transmission electron microscopy (TEM) can provide direct imaging, but sample preparation is complex and the sampling volume is limited, making it difficult to obtain quantitative data on continuous depths penetrating the thickness. Conventional sealed-source PAS mostly provides bulk average values, lacking depth resolution. In contrast, slow positron beams, by adjusting the incident energy to select different average injection depths, can establish a relationship between slow positron observations and depth distribution parameters by analyzing the relationship between slow positrons and depth distribution in different materials.
[0004] Currently, no patents directly utilize slow positron beams to achieve tomographic resolution of helium bubble size and density. While slow positrons are sensitive probes for identifying atomic-scale defects, limitations in laboratory conditions make it difficult to determine how to couple and correlate slow positron annihilation multi-parameter spectra and establish a mapping relationship between helium bubble size, density, and slow positron beam observations. This invention, based on a comprehensive slow positron beam measurement platform, is the first to perform simultaneous analysis of slow positron annihilation multi-parameter spectra (DBS, CDB, PALS) and combine it with first-principles calculations as a theoretical reference. This is the first analytical method for helium bubble size and density based on slow positron beams. Summary of the Invention
[0005] To address the problems existing in the prior art, the present invention aims to provide a depth-resolved helium bubble size and density analysis method based on slow positron beams. By acquiring observations such as positron annihilation lifetime spectrum (PALS), Doppler broadening spectrum (DBS), and coincidence Doppler spectrum (CDB) at different incident energies, and combining them with first-principles calculations to obtain a theoretical reference for helium bubble defects, a depth distribution mapping from slow positron beam observations to helium bubble radius R and density N is established by combining the slow beam results with the theoretical reference.
[0006] The technical solution of this invention is a method for analyzing the size and density of helium bubbles based on slow positron beam tomography, the steps of which include: 1) Measure the Doppler broadening DBS of the material under test using a slow positron beam, and calculate the low momentum annihilation ratio S and high momentum annihilation ratio W at each energy point in the Doppler broadening DBS; 2) Determine the energy points where helium bubbles exist based on the low momentum annihilation ratio S and the high momentum annihilation ratio W; then, for the energy points where helium bubbles exist, use a slow positron beam to measure the lifetime spectrum PALS of the corresponding energy points of the material under test, and use LT9 to deconvolve and fit the lifetime spectrum PALS to obtain the lifetime value of each helium bubble in the material under test. 3) Analyze the depth distribution of each helium bubble in the material under test to obtain the average injection depth of each helium bubble. ; 4) Obtain the lifetime values and average lifetime values of helium bubbles of different sizes in the test material using first-principles simulations. Then, compare the lifetime values of each helium bubble in the test material obtained in step 2) with the simulated lifetime values. By comparison, the type of helium bubble in the material to be tested is obtained; using the atomic volume Ω of the material to be tested as a scale, the radius of each helium bubble is converted into the radius of a sphere to obtain the size of the helium bubble in the material to be tested. 5) Based on the helium bubble size within the test material and the matrix lifetime of the test material. Lifetime of a helium bubble Average lifespan of helium bubbles Through a two-state capture model Calculate the density of the helium bubble at its corresponding injection depth. , denoted as the positron capture rate of the helium bubble in the test material system.
[0007] Preferably, the lifetime values of different types of helium bubbles are calculated using first-principles calculations. The method is as follows: First, construct a supercell containing helium bubbles within the framework of density functional theory to obtain the ground-state electron density. Then, in the two-component density functional, a selected electron-positron correlation potential and enhancement factor are used. Solving for the positron ground state Calculate the annihilation rate and the lifetime value of helium bubbles .
[0008] Preferred, according to Calculate annihilation rate and the lifetime value of helium bubbles .
[0009] Preferred energy points Low momentum annihilation ratio Energy Points High momentum annihilation ratio ;in, The center momentum window is used for the central momentum window, while the wings are used for the high momentum side wing windows. The energy of the incident slow positron is Hourly momentum is The count at the location, where peak represents the Doppler peak region.
[0010] Preferred capture rate ;in, The average radius of the helium bubble. The positron diffusion coefficient of the material under test is denoted as . These are the boundary conditions for the helium bubble.
[0011] Preferably, by comparing the low-momentum annihilation ratio S and high-momentum annihilation ratio W at different energy points, the energy ranges in which helium bubbles cause significant changes are determined. For each energy range with significant changes, the coincidence Doppler broadening (CDB) of the test material is measured using a slow positron beam of the corresponding energy. The measured CDB is normalized to the CDB of the standard sample to obtain a ratio curve. The calculation ranges of the S and W parameters at each energy point in the energy range with significant changes are corrected based on the ratio curve, and the low-momentum annihilation ratio S and high-momentum annihilation ratio W at the corresponding energy point are recalculated based on the corrected ranges.
[0012] Preferably, the depth distribution of each helium bubble is analyzed using the Makhov distribution; the average injection depth ;in, For slow positron energy, The density of the material to be tested is . This represents the empirical coefficient of the material to be tested.
[0013] This invention proposes a joint analysis method that uses slow beam as the primary method and first-principles calculation as a supplement. It constructs a unified analysis system for observations such as PALS, DBS, and CDB at depth-resolved slow positron energies, and establishes a one-to-one mapping from the observations to the helium bubble radius R(z) and helium bubble density N(z), so that the depth distribution of helium bubble size and density can be obtained solely from slow beam data.
[0014] This method utilizes the energy distribution E1~E K A slow positron beam was used to measure the Doppler broadening (DBS) of the material under test, and the S and W parameters at each energy point were calculated using the following formula.
[0015] in For the central momentum window (generally taken as...) Wings are high-momentum side wing windows (typically 1.8-2.2). ), The energy of the incident slow positron is At that time, the momentum is The count at the point, where peak indicates that the integration region is the entire Doppler peak region. Momentum is represented by a value calculated from the energy value of the annihilation gamma deviating from 511 keV. For example... Figure 2 As shown, S represents the proportion of low-momentum (valence / free electron) annihilation, and W represents the proportion of high-momentum (matrix core electron) annihilation. For open-pore defects like helium bubbles, positrons are more localized in low-electron-density cavities. Both increasing the size and density of the helium bubble lead to an increase in the S parameter and a decrease in the W parameter.
[0016] The above calculations yielded the following results. By comparing the S and W parameters at different energy points, the energy range in which the helium bubble causes significant changes can be determined. At energy points corresponding to the depth where the helium bubble exists, the S parameter will increase significantly, while the W parameter will decrease. For the energy range with significant changes, the coincidence Doppler broadening (CDB) of the test material is measured using a slow positron beam at the corresponding energy. The CDB result obtained is normalized to the CDB result of the standard sample. The calculation range of the S and W parameters at that energy point can be corrected by the ratio curve. The interval in the CDB ratio curve where the low momentum region and the high momentum region are significantly different is the interval where the helium bubble characteristics are significantly different. By recalculating the S and W parameters according to the aforementioned formula in the corrected interval, an energy range with more obvious comparison can be obtained.
[0017] The energy points where helium bubbles exist are determined based on the low momentum annihilation ratio S and the high momentum annihilation ratio W. Then, for the energy points where helium bubbles exist, the lifetime spectrum PALS of the corresponding energy points of the material under test is measured using a slow positron beam. The lifetime spectrum is then deconvolved and fitted using LT9 (an internationally recognized lifetime spectrum analysis software). The model principle is as follows:
[0018] Lifetime spectra reflect the local electron density during positron annihilation: longer lifetimes indicate lower local electron density and larger open volumes (vacancies / vacancy clusters / cavities, helium bubbles, etc.); shorter lifetimes indicate a matrix or high electron density environment. (Intensity of each component) It represents the relative probability of the corresponding annihilation channel, which is related to the defect capture rate and concentration.
[0019] The depth distribution corresponding to the Makhov distribution is analyzed, thus achieving a mapping between slow positron observations and the depth distribution. A commonly used analytical approximation model for the injection depth distribution of Makhov distributed slow positrons in solids has the following average injection depth:
[0020] in These are the slow positron energy and the material density, respectively. For empirical coefficients of materials (e.g., in metals: ).
[0021] The above steps completed the measurement of the helium bubble sample by the slow positron beam, and the helium bubble depth distribution was determined by multispectral coupling analysis, resulting in a high-precision annihilation lifetime value. Next, the lifetime value and average lifetime value corresponding to helium bubble defects of different sizes were obtained by first-principles simulation (DFT+TCDFT). Then, the helium bubble density was obtained by combining the lifetime value with the trapping model.
[0022] The first-principles simulation steps are as follows: First, construct a helium-containing bubble (explicitly placed inside the cavity) within the framework of density functional theory (DFT). The supercell (containing 10 He atoms) acquires the ground-state electron density. Subsequently, in the two-component density functional (TCDFT), a selected electron-positron correlation potential and enhancement factor were used. Solving for the positron ground state And calculate the annihilation rate according to the following formula. and lifespan value .
[0023]
[0024] By calculating the positron annihilation lifetimes of different types of helium bubbles (containing different vacancy defects with varying numbers of He atoms) using first-principles calculations, and then correlating the lifetime values obtained from the previous slow positron lifetime measurements with the simulated lifetime values, we can obtain multiple possible helium bubble types within the material under test. (m He atoms in n vacancy) is equivalent to an open volume. Using the atomic volume Ω of the material as a scale, and then converting it to the radius of a sphere, we can obtain the various possible helium bubble sizes inside the material to be tested.
[0025] The above steps yielded the helium bubble size. Next, the helium bubble density was analyzed, and the matrix lifetime was determined based on measurements from the slow positron beam. Helium bubble defect lifetime Average lifespan Since the helium bubble acts as an independent "deep trap" for positrons, the system only has "matrix annihilation" and "helium bubble annihilation". The capture dynamics can be equivalent to a two-state capture model, as shown in the following equation:
[0026] in Let be the density of the helium bubble at its corresponding injection depth. The energy level represents the positron capture rate of the helium bubble in the test material system. Each energy point represents an injection depth.
[0027] The capture rate of positrons by the helium bubble in the test material system can be calculated using the following formula:
[0028] in To obtain the radius of the helium bubble, The value is the positron diffusion coefficient of the material to be tested (the diffusion coefficients of different materials are generally available in the literature). The boundary conditions for helium bubbles (empirical values vary for different materials; for metals, the empirical value is approximately 10). 5 ~10 7 The helium bubble density can be calculated by combining the calculated capture rate with the various lifetime values measured by the slow positron beam (cm / s).
[0029] The helium bubble size and density mentioned above were obtained by mapping the slow positron beam measurement results with the theoretical calculation results, thereby realizing the construction of the helium bubble size and density analysis model in different material systems.
[0030] The advantages of this invention are as follows: 1) The size and density of helium bubbles can be determined using only slow positron beams and first-principles calculations; 2) Combining first-principles calculations improves the accuracy of the analysis results; 3) Establish analytical parameters for different material systems, such as capture rate and correction coefficient. Only one measurement needs to be performed on a certain material system to simplify the subsequent measurement steps and facilitate future engineering applications. Attached Figure Description
[0031] Figure 1 This is a flowchart of the process for analyzing the size and density of helium bubbles based on positron annihilation multi-parameter analysis; Figure 2 A schematic diagram illustrating the calculation of S and W parameters in positron annihilation Doppler; Figure 3 This is a schematic diagram illustrating the analytical interpretation of the positron annihilation lifetime spectrum. Detailed Implementation
[0032] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.
[0033] Figure 1The following is a detailed flowchart of the helium bubble size and density analysis method based on slow positron beam tomography. The specific operation of each step will be described in detail below. The material to be tested is a certain metal. After the sample is prepared under certain irradiation conditions, slow positron beams of different energies are selected to perform Doppler broadening measurements (DBS) on the sample to be tested. Then, the changes of the corresponding S and W parameters with energy are calculated based on the different regions of each energy point peak. The energy range in which the helium bubble causes significant changes is determined. At the energy point at the corresponding depth where the helium bubble exists, the S parameter will increase significantly, while the W parameter will decrease.
[0034] Energy points with significant differences were selected for measurement of coincidence Doppler broadening (CDB), and the irradiated sample was normalized and compared with the original sample. Simultaneously, based on the energy points with significant differences, the slow positron lifetime spectrum was measured, and the defect lifetime was analyzed using LT9 software. The irradiation lifetime spectrum and analysis results are illustrated in the figure below. Figure 3 As shown, the matrix lifetime, helium bubble lifetime, and mean lifetime of the three materials are obtained, and the helium bubble type corresponding to the given lifetime value is calculated based on first-principles calculations.
[0035] Based on the obtained helium bubble size, the positron diffusion coefficient of the corresponding material was obtained by consulting the literature based on the two-state trapping model. The trapping rates of the two helium bubble size samples were calculated respectively. The density of the helium bubble material of the two sizes was obtained based on the matrix lifetime, helium bubble lifetime and mean lifetime obtained by the slow positron lifetime spectrum analysis.
[0036] In the future, for this metal under these irradiation conditions, the slow positron beam current can be directly measured to obtain helium bubble density information.
[0037] Industrial applicability This method, based on the tunable energy of a slow positron beam platform, enables depth-resolved output of helium bubble size and density. The entire process is parameterized, reproducible, and transferable, and is applicable to various materials containing helium bubbles, including but not limited to reactor components and first wall materials of fusion devices, gradient structures formed by ion implantation, and process quality control and in-service life assessment of coating / thin film systems. It has significant industrial application value and potential for standardization and promotion.
[0038] This invention acquires observations from multiple energy points using PALS, DBS, and CDB, establishes a correspondence between energy points and depth distributions based on analytical injection depth distributions, and utilizes slow positron beam measurements as a foundation. A helium bubble type database, derived from first-principles calculations, serves as a theoretical reference to identify the helium bubble type of the test material system and establish a helium bubble measurement model for that system. Simultaneously, based on the obtained helium bubble size, the positron capture rate for that type of helium bubble is calculated, yielding the corresponding helium bubble density, thus realizing a helium bubble density analysis model for the test material system. Once the model is constructed, this method can obtain a quantitative analysis of the helium bubble size and density of a test material system using only slow positron beam data. It is applicable to various materials containing helium bubbles, including but not limited to metals, semiconductors, coatings, and polymers, for irradiation damage assessment and quality control.
[0039] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.
Claims
1. A helium bubble size and density analysis method based on slow positron beam tomography, comprising the steps of: 1) measuring the Doppler broadening (DBS) of the material to be measured using a slow positron beam, and calculating the low momentum annihilation fraction (S) and the high momentum annihilation fraction (W) of each energy point in the Doppler broadening (DBS); 2) determining the energy points where helium bubbles exist according to the low momentum annihilation fraction (S) and the high momentum annihilation fraction (W); then, for the energy points where helium bubbles exist, measuring the lifetime spectrum (PALS) of the corresponding energy points of the material to be measured using a slow positron beam, and deconvolving and fitting the lifetime spectrum (PALS) using LT9 to obtain the lifetime value of each helium bubble in the material to be measured; 3) Analyzing the depth distribution of each helium bubble in the material to be measured to obtain the average injection depth of each helium bubble ; 4) obtaining the life values of the helium bubbles of different sizes in the material to be tested and the average life value of the helium bubbles by first principle simulation, and then comparing the life values of the helium bubbles in the material to be tested obtained in step 2) with the life values obtained by simulation carrying out comparison to obtain the helium bubble types in the material to be tested; using the atomic volume Ω of the material to be tested as a scale, converting the radii of the helium bubbles into spherical radii to obtain the helium bubble sizes of the helium bubbles in the material to be tested; 5) the size of the helium bubble in the material to be measured, the base life of the material to be measured , the life value of the helium bubble , the average life of the helium bubble , by two-state capture model Calculate the density of the helium bubble to be solved at its corresponding injection depth , The capture rate of the positron by the helium bubble of the material system to be measured.
2. The method of claim 1, wherein, The lifetime values of different types of helium bubbles are obtained by first principle calculation The method is as follows: firstly, constructing a supercell containing helium bubbles under the framework of density functional theory to obtain the ground state electron density ; then, in the two-component density functional, the selected electron-positron correlation potential and the enhancement factor are used to solve the positron ground state , calculate the annihilation rate and the lifetime value of the helium bubble .
3. The method of claim 2, wherein, According to The annihilation rate is calculated And the lifetime values of the helium bubbles .
4. The method according to claim 1 or 2 or 3, characterized in that, Energy point Low momentum annihilation fraction Energy point High momentum annihilation fraction ; wherein, is the central momentum window, wings are the high momentum side wing windows, is the incident slow positron energy is momentum is count at, peak indicates the Doppler peak region.
5. The method according to claim 1 or 2 or 3, characterized in that, Capture rate ; where, is the average helium bubble radius, is the positron diffusion coefficient of the material under test, is the boundary condition of the helium bubble.
6. The method of claim 1, wherein, comparing the low momentum annihilation fraction (S) and the high momentum annihilation fraction (W) of different energy points to determine the energy interval where the helium bubbles cause significant changes; for each significant change energy interval, measuring the coincidence Doppler broadening (CDB) of the material to be measured using a slow positron beam of the corresponding energy; normalizing the measured coincidence Doppler broadening (CDB) with the coincidence Doppler broadening (CDB) of a standard sample to obtain a ratio curve; correcting the S and W parameter calculation interval of each energy point in the significant change energy interval according to the ratio curve, and recalculating the low momentum annihilation fraction (S) and the high momentum annihilation fraction (W) of the corresponding energy points according to the corrected interval.
7. The method of claim 1, wherein, The depth distribution of each helium bubble is analyzed by using Makhov distribution; average implantation depth ; wherein, is the slow positron energy, is the material density of the material to be measured, is the empirical coefficient of the material to be measured.