A theoretical calculation and data-driven combined method for musbauer spectrum research

Abstract

This invention relates to the interdisciplinary field of materials computation and spectroscopic analysis. To address the problems of low experimental throughput, high computational cost, and difficulties in analysis caused by a lack of standard spectral libraries in existing technologies, it provides a Mössbauer spectral research method that combines theoretical calculation with data-driven approaches. This invention obtains and predicts candidate crystal structures from a historical crystal structure database, performs thermodynamic stability screening and all-electron quantum chemical calculations to acquire their Mössbauer spectral parameters, and then uses a symbolic regression algorithm to construct a predictive model between structural features and spectroscopic parameters after structural feature extraction. This enables second-level spectral parameter prediction, expands the theoretical standard library, and is used for accurate analysis of experimental spectra. This invention significantly improves prediction efficiency and analytical accuracy, and provides physical insights for materials design.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of materials computation and spectroscopic analysis, specifically to a Mössbauer spectroscopy research method that combines theoretical calculation with data-driven approaches. Background Technology

[0002] Mössbauer spectroscopy is a microscopic detection technique based on the recoilless resonance effect of atomic nuclei. By analyzing hyperfine parameters such as isomorphic shifts, quadrupole splitting, and hyperfine magnetic fields, it can accurately characterize the valence state, coordination environment, and magnetic structure of specific elements in materials, and is considered the "gold standard" for atomic-scale local structure analysis. Currently, this technique mainly relies on experimental measurements combined with first-principles calculations based on density functional theory. Experimentally, signals are collected using radioactive sources, while theoretically, spectroscopic parameters are simulated through quantum mechanical calculations.

[0003] However, existing methods have significant limitations: in terms of experimental measurements, signal acquisition throughput is low and time-consuming, making it difficult to achieve high-throughput detection; for complex systems with low content, metastable states, and multiphase mixtures, experimental spectra are prone to peak overlap and noise interference, making analysis difficult; at the same time, traditional density functional theory (DFT) is computationally expensive and time-consuming when dealing with large systems or low-symmetry structures, failing to meet the requirements of high-throughput screening. Furthermore, existing standard spectral databases are severely insufficient, resulting in a lack of corresponding reference data for many novel materials and metastable phases, leading to analytical dilemmas of "spectral data without structure" or "structure without spectrum."

[0004] To overcome the above-mentioned shortcomings, this invention proposes a Mössbauer spectral research method that combines theoretical calculation with data-driven approaches. By constructing a nonlinear mapping model between structural feature descriptors and Mössbauer spectral parameters through machine learning, it achieves rapid prediction and high-precision analysis of Mössbauer spectral parameters, thereby supplementing and improving the theoretical spectral database and enhancing the analysis efficiency and reliability of complex material systems. Summary of the Invention

[0005] In order to solve at least one of the above-mentioned technical problems in the prior art, the present invention provides a method for studying Mössbauer spectroscopy that combines theoretical calculation with data-driven approaches.

[0006] This invention provides a method for studying Mössbauer spectroscopy that combines theoretical calculations with data-driven approaches. The method includes: Obtain all crystal structures containing the target element from the historical crystal structure database, and use a structure prediction program to predict the chemical composition ratios not covered in the historical crystal structure database to generate candidate crystal structures. Based on density functional theory, the candidate crystal structures were screened for thermodynamic stability and geometrically optimized to obtain stable and metastable structures. Mössbauer spectral parameters of some of the stable and metastable structures were obtained by all-electronic quantum chemical calculations. The Mössbauer spectral parameters include isotropic shifts, quadrupole splitting, and hyperfine magnetic fields. Multidimensional structural feature descriptors of the stable and metastable structures are extracted, and a symbolic regression algorithm is used to model the nonlinear correlation between the structural feature descriptors and the Mössbauer spectral parameters to train a prediction model. Based on the prediction model, the Mössbauer spectral parameters of all target crystals are predicted, and the historical theoretical Mössbauer spectral standard library is supplemented according to the prediction results. Based on the supplemented historical theoretical Mössbauer spectral standard library, the Mössbauer spectrum to be tested is analyzed to determine the phase composition and structural information contained in the Mössbauer spectrum to be tested.

[0007] In one optional implementation, a structure prediction program is used to predict the chemical composition ratios not covered in the historical crystal structure database, including: Candidate crystal structures with different space group symmetries and different central atom coordination environments are generated by using the USPEX program based on evolutionary algorithms or the symmetry search program based on group theory, wherein the central atom coordination environment includes octahedral, tetrahedral or triangular prism coordination.

[0008] In one optional implementation, the candidate crystal structure is subjected to thermodynamic stability screening and geometric optimization based on density functional theory, including: Using the VASP software package, the projected fused wave method and PBE functional were used for geometry optimization until the atomic forces of the candidate crystal structure were less than a preset force threshold and the lattice stress converged. Using R 2 SCAN functional calculations are performed on the formation energy of each structure contained in the candidate crystal structure, and the energy difference of each structure relative to the thermodynamically stable phase is calculated by convex hull analysis. Candidate crystal structures with energy differences below a preset threshold are retained to complete the thermodynamic stability screening. Based on the results of geometric optimization and thermodynamic stability screening, stable and metastable structures were obtained.

[0009] In one optional implementation, the thermodynamic stability screening further includes: Phonon spectra of the selected candidate crystal structures were calculated using the VASP software package in conjunction with Phonopy software. Based on the calculation results, candidate crystal structures without imaginary frequencies in the phonon spectra were selected.

[0010] In one optional implementation, the Mössbauer spectral parameters of the stable and metastable structures are obtained through all-electron quantum chemical calculations, including: The calculations were performed using WIEN2k software based on the all-electronic augmented plane wave method.

[0011] In one optional implementation, a symbolic regression algorithm is used to model the nonlinear correlation between the structural feature descriptor and the Mössbauer spectral parameters, including: The SISSO algorithm is used to combine multi-dimensional structural feature descriptors using basic mathematical operators to generate a high-order candidate descriptor space. Using neural compressed sensing technology, one or more structural feature descriptors that are most strongly correlated with the Mössbauer spectral parameters are selected from the higher-order candidate descriptor space. Based on the selected structural feature descriptors, a mapping function with a clear mathematical analytical form is generated as the prediction model.

[0012] In one alternative implementation, the Mössbauer spectrum to be measured is analyzed based on a supplemented historical theoretical Mössbauer spectral standard library, including: The historical theoretical Mössbauer spectral standard library is used as the initial fitting model and input into the spectrum fitting software. The experimental spectrum obtained by the spectrum fitting software is decomposed into a superimposed spectrum composed of one or more phase spectra from the historical theoretical Mössbauer spectral standard library by least squares fitting. Based on the superimposed spectrum, the phase composition and corresponding structural information contained in the target crystal are determined.

[0013] Compared with the prior art, the beneficial effects of the present invention are: This invention establishes a predictive model based on the structural feature descriptors and Mössbauer spectral parameters by integrating high-throughput first-principles calculations and symbolic regression machine learning. This improves the efficiency of traditional computations that take several days by several orders of magnitude. Furthermore, it can accurately analyze complex and multiphase experimental spectra based on a supplemented historical theoretical Mössbauer spectral standard library, effectively identifying phase composition and structural information.

[0014] Furthermore, the prediction model constructed in this invention is physically interpretable and can output explicit mathematical expressions that reveal the correlation between microstructure and spectroscopic parameters. This not only provides theoretical guidance for material design but also systematically fills the gaps in experimental spectra in metastable phases and other aspects, forming a complete technical closed loop of "theoretical prediction - data generation - experimental analysis," fundamentally improving the overall capabilities of Mössbauer spectroscopy. Attached Figure Description

[0015] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating a method for studying Mössbauer spectroscopy that combines theoretical calculations with data-driven approaches, according to an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] By precisely analyzing three hyperfine parameters in the Mössbauer spectroscopy spectrum—isomorphic shift, quadrupole splitting, and hyperfine magnetic field—researchers can quantitatively resolve the electronic structure, chemical bond covalentity, symmetry evolution, and phase composition of materials.

[0019] Although Mössbauer spectroscopy has wide applications in heterogeneous catalysis, secondary batteries, geological minerals, and biogenic ferritin, its practical applications are still limited by the following bottlenecks due to the physical principles involved: (1) Extremely low signal acquisition throughput: limited by the radioactive source (e.g. 57 Due to the intrinsic activity of Co and the limitations of its nuclear resonance cross section, obtaining spectra with high signal-to-noise ratio (SNR) usually requires continuous counting for several hours to several days, which severely restricts the detection efficiency of samples.

[0020] (2) Difficulty in measuring complex systems: For supported nanocatalysts with low iron content and high dispersion or complex heterojunction interfaces, experimental spectra often show severe baseline fluctuations and highly overlapping characteristic peaks at multiple sites, which makes the effective physical signal easily submerged by background noise.

[0021] (3) Insufficient spatiotemporal resolution: The long sampling period makes it difficult for this technology to capture the transient evolution of materials during the reaction process, and it cannot achieve true high time resolution in-situ / operando dynamic tracking.

[0022] Currently, theoretical calculations and numerical simulations primarily rely on first-principles calculations using DFT to compute Mössbauer spectral parameters. However, traditional computational simulations reveal the following drawbacks: a contradiction between computational cost and system scale: for complex systems with low symmetry, disordered doping, or large unit cells, the time required for DFT calculations of the electric field gradient (EFG) and electron density increases exponentially, making it difficult to support high-throughput screening in materials genome engineering.

[0023] The existing "experimental measurement + theoretical calculation" model suffers from drawbacks such as long R&D cycles, limited analytical dimensions, and low efficiency. More critically, these limitations result in a severe shortage of existing theoretical Mössbauer spectral libraries (Standard Database). Many novel structures and metastable phases lack corresponding standard data, creating a gap where there are either spectra without structures or structures without spectra. Currently known experimental standard libraries are insufficient to meet the needs for accurate spectral interpretation. Therefore, developing a machine learning-based data-driven method to construct a high-dimensional "structure-spectroscopy" nonlinear mapping model to achieve millisecond-level rapid prediction of Mössbauer spectral parameters, and thereby supplementing and improving the historical theoretical Mössbauer spectral standard library, is of extremely urgent practical significance for breaking through the analytical bottleneck in new material development and realizing intelligent qualitative and quantitative analysis of complex systems.

[0024] According to an embodiment of the present invention, an embodiment of a method for studying Mössbauer spectroscopy that combines theoretical calculation with data-driven approaches is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0025] This embodiment provides a method for studying Mössbauer spectroscopy that combines theoretical calculations with data-driven approaches, and can be used on the aforementioned mobile terminal. Figure 1 This is a flowchart of a Mössbauer spectroscopy research method combining theoretical calculation and data-driven approaches according to an embodiment of the present invention, as shown below. Figure 1 As shown, the process includes the following steps: S1: Obtain all crystal structures containing the target element from the historical crystal structure database, and use a structure prediction program to predict the chemical composition ratios not covered in the historical crystal structure database to generate candidate crystal structures.

[0026] In this embodiment, all binary or multi-element inorganic crystal structures containing the target element are retrieved from authoritative historical crystal structure databases such as the Materials Project, The Cambridge Structural Database, The Inorganic Crystal Structure Database, and the Crystallography Open Database, and their unit cell parameters and atomic coordinates are obtained.

[0027] Optionally, a structure prediction program is used to predict the chemical group ratios not covered in the historical crystal structure database, including: using the USPEX program based on evolutionary algorithms or the symmetry search program based on group theory to generate candidate crystal structures with different space group symmetries and different central atom coordination environments, wherein the central atom coordination environment includes octahedral, tetrahedral or triangular prism coordination.

[0028] In this embodiment, for chemical composition ratios not covered by the historical crystal structure database (such as unconventional ratios in the Fe-S and Fe-C systems), the USPEX program based on evolutionary algorithms or the symmetry search program based on group theory is used to generate candidate crystal structures with different space group symmetries and different central atom coordination environments.

[0029] S2: Based on density functional theory, the candidate crystal structures are screened for thermodynamic stability and geometrically optimized to obtain stable and metastable structures.

[0030] Optionally, the candidate crystal structure is subjected to thermodynamic stability screening and geometric optimization based on density functional theory, including: using the VASP software package, employing the projected fused wave method and PBE functional to perform geometric optimization until the atomic forces on the candidate crystal structure are less than a preset force threshold and the lattice stress converges; using R... 2 The SCAN functional calculates the formation energy of each structure contained in the candidate crystal structure, and calculates the energy difference of each structure relative to the thermodynamically stable phase through convex hull analysis. Candidate crystal structures with energy differences below a preset threshold are retained to complete the thermodynamic stability screening. Based on the geometric optimization results and the thermodynamic stability screening results, stable and metastable structures are obtained.

[0031] Optionally, the thermodynamic stability screening further includes: using the VASP software package in conjunction with Phonopy software to calculate the phonon spectrum of the screened candidate crystal structures, and selecting candidate crystal structures that do not have imaginary frequencies in the phonon spectrum based on the calculation results.

[0032] In this embodiment, the Vienna Ab-initio Simulation Package (VASP), which performs electronic structure calculations and quantum mechanical-molecular dynamics simulations, is used. The Projector Augmented Wave (PAW) method and Perdew-Burke-Ernzerhof Functional (PBE) are employed to perform high-precision geometric optimization on all candidate crystal structures until the atomic forces and crystal orientation stresses reach the convergence criteria (e.g., atomic forces are less than 0.03 eV / Å).

[0033] Using R 2 SCAN functional calculations were performed on the formation energies of each structure, and the energy difference between the candidate crystal structure and the thermodynamically stable phase was calculated using the convex hull analysis method. An energy difference threshold (e.g., energy difference E) was then set. hull (<0.2 eV / atom), retaining stable and metastable structures that meet this condition.

[0034] Furthermore, the phonon spectra of these stable and metastable structures were calculated using the VASP software package and the Phonopy software for calculating material lattice dynamics, and stable and metastable structures without imaginary frequencies were selected as inputs for subsequent spectroscopic calculations.

[0035] S3: Obtain Mössbauer spectral parameters of some of the stable and metastable structures through all-electron quantum chemical calculations. The Mössbauer spectral parameters include isomorphic shifts, quadrupole splitting, and hyperfine magnetic fields.

[0036] Optionally, the Mössbauer spectral parameters of some of the stable and metastable structures can be obtained through all-electron quantum chemical calculations, including calculations using WIEN2k software based on the all-electron augmented plane wave method.

[0037] In this embodiment, the Augmented Plane Wave plus Local Orbitals (APW+lo) method is employed, utilizing the quantum chemistry software WIEN2k for precise DFT calculations of stable and metastable structures. This method accurately handles wave function variations near the nuclei in both stable and metastable structures, yielding Mössbauer spectral parameters. Specifically, isotropic displacements are calculated by measuring the electron contact density at the nucleus and calibrating using a standard reference (e.g., metallic iron); quadrupole splitting is calculated by measuring the electric field gradient tensor (EFG) at the nucleus and combining it with the nuclear quadrupole moment to obtain the corresponding splitting value; and the hyperfine magnetic field is calculated by spin polarization, considering contact interactions, orbital contributions, and dipole contributions.

[0038] In this embodiment, the formula for calculating the isomer shift (IS) is as follows: In the formula, The nuclear constant; This represents the electron density at the atomic nucleus of the sample; This represents the electron contact density at the atomic nuclei of metallic iron.

[0039] The formula for calculating quadrupole splitting (QS) is: In the formula, The value represents the nuclear quadrupole splitting value, reflecting the energy level splitting of the atomic nucleus in a non-cubic symmetric electric field environment. It is in an excited state. 57 The nuclear quadrupole moment of an Fe atom nucleus (spin quantum number I>1) characterizes the degree to which the nuclear charge distribution deviates from a spherical shape. In this embodiment, Q = 0.16 × 10⁻⁶. -28 m 2 ; It is the elementary charge; It is the principal axis component of the electric field gradient tensor, which describes the magnitude of the electric field gradient at the atomic nucleus; It is an asymmetric parameter used to describe the asymmetry of the electric field gradient.

[0040] Hyperfine field (B hf The formula for calculating ) is: In the formula, This represents the Fermi contact term, which is the main contributing term, originating from the imbalance in the probability density distribution of s electrons at the atomic nucleus (spin polarization). Represents the orbital term, which originates from the magnetic field generated by the orbital angular momentum of the electron; Represents the dipole term, which originates from the magnetic dipole interaction between the electron spin magnetic moment and the nuclear magnetic moment.

[0041] S4: Extract the multi-dimensional structural feature descriptors of the stable and metastable structures, and use the symbolic regression algorithm to perform nonlinear correlation modeling between the structural feature descriptors and the Mössbauer spectral parameters to train and obtain the prediction model.

[0042] In this embodiment, Python scripts and materials informatics toolkits (such as Pymatgen) are used to perform feature engineering on the optimized stable and metastable structures. Centered on the iron atom, the first coordinating shell atom is identified through Voronoi polyhedron analysis or a fixed cut radius to determine the coordination number. The average bond length, standard deviation of bond length, and bond angle distortion index between the iron atom and the ligand atoms are calculated to quantify the symmetry breaking of the coordination polyhedron. Features such as electronegativity, atomic radius, and atomic number of the coordinating atoms are introduced to construct a multi-dimensional structural feature descriptor that reflects differences in the chemical environment.

[0043] Optionally, a symbolic regression algorithm is used to model the nonlinear correlation between the structural feature descriptors and the Mössbauer spectral parameters, including: using the SISSO algorithm to combine multi-dimensional structural feature descriptors through basic mathematical operators to generate a higher-order candidate descriptor space; using neural compressed sensing technology to select one or more structural feature descriptors that are most strongly correlated with the Mössbauer spectral parameters from the higher-order candidate descriptor space; and generating a mapping function with a clear mathematical analytical form based on the selected structural feature descriptors as the prediction model.

[0044] In this embodiment, the Sure Independence Screening and Sparsifying Operator (SISSO) algorithm is used to nonlinearly combine multi-dimensional structural feature descriptors using mathematical operators (such as +, -, ×, ÷, exp, log, etc.) to generate a space of hundreds of millions of high-order candidate descriptors. The core operator with the strongest correlation in Mössbauer spectral parameters is employed using neural compressed sensing technology to ultimately output a relational expression with a clear mathematical form, thus obtaining the prediction model. In practical applications, the Hyperfine Field (B) is derived. hf An analytical function varying with the effective coordination number or average bond length is used. Leave-one-out cross-validation is employed to evaluate the prediction accuracy of the model, ensuring it can perform rapid spectroscopic predictions of new structures within seconds. The advantage of using the SISSO algorithm for modeling lies in its applicability to small sample data, making it particularly suitable for computationally intensive Mun spectrum modeling. Starting from basic physical input features, it constructs analytical formulas to predict target properties through a combination of mathematical operations. These formulas are based on underlying physical laws, thus possessing strong generalization capabilities and can be extrapolated to other systems.

[0045] S5: Based on the prediction model, predict the Mössbauer spectral parameters of all target crystals, and supplement the historical theoretical Mössbauer spectral standard library according to the prediction results. Based on the supplemented historical theoretical Mössbauer spectral standard library, analyze the Mössbauer spectrum to be tested to determine the phase composition and structural information contained in the Mössbauer spectrum to be tested.

[0046] Optionally, the analysis of the Mössbauer spectrum to be tested is performed based on the supplemented historical theoretical Mössbauer spectral standard library, including: using the historical theoretical Mössbauer spectral standard library as an initial fitting model, inputting it into the spectrum fitting software, fitting it using the least squares method, decomposing the experimental spectrum obtained by the spectrum fitting software into a superimposed spectrum composed of one or more phase spectra from the historical theoretical Mössbauer spectral standard library, and determining the phase composition and corresponding structural information contained in the target crystal based on the superimposed spectrum.

[0047] To further describe the technical solution of this application, the following specific embodiments illustrate the Mössbauer spectrum analysis process of iron sulfide based on theoretical calculation data.

[0048] Step 1: Obtaining the structure of iron sulfide. First, collect experimentally known iron sulfide crystal structures from existing open-source crystal structure databases (such as MaterialsProject, COD, etc.). At the same time, use structure prediction programs (such as USPEX, etc.) to theoretically predict experimentally unreported iron sulfide phases and generate candidate crystal structures. Step 2: Using the VASP software package, combined with R 2 The SCAN functional optimizes candidate crystal structures of iron sulfide and calculates the thermodynamic formation energy, and plots the convex hull based on the calculation results. Step 3: Based on the calculated convex hull, using the point with the lowest formation energy as the reference standard, set an energy difference threshold of 0.2 eV / atom. If the formation energy of a candidate crystal structure is within this range, it is considered to be thermodynamically stable. If the formation energy is not within this range, these structures are considered to be thermodynamically unstable and need to be discarded. Step 4: Based on the screening results of the formation energy, use the VASP software package in conjunction with Phonopy to calculate the phonon spectrum of the candidate crystal structures to determine whether these candidate crystal structures have imaginary frequencies. If imaginary frequencies are present, these structures are considered to be kinetically unstable, so structures with imaginary frequencies should be discarded. Step 5: Determine the final candidate crystal structure based on the calculation results of the formation energy and phonon spectrum; Step 6: Use the quantum chemistry software WIEN2k to analyze the Mössbauer spectral parameters (isotropic shift IS, quadrupole splitting QS, hyperfine magnetic field B) of a small number of candidate crystal structures. hf The calculations were performed, and the structural features of these crystals (coordination number of the central iron atom, structural symmetry of the central iron atom, chemical bond length of Fe-Fe, chemical bond length of Fe-S, etc.) were extracted using Python scripts and the Pymatgen package. Step 7: Using the symbolic regression algorithm, the extracted basic features are nonlinearly combined through mathematical operators to generate a space of hundreds of millions of high-order candidate descriptors; using neural compressed sensing technology, the core operators with the strongest correlation to the Mössbauer spectral parameters of iron sulfide are screened from the huge space of high-order candidate descriptors, and finally the relation with a clear mathematical form is output as the prediction model.

[0049] In the formula, This represents the predicted value of the isotropic displacement from the prediction model. This represents the average bond length of the corresponding crystal structure. This represents the coordination number between atoms in the corresponding crystal structure. This represents the generalized coordination number between atoms in the corresponding crystal structure; This represents the quadrupole splitting prediction value of the prediction model; This represents the ultra-fine magnetic field prediction value of the prediction model.

[0050] Step 8: Use this prediction model to quickly predict the Mössbauer spectral parameters of all iron sulfide crystal structures and improve the Mössbauer spectral parameter standard database for iron sulfide. Step 9: Using the spectra obtained from the experimental characterization, the experimental spectra were fitted, analyzed, and visualized using the spectral fitting software Mosswin, combined with a historical theoretical Mössbauer spectral standard library. The spectral lines corresponding to isotropic shifts, quadrupole splitting, and hyperfine magnetic fields were superimposed to obtain the superimposed spectrum. The phase and composition information of the experimental sample were determined using the superimposed spectrum. The proportions of each component are as follows: Fe7S8: 40%; FeS2: 2.9%; Fe3S4: 47.2%; Fe9S... 10 5.8%; Fe9S 11 4.1%.

[0051] This invention achieves physically interpretable explicit correlation modeling, unlike traditional "black box" machine learning models. Employing a symbolic regression algorithm based on neural compressed sensing, this invention successfully derives analytical mathematical expressions for ultrafine magnetic fields, isotropic displacement, and quadrupole splitting. These explicit functions establish a quantitative mapping between local structural features and Mössbauer spectral parameters, making complex physical correlations intuitive and computable. Through the established nonlinear mapping model, this invention achieves second-level predictions from crystal structure features to Mössbauer spectral parameters. Compared to first-principles all-electronic calculations that take several days, this invention improves computational efficiency by several orders of magnitude while maintaining high accuracy, meeting the real-time processing needs of massive data in materials genome engineering. This invention not only performs numerical predictions but also reveals the physical essence through mathematical expressions. For example, it quantitatively analyzes the influence of coordination number, chemical bond length, and local symmetry breaking on the magnetic properties and charge distribution of iron-based materials. This physical interpretability provides theoretical guidance for the design and performance regulation of novel magnetic materials. Utilizing the high-throughput prediction capabilities of this invention, a theoretical Mössbauer spectral reference database containing a large number of stable and metastable phases has been constructed. This fills the gap in the experimental standard library regarding extreme conditions or metastable phases, providing a precise basis for attributing unknown phases discovered in experiments. This invention can identify trace phases or evolutionary intermediates that are difficult to detect using traditional methods, effectively reducing the subjectivity of manual fitting and achieving precise analysis of complex kinetic reaction processes.

[0052] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for studying Mössbauer spectroscopy that combines theoretical calculations with data-driven approaches, characterized in that: The method includes: Obtain all crystal structures containing the target element from the historical crystal structure database, and use a structure prediction program to predict the chemical composition ratios not covered in the historical crystal structure database to generate candidate crystal structures. Based on density functional theory, the candidate crystal structures were screened for thermodynamic stability and geometrically optimized to obtain stable and metastable structures. Mössbauer spectral parameters of some of the stable and metastable structures were obtained by all-electronic quantum chemical calculations. The Mössbauer spectral parameters include isotropic shifts, quadrupole splitting, and hyperfine magnetic fields. Multidimensional structural feature descriptors of the stable and metastable structures are extracted, and a symbolic regression algorithm is used to model the nonlinear correlation between the structural feature descriptors and the Mössbauer spectral parameters to train a prediction model. Based on the prediction model, the Mössbauer spectral parameters of all target crystals are predicted, and the historical theoretical Mössbauer spectral standard library is supplemented according to the prediction results. Based on the supplemented historical theoretical Mössbauer spectral standard library, the Mössbauer spectrum to be tested is analyzed to determine the phase composition and structural information contained in the Mössbauer spectrum to be tested.

2. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 1, characterized in that, The structure prediction program is used to predict the chemical composition ratios not covered in the historical crystal structure database, including: Candidate crystal structures with different space group symmetries and different central atom coordination environments are generated by using the USPEX program based on evolutionary algorithms or the symmetry search program based on group theory, wherein the central atom coordination environment includes octahedral, tetrahedral or triangular prism coordination.

3. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 1, characterized in that, The candidate crystal structures were screened for thermodynamic stability and their geometry optimized based on density functional theory, including: Using the VASP software package, the projected fused wave method and PBE functional were used for geometry optimization until the atomic forces of the candidate crystal structure were less than a preset force threshold and the lattice stress converged. Using R 2 SCAN functional calculations are performed on the formation energy of each structure contained in the candidate crystal structure, and the energy difference of each structure relative to the thermodynamically stable phase is calculated by convex hull analysis. Candidate crystal structures with energy differences below a preset threshold are retained to complete the thermodynamic stability screening. Based on the results of geometric optimization and thermodynamic stability screening, stable and metastable structures were obtained.

4. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 3, characterized in that, The thermodynamic stability screening also includes: Phonon spectra of the selected candidate crystal structures were calculated using the VASP software package in conjunction with Phonopy software. Based on the calculation results, candidate crystal structures without imaginary frequencies in the phonon spectra were selected.

5. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 1, characterized in that, The Mössbauer spectral parameters of the stable and metastable structures were obtained through all-electron quantum chemical calculations, including: The calculations were performed using WIEN2k software based on the all-electronic augmented plane wave method.

6. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 1, characterized in that, The nonlinear correlation model between the structural feature descriptor and the Mössbauer spectral parameters is performed using a symbolic regression algorithm, including: The SISSO algorithm is used to combine multi-dimensional structural feature descriptors using basic mathematical operators to generate a high-order candidate descriptor space. Using neural compressed sensing technology, one or more structural feature descriptors that are most strongly correlated with the Mössbauer spectral parameters are selected from the higher-order candidate descriptor space. Based on the selected structural feature descriptors, a mapping function with a clear mathematical analytical form is generated as the prediction model.

7. The Mössbauer spectroscopy research method combining theoretical calculation and data-driven approach according to claim 1, characterized in that, Based on the supplemented historical theoretical Mössbauer spectral standard library, the Mössbauer spectra to be tested were analyzed, including: The historical theoretical Mössbauer spectral standard library is used as the initial fitting model and input into the spectrum fitting software. The experimental spectrum obtained by the spectrum fitting software is decomposed into a superimposed spectrum composed of one or more phase spectra from the historical theoretical Mössbauer spectral standard library by least squares fitting. Based on the superimposed spectrum, the phase composition and corresponding structural information contained in the target crystal are determined.

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