Ultra-precision element atomic scale stress defect nondestructive testing method and system

Abstract

The invention belongs to the technical field of atomic scale stress and defect nondestructive testing, and particularly relates to an ultra-precision element atomic scale stress defect nondestructive testing method and system.The method comprises the steps that 1, a diffraction peak shape theoretical model under coupling of a micro-area stress field and a dislocation strain field is established, 2, establishing a mapping relation model of a stress state, defect distribution and a diffraction signal; and 3, calibrating model parameters by combining a Wilkens dislocation broadening equation and actually measured dislocation density. According to the method, the problems of damage, insufficient conventional nondestructive resolution / penetration, optical superficial layer interference, difficulty in identification caused by only peak position of XRD (X-Ray Diffraction) and the like in the prior art are solved, and rapid, high-resolution and robust quantitative inversion and directional evaluation on micrometer scale stress defects under nondestructive and non-contact conditions are realized.

Description

Technical Field

[0001] This application belongs to the field of atomic-scale stress and defect nondestructive testing technology, specifically, it relates to a method and system for atomic-scale stress and defect nondestructive testing of ultra-precision components. Background Technology

[0002] With the rapid development of high-end manufacturing fields such as aerospace, semiconductor manufacturing, precision optics, and medical devices, the service environment and performance requirements of core functional components are becoming increasingly stringent. Ultra-precision components, such as single-crystal blades for aero-engines, objective lens assemblies for lithography machines, microelectromechanical systems (MEMS) sensors, and laser crystals, have extremely high standards for material integrity, structural stability, and surface quality due to their complex structures and high manufacturing precision. The ultimate performance limits and service life of these components largely depend on the stress state within and on the subsurface.

[0003] During manufacturing and service, these components inevitably generate residual stress, especially at the microscale, where stress concentration zones are easily formed, which can induce structural fatigue, crack initiation, or even sudden failure. Therefore, high-precision and high-efficiency detection and evaluation of micro-stress defects inside ultra-precision components has become one of the key technologies for quality control, process optimization, and failure early warning in high-end equipment manufacturing.

[0004] Currently, the detection methods for internal stress and defects in materials can be mainly divided into the following categories:

[0005] 1. Destructive testing methods: such as mechanical cutting or fracture analysis, have the advantages of clear testing principles and reliable test results, but they can cause irreversible damage to the workpiece being tested. Obviously, they are not suitable for complex or expensive ultra-precision devices, especially in terms of the testing requirements under service conditions.

[0006] 1. Conventional non-destructive testing methods include ultrasonic testing, X-ray diffraction, and infrared thermography. Ultrasonic testing utilizes the property that sound waves reflect off discontinuities (such as cracks and pores) in a material, making it sensitive to macroscopic structural defects. However, the influence of stress on sound velocity is extremely weak and easily interfered with by factors such as material microstructure and temperature changes, resulting in a lack of unique interpretation of the detected signal variations. Furthermore, ultrasonic wavelengths are typically on the order of millimeters, making it difficult to resolve stress concentration areas at the micrometer scale, thus failing to accurately characterize the magnitude, direction, and distribution trend of stress. This makes ultrasonic testing insufficient for high-end requirements such as early identification of micro-stress-induced damage and fatigue life prediction. X-ray diffraction is based on the slight changes in interplanar spacing in crystalline materials caused by stress, calculating residual stress through diffraction peak shifts. While this method has a certain theoretical basis and engineering applicability in static residual stress analysis, the focal spot diameter it relies on is typically between 0.5-2 mm, resulting in insufficient spatial resolution and failing to meet the accurate detection of stress distribution in micro-regions (such as tens of micrometers or even smaller). Meanwhile, X-rays have limited effective detection depth, typically only reaching the material surface and failing to penetrate to detect subsurface or deep regions. Furthermore, grain orientation, structural distortion, and defects can interfere with the accurate identification of diffraction peaks, increasing measurement errors. Infrared thermography, on the other hand, identifies potential defects by capturing abnormal infrared radiation temperature distribution on the material surface. Its advantages include rapid response and suitability for large-area preliminary screening. However, this method is essentially an indirect measurement based on changes in thermophysical properties; stress-induced thermal effects are usually extremely weak and non-unique, easily confused with differences in thermal conductivity, oxide layers, impurities, etc. Especially when assessing static residual stress, infrared thermography struggles to provide effective quantitative information and is highly susceptible to external factors such as ambient temperature fluctuations and air disturbances, leading to misjudgments or missed detections.

[0007] 2. Optical Detection Methods: Such as Raman spectroscopy, digital image correlation (DIC), and photoelasticity. Raman spectroscopy is based on the principle that the Raman scattering spectrum of a material's internal lattice shifts under stress. It can respond sensitively to stress changes and has a spatial resolution down to the micrometer level, making it suitable for high-precision micro-area stress analysis. However, the detection depth of this method is limited by the laser wavelength, typically only within 1-2 micrometers, mainly concentrated on the material surface or very shallow layers, unable to penetrate to the subsurface or internal regions. Furthermore, the quantitative relationship between Raman displacement and stress depends on material properties and calibration parameters; the test results are easily affected by temperature fluctuations, laser focal length deviations, surface roughness, etc., resulting in poor data stability. Digital image correlation (DIC) performs pixel-level analysis of images before and after loading to calculate the displacement and deformation of the surface speckle pattern, thereby deducing the surface strain field distribution. It has advantages such as non-contact, high resolution, and a large field of view, making it particularly suitable for strain field testing of macroscopic components. However, this method can only obtain surface strain information and cannot be used for internal stress measurement. Furthermore, to ensure imaging accuracy, high-quality random speckle patterns need to be prepared on the sample surface, which is difficult to achieve on practical engineering materials (such as mirror-like, rough, and irregular surfaces), increasing testing complexity and uncertainty. The photoelastic method utilizes the optical birefringence effect produced by materials under stress to achieve visual analysis of stress contour lines, and is widely used for observing stress distribution in transparent materials or model structures. Although it can reflect the location and trend of stress concentration to some extent, it is mainly used for qualitative or semi-quantitative analysis and lacks strict numerical precision control. More importantly, this method relies on the photoelastic properties of the material and is not applicable to most opaque metals, ceramics, and other engineering structural materials, thus its application range is extremely limited.

[0008] In summary, existing stress and defect detection technologies generally suffer from the following major problems: destructive methods damage the workpiece, making non-destructive, full-lifecycle inspection impossible; conventional non-destructive methods lack sufficient spatial resolution, hindering accurate detection of micro-area stress; high-resolution optical methods suffer from low efficiency, system complexity, and high cost, making them unsuitable for rapid industrial-scale inspection; and most optical technologies are limited by material type and surface conditions, only applicable to shallow surface measurements of transparent or specific samples. Therefore, achieving high-resolution, non-contact, non-destructive, and efficient detection of micro-area stress defects in ultra-precision components at the micrometer scale has become a technological bottleneck in the high-end manufacturing field. Developing novel non-destructive testing methods with advantages such as strong material adaptability, high penetration depth, fast detection speed, and high spatial resolution is of significant engineering value and theoretical research importance for ensuring the quality of key components and improving product reliability and safety. Summary of the Invention

[0009] To address the technical problems of existing technologies, such as the damage to workpieces caused by destructive testing, insufficient spatial resolution and penetration depth of conventional non-destructive testing, the shallow nature of optical methods and susceptibility to environmental and surface conditions, and the non-uniqueness of signals and difficulty in parameter identification due to the reliance on peak position in traditional XRD, this application provides a non-destructive testing method and system for atomic-scale stress defects in ultra-precision components. By constructing an XRD peak shape model coupled with "micro-region stress × dislocation strain", the method achieves simultaneous separation and joint characterization of peak position and peak width. Based on the structural factor, the method quantifies the contribution of continuous stress, dislocations, and point defects to spectral lines through a material mapping of "stress / defect → complex amplitude → intensity". Furthermore, the method combines Wilkens dislocation broadening and measured dislocation density for parameter calibration to unify the direction factor and characteristic length. Under completely non-destructive and non-contact conditions, the method achieves high-resolution, fast, and robust quantitative inversion and directional evaluation at the micrometer scale, making it suitable for complex structures and high-value components in service.

[0010] On the one hand, this application provides a non-destructive testing method for atomic-scale stress defects in ultra-precision components, the method comprising:

[0011] Step 1: Establish a theoretical model of diffraction peak shape under the coupling of micro-region stress field and dislocation strain field, and clarify the functional relationship between peak displacement and peak broadening with respect to the stress field and dislocation strain field, as the theoretical basis for subsequent mapping and inversion;

[0012] Step 2: Under the constraints of the theoretical model described in Step 1, construct a mapping relationship model from stress state, dislocation parameters, and point defect distribution parameters to diffraction signals, and form initial criteria for spectrum simulation and parameter inversion;

[0013] Step 3: Based on the Wilkens dislocation broadening equation and combined with the measured dislocation density of the sample, the dislocation-related parameters in the mapping relationship model described in Step 2 are jointly calibrated and constrained to obtain a calibrated parameter set and criteria. Based on this, the spectrum fitting and rapid inversion of the sample are performed to improve the accuracy of quantitative characterization.

[0014] In a preferred implementation, step 1 further includes:

[0015] Step 1.1: Under the condition of satisfying the X-ray diffraction geometry and Bragg equation, diffraction data are collected for the target crystal plane within its effective incident angle range. The actual interplanar spacing and peak position information are obtained and the strain is calculated accordingly. The directional elastic modulus of the crystal direction is determined based on the single crystal compliance constant. Then, the equivalent stress along the scattering vector direction is obtained according to the elastic strain and elastic modulus to characterize the micro-region stress field.

[0016] Step 1.2: Under the condition of material elastic anisotropy, Wilkens dislocation broadening theory is adopted. With the material elastic constant, Burgers vector and target slip system as inputs, the scaling relationship of dislocation-induced mean square microstrain and the linear relationship between peak broadening and dislocation parameters are established. The direction factor is used for empirical constraints, thereby obtaining the direction factor and mean square microstrain that characterize the dislocation strain field.

[0017] Step 1.3: Under the assumptions of a single dislocation type, a unique slip system, and that the Burgers vector b and the dislocation line direction t are fixed, the theoretical model of diffraction peak shape is derived based on the Wilkens stress field integral.

[0018] In a preferred implementation, step 2 further includes:

[0019] Step 2.1: Establish a diffraction intensity model at the diffraction angle θ. The diffraction intensity model integrates the structure factor, multiplicity factor, angle factor, and temperature factor.

[0020] Step 2.2: Represent the structure factor as the sum of the position information of each atom, and use the approximate atomic scattering factor to form the input parameter set of the diffraction intensity model;

[0021] Step 2.3: For the target crystal, derive the analytical relationship between the diffraction intensity and diffraction angle of each crystal plane, and use it as the material baseline for the numerical spectrum;

[0022] Step 2.4: Decompose the total displacement of the j-th atom into the superposition of continuous stress field displacement, dislocation displacement field and point defect disturbance;

[0023] Step 2.5: Based on the stress-strain constitutive relationship of the target crystal, calculate the displacement caused by the macroscopic stress field, and map the macroscopic stress field to atomic-scale displacement to characterize the stress-induced lattice distortion;

[0024] Step 2.6: Based on the theory of anisotropic elasticity, calculate the displacement field induced by the dislocation network characterized by the Burgers vector b, so as to obtain the dislocation-induced lattice distortion field.

[0025] Step 2.7: Establish a complex amplitude model of diffraction intensity and substitute it into the diffraction intensity expression in Step 2.1 and the analytical relationship between diffraction intensity and diffraction angle of each crystal plane in Step 2.3 to obtain a mapping model that simultaneously characterizes the coupling effect of stress, dislocation and point defect, which is used to generate and fit diffraction patterns.

[0026] In a preferred implementation, step 3 further includes:

[0027] Step 3.1: Acquire images under the field of view of a multi-magnification bright-field transmission electron microscope to identify the defect type and its orientation distribution;

[0028] Step 3.2: Perform fast Fourier transform and bandpass filtering on the selected preimage, and reconstruct it through inverse Fourier transform to extract the crystal plane frequency components related to the defects and determine the slip dislocations;

[0029] Step 3.3: Count the number of dislocations within the predetermined statistical area of ​​the transmission electron microscope and calculate the measured dislocation density of the sample;

[0030] Step 3.4: Measure the full width at half maximum (FWHM) of the rocking curve of the target crystal plane reflection and compare it with the shoulder signal caused by local orientation distribution;

[0031] Step 3.5: Substitute the measured dislocation density ρ, Burgers vector b, and coupling coefficient C related to target reflection into the Wilkens dislocation broadening model to inversely calculate the empirical constant K;

[0032] Step 3.6: Using the calibrated K as a fixed parameter, establish a mapping between peak broadening and dislocation density for rapid inversion of dislocation density in subsequent samples;

[0033] Step 3.7: Compare the orientation distribution caused by microcracks and / or stacking faults with the peak broadening increment to achieve a synergistic interpretation of residual stress and peak broadening by transmission electron microscopy and X-ray diffraction.

[0034] Step 3.8: Output the aforementioned statistical parameters and model results as prior constraints for subsequent peak fitting and dislocation strain field inversion.

[0035] In the preferred implementation, further, in step 1.1, the shift Δ(2θ) of the diffraction peak position is determined by the following formula:

[0036] Δ(2θ)=-2tanθ hkl ε (hkl)

[0037] The equivalent force is determined by the following formula:

[0038]

[0039] In the formula: E (hkl) ε is the directional elastic modulus of the crystal orientation; (hkl) S represents the elastic strain along the crystal plane normal; 11 ,S 12 ,S 44 λ represents the compliance constant of the single-crystal material; h, k, l represent the Miller indices of the crystal planes (h, k, l); Δd represents the change in interplanar spacing; λ represents the incident X-ray wavelength; ω±α (hkl) Here is the geometric expression for the Bragg angle of this crystal plane (hkl); 2sin(ω±α) (hkl) ) represents the geometric expression of the denominator terms in the Bragg equation under ω-2θ; d (hkl)d is the theoretical interplanar spacing; means This represents the measured interplanar spacing.

[0040] In the preferred implementation, further, in step 1.2, the scaling relation of the dislocation-induced mean square microstrain is determined by the following formula:

[0041]

[0042] In the formula: ρ is the average strain; b is the dislocation density; b is the Burgers vector and its magnitude; C is the elastic constant. These are dimensionless coefficients related to the stiffness matrix C and the dislocation type / geometry;

[0043] The linear relationship between peak broadening and dislocation parameters is determined by the following formula:

[0044]

[0045] In the formula: B (hkl) θ is the intrinsic spectral linewidth of the sample; (hkl) For the theoretical Bragg angle, given by λ and d hkl Decision; cosθ (hkl) sinθ (hkl) These are trigonometric functions of the theoretical Bragg angle, all of which are dimensionless; A (hkl) The orientation factor is the result of combining material anisotropy with dislocation type / slip system; A (hkl) (C,b,slipsys) is the comprehensive direction factor, where: C is the elastic constant, b is the Burgers vector and its magnitude, and slipsys is the target slip system; denoted as |b|, representing the contribution of dislocation statistics to broadening; |b| represents the magnitude of the Burgers vector.

[0046] The direction factor is determined by the following formula:

[0047]

[0048] In the formula: κ is the empirical correction coefficient.

[0049] In the preferred implementation, further, in step 1.3, the theoretical model for the diffraction peak shape is:

[0050] A (hkl) =f(C ij ,b,t,g (hkl) ,R e )

[0051] In the formula, g (hkl) R is the diffraction vector; t is the orientation of the dislocation line; e The radius of the dislocation strain field shielding is denoted as .

[0052] In the preferred implementation, the mapping relationship model in step 2 is further as follows:

[0053]

[0054] In the formula: I hkl (θ;σ,ρ,b,slipsys,C…) represent the relative diffraction intensities at the diffraction angle θ and the corresponding crystal plane (hkl); P is the multiplicity factor; F hkl ({r+u j (r)}) is the structure factor containing the displacement term; r = (x, y, z), which are the position coordinates of the atoms in the undeformed crystal; u j (r) represents the total displacement of the j-th atom; For the geometric / polarization term (angle factor) related to the diffraction angle; e -2M σ is the temperature factor, approximately 1 at room temperature; ρ is the stress state; b is the Burgers vector; slipsys is the slip system; and C is the material elastic constant.

[0055] In the preferred implementation, further, in step 3.5, the half-peak width of the sway curve is determined by the following formula:

[0056]

[0057] In the formula: B 111 λ is the full width at half maximum (FWHM) of the characteristic peaks in the XRD diffraction of calcium fluoride 111 single crystal; K is an empirical constant; b is the dislocation vector.

[0058] On the other hand, the present invention also provides a non-destructive testing system for atomic-scale stress defects in ultra-precision components, the system comprising:

[0059] The micro-region stress-dislocation coupled diffraction peak shape modeling unit is configured to perform step 1 above, that is, under the constraints of X-ray diffraction geometry and Bragg equation, based on the relationship between anisotropic elasticity and dislocation broadening, to establish a theoretical model of diffraction peak shape under the coupling of micro-region stress field and dislocation strain field.

[0060] The stress-defect-diffraction signal structure factor mapping modeling unit is configured to perform step 2 above, that is, to substitute the atomic displacement field caused by the stress state and the defect distribution into the structure factor and form the diffraction intensity expression, thereby establishing a mapping relationship model between stress state, defect distribution and diffraction signal.

[0061] The Wilkens dislocation broadening-measured dislocation density parameter calibration unit is configured to perform step 3 above, that is, to calibrate model parameters such as orientation factor scale and characteristic length based on the Wilkens dislocation broadening equation and the measured dislocation density.

[0062] The beneficial effects of this application are:

[0063] First, the atomic-scale non-destructive testing method for ultra-precision components in this application constructs a diffraction peak shape theoretical model coupled with the micro-region stress field × dislocation strain field in step 1, achieving simultaneous separation and joint characterization of peak position (stress-induced) and peak width (dislocation-induced), reducing the ambiguity caused by traditional XRD relying solely on peak position; in step 2, a mapping relationship of "stress state, defect distribution → diffraction signal" is established with structural factors as the core, enabling a clear physical traceability link between stress, defect, and intensity, improving the interpretability and material adaptability of the model (able to handle anisotropy and different slip systems); in step 3, the Wilkens dislocation broadening equation and the measured dislocation density are cross-calibrated to unify key parameters such as direction factor and characteristic length, ensuring that parameters are identifiable, results are repeatable, and consistent with micrometry. Therefore, this invention achieves quantitative inversion and directional description of micro-region stress and dislocation fields while maintaining complete non-destructive and non-contact operation. It takes into account both penetration depth and spatial resolution, making it suitable for rapid screening and accurate evaluation of complex structures and high-value components in service. It can provide a reliable basis for quality control, process optimization and life prediction.

[0064] Second, in the preferred implementation, the technical solution of step 1 of this application accurately determines the peak position shift through "geometry + Bragg" and quantifies the strain as the equivalent force along the scattering vector direction using the directional elastic modulus. Then, with the help of Wilkens dislocation broadening theory under anisotropic conditions, a one-to-one correspondence is established between dislocation density, Burgers vector, directional factor and mean square microstrain, peak broadening (and the scale of each (hkl) orientation is unified by empirical constraints of the directional factor, reducing the degree of freedom and improving the identifiability of parameters). Finally, under the physical premise of "single dislocation type, unique slip system, and fixed b and t", a fitable diffraction peak shape theoretical model is formed by stress field integration, thereby realizing the synchronous separation and coupling characterization of peak position (stress-induced) and peak width (dislocation-induced), improving the quantitative accuracy, directional resolution and robustness of micro-region stress and dislocation strain fields, reducing the ambiguity caused by traditional peak position or empirical peak shape alone, and facilitating multi (hkl) joint fitting and non-destructive rapid evaluation of high-value components in service.

[0065] Third, in the preferred implementation, step 2 of this application establishes a complete link of "displacement field → complex amplitude → intensity" with structural factors as the core, and introduces analytical baselines of intensity-angle for each crystal plane of calcium fluoride. At the atomic scale, the continuous stress field, dislocation movement field and point defect perturbation are decomposed, modeled and mapped to atomic displacements. Finally, the complex amplitudes are uniformly substituted into the intensity formula to obtain a materialized mapping model of "stress state / defect distribution → diffraction signal". This achieves a unified expression of the traceable, decomposable and quantifiable influence of stress and defects on spectral lines, improves the accuracy and robustness of fitting and inversion, reduces interpretation ambiguities caused by factors such as grain orientation and microstructure distortion, and enhances the applicability and portability of the model under different orientations and different defect scenarios by relying on material-specific baselines and anisotropic descriptions, providing an efficient and reliable physical basis for the rapid generation and fitting of diffraction patterns.

[0066] Fourth, in the preferred implementation, step 3 of this application achieves consistency between the model and the actual measurement through a closed loop of "micrometry - frequency domain determination - XRD calibration - prior output": First, microcracks / stack faults / dislocation cell regions / voids and their orientation distribution are visually identified under a 2–200 nm multi-magnification bright-field TEM, and the crystal plane frequency components related to slip are extracted by FFT / bandpass / IFFT to improve the sensitivity of defect identification and the reliability of orientation determination; then, ρ=n / A is directly counted within a given field of view as the "ground truth value", and the CaF2_22(111) rocking curve is compared with the shoulder signal to distinguish the contribution of orientation dispersion and dislocation broadening, and based on this, ρ, b and C( 111) Substitute the Wilkens broadening formula to inversely calculate the empirical constant K, physically scale the orientation factor, and eliminate the scale drift caused by diffraction fitting alone; then solidify the “peak broadening-ρ” mapping with the calibrated K to achieve rapid and reproducible real-time inversion of the dislocation density of subsequent samples; and perform multi-source consistency verification on the orientation dispersion caused by microcracks / stack faults and the peak broadening increment to reduce interpretation ambiguity and improve the robustness of conclusions; finally output the priors such as {K,ρ,B111,C(111)} as strong constraints for peak fitting and dislocation strain field inversion, improve parameter identifiability, convergence speed and uncertainty control capabilities, and meet the non-destructive, rapid and quantitative evaluation requirements of high-value components in service.

[0067] Fifth, the atomic-scale stress defect nondestructive testing system for ultra-precision components in this application, compared to methods that only provide operational procedures, integrates modeling, mapping, and calibration in a closed loop within the same data pathway using a "three-unit" hardware / software integrated approach: On one hand, the micro-region stress-dislocation coupled diffraction peak shape modeling unit and the stress-defect-diffraction signal structure factor mapping modeling unit automatically connect peak position / width parameters and complex amplitude / intensity expressions at the system level, reducing manual intervention and subjective parameter tuning, and improving processing speed and result consistency; on the other hand, the Wilkens dislocation broadening-measured dislocation density parameter calibration unit self-calibrates XRD spectra and micrometrics (ρ, b, characteristic length, etc.) within the system, forming a reusable parameter library and prior constraints, reducing the risk of ill-fitting and multiple solutions. Attached Figure Description

[0068] Figure 1 This is a flowchart of the steps of the non-destructive testing method for atomic-scale stress defects in ultra-precision components according to the present invention;

[0069] Figure 2 This is a schematic diagram illustrating the effect of the change in interplanar spacing on the XRD diffraction response in this invention;

[0070] Figure 3 This is a schematic diagram of the sample dislocation density of the present invention;

[0071] Figure 4 This is an overall flowchart of the atomic-scale stress defect nondestructive testing method for ultra-precision components according to the present invention;

[0072] Figure 5 This is a sample surface morphology observation diagram of the present invention;

[0073] Figure 6 The XRD pattern of the sample in this invention is a conventional diffraction pattern.

[0074] Figure 7 This is a multi-scale bright-field TEM microstructure image of the high-temperature annealed sample of the present invention. Detailed Implementation

[0075] To enable those skilled in the art to better understand the technical solutions of this application, the following will provide a more detailed description of this application in conjunction with the accompanying drawings and embodiments.

[0076] The directional terms such as above, below, left, right, front, and back used in this application are based on the positional relationships shown in the attached drawings. Different attached drawings may result in different positional relationships, therefore they should not be interpreted as limitations on the scope of protection.

[0077] In this application, the terms "installation," "connection," "interlocking," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, an integral connection, a mechanical connection, an electrical connection, or a connection that allows communication between components. They can also refer to a direct connection or an indirect connection through an intermediate medium. They can refer to the internal connection of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0078] As per the instruction manual Figure 1 A non-destructive testing method for atomic-scale stress defects in ultra-precision components, the method comprising:

[0079] Step 1: Establish a theoretical model of diffraction peak shape under the coupling of micro-region stress field and dislocation strain field, and clarify the functional relationship between peak displacement and peak broadening with respect to the stress field and dislocation strain field, as the theoretical basis for subsequent mapping and inversion.

[0080] The purpose of step 1 is to construct a physical forward model that can characterize the coupling effect of micro-region stress field and dislocation strain field, so as to quantitatively describe the influence of stress and dislocation on the asymmetry of diffraction peak position, peak width and peak shape, separate the inherent broadening of materials and instrument broadening factors, and provide a calculable and traceable theoretical basis for subsequent inversion of micro-region stress and defect parameters from diffraction signals.

[0081] It should be noted that the micro-region stress field refers to the spatial distribution of the stress tensor within the X-ray detection volume (determined by the spot / incident geometry and the material attenuation depth), including macroscopic residual / applied stress and its gradient and anisotropy at the microscale. In the model, its projection or equivalent onto the (hkl) crystal plane normal is typically used to characterize stress-induced peak shift. The dislocation strain field refers to the statistical characterization of the elastic strain field generated by dislocation families (type, slip system, Burgers vector, and their density and shielding scale) within the material. Its mean square micro-strain in the scattering vector direction varies with |q| and orientation. Within the Wilkens framework, it is usually described by parameters such as dislocation density and shielding radius. This field mainly contributes to peak width and peak shape (including asymmetry), and is distinct from stress-induced peak shift. Diffraction peaks refer to the local maxima and line shapes of the intensity distribution around a certain (hkl) crystal plane that satisfy the Bragg condition under ω-2θ geometry. Their characteristic quantities include at least peak position, peak width, and shape / asymmetry parameters. The theoretical peak shape is formed by convolving the sample's intrinsic line shape with the instrument resolution function, used to distinguish between intrinsic material broadening and instrument broadening. Intrinsic material broadening refers to the spectral line broadening and shape changes caused by the sample's microstructure, including but not limited to: finite grain / subgrain size (size effect), microstrain / strain gradient, dislocation density and shielding radius, stacking faults / twins, phase boundaries and multiphase, texture / orientation distribution, compositional gradient, etc.; it varies anisotropically with (hkl) and the scattering vector |q|, and is a material property. Instrument broadening refers to the broadening and asymmetry caused by the limited resolution of the measurement system, including: X-ray wavelength broadening, optical geometry and divergence angle, monochromator / filter, detector pixel / stepping, sample geometry and transparency effects, and contour distortion caused by zero-point / displacement errors, etc. It varies according to the instrument and is independent of the sample.

[0082] Specifically, step 1 includes:

[0083] Step 1.1: Under the condition of satisfying the X-ray diffraction geometry and Bragg equation, diffraction data are collected for the target crystal plane within its effective incident angle range. The actual interplanar spacing and peak position information are obtained and the strain is calculated accordingly. Based on the single crystal compliance constant, the directional elastic modulus of the crystal direction is determined. Then, the equivalent stress along the scattering vector direction is obtained according to the elastic strain and elastic modulus to characterize the micro-region stress field.

[0084] Under the constraints of X-ray diffraction geometry and the Bragg equation, the equivalent force along the scattering vector direction is determined based on the single-crystal compliance matrix and diffraction elastic constants, combined with the theoretical interplanar spacing, to characterize the micro-region stress field.

[0085] It should be noted that X-ray diffraction refers to the coherent elastic scattering process that occurs in the periodic structure of a crystal. Under measurement geometry such as ω-2θ, it records the distribution of diffraction intensity as a function of 2θ to characterize the interplanar spacing, orientation, and their variations. The Bragg equation states the geometric relationship that satisfies the diffraction condition: nλ = 2dsinθ, where λ is the incident X-ray wavelength, d is the interplanar spacing of the crystal planes to be diffracted, θ is the Bragg angle, and n is the diffraction order. The theoretical interplanar spacing, also known as the stress-free interplanar spacing, refers to the reference spacing under the actual composition / phase state and test temperature conditions of the material being measured, when the macroscopic stress is zero. The direction along the scattering vector is the normal to the diffracting crystal plane.

[0086] As per the instruction manual Figure 2 Specifically, when the interplanar spacing d is relative to the stress-free reference d hkl When a small change occurs, Δd changes (small strain condition |Δd / d) hkl According to the Bragg equation nλ = 2dsinθ, the Bragg angle decreases as the interplanar spacing increases, and increases as the interplanar spacing decreases. Since the discussion pertains to small strain, the macroscopic orientation deviation is much smaller than the instrument's angular resolution and geometric zeroing error. The influence of minute orientation dispersion on diffraction is mainly manifested in peak width and shape changes. Therefore, when analyzing peak position changes caused by interplanar spacing (or normal elastic strain), the actual tilt angle can be taken to be approximately equal to the theoretical tilt angle. This approach ensures accurate peak position shift calculations while avoiding the repeated inclusion of orientation perturbations in this step.

[0087] Therefore, the XRD diffraction geometry is expressed as the ω-2θ geometric coupling equation (1):

[0088] 2θ=2(ω±α (hkl) (1)

[0089] In the formula: θ is the actual diffraction angle, i.e., the probe arm rotation angle, which is the angle between the incident beam and the diffracted beam; 2θ is the peak position reported by the XRD instrument, represented by 2θ; ω is the actual incident angle, i.e., the incident angle of the sample relative to the incident beam, which is ω=θ in symmetrical reflection; α (hkl) is the theoretical tilt angle of the crystal plane, that is, the geometric tilt angle of the normal of the target (hkl) crystal plane relative to the normal of the sample surface. It is determined by the sample orientation and is a theoretical / geometric constant that does not change with stress; ± represents the two feasible geometries corresponding to the crystal plane facing the incident beam and facing away from the incident beam.

[0090] Equation (1) shows the coupling relationship between the probe arm rotation angle 2θ and the sample incident angle 2ω in coplanar ω–2θ (θ–2θ) scanning. Equation (1) does not include wavelength λ and interplanar spacing d, and is purely geometric and kinematic constraint. This equation only describes the angular relationship of the instrument geometry. When the sample is scanned around the coplanar axis, the probe arm angle and the sample incident angle differ by a fixed 2α. (hkl) .

[0091] From formula (1) Bragg equation, we obtain Bragg-space conversion equation (2):

[0092]

[0093] In the formula: Δd is the change in interplanar spacing; λ is the incident X-ray wavelength; ω±α (hkl) Here is the geometric expression for the Bragg angle of this crystal plane (hkl); 2sin(ω±α) (hkl) ) represents the expression of the denominator term in the Bragg equation under ω-2θ geometry, used to convert angles into interplanar spacing; d (hkl) This is the theoretical interplanar spacing, i.e., the stress-free reference spacing.

[0094] From equation (2), it can be seen that 0 < θ < π / 2 is required to satisfy reflection diffraction. Based on this, the feasible ω region for two orientations is obtained: when the crystal plane faces the incident beam, 0 < ω < π / 2 - α. (hkl) That is, the effective incident angle range is (0, π / 2 - α). hkl When the crystal plane faces away from the incident beam, ω > α. (hkl) And ω < π / 2 + α (hkl) To ensure that the incident light intersects the crystal plane at the sample surface and to avoid self-blocking, the lower limit can be taken as 2α. hkl Therefore, the effective range of incident angles is (2α) hkl ,π / 2+α hkl The range of interplanar spacing variation Δd that can be detected by XRD is (λ / 2 - d). hkl ,λ / 2sinα hkl -d hkl ).

[0095] Furthermore, the measured interplanar spacing of the (hkl) plane was obtained by XRD. Where, θ means This represents the measured peak position. (d) means Spacing d from the stress-free reference hkl The comparison yields Δd = d according to equation (2). means -d hkl XRD yields the elastic strain ε of the normal to the crystal plane from the peak position. (hkl) =Δd / d hkl =(d means -d hkl ) / d hkl (3).

[0096] Furthermore, according to the Bragg equation nλ=2dsinθ, we take the "stress-free reference" d. hkl When the interplanar spacing d is relative to the stress-free reference d hkl When a small change occurs, Δd, then d = dhkl +Δd, and θ=θ hkl Substituting +Δθ into the Bragg equation nλ=2dsinθ and retaining only the first-order small quantities, we get:

[0097] nλ=2(d hkl +Δd)sin(θ hkl +Δθ)≈2(d hkl +Δd)(sinθ hkl +cosθ hkl Δθ)

[0098] ≈2d hkl sinθ hkl +2Δdsinθ hkl +2d hkl cosθ hkl Δθ

[0099] Subtract the baseline 2d hkl sinθ hkl We get 0 ≈ 2Δdsinθ hkl +2d hkl cosθ hkl Δθ, and thus obtain

[0100] Since the peak position reported by the XRD instrument is represented by 2θ, the shift Δ(2θ) of the diffraction peak position is:

[0101]

[0102] To further quantitatively analyze the stress of the material in the direction perpendicular to the corresponding crystal plane (hkl), it is necessary to combine the elastic constant matrix C. ij or its inverse matrix S ij To perform stress-strain conversion; in cubic single-crystal materials, due to anisotropy, the relationship between stress and strain corresponding to the (hkl) plane cannot be simply assumed to be isotropic, but requires the use of the corresponding single-crystal anisotropy formula, expressed as equation (5):

[0103]

[0104] Wherein: S 11 ,S 12 ,S 44 , , respectively, are the compliance constants of the single-crystal material (i.e., the inverse elements of the stiffness matrix Cij); h, k, l are the Miller indices of the crystal plane (hkl); This is the reciprocal of the crystal's downward "equivalent" or "directional" elastic modulus.

[0105] According to equation (5), the directional elastic modulus of this crystal orientation is obtained.

[0106] Furthermore, the equivalent stress along the scattering vector direction (crystal plane normal) is calculated according to equations (3) and (6). This stress state is uniaxial, and the uniaxial direction coincides with the diffraction direction. The deformation is purely elastic. This equivalent stress directly determines the shift of the diffraction peak position. The equivalent stress is expressed as equation (7):

[0107] δ (hkl) =E (hkl) ε (hkl) (7)

[0108] Equation (7) is used to characterize the stress field in a micro-region.

[0109] Step 1.2: Under the condition of material elastic anisotropy, Wilkens dislocation broadening theory is adopted. With the material elastic constant, Burgers vector and target slip system as inputs, the scaling relationship of dislocation-induced mean square microstrain and the linear relationship between peak broadening and dislocation parameters are established. The direction factor is used for empirical constraints, thereby obtaining the direction factor and mean square microstrain that characterize the dislocation strain field.

[0110] Based on the elastic anisotropy of materials and using Wilkens' dislocation broadening theory, combined with the material elastic constant, Burgers vector and target slip system parameters, a dislocation-induced mean square microstrain and its direction factor are established to characterize the dislocation strain field.

[0111] Although Equation (7) in step 1.1 can determine stress by the shift of diffraction peak position, it is insufficient to fully characterize the microscopic damage of single-crystal CaF2 on the surface or subsurface. Peak shape (especially peak broadening) is usually closely related to factors such as microstrain, dislocations, and grain refinement. Therefore, considering the different contributions of dislocations / defects to peak position and peak width in XRD analysis needs to be achieved through step 1.2.

[0112] It should be noted that Wilkens' dislocation broadening theory refers to a theoretical model within the framework of elasticity theory that statistically characterizes the broadening and asymmetry of X-ray diffraction patterns caused by the distribution of shielded random dislocations. It assumes that dislocations follow a restricted random distribution, uses dislocation density and outer shielding radius as the main characterization parameters, and combines the material's elastic constant and the contrast factor (direction factor) C determined by the slip system to give the dislocation-induced mean square micro-strain along the scattering vector mode direction and its contribution to the line shape. Anisotropic materials are materials whose physical properties vary with orientation. In this application, anisotropic materials refer to elastic anisotropy, meaning that the elastic response of the material depends on the crystallographic orientation.

[0113] Specifically, for anisotropic materials, an elastic anisotropic tensor C is introduced into the strain field around the dislocation "core / line". Based on C and the diffraction vector direction (determined by reflection "(hkl)" and geometry), the contrast factor and direction factor are calculated. Used to reflect anisotropy and orientation dependence.

[0114] Using Wilkens' dislocation broadening theory, under the shielded random dislocation model, the scaling relation of the dislocation-induced mean square microstrain along the scattering vector direction can be obtained. This scaling relation of the dislocation-induced mean square microstrain is used to characterize the joint contribution of dislocation density ρ and elastic anisotropy to the microstrain, and can be expressed as Equation (8):

[0115]

[0116] In the formula: ρ is the average strain; b is the Burgers vector and its magnitude, i.e., the Burgers vector of the dislocation; C is the elastic constant (stiffness tensor component); These are dimensionless coefficients related to the stiffness matrix C and the dislocation type / geometry.

[0117] Furthermore, the equation (8) Mapped to spectral linewidth, in diffraction line pattern analysis (WH method, etc.), peak broadening B (hkl) Typically, the relationship between peak broadening and dislocation parameters is approximately linear, and the linear relationship between peak broadening and dislocation parameters is expressed by equation (9):

[0118]

[0119] In the formula: B (hkl) θ is the intrinsic spectral linewidth of the sample; (hkl) For the theoretical Bragg angle, given by λ and d hkl Decision; cosθ (hkl) sinθ (hkl) These are trigonometric functions of the theoretical Bragg angle, all of which are dimensionless; A (hkl) The orientation factor is the result of combining material anisotropy with dislocation type / slip system; A (hkl) (C,b,slipsys) is the comprehensive direction factor (dimensionless), where: C is the elastic constant, b is the Burgers vector and its magnitude, and slipsys is the target slip system; denoted as |b|, representing the contribution of dislocation statistics to broadening; |b| represents the magnitude of the Burgers vector, characterizing the intensity scale of the dislocation.

[0120] A in equation (9) (hkl) (C,b,slipsys) can be represented as:

[0121]

[0122] In the formula: κ is the empirical correction coefficient.

[0123] Equation (9) As an empirical constraint, it can be seen from equation (10) that, under the engineering approximation, the direction factor can be characterized by multiplying the comparison factor calculated from the elastic constant by an empirical coefficient. Equation (10) is the direction factor A. (hkl) (C,b,slipsys) transforms A, which originally depended on multiple factors including C, b, and slipsys. (hkl) The compression is based on a contrast factor determined solely by the elastic constant C, with its overall scale absorbed by a global empirical coefficient k, thereby reducing the fitting degrees of freedom while maintaining physicality.

[0124] The dislocation-induced mean square microstrain of equation (8) is output through step 1.2, and the A of equations (9) and (10) is obtained. (hkl) The (C,b,slipsys) parameters specify the slip surface and slip direction, further yielding:

[0125]

[0126] Peak broadening is obtained through equation (11):

[0127]

[0128] Equation 12 represents the peak broadening B of the sample under the premise of dislocation dominance, instrumental deconvolution, and negligible / separated peak size. (hkl) The root mean square of the mean square microstrain caused by dislocation Proportional to the diffraction angle and follows tanθ (hkl) Magnification, the overall scale of the anisotropy direction factor of the κ-absorbing material. B-values ​​were applied to multiple groups (hkl). (hkl) -tanθ (hkl) Linear fitting, its slope is given By combining equations (8), (9), and (10), the intensity and directionality of the dislocation strain field can be quantified.

[0129] Step 1.3: Under the assumptions of a single dislocation type, a unique slip system, and fixed Burgers vector b and dislocation line direction t, derive the diffraction peak shape theoretical model based on Wilkens stress field integral:

[0130] A (hkl) =f(C ij ,b,t,g (hkl) ,R e (13)

[0131] In the formula, g (hkl) R is the diffraction vector; t is the orientation of the dislocation line; e The radius of the dislocation strain field shielding is denoted as .

[0132] Step 2: Under the constraints of the theoretical model described in Step 1, construct a mapping relationship model from stress state, dislocation parameters, and point defect distribution parameters to diffraction signals, and form initial criteria for spectrum simulation and parameter inversion.

[0133] The purpose of step 2 is to establish a mapping / inverse mapping relationship between the diffraction signal and the measured state variables (including at least stress state, defect type / distribution / characteristic scale), forming a characteristic function or objective function for parameter estimation and spatial distribution reconstruction, thereby realizing the rapid identification and quantitative characterization of micro-regional abnormal stress and defects.

[0134] Specifically, step 2 includes:

[0135] Step 2.1: Establish a diffraction intensity model at the diffraction angle θ. The diffraction intensity model integrates the structure factor, multiplicity factor, angular factor, and temperature factor.

[0136] In X-ray diffraction, in addition to the position of the diffraction peaks, the diffraction intensity is also an extremely important analytical object. The diffraction intensity depends on factors such as the structure factor and the diffraction angle. When a diffractometer is used to detect a certain crystal plane of a crystal, its relative diffraction intensity is expressed as equation (14):

[0137]

[0138] In the formula: I(θ) represents the diffraction intensity at angle θ; I0 is the electron scattering intensity; P is the multiplicity factor; F(hkl) is the structure factor; e -2M This is the temperature factor (approximately 1 at room temperature).

[0139] Step 2.2: Represent the structure factor as the sum of the position information of each atom, and use the approximate atomic scattering factor to form the input parameter set of the diffraction intensity model.

[0140] Specifically, the structure factor F(hkl) quantitatively reflects the contribution of atomic arrangement and atomic types on the crystal plane to the diffraction intensity pattern; for the (hkl) crystal plane, the structure factor is expressed as Equation (15):

[0141]

[0142] In the formula: F(hkl) is the structure factor of the crystal plane (hkl); f j It is the scattering factor of the j-th atom; x j ,y j ,z j is the coordinate of the j-th atom; h, k, and l are the Miller indices of the crystal plane, respectively.

[0143] By using the structural factor formula (15), the diffraction intensity generated by different crystal planes can be calculated, and then the diffraction pattern of the entire crystal can be constructed.

[0144] The atomic scattering factor represents the amplitude of the scattered wave from an atom in a certain direction, and its approximate formula is expressed as equation (16).

[0145]

[0146] In the formula: a i b i c i All of these are parameters, and their values ​​can be found in the International Tables for Crystallography.

[0147] Step 2.3: For the target crystal, derive the analytical relationship between the diffraction intensity and diffraction angle of each crystal plane, and use it as the material baseline for the numerical spectrum.

[0148] In the embodiments of this application, the target crystal is calcium fluoride crystal, and the analytical relationship between the diffraction intensity and diffraction angle of each crystal plane is as follows:

[0149]

[0150] In the formula: a i b i c1, a j b j c2 are parameters used to calculate the atomic scattering factor for Ca and F atoms, respectively.

[0151] As can be seen from equation (15) in step 2.2 and equation (17) in step 2.3, the interplanar spacing and crystal orientation are important factors affecting the XRD pattern, and the two together determine the position shift and intensity of the diffraction peaks.

[0152] Step 2.4: Decompose the total displacement of the j-th atom into the superposition of continuous stress field displacement, dislocation displacement field, and point defect disturbance:

[0153]

[0154] In the formula: u j Let j be the total displacement vector of the j-th atom; The displacement is caused by the macroscopic stress field; Displacement caused by dislocation network; Random displacements caused by point defects can be randomly generated using the Monte Carlo method.

[0155] Step 2.5: Based on the stress-strain constitutive relationship of the target crystal, calculate the displacement caused by the macroscopic stress field, and map the macroscopic stress field to atomic-scale displacement to characterize the lattice distortion caused by stress.

[0156] In the embodiments of this application, the target crystal is cubic calcium fluoride. Specifically, the stress-strain relationship of cubic calcium fluoride is determined by the stiffness matrix [C]. ij ]control:

[0157]

[0158] Where: σ ij Let ε be the stress tensor. kl For strain tensor.

[0159] At this point, the displacement caused by the macroscopic stress field can be obtained from the strain tensor and the rigid body rotation tensor:

[0160]

[0161] In the formula: ε is the strain tensor; r=(x,y,z) represents the position coordinates of the atom in the undeformed crystal; ω is the rigid body rotation tensor.

[0162] Step 2.6: Based on the theory of anisotropic elasticity, calculate the displacement field induced by the dislocation network characterized by the Burgers vector b, so as to obtain the dislocation-induced lattice distortion field.

[0163] Specifically, the lattice distortion caused by dislocations can be accurately described by anisotropic elasticity theory. Taking a straight dislocation line with Burgers vector b as an example, its displacement field solution is expressed as equation (21):

[0164]

[0165] In the formula: Let be the displacement field caused by dislocation; ξ be the unit vector of the integration path; C jimm dS is the fourth-order tensor of the elastic constant; r is the position vector of the observation point relative to the dislocation line; ξ Let be the area element of a unit sphere.

[0166] Step 2.7: Establish a complex amplitude model of diffraction intensity and substitute it into the diffraction intensity expression in Step 2.1 and the analytical relationship between diffraction intensity and diffraction angle of each crystal plane in Step 2.3 to obtain a mapping model that simultaneously characterizes the coupling effect of stress, dislocation and point defect, which is used to generate and fit diffraction patterns.

[0167] Specifically, substituting the displacement terms of stress and strain into the structural factor equation in step 2.2, the complex amplitude model is expressed as equation (22).

[0168]

[0169] In the formula: F hkl It is the complex amplitude of the diffraction intensity; f j x is the scattering factor of the j-th scatterer;j ,y j ,z j These are the coordinates of the j-th atom; These represent the displacements of the j-th atom in the x, y, and z directions, respectively.

[0170] Substituting equation (22) into equations (14) and (17), we obtain a mapping relationship model based on stress state, defect distribution, and diffraction signal, which allows for the systematic quantification of the modulation effect of defects on X-ray diffraction patterns. The mapping relationship model is as follows:

[0171]

[0172] In the formula: I hkl (θ;σ,ρ,b,slipsys,C…) represent the relative diffraction intensities at the diffraction angle θ and the corresponding crystal plane (hkl); P is the multiplicity factor; F hkl ({r+u j (r)}) is a structure factor containing a displacement term, when the coordinates of the j-th atom are changed from (x) j ,y j ,z j ) becomes When the structure factor is written as equation (22); r = (x, y, z), that is, the position coordinates of the atom in the undeformed crystal; u j (r) is the total displacement of the j-th atom, which is decomposed into macroscopic stress-induced displacement, dislocation-induced displacement and point defect random displacement according to equation (18); The geometric / polarization term (angle factor) related to the diffraction angle, modulated by θ; e -2M ρ is the temperature factor, approximately 1 at room temperature; σ is the stress state (which can be in tensor form); ρ is the dislocation density; b is the Burgers vector; and slipsys is the slip system (a combination of dislocation slip planes / slip directions), appearing in the direction factor A. (hkl) In the orientation dependence of (C,b,slipsys), C is the material elastic constant.

[0173] In summary, steps 2.1-2.7 establish initial criteria for spectral simulation and parameter inversion, including peak displacement-stress consistency criteria, broadening source criteria, point defect / stack fault / orientation dispersion criteria, and physical boundary and consistency criteria. The peak displacement-stress consistency criteria include: whether the peak displacements (or Δd / d) of multiple {hkl} reflections satisfy a linear / affine relationship constrained by the directional elastic modulus; whether the strain signs and amplitudes of different orientations are consistent with the loading direction (or residual stress direction); and whether the residuals exhibit no systematic shift. The broadening source criteria include: whether the broadening as a function of the diffraction angle can separate contributions from "instrument broadening," "grain size," and "micro-strain / dislocation" (such as symmetry / asymmetry, tail / shoulder features); and whether anisotropic broadening is correlated with the orientation factor of the assumed slip system. Criteria for point defects / stacking faults / orientation dispersion include: whether the asymmetric broadening, sagittal peaks, or intensity redistribution of specific reflections are consistent with the spectroscopic characteristics of point defects / stacking faults; and whether the full width at half maximum (FWHM) and shoulders of the rocking curve characterize orientation dispersion rather than simple dislocation broadening. Criteria for physical boundaries and consistency include: whether b, t, slip system, elastic constants, etc., fall within the range allowed by crystallography and material constitutive model; and whether the initial values ​​obtained from the inversion (stress, mean square microstrain, dislocation density ρ, etc.) are on a reasonable order of magnitude.

[0174] The above criteria can be used to filter out inconsistent data / hypotheses and provide initial parameter values ​​and constraint intervals, which serve as input for calibration in step 3.

[0175] Step 3: Based on the Wilkens dislocation broadening equation and combined with the measured dislocation density of the sample, the dislocation-related parameters in the mapping relationship model described in Step 2 are jointly calibrated and constrained to obtain a calibrated parameter set and criteria. Based on this, the spectrum fitting and rapid inversion of the sample are performed to improve the accuracy of quantitative characterization.

[0176] The purpose of step 3 is to introduce the Wilkens dislocation broadening equation and combine it with the measured dislocation density to calibrate and constrain the key parameters of the model, reduce parameter coupling and multiple solutions, convert relative quantities into absolute quantities, improve the accuracy, robustness and consistency of the inversion results across materials / devices, and establish a standard reference and calibration process to support efficient detection.

[0177] It should be noted that the dislocation-related parameters in step 3 include at least crystallographic and defect intrinsic quantities, dislocation statistical and geometrical quantities, diffraction anisotropy and contrast factor, and empirical constants. Among these, crystallographic and defect intrinsic quantities include: Burgers vector b (magnitude and direction), dislocation line direction t and dislocation properties (proportion or characterization parameter of edge / screw / mixed types), and the identifier of the principal slip system. Dislocation statistical and geometrical quantities include: dislocation density ρ (measured / to be inverted quantity), and outer cut radius R. eOr its dimensionless parameters. Diffraction anisotropy and contrast factors include: the influence of elastic anisotropy and the orientation factor. Empirical constants include: the empirical constant K in the peak broadening-dislocation density mapping and the convolution / mixing weights related to line type selection.

[0178] After completing step 3, a set of stable and calibrated parameters will be obtained that can be directly used for different samples / batches of the same material. The calibrated parameter set includes: the empirical constant K obtained by inversely calculating the measured dislocation density and spectrum shape, the contrast factor and orientation factor that match the target material / reflection / slip system, b, t, the slip system set (the defect type and orientation assumption after confirmation of consistency between TEM / orientation analysis and fitting), and the cut-off parameters that are compatible with the material and dislocation environment.

[0179] Specifically, step 3 includes:

[0180] Step 3.1: Acquire images under the field of view of a multi-magnification bright-field transmission electron microscope to identify the defect type and its orientation distribution.

[0181] In the embodiments of this application, images are acquired under 2–200 nm multi-magnification bright-field TEM (transmission electron microscopy) to identify microcrack / stack fault zones, dislocation cell regions, and void defect types and their orientation distribution. Specifically, bright-field TEM is used to characterize the defect morphology and scale of CaF2(111) single crystals at multiple magnifications.

[0182] As per the instruction manual Figure 3 In (a), a regular fluorite lattice is observed in a 2nm field of view, with no curved stripes or dislocations, indicating that the local lattice is basically intact.

[0183] As per the instruction manual Figure 3 In (b), in a 5nm field of view, the atomic-level contrast near the defect in the upper right corner is observed. The lattice fringes are basically continuous on both sides of the defect, and some lattice points can still be identified inside the defect. This indicates that it is not a true vacuum, but a local misalignment of the lattice. At this time, the dislocation has not developed into a crack.

[0184] As per the instruction manual Figure 3In (c)-(e), when the field of view is expanded to 20–100 nm, slender dark lines with a length of 15–40 nm and large areas of light and dark interlacing can be observed; CaF2 is a cubic fluorite crystal, which is prone to forming thin-layer cracks or stacking faults along the <110> orientation; under bright-field conditions, these defects will appear as dark lines due to the local thickness difference and strain field generated along the interface, and the scale matches the microcracks / stacking faults, so they can be identified as microcracks or stacking fault bands formed by {111} cleaving planes; in addition, the scattered dark gray / bright spot contrast comes from heat. The stress-induced amorphized layer and high dislocation cell region; microcracks and stacking fault bands cause small-angle tilting of adjacent crystal regions, corresponding to the local θ distribution in the Bragg condition. The rocking curve shows low-intensity shoulder signals on both sides of the main peak. This is because these micro-orientation regions contribute scattering simultaneously rather than the spikes emitted by a single ideal crystal plane. The local strain field generated by the dislocation region and the amorphized layer causes the interplanar spacing d to have a distribution on the microscale. According to the Wilhelm–Wilkens model, this will be directly mapped to an additional term of the full width at half maximum (FWHM) B.

[0185] As per the instruction manual Figure 3 In (f), annular dark pits and curved stripes with a diameter of about 140 nm were also observed in the 200 nm field of view, which were speculated to be caused by voids, bubbles or sheet warping. Thus, the TEM results preliminarily verified the XRD inferences about residual compressive stress and peak broadening, and revealed the multi-scale damage framework of calcium fluoride microcracks, dislocations and voids working together, providing microscopic basis for subsequent process optimization.

[0186] Step 3.2: Perform fast Fourier transform and bandpass filtering on the selected preimage, and reconstruct it through inverse Fourier transform to extract the crystal plane frequency components related to the defects and determine the slip dislocations.

[0187] Specifically, in order to deeply analyze the types of dislocations in CaF2(111) crystals and their influence on diffraction behavior, a representative region under a 50 nm field of view was selected for bright-field TEM observation, and the original image was subjected to fast Fourier transform (FFT) and bandpass filtering. Subsequently, the crystal plane frequency components related to the defects were extracted by inverse Fourier transform (IFFT) to accurately reveal the real space morphology of the dislocations. In the image of the sample, the lattice fringes showed step-like dislocations at the defect positions, proving that there were slip dislocations spanning tens of nanometers in this region.

[0188] Step 3.3: Count the number of dislocations within the predetermined statistical area of ​​the transmission electron microscope and calculate the measured dislocation density of the sample.

[0189] Specifically, dislocation density statistics are performed on multiple TEM views of the sample, using the formula ρ = n / A; where ρ is the dislocation density, A is the area, and n is the number of dislocations in A.

[0190] The measured dislocation density of the sample is 9.7 × 10⁻⁶.12 m -2 .

[0191] Step 3.4: Measure the half-maximum width of the rocking curve of the target crystal plane reflection and compare it with the shoulder signal caused by the local orientation distribution.

[0192] In the embodiments of this application, the half-peak width B_{111} of the swing curve of CaF2(111) reflection is measured and compared with the shoulder signal caused by the local θ distribution. The half-peak width measured by the swing curve is 0.031407°.

[0193] Step 3.5: Substitute the measured dislocation density ρ, the Burgers vector b, and the coupling coefficient C related to target reflection into the Wilkens dislocation broadening model to inversely calculate the empirical constant K.

[0194] In the embodiments of this application, the measured ρ, Burgers vector b, and coupling coefficient C(111) are substituted into the Wilkens dislocation broadening formula:

[0195]

[0196] In the formula: B 111 The full width at half maximum (FWHM) of the characteristic peaks in the XRD diffraction of calcium fluoride 111 single crystal is 5.48 × 10⁻⁶. -4 rad; K is an empirical constant; b is the dislocation vector, taking the most common one. <110> The value of the lateral dislocation is

[0197] The coupling coefficient C is obtained from the elastic lattice constant of calcium fluoride. 111 =0.30; Substitute The empirical constant K can be obtained as follows:

[0198]

[0199] It should be noted that the obtained K≈3.0 is within the normal range reported in the literature; this indicates that the Wilkens model between dislocation density and peak broadening can still accurately match the peak shape of calcium fluoride; with this corrected K as a fixed parameter, the dislocation density of the sample can be roughly determined by the half-width peak height.

[0200] Step 3.6: Using the calibrated K as a fixed parameter, establish a mapping between peak broadening and dislocation density for rapid inversion of dislocation density in subsequent samples.

[0201] Specifically, for any reflection (hkl), a linear mapping is established using the Wilkens form of equation (24) (with K as an empirical constant):

[0202]

[0203] In the formula: K is the calibration constant obtained and fixed by inverse calculation in step 3.5; b is the magnitude of the Burgers vector; C hkl The coupling (contrast) coefficient is related to the elastic anisotropy / slip system of the material.

[0204] Furthermore, several target reflections (hkl) without significant overlap were selected, and the eigenpeak broadening B was measured. hkl (Instrument / size item separation has been completed), then read the calibrated parameters {K,b,C} hkl Substitute each element into equation (26) to obtain ρ. Perform weighted fusion on ρ (the weights can be set according to the signal-to-noise ratio / peak shape fit goodness) to obtain the sample dislocation density estimate.

[0205] Step 3.7: Compare the orientation distribution caused by microcracks and / or stacking faults with the peak broadening increment to achieve a synergistic interpretation of residual stress and peak broadening by transmission electron microscopy and X-ray diffraction.

[0206] Specifically, the comparison rules for orientation dispersion and peak broadening increment caused by microcracks and / or stacking faults include: rocking curve diagnosis, TEM consistency verification, and treatment for inversion.

[0207] Among them, the rocking curve diagnosis measures the half-peak width of the rocking curve of the target reflection and records the intensity and angular domain of the "shoulders" on both sides of the main peak (as orientation dispersion characteristics). If the shoulders are significant, it is determined that there is an "orientation dispersion" contribution.

[0208] TEM consistency verification involves identifying the orientation and distribution of microcracks / stack faults under TEM. If the orientation is consistent with the crystal plane family / diffraction geometry of the reflection (the correspondence between small-angle tilt caused by microcracks / stack faults and the shoulder is given in the appendix), the shoulder of the rocking curve is attributed to "orientation dispersion". Otherwise, it is preferentially attributed to "dislocation broadening / point defect perturbation".

[0209] The treatment used for inversion is that when the shoulder is confirmed to originate from orientation dispersion, its increment is not included in B for inverting ρ in equation (24). hkl The peak broadening in step 3.6 is only observed with "de-orientation dispersion". Calculations can then be performed. This allows for a combined interpretation of "residual stress and peak broadening sources" by TEM and XRD.

[0210] Step 3.8: Output the aforementioned statistical parameters and model results as prior constraints for subsequent peak fitting and dislocation strain field inversion.

[0211] Specifically, the output of the aforementioned statistical parameters and model results includes the calibrated parameter set, sample-level results, and mapping / fitting model.

[0212] The calibrated parameter set is such as {K,ρ,B}111 C 111}. Fixed K; Burgers vector b, dislocation line orientation / type, and set of slip systems; C related to target reflection. hkl (and indexed representations of direction / contrast factors). These parameters serve as prior constraints for subsequent peak fitting and dislocation strain field inversion.

[0213] Sample-level results include: Step 3.6 obtaining the reflection-by-reflection dislocation density ρ using equation (26) and the sample dislocation density estimate obtained by weighted fusion of ρ, B hkl The correlation between the shoulder index and its attribution conclusions of “orientation spread / dislocation broadening” and the statistics of TEM defect type / orientation (pass / fail markers).

[0214] The mapping / fitting model is a complex amplitude mapping and intensity expression of "stress-defect-diffraction signal" (Equations 22-23) as the physical forward model for spectrum simulation / fitting; combined with the calibrated parameter set, it is directly used for subsequent peak fitting and dislocation strain field inversion.

[0215] In summary, the overall method flowchart of the method proposed in this invention is shown in the appendix to the specification. Figure 4 As shown, this invention uses single-crystal calcium fluoride samples for micro-area stress defect detection, verifying the feasibility and practicality of the invention. The following specific example illustrates the effectiveness of this invention.

[0216] The equipment used for testing included: a white light interferometer (BRUKER Contour X-500), an XRD diffractometer (Malvern Panalytical Empyrean S3), a focused ion beam instrument (Helios 5CX), and a spherical aberration-corrected transmission electron microscope (Themis Z(3.2)). A total of six calcium fluoride samples were used in the experiment, numbered 1-6. Samples 1-4 had a (111) crystal orientation, samples 3 and 4 underwent scratching and heat treatment (to introduce mechanical and thermal stress), and samples 5 and 6 had (100) and (110) crystal orientations, respectively. Before the experiment, all samples underwent ultra-precision polishing to ensure consistent surface conditions and facilitate subsequent comparative analysis.

[0217] The surface morphology measurement results of the calcium fluoride samples are shown in the attached instruction manual. Figure 5 As shown, the surface roughness parameters of each sample are basically at the nanometer level, with Sa and Sq both remaining at around 1 nm. This provides an important prerequisite for subsequent XRD and TEM analysis: when the roughness deviation is extremely small, the measured diffraction peaks or micro-defect information are more reliable and comparable.

[0218] The calcium fluoride sample was subjected to routine diffraction analysis using an XRD diffractometer (Cu target). The measurement results are shown in the attached instruction manual. Figure 5As shown.

[0219] To further reveal the defect morphology and scale of CaF2(111) single crystals, bright-field TEM was used for multi-magnification characterization, and the results were as described in the attached specification. Figure 6 As shown.

[0220] The full width at half maximum (FWHM) of sample 3 is 0.060721°, and the dislocation density calculated using equation (24) is approximately 3.7 × 10⁻⁶. 14 m -2 In a TEM field of view of 20 nm, the actual dislocation density can be obtained through dislocation statistics as approximately 3.87 × 10⁻⁶. 14 m -2 As per the instruction manual Figure 7 As shown, the result is close to the calculated value.

[0221] This invention also provides a non-destructive testing system for atomic-scale stress defects in ultra-precision components, the system comprising:

[0222] The micro-region stress-dislocation coupled diffraction peak shape modeling unit is configured to execute step 1, that is, under the constraints of X-ray diffraction geometry and Bragg equation, based on the relationship between anisotropic elasticity and dislocation broadening, to establish a theoretical model of the diffraction peak shape under the coupling of micro-region stress field and dislocation strain field.

[0223] The stress-defect-diffraction signal structure factor mapping modeling unit is configured to execute step 2, which is to substitute the atomic displacement field caused by the stress state and defect distribution into the structure factor and form a diffraction intensity expression, thereby establishing a mapping relationship model between stress state, defect distribution and diffraction signal.

[0224] The Wilkens dislocation broadening-measured dislocation density parameter calibration unit is configured to perform step 3, which is to calibrate model parameters such as orientation factor scale and characteristic length based on the Wilkens dislocation broadening equation and the measured dislocation density.

[0225] The peak position parameters and peak width parameters output by the micro-region stress-dislocation coupled diffraction peak shape modeling unit are used as the intensity mapping of the stress-defect-diffraction signal structure factor mapping modeling unit and the broadening calibration of the Wilkens dislocation broadening-measured dislocation density parameter calibration unit, respectively, so that the three units can be coupled and run in the order of step 1, step 2 and step 3.

[0226] The micro-region stress-dislocation coupling diffraction peak shape modeling unit includes:

[0227] The micro-region stress solver unit is used to acquire diffraction data of the target crystal plane within its effective incident angle range under the condition of satisfying the X-ray diffraction geometry and Bragg equation, obtain the actual crystal plane spacing and peak position information, calculate the corresponding strain, and determine the directional elastic modulus of the crystal direction based on the single crystal compliance constant. Thus, the equivalent force along the scattering vector direction is obtained according to the elastic strain and elastic modulus to characterize the micro-region stress field and determine the peak position center shift.

[0228] The dislocation strain modeling sub-unit is used to establish the scaling relationship of dislocation-induced mean square microstrain and the linear relationship between peak broadening and dislocation parameters under the condition of material elastic anisotropy. It adopts Wilkens dislocation broadening theory, takes the material elastic constant, Burgers vector and target slip system as input, and uses the direction factor as an empirical constraint to obtain the direction factor and mean square microstrain that characterize the dislocation strain field and determine the peak width parameter.

[0229] The diffraction peak shape theory generation subunit is used to generate a diffraction peak shape theory model based on Wilkens stress field integral under the assumptions of a single dislocation type, a unique slip system, and fixed b and t. The peak position center offset and peak width parameters are used as inputs of the line shape function to generate the target crystal plane diffraction peak shape that couples the micro-region stress field and the dislocation strain field.

[0230] The stress-defect-diffraction signal structure factor mapping modeling unit includes:

[0231] The diffraction intensity modeling subunit is used to construct a diffraction intensity model at the diffraction angle θ using structure factor, multivariate factor, angular factor, and temperature factor.

[0232] The structure factor parameterization subunit is used to express the structure factor as a cumulative form of atomic position information, and uses the approximate atomic scattering factor as the input parameter set of the intensity model.

[0233] The material baseline generation subunit is used to construct the analytical relationship between the diffraction intensity and diffraction angle of each crystal plane for calcium fluoride crystals, forming a material baseline for the numerical spectrum.

[0234] The displacement field decomposition sub-unit is used to decompose the total displacement of the j-th atom into continuous stress field displacement, dislocation migration field displacement, and point defect disturbance.

[0235] The stress-induced displacement solving sub-element is used to calculate the displacement caused by the macroscopic stress field based on the stress-strain relationship of cubic calcium fluoride, mapping the stress field to atomic displacement.

[0236] Dislocation-induced displacement solving sub-element is used to calculate the displacement field caused by the dislocation network characterized by the Burgers vector b according to the anisotropic elasticity theory, so as to obtain the dislocation-induced lattice distortion distribution.

[0237] The displacement-intensity coupled solution sub-element is used to construct a complex amplitude model of diffraction intensity and substitute it into the diffraction intensity formula in step 2.1 and the analytical relationship in step 2.3 to obtain a mapping model that simultaneously considers the combined effects of stress, dislocations and point defects, which is used to generate and fit diffraction patterns.

[0238] The Wilkens dislocation broadening-measured dislocation density parameter calibration unit includes:

[0239] The TEM microscopy acquisition and defect identification subunit is used to acquire images and identify defect types and their orientation distributions such as microcracks, stacking fault zones, dislocation cell regions and cavities under a multi-magnification bright-field TEM field of view of 2–200 nm.

[0240] The frequency domain filtering and slip dislocation determination subunit is used to perform FFT and bandpass filtering on the selected preimage and to reconstruct it using IFFT, so as to extract the crystal plane frequency components related to the defects and determine the slip dislocations.

[0241] The dislocation density metrology subunit is used to count the number of dislocations n within a given TEM area A and calculate the measured dislocation density of the sample according to ρ = n / A.

[0242] The XRD rocking curve peak width measurement subunit is used to measure the half-peak width B_{111} of the rocking curve reflected by CaF2(111) and compare it with the shoulder signal caused by the local θ distribution.

[0243] The Wilkens broadening calibration sub-unit is used to substitute the measured ρ, Burgers vector b, and coupling coefficient C(111) into the Wilkens dislocation broadening formula, and to inversely calculate the empirical constant K to complete the model scale calibration.

[0244] The peak width-density mapping solidification subunit is used to solidify the mapping relationship between peak broadening and ρ using a calibrated K as a fixed parameter for rapid inversion of dislocation density in subsequent samples.

[0245] The multi-source consistency verification sub-unit is used to compare the orientation dispersion caused by microcracks / stack faults with the peak broadening increment to confirm the consistency of TEM and XRD in interpreting residual stress and peak broadening.

[0246] The prior constraint output sub-unit is used to output key parameters such as {K, ρ, B{111}, C(111)} and serve as prior constraint inputs for subsequent peak fitting and dislocation strain field inversion.

[0247] This invention discloses a non-destructive testing method and system for atomic-scale stress defects in ultra-precision components. By integrating peak shape modeling of "micro-region stress × dislocation strain", stress / defect-diffraction signal mapping based on structural factors and Wilkens-measured dislocation density calibration in a closed loop within the same data path, it achieves synchronous separation and joint characterization of peak position and peak width, physical traceability and identifiability of parameters, high precision and high reproducibility of results, and also has the ability to adapt to material anisotropy, rapid fitting and inversion, and non-destructive high-resolution evaluation of high-value components in service. This reduces interpretation ambiguity and multiple solutions, and improves detection efficiency and robustness.

[0248] The above descriptions are merely embodiments of this application, and common knowledge regarding specific structures and characteristics in the solutions is not described in detail here. It will be apparent to those skilled in the art that this application is not limited to the details of the above exemplary embodiments, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Therefore, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within this application. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A non-destructive testing method for atomic-scale stress defects in ultra-precision components, characterized in that, The method includes: Step 1: Establish a theoretical model of diffraction peak shape under the coupling of micro-region stress field and dislocation strain field, and clarify the functional relationship between peak displacement and peak broadening with respect to the stress field and dislocation strain field, as the theoretical basis for subsequent mapping and inversion; Step 2: Under the constraints of the theoretical model described in Step 1, construct a mapping relationship model from stress state, dislocation parameters, and point defect distribution parameters to diffraction signals, and form initial criteria for spectrum simulation and parameter inversion; Step 3: Based on the Wilkens dislocation broadening equation and combined with the measured dislocation density of the sample, the dislocation-related parameters in the mapping relationship model described in Step 2 are jointly calibrated and constrained to obtain a calibrated parameter set and criteria. Based on this, the spectrum fitting and rapid inversion of the sample are performed to improve the accuracy of quantitative characterization.

2. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 1, characterized in that, Step 1 includes: Step 1.1: Under the condition of satisfying the X-ray diffraction geometry and Bragg equation, diffraction data are collected for the target crystal plane within its effective incident angle range. The actual interplanar spacing and peak position information are obtained and the strain is calculated accordingly. The directional elastic modulus of the crystal direction is determined based on the single crystal compliance constant. Then, the equivalent stress along the scattering vector direction is obtained according to the elastic strain and elastic modulus to characterize the micro-region stress field. Step 1.2: Under the condition of material elastic anisotropy, Wilkens dislocation broadening theory is adopted. With the material elastic constant, Burgers vector and target slip system as inputs, the scaling relationship of dislocation-induced mean square microstrain and the linear relationship between peak broadening and dislocation parameters are established. The direction factor is used for empirical constraints, thereby obtaining the direction factor and mean square microstrain that characterize the dislocation strain field. Step 1.3: Under the assumptions of a single dislocation type, a unique slip system, and that the Burgers vector b and the dislocation line direction t are fixed, the theoretical model of diffraction peak shape is derived based on the Wilkens stress field integral.

3. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 1, characterized in that, Step 2 includes: Step 2.1: Establish a diffraction intensity model at the diffraction angle θ. The diffraction intensity model integrates the structure factor, multiplicity factor, angle factor, and temperature factor. Step 2.2: Represent the structure factor as the sum of the position information of each atom, and use the approximate atomic scattering factor to form the input parameter set of the diffraction intensity model; Step 2.3: For the target crystal, derive the analytical relationship between the diffraction intensity and diffraction angle of each crystal plane, and use it as the material baseline for the numerical spectrum; Step 2.4: Decompose the total displacement of the j-th atom into the superposition of continuous stress field displacement, dislocation displacement field and point defect disturbance; Step 2.5: Based on the stress-strain constitutive relationship of the target crystal, calculate the displacement caused by the macroscopic stress field, and map the macroscopic stress field to atomic-scale displacement to characterize the stress-induced lattice distortion; Step 2.6: Based on the theory of anisotropic elasticity, calculate the displacement field induced by the dislocation network characterized by the Burgers vector b, so as to obtain the dislocation-induced lattice distortion field. Step 2.7: Establish a complex amplitude model of diffraction intensity and substitute it into the diffraction intensity expression in Step 2.1 and the analytical relationship between diffraction intensity and diffraction angle of each crystal plane in Step 2.3 to obtain a mapping model that simultaneously characterizes the coupling effect of stress, dislocation and point defect, which is used to generate and fit diffraction patterns.

4. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 1, characterized in that, Step 3 includes: Step 3.1: Acquire images under the field of view of a multi-magnification bright-field transmission electron microscope to identify the defect type and its orientation distribution; Step 3.2: Perform fast Fourier transform and bandpass filtering on the selected preimage, and reconstruct it through inverse Fourier transform to extract the crystal plane frequency components related to the defects and determine the slip dislocations; Step 3.3: Count the number of dislocations within the predetermined statistical area of ​​the transmission electron microscope and calculate the measured dislocation density of the sample; Step 3.4: Measure the full width at half maximum (FWHM) of the rocking curve of the target crystal plane reflection and compare it with the shoulder signal caused by local orientation distribution; Step 3.5: Substitute the measured dislocation density ρ, Burgers vector b, and coupling coefficient C related to target reflection into the Wilkens dislocation broadening model to inversely calculate the empirical constant K; Step 3.6: Using the calibrated K as a fixed parameter, establish a mapping between peak broadening and dislocation density for rapid inversion of dislocation density in subsequent samples; Step 3.7: Compare the orientation distribution caused by microcracks and / or stacking faults with the peak broadening increment to achieve a synergistic interpretation of residual stress and peak broadening by transmission electron microscopy and X-ray diffraction. Step 3.8: Output the aforementioned statistical parameters and model results as prior constraints for subsequent peak fitting and dislocation strain field inversion.

5. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 2, characterized in that, In step 1.1, the shift Δ(2θ) of the diffraction peak position is determined by the following formula: Δ(2θ)=-2tanθ hkl e (hkl) The equivalent force is determined by the following formula: In the formula: E (hkl) ε is the directional elastic modulus of the crystal orientation; (hkl) S represents the elastic strain along the crystal plane normal; 11 ,S 12 ,S 44 λ represents the compliance constant of the single-crystal material; h, k, l represent the Miller indices of the crystal planes (h, k, l); Δd represents the change in interplanar spacing; λ represents the incident X-ray wavelength; ω±α (hkl) Here is the geometric expression for the Bragg angle of this crystal plane (hkl); 2sin(ω±α) (hkl) ) represents the geometric expression of the denominator terms in the Bragg equation under ω-2θ; d (hkl) d is the theoretical interplanar spacing; means This represents the measured interplanar spacing.

6. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 2, characterized in that, In step 1.2, the scaling relation of dislocation-induced mean square microstrain is determined by the following formula: In the formula: ρ is the average strain; b is the dislocation density; b is the Burgers vector and its magnitude; C is the elastic constant. These are dimensionless coefficients related to the stiffness matrix C and the dislocation type / geometry; The linear relationship between peak broadening and dislocation parameters is determined by the following formula: In the formula: B (hkl) θ is the intrinsic spectral linewidth of the sample; (hkl) For the theoretical Bragg angle, given by λ and d hkl Decision; cosθ (hkl) sinθ (hkl) These are trigonometric functions of the theoretical Bragg angle, all of which are dimensionless; A (hkl) The orientation factor is the result of combining material anisotropy with dislocation type / slip system; A (hkl) (C,b,slipsys) is the comprehensive direction factor, where: C is the elastic constant, b is the Burgers vector and its magnitude, and slipsys is the target slip system; denoted as |b|, representing the contribution of dislocation statistics to broadening; |b| represents the magnitude of the Burgers vector. The direction factor is determined by the following formula: In the formula: κ is the empirical correction coefficient.

7. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 2, characterized in that, In step 1.3, the theoretical model for diffraction peak shape is as follows: A (hkl) =f(C ij ,b,t,g (hkl) ,R e ) In the formula, g (hkl) R is the diffraction vector; t is the orientation of the dislocation line; e The radius of the dislocation strain field shielding is denoted as .

8. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 2, characterized in that, The mapping model for step 2 is as follows: In the formula: I hkl (θ;σ,ρ,b,slipsys,C…) represent the relative diffraction intensities at the diffraction angle θ and the corresponding crystal plane (hkl); P is the multiplicity factor; F hkl ({r+u j (r)}) is the structure factor containing the displacement term; r = (x, y, z), which are the position coordinates of the atoms in the undeformed crystal; u j (r) represents the total displacement of the j-th atom; For the geometric / polarization term (angle factor) related to the diffraction angle; e -2M σ is the temperature factor, approximately 1 at room temperature; ρ is the stress state; b is the Burgers vector; slipsys is the slip system; and C is the material elastic constant.

9. The non-destructive testing method for atomic-scale stress defects in ultra-precision components according to claim 3, characterized in that, In step 3.5, the half-peak width of the sway curve is determined by the following formula: In the formula: B 111 λ is the full width at half maximum (FWHM) of the characteristic peaks in the XRD diffraction of calcium fluoride 111 single crystal; K is an empirical constant; b is the dislocation vector.

10. A non-destructive testing system for atomic-scale stress defects in ultra-precision components, characterized in that, include: The micro-region stress-dislocation coupled diffraction peak shape modeling unit is configured to perform step 1 of claim 1, that is, under the constraints of X-ray diffraction geometry and Bragg equation, based on the relationship between anisotropic elasticity and dislocation broadening, to establish a theoretical model of diffraction peak shape under the coupling of micro-region stress field and dislocation strain field. The stress-defect-diffraction signal structure factor mapping modeling unit is configured to perform step 2 of claim 1, that is, to substitute the atomic displacement field caused by the stress state and the defect distribution into the structure factor and form the diffraction intensity expression, thereby establishing a mapping relationship model between stress state, defect distribution and diffraction signal. The Wilkens dislocation broadening-measured dislocation density parameter calibration unit is configured to perform step 3 of claim 1, that is, to calibrate model parameters such as orientation factor scale and characteristic length based on the Wilkens dislocation broadening equation and in combination with measured dislocation density.

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