Cmas glassy structure first-principles modeling method, apparatus, and medium

Abstract

This invention discloses a first-principles modeling method, apparatus, and medium for CMAS glassy structures. The method includes determining the number of atoms in the system based on the chemical composition of CMAS and constructing an initial atomic model; setting first-principles calculation parameters based on density functional theory; in an NVT canonical ensemble, heating the initial atomic model to the melting temperature for melt relaxation to obtain a molten state model; cooling the molten state model from the melting temperature to room temperature for quenching to obtain a room-temperature glassy state model; switching the ensemble to an NPT ensemble, relaxing the room-temperature glassy state model to eliminate internal stress, and performing static geometric optimization to obtain a CMAS glassy ground-state model. This invention has the advantages of being based on first-principles molecular dynamics methods, accurately describing interatomic electronic interactions at the atomic scale without relying on empirical parameters, and constructing a standardized, high-precision, and repeatable CMAS glassy structure model through a "melt-quench" process.

Description

Technical Field

[0001] This invention relates to the fields of computational materials science and high-temperature corrosion technology, specifically to a first-principles modeling method, device, and medium for CMAS glassy structures. Background Technology

[0002] Thermal barrier coatings (TBCs) are crucial for achieving high thrust-to-weight ratios and long service lives in hot-end components of modern aero-engines, such as turbine blades. Typically, these components are coated with a ceramic layer, such as yttrium-stabilized zirconia (YSZ), to insulate against high-temperature combustion gases and reduce the operating temperature of the metal substrate. However, in actual service environments, dust, volcanic ash, and impurities in the fuel ingested by the engine melt at high temperatures (typically above 1200°C), forming a calcium magnesium aluminum silicate (CMAS) melt with a low eutectic point. This melt rapidly wets and penetrates along the micropores and grain boundaries of TBCs, undergoing a violent physicochemical reaction with YSZ, leading to coating phase transformation, peeling, and ultimately, failure. Therefore, CMAS corrosion has become the primary factor limiting the lifespan of thermal barrier coatings. A deep understanding of the glassy structure of CMAS and its interfacial reaction mechanism with TBCs at the atomic scale is of significant scientific and engineering value for the development of novel corrosion-resistant coatings.

[0003] Currently, research on the glassy structure of CMAS mainly faces the following limitations:

[0004] 1. Limitations of experimental characterization methods

[0005] CMAS forms a typical multi-component disordered glassy material at high temperatures. Its atomic structure lacks long-range order, making it difficult to accurately characterize it at the atomic scale using traditional crystal structure analysis techniques, such as X-ray diffraction (XRD). Furthermore, CMAS corrosion is a dynamic, high-temperature, and highly corrosive process, and current experimental techniques struggle to achieve in-situ, real-time monitoring of the internal structure of molten CMAS, ion diffusion behavior, and its interface with TBCs at the atomic scale. This lack of microscopic observation methods severely restricts a deeper understanding of the CMAS corrosion mechanism.

[0006] 2. The accuracy of traditional calculation methods is insufficient.

[0007] To theoretically explore the microstructure of CMAS, existing techniques attempt to employ molecular dynamics (MD) simulations based on empirical force fields. However, these methods have inherent limitations: the force fields used (such as the BKS potential and Tossell potential) are typically fitted from the physical properties of specific crystal structures or simple oxide systems. When applied to amorphous systems like CMAS, which contain multiple elements such as Ca, Mg, Al, Si, and O, exhibit complex interatomic interactions, and have highly disordered structures, their accuracy and transferability are severely inadequate. The results obtained from simulations using different force fields often differ significantly, making it difficult to guarantee the reliability of the simulations and failing to provide a credible physical picture of the microstructure of CMAS.

[0008] 3. Lack of first-principles modeling methods

[0009] First-principles calculations, especially those based on density functional theory (DFT), have become the "gold standard" for studying the microstructure of materials because they do not rely on empirical parameters and can accurately describe the electronic interactions between atoms. Theoretically, the glassy structure of CMAS can be constructed from first-principles starting points through "melt-quench" molecular dynamics simulations. However, in practical applications, this method faces significant challenges: a lack of standardized procedures. Currently, there is a lack of a publicly available, systematic, and standardized first-principles-based "melt-quench" modeling method. Existing publications typically only report the final calculation results, while remaining tight-lipped about key parameters in the model construction process, such as melting temperature, relaxation time, quenching rate, and ensemble selection. This lack of a technical solution makes model construction in this field difficult to reproduce, casting doubt on the reliability of the results, and significantly hindering further progress in in-depth research on the corrosion mechanism of CMAS based on first-principles molecular dynamics (AIMD). Summary of the Invention

[0010] To address the limitations of existing experimental techniques in characterizing disordered glassy structures, the insufficient accuracy of traditional empirical force field methods, and the lack of a systematic process in first-principles modeling, this invention provides a standardized, high-precision, and repeatable first-principles modeling method, apparatus, and medium for CMAS glassy structures. The method is based on first-principles molecular dynamics, accurately describing interatomic electron interactions at the atomic scale without relying on empirical parameters, and constructing a CMAS glassy structure model through a "melt-quench" method.

[0011] To address the aforementioned technical problems, the present invention provides a first-principles modeling method for CMAS glassy structures, comprising:

[0012] Based on the chemical composition of the CMAS to be modeled, the number of each atom in the system is determined, and an initial atomic model that satisfies the boundary conditions of electroneutrality and periodicity is constructed.

[0013] Based on density functional theory, first-principles calculation parameters are set, including electron exchange correlation energy, pseudopotential type, plane wave basis set cutoff energy, and Brillouin zone sampling method.

[0014] In the NVT canonical ensemble, the initial atomic model is heated to the melting temperature. Then, melt relaxation is performed until the system reaches thermodynamic equilibrium to obtain the molten state model;

[0015] The molten state model is based on the melting temperature. Cool down to room temperature Quenching was performed to obtain a room temperature glassy model;

[0016] The ensemble is switched to the NPT isothermal and isobaric ensemble, and the room temperature glassy state model is relaxed to eliminate internal stress and static geometric optimization is performed until the force on each atom converges to obtain the CMAS glassy ground state model.

[0017] In a preferred embodiment, the method further includes performing structural analysis on the CMAS glassy ground state model. If the structural analysis results conform to the characteristics of the glassy state, the CMAS glassy ground state model is determined to be completed.

[0018] The structural analysis includes radial distribution analysis of atomic pairs, coordination number analysis, and bond angle analysis.

[0019] In a preferred embodiment, the atomic pair radial distribution analysis includes Atomic pairs Atomic pairs and The radial distribution of atomic pairs, if The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, and the radial distribution function is greater than If the distance tends to 1.0 without obvious oscillation, it is determined to meet the long-range disorder characteristics of the glassy state.

[0020] In a preferred embodiment, the melting temperature The temperature is set to 3000K to 4500K, the melt relaxation time is greater than or equal to 15 ps, and the time step is set to 1.0 fs to 2.0 fs;

[0021] If the total energy of the system and the mean square displacements of silicon and aluminum atoms are detected, and the total energy of the system fluctuates within the mean, and the mean square displacements of silicon and aluminum atoms increase linearly with time, then the system is determined to have reached thermodynamic equilibrium.

[0022] In a preferred embodiment, the molten state model employs a preset quenching rate. From melting temperature Continuous linear cooling to room temperature The quenching rate Set to 100K / ps to 500K / ps;

[0023] Alternatively, the molten state model may employ a preset temperature interval. From melting temperature Cool down to room temperature in stages And isothermal relaxation of the NVT canonical ensemble is performed at each temperature node, the temperature interval Set it to 300K to 500K.

[0024] In a preferred embodiment, in an NPT isothermal-isobaric ensemble, the target pressure is set to 0 GPa, the cell volume and shape are set to be variable, and a constant pressure control method is used for relaxation until volume convergence, thereby eliminating internal stress.

[0025] In a preferred embodiment, the static geometry optimization specifically includes the following steps:

[0026] The last frame of the room-temperature glassy state model after eliminating internal stress was used as the starting point for optimization, and molecular dynamics thermal motion was stopped.

[0027] Iterative optimization is performed using the conjugate gradient method or the quasi-Newton method, simultaneously optimizing the atomic positions and unit cell size until each atom is force-converged, thus obtaining the final CMAS glassy ground state model;

[0028] If the residual force acting on an atom is less than a preset threshold, then the atom is determined to have converged force. The preset threshold is set to... to .

[0029] In a preferred embodiment, the electron exchange correlation energy is a PBE functional under the generalized gradient approximation, the plane wave basis set cutoff energy is greater than 400 eV, and the Brillouin zone sampling method is to sample at the Γ point in the Brillouin zone.

[0030] The present invention also provides a computer device, comprising: a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor communicates with the memory via the bus, and when the machine-readable instructions are executed by the processor, the steps of the first-principles modeling method for CMAS glassy structures as described in any of the preceding claims are performed.

[0031] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the first-principles modeling method for CMAS glassy structures as described in any of the preceding claims.

[0032] Compared with existing technologies, the first-principles modeling method, device, and medium for CMAS glassy structures disclosed in this invention have the following advantages:

[0033] This invention discloses a first-principles modeling method for the glassy structure of CMAS (Chemical Molecular Assay). The method includes determining the number of atoms in the system based on the chemical composition of the CMAS to be modeled, constructing an initial atomic model that satisfies both electroneutrality and periodicity boundary conditions, and ensuring the physical rationality of the initial model state by clearly defining the stoichiometry and strictly adhering to the electroneutrality principle. The setting of periodic boundary conditions makes the model suitable for first-principles molecular dynamics simulations, providing a standardized starting point for subsequent melting-quenching processes and ensuring the repeatability of model construction from the outset.

[0034] Based on density functional theory, first-principles calculation parameters are set, including electron exchange correlation energy, pseudopotential type, plane-wave basis set cutoff energy, and Brillouin zone sampling method. On the one hand, by adopting density functional theory and starting from first principles, the reliance on empirical parameters is completely eliminated; on the other hand, by clearly defining key parameters such as exchange correlation functional, pseudopotential, cutoff energy, and sampling method, the accuracy and reproducibility of electronic structure calculations are ensured, laying the foundation for accurately describing the complex electronic interactions between elements such as Ca, Mg, Al, Si, and O in the CMAS system.

[0035] In the NVT canonical ensemble, the initial atomic model is heated to the melting temperature. The system undergoes melt relaxation until it reaches thermodynamic equilibrium, resulting in a molten state model. Temperature is controlled by the NVT ensemble, allowing for prolonged relaxation at temperatures far exceeding the material's physical melting point. The thermodynamic equilibrium criterion is explicitly defined as the stability of the system's total energy and the linear increase in the mean square displacement of Si, Al, and other network-forming ions. This ensures that artificial "memory" in the initial structure is completely eliminated, atoms are fully mixed, and a reliable liquid precursor is provided for subsequent quenching to obtain a true glassy structure.

[0036] The molten state model is based on the melting temperature. Cool down to room temperature Quenching is performed to obtain a room-temperature glassy model. Through a cooling quenching step, the high-temperature molten state is "frozen" into a room-temperature amorphous state, completely reproducing the transformation process of CMAS material from melt to glass. This core technical operation of quenching differs from traditional modeling methods that only perform simple relaxation on the crystal structure, ensuring that the final model can truly reflect the long-range disorder characteristics of the CMAS glassy state.

[0037] The ensemble was switched to the NPT isothermal-isobaric ensemble, and the room-temperature glassy model was relaxed to eliminate internal stress. Static geometric optimization was then performed until the forces on each atom converged to obtain the CMAS glassy ground-state model. NPT ensemble relaxation allows for free adjustment of the cell volume and shape, effectively eliminating non-physical internal stresses generated during quenching due to volume fixation, and causing the model density to converge to the true value. Further static geometric optimization relaxes the atomic positions to the lowest energy configuration, ensuring that the final CMAS glassy ground-state model meets first-principles accuracy requirements in terms of structural stability and energy rationality, providing a reliable initial configuration for subsequent calculations of ion diffusion, interfacial reactions, and other properties. Attached Figure Description

[0038] Figure 1 This is an overall flowchart illustrating an embodiment of the first-principles modeling method, device, and medium for CMAS glassy structures of the present invention.

[0039] Figure 2 A schematic diagram of the temperature-time trajectory of initial heating, melt relaxation, and cooling quenching in an embodiment of the first-principles modeling method, equipment, and medium for the CMAS glassy structure of the present invention.

[0040] Figure 3 The graphs showing the changes in total energy and mean square displacement (MSD) of the CMAS system over time in an embodiment of the first-principles modeling method, device and medium for CMAS glassy structures of the present invention.

[0041] Figure 4 A schematic diagram of the ground state model of the CMAS glassy structure, which is an embodiment of the first-principles modeling method, device and medium of the CMAS glassy structure of the present invention;

[0042] Figure 5 A schematic diagram of the radial distribution function of an embodiment of the first-principles modeling method, device and medium for CMAS glassy structure of the present invention;

[0043] Figure 6 This is a schematic diagram of the device principle of an embodiment of the CMAS glassy structure first-principles modeling method, device and medium of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0045] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the specification of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0047] Furthermore, in this invention, the use of terms such as "first" and "second" is for descriptive purposes only and does not specifically refer to any order or sequence, nor is it intended to limit the invention. They are merely used to distinguish components or operations described using the same technical terms, and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of various embodiments can be combined with each other, but only if they are feasible for those skilled in the art. If a combination of technical solutions is contradictory or impossible to implement, such a combination should be considered nonexistent and not within the scope of protection claimed by this invention.

[0048] Example 1

[0049] The first-principles modeling method for the CMAS glassy state structure in this embodiment is based on first-principles molecular dynamics AIMD expansion. In AIMD simulations, although the motion of atomic nuclei follows classical Newtonian mechanics, the interaction forces driving atomic motion do not originate from pre-fitted empirical potential functions. Instead, they are precisely calculated based on the real-time electronic structure, i.e., the electron cloud distribution, by solving the Schrödinger equation of the system in real time at each time step. Specifically, CMAS is a complex, multi-component, highly disordered oxide system that undergoes complex chemical bond breaking and recombination during its transition from a high-temperature melt to an amorphous glassy state. The AIMD method eliminates the dependence on any empirical parameters. It can adaptively and accurately describe the electronic-level interactions between various network-forming ions (Si, Al) and network-modifying ions (Ca, Mg) and oxygen atoms in the system according to the real-time chemical environment. This is crucial for accurately reproducing the dynamic changes in atomic bonding states at high temperatures, capturing real local short-range ordered structures, and thus constructing a physically reliable and highly accurate CMAS glassy state model.

[0050] The first-principles modeling method for the CMAS glassy structure in this embodiment, such as Figure 1 As shown, it includes at least the following steps:

[0051] Step S1: Based on the chemical composition of the CMAS to be modeled, determine the number of each atom in the system and construct an initial atomic model that satisfies the boundary conditions of electroneutrality and periodicity.

[0052] Specifically, CMAS systems typically contain multiple elements such as calcium, magnesium, aluminum, silicon, and oxygen. The general chemical formula of CMAS corrosion deposits is:

[0053] ,

[0054] in, This is the molar coefficient of calcium oxide. is the molar coefficient of magnesium oxide. This is the molar coefficient of aluminum oxide. This represents the molarity coefficient of silicon dioxide. The number of various atoms within the simulation chamber needs to be accurately calculated based on the target stoichiometry. When constructing the model, the principle of electroneutrality must be strictly adhered to; that is, the total positive charge of all cations in the system must equal the total negative charge of oxygen ions. This is a fundamental physical premise for density functional theory calculations of electronic structure. If the system's charge is unbalanced, the calculation will fail to converge or the results will be physically meaningless. Simultaneously, to simulate the properties of macroscopic bulk materials using a limited number of atoms, this embodiment employs periodic boundary conditions to construct a supercell. Periodic boundary conditions eliminate surface effects at the boundaries of the simulation chamber, allowing atoms to enter from the opposite boundary when crossing one side of the chamber, thus simulating the bulk environment of an infinitely large system and avoiding interference from free surfaces on the atomic structure. When constructing the initial atomic model, a random filling method or a crystal structure-based substitution method can be used, and a reasonable initial density must be preset to avoid initial calculation collapse caused by excessively close atomic spacing.

[0055] Step S2 involves setting first-principles calculation parameters based on density functional theory. These parameters include electron exchange correlation energy, pseudopotential type, plane-wave basis set cutoff energy, and Brillouin zone sampling method. Specifically, this embodiment uses density functional theory (DFT) as the core of the calculation. Its advantage lies in the fact that it does not rely on empirical potential functions and can accurately describe the interatomic interaction forces by solving the Schrödinger equation for multi-electron systems. In terms of parameter settings, the electron exchange correlation energy is usually achieved using the PBE functional under the generalized gradient approximation (GGA), which exhibits good accuracy when dealing with oxide systems. The pseudopotential type is preferably the projected decorated wave (PAW) method, which freezes core electrons and only deals with valence electrons, thereby significantly reducing the computational load while ensuring accuracy. The cutoff energy of the plane wave basis set determines the completeness of the wave function expansion and needs to be set to a sufficiently high value to ensure computational accuracy. The Brillouin zone sampling method is designed for the characteristics of large-size supercells in amorphous systems, and sampling is usually performed only at the Γ point in the Brillouin zone. This not only conforms to the physical characteristics of amorphous systems lacking translational symmetry, but also significantly improves computational efficiency.

[0056] Step S3: In the NVT canonical ensemble, heat the initial atomic model to the melting temperature. The system undergoes melt relaxation until it reaches thermodynamic equilibrium, resulting in a molten model. Specifically, this step uses an NVT ensemble (constant number of atoms N, volume V, temperature T) for high-temperature melting simulation. The NVT ensemble is chosen because maintaining a constant volume during melting and subsequent quenching helps control the shape of the simulation chamber, preventing drastic deformation or collapse at high temperatures. The heating process raises the system temperature from room temperature to a melting temperature far exceeding the physical melting point of CMAS. This aims to impart extremely high kinetic energy to the atoms, enabling them to overcome interatomic barriers and completely break down crystal memory or unreasonable bonding in the initial artificially constructed structure, achieving full diffusion and mixing of atoms. The melt relaxation process must continue for a sufficiently long time until the system reaches thermodynamic equilibrium. At this point, the total energy of the system fluctuates around the mean, and the diffusion behavior of atoms tends to stabilize, indicating that the system has entered a homogeneous, disordered liquid equilibrium phase.

[0057] Step S4, change the molten state model from the melting temperature Cool down to room temperature Quenching is performed to obtain a room-temperature glassy model. Specifically, the quenching process is a crucial step in "freezing" the high-temperature liquid structure into an amorphous solid. Rapid cooling prevents atoms from undergoing long-range diffusion and rearrangement to form an ordered crystal structure, thus preserving the short-range ordered and long-range disordered structural characteristics of the liquid state. Quenching is performed within the NVT ensemble, maintaining the volume and ensuring the stability of the simulation box dimensions. The cooling process can employ continuous linear cooling or stepwise cooling strategies, the core of which lies in controlling the cooling rate—it must be fast enough to suppress crystallization while ensuring sufficient relaxation time for atoms to adjust their local structures.

[0058] Step S5 involves switching the ensemble to the NPT isothermal-isobaric ensemble, relaxing the room-temperature glassy model to eliminate internal stress, and performing static geometry optimization until each atom converges to obtain the CMAS glassy ground-state model. Specifically, since the preceding steps were all performed under the NVT ensemble (constant volume), although the quenched model exhibits an amorphous structure, its density remains fixed at the initial preset value, and non-physical internal stresses generated by rapid cooling may remain internally. Therefore, this step switches the ensemble to the NPT ensemble (constant number of atoms N, pressure P, temperature T), setting the target pressure to 0 GPa (i.e., standard atmospheric pressure), allowing changes in the volume and shape of the unit cell. Relaxation under the NPT ensemble automatically adjusts the unit cell size until the internal and external pressures are balanced, thereby obtaining the true equilibrium density of the CMAS glassy state of this composition at the current temperature and effectively eliminating internal stress. Subsequently, molecular dynamics thermal motion is turned off, and static geometry optimization is performed. This process, conducted at 0K, uses an iterative algorithm to adjust atomic positions and unit cell parameters, searching for local energy minima of the system until the residual force on each atom is less than a preset convergence threshold. This yields a structurally stable, lowest-energy CMAS glassy ground-state model, providing a reliable atomic model basis for subsequent microstructure analysis and property calculations.

[0059] Example 2

[0060] This embodiment, based on Embodiment 1, adds a structural analysis verification step to the final obtained CMAS glassy ground-state model. This is to ensure that the model not only converges energyally but also structurally conforms to the physical characteristics of the glassy state, preventing the model from containing crystal residues or structural defects in reality, even if the calculation shows convergence.

[0061] Step S6, after obtaining the CMAS glassy ground-state model, also includes structural analysis of the CMAS glassy ground-state model. If the structural analysis results conform to the characteristics of the glassy state, the CMAS glassy ground-state model is considered to have been successfully constructed. The structural analysis includes radial distribution analysis of atomic pairs, coordination number analysis, and bond angle analysis.

[0062] This step is crucial because first-principles calculations can only guarantee that the model is at a local energy minimum, but cannot automatically guarantee the correctness of its microscopic topology. For example, if the quenching rate is too slow or the melting is insufficient, the system may undergo local crystallization, forming a structure with lower energy but not the target glassy state. This will render subsequent calculations of diffusion coefficients or reaction barriers meaningless.

[0063] For the radial distribution analysis of atom pairs, such as Figure 5 As shown, its core lies in verifying the characteristic of "short-range order and long-range disorder." Atom pair radial distribution analysis includes... Atomic pairs Atomic pairs and The radial distribution of atomic pairs, if The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, and the radial distribution function is greater than If the distance tends to 1.0 without obvious oscillation, it is determined to meet the long-range disorder characteristics of the glassy state.

[0064] Specifically, bond length and bond length The numerical range corresponds to the typical covalent bond lengths of silicon-oxygen tetrahedra and aluminum-oxygen tetrahedra. In the CMAS glass network, silicon and aluminum, as network formers, mainly form tetrahedral coordination structures with oxygen atoms through sp3 hybridization. If the position of the first characteristic peak deviates from this range (e.g., a significant increase in the Si-O bond length), it suggests the possible existence of defect structures with high coordination numbers (e.g., five-coordinate or six-coordinate silicon), which is usually an unreasonable glassy structure. Meanwhile, the radial distribution function in the long-range is greater than... The value tends towards 1.0 and shows no obvious oscillations, intuitively reflecting that the probability of atomic arrangement over long distances tends to be randomly distributed, and there are no periodic crystal structure peaks. This criterion proves the long-range disorder of the model from a statistical physics perspective, ruling out the possibility of local crystallization.

[0065] Furthermore, for coordination number analysis, this embodiment uses... and The first peak of the radial distribution function is integrated to calculate the average coordination number. In a reasonable glassy model, the average coordination number of Si and Al should be close to 4.0, indicating that they exist in the network skeleton in a tetrahedral form. If the coordination number deviates significantly from 4.0, it indicates that the network structure has been distorted or disintegrated. For bond angle analysis, the main focus is on... and Bond angle distribution. The bond angle distribution should be around 109.5° and have a certain distribution width, which reflects the preservation of the internal structure of the tetrahedron and its distortion in the amorphous state; The bond angle distribution reflects the connection method between tetrahedra, and its distribution is usually wide (e.g., 120°-180°), reflecting the flexibility of glassy network connections. Through the above multi-dimensional structural analysis, a strict "structural rationality" judgment criterion was established to ensure that the final model can truly reflect the microscopic topological characteristics of the CMAS glassy state.

[0066] Example 3

[0067] This embodiment, based on Embodiment 1, provides a further detailed explanation of the specific parameter settings and system equilibrium criteria for high-temperature melt relaxation in step S3. Melting temperature Set to 3000K to 4500K, with a melt relaxation time greater than or equal to 15 ps and a time step of 1.0 fs to 2.0 fs.

[0068] Specifically, the physical melting point of the CMAS system is typically around 1500K. Setting the melting temperature to a range of 3000K to 4500K, which is far above the physical melting point, has the physical significance of imparting extremely high kinetic energy to the atoms. At such high temperatures, the thermal motion of atoms is extremely rapid, enabling them to overcome the potential barriers formed between atoms. This completely breaks down any crystal structure memory or unreasonable chemical bonds that may exist in the initial model, ensuring that the system enters a completely disordered liquid state. If the temperature is set too low, the atoms may not be able to overcome the energy barrier, resulting in the inability to eliminate the ordered regions in the initial structure. The final model may contain crystal residues and cannot represent the true glassy structure. Simultaneously, by detecting the total energy of the system and the mean square displacements of silicon and aluminum atoms, if the total energy of the system fluctuates within the mean and the mean square displacements of silicon and aluminum atoms increase linearly with time, the system is determined to have reached thermodynamic equilibrium.

[0069] like Figure 3 As shown, the total energy of the system fluctuates around the mean without a long-term drift trend, indicating that the thermodynamic state of the system has stabilized and the temperature control is effective. More importantly, silicon and aluminum atoms, as the main constituents of the CMAS glass network, exhibit linearly increasing mean square displacements over time, a typical characteristic of fluid behavior. In solids or crystals, atoms are confined to vibrate near their lattice positions, and the mean square displacement usually tends to saturate or fluctuates only within a limited range; however, in liquids, atoms undergo long-range diffusion, and the mean square displacement shows a linear increase over time. Therefore, only when the mean square displacement curves of silicon and aluminum atoms show linear growth can it be proven that the network structure has fully disintegrated and the system has reached a thermodynamically balanced molten state. This provides a physically reasonable starting structure for the subsequent quenching process and prevents defects such as local crystallization in the model due to insufficient melting.

[0070] Example 4

[0071] This embodiment provides a detailed explanation of the specific implementation strategy for quenching and cooling in step S4. Quenching is a crucial step in freezing a high-temperature molten structure into an amorphous glassy state. Its core lies in suppressing long-range diffusion and ordered arrangement of atoms through rapid cooling, thereby preserving the disordered structure in the liquid state. This embodiment provides two parallel quenching and cooling strategies to adapt to different computational needs and accuracy requirements.

[0072] In the first implementation method, the molten state model adopts a preset quenching rate. From melting temperature Continuous linear cooling to room temperature The quenching rate The temperature is set to between 100K / ps and 500K / ps. Specifically, in this strategy, the simulation system, under the NVT ensemble, exhibits a linear temperature decrease over time, without any isothermal relaxation plateau. For example... Figure 2 As shown, the temperature curve is a smoothly descending sloping line. The advantage of this continuous linear cooling strategy lies in its simplicity and high computational efficiency, enabling the transition from the molten state to the glassy state in the shortest possible computation time. For the quenching rate, this embodiment strictly limits it to the range of 100 K / ps to 500 K / ps. This rate range is much higher than the natural cooling rate, and its physical significance lies in depriving atoms of the time window required for long-range diffusion and lattice rearrangement. If the cooling rate is too slow (e.g., close to the equilibrium cooling rate), atoms have sufficient time to overcome the energy barrier and migrate to lower-energy lattice positions during cooling, leading to crystallization and the formation of a crystal rather than the desired glassy state. Conversely, although theoretically a faster quenching rate is more beneficial for preserving the disordered structure, due to the time step size of first-principles molecular dynamics (typically femtoseconds) and computational resources, an excessively high quenching rate may result in too few simulation steps, leaving atoms insufficient time for local structural adjustments, thus freezing too many high-energy defect structures. Therefore, the rate range selected in this embodiment is an optimal balance between suppressing crystallization and ensuring local relaxation of the structure.

[0073] In a second implementation, the molten state model is cooled stepwise from the melting temperature to room temperature at preset temperature intervals, with isothermal relaxation performed using an NVT canonical ensemble at each temperature node. These temperature intervals are set to 300K to 500K. Specifically, this strategy divides the entire cooling process into several temperature steps, for example, setting a temperature node every 300K decrease from the melting temperature. At each temperature node, the system undergoes short-term isothermal relaxation under the NVT ensemble (e.g., running hundreds to thousands of steps). Figure 2 As shown, the temperature curve exhibits a stepped decrease. The physical significance of this stepwise cooling strategy lies in the fact that it allows atoms to undergo a certain degree of local structural adjustment and energy relaxation at each temperature step, resulting in a more reasonable local topology and a more uniform distribution of internal stress in the final glassy structure. Compared to continuous cooling, stepwise cooling, although slightly increasing the computational cost, can yield a glassy model with more complete structural relaxation and a lower energy state, making it suitable for research scenarios requiring high accuracy of the model structure.

[0074] It should be understood that both of the above quenching strategies can achieve the goal of transforming the molten state model into a room-temperature glassy state model, and researchers can flexibly choose according to specific computational resources and research objectives. Regardless of the strategy used, the essence is to control the cooling rate so that the liquid structure is rapidly "frozen" before the atoms have time to arrange themselves into a long-range ordered state, thereby ensuring that the final model possesses the long-range disorder characteristics of the glassy state.

[0075] Example 5

[0076] This embodiment, based on the above embodiments, provides a detailed explanation of the specific parameter settings for NPT ensemble relaxation in step S5 and the key parameter configuration for first-principles calculations in step S2. The selection of these parameters directly affects the accuracy and efficiency of the calculation results and is an important guarantee for constructing a high-quality CMAS glassy state model.

[0077] For the NPT ensemble relaxation process, in the NPT isothermal and isobaric ensemble, the target pressure is set to 0 GPa, and the cell volume and shape are set to be variable. A constant-pressure control method is used for relaxation until volume convergence, thereby eliminating internal stress. Specifically, in the quenching process under the aforementioned NVT ensemble, the volume of the simulation box is fixed, which leads to artificial constraints on the system's contraction or expansion during cooling, resulting in the accumulation of non-physical stresses internally. By switching the ensemble to NPT and setting the target pressure to 0 GPa, the cell volume and shape are allowed to be freely adjusted, and the system can automatically find the true equilibrium density at that temperature. Using constant-pressure control methods such as the Parrinello-Rahman or Langevin pistons ensures the thermodynamic stability of the pressure control. When volume convergence no longer changes, it means that the internal stress of the system has been released, and the density has reached the physical equilibrium value, providing a reasonable structural basis for subsequent static geometry optimization.

[0078] For the static geometry optimization process, the last frame of the room-temperature glassy state model after eliminating internal stress is used as the starting point for optimization, and molecular dynamics thermal motion is stopped. Iterative optimization is performed using the conjugate gradient method or the quasi-Newton method, simultaneously optimizing atomic positions and cell sizes until the forces acting on each atom converge, resulting in the final CMAS glassy ground-state model. If the residual force acting on an atom is less than a preset threshold, the atom is considered to have converged. The preset threshold is set to... to .

[0079] Specifically, static geometry optimization seeks local minima on the energy surface of the system at 0K. Stopping molecular dynamics means disregarding temperature-induced atomic vibrations and focusing instead on the forces acting on atoms. The conjugate gradient method and the quasi-Newton method are two commonly used optimization algorithms; the former offers better robustness, while the latter converges faster. Convergence threshold. to The threshold is a crucial accuracy indicator. If the threshold is too high, the forces on the atoms are not fully released, and the model is in a high-energy metastable state. If the threshold is too low, although the accuracy is higher, the computational cost will increase exponentially and the improvement in physical meaning will be limited. This range ensures that the model is in the ground state (the lowest energy point) while also taking into account computational efficiency.

[0080] For first-principles calculations, the electron exchange correlation energy is calculated using the PBE functional under the generalized gradient approximation, the plane-wave basis set cutoff energy is greater than 400 eV, and the Brillouin zone sampling method uses sampling at the Γ point in the Brillouin zone. Specifically, the PBE (Perdew-Burke-Ernzerhof) functional is one of the most widely used functionals in the generalized gradient approximation (GGA). For oxide systems like CMAS, the PBE functional can well describe the electron correlation effects in transition metal oxides and main group oxides, accurately predict lattice constants and bond lengths, and its calculation accuracy has been verified by a large number of publications. The plane-wave basis set cutoff energy determines the completeness of the wave function expansion; setting it to greater than 400 eV ensures the calculation accuracy of the stress tensor during variable cell optimization (NPT and static optimization), avoiding the "Pulay stress" error caused by insufficient cutoff energy. For Brillouin zone sampling, since the CMAS glassy model typically contains hundreds of atoms, belonging to a large-size supercell, and the amorphous structure lacks long-range periodicity, the wave vector distribution in the reciprocal space is very dense. Therefore, sampling only at the Γ point (k=0) is sufficient to meet the accuracy requirements. This greatly reduces the computational load compared to multi-point sampling, significantly improves the efficiency of AIMD simulation, and is the standard practice for handling large-size amorphous systems.

[0081] Example 6

[0082] To further verify the effectiveness and versatility of the first-principles modeling method for CMAS glassy structures provided by this invention, this embodiment selects the silicon-rich CMAS system, which is commonly used in the study of corrosion of thermal barrier coatings in aero-engines, as a specific application scenario, and demonstrates in detail the entire modeling process and the structural features of the final model.

[0083] Specifically, the target model constructed in this embodiment has the chemical composition of Ca. 20 Mg 10 Al 20 Si 50 O 155 First, step S1 is executed. Based on the chemical composition, the number of atoms in the system is determined as follows: 20 calcium atoms, 10 magnesium atoms, 20 aluminum atoms, 50 silicon atoms, and 155 oxygen atoms, for a total of 255 atoms. When constructing the initial atomic model that satisfies the boundary conditions of electroneutrality and periodicity, the initial density is set to 2.90 g / cm³, and the calculated edge length of the cubic supercell is... Atomic coordinates were randomly generated within the unit cell using Packmol software, and the minimum interatomic distance tolerance was set to [value missing]. This is to avoid initial computational crashes caused by excessively close internuclear spacing in the initial configuration, thereby completing the construction of the initial atomic model.

[0084] Step S2 is then executed, setting the first-principles calculation parameters based on density functional theory. This embodiment uses the VASP software package for calculations, employing the PBE functional under the generalized gradient approximation for the electron exchange correlation energy, and selecting the PAW-PBE standard pseudopotential set as the pseudopotential type. The plane-wave basis set cutoff energy is set to 500 eV, exceeding the minimum requirement of 400 eV, to ensure computational accuracy. The Brillouin zone sampling method uses sampling at the Γ point in the Brillouin zone to accommodate the computational efficiency requirements of large-size amorphous cells.

[0085] Next, step S3 is performed, involving high-temperature melt relaxation within the NVT canonical ensemble. The initial atomic model is heated to a melting temperature of 3500 K, which falls within the preferred range of 3000 K to 4500 K, significantly higher than the physical melting point of CMAS. The melt relaxation time is set to 20 ps, ​​and the time step is set to 2.0 fs. By monitoring the total energy of the system and the mean square displacements of silicon and aluminum atoms, the results show that the total energy of the system fluctuates stably around the mean, and the mean square displacements of silicon and aluminum atoms increase linearly with time, indicating that the system has reached thermodynamic equilibrium, the initial crystal memory has been completely eliminated, and a molten state model is obtained.

[0086] Then, step S4 is executed to quench the molten model by cooling it from the melting temperature to room temperature. This embodiment employs a step-by-step cooling strategy, specifically: linear cooling from 3500K to 3000K, followed by isothermal relaxation; then cooling to 2500K, followed by isothermal relaxation; and so on, until finally cooling to 300K. The total equivalent quenching rate is approximately 250K / ps, falling within the preferred range of 100K / ps to 500K / ps. This strategy effectively suppresses the crystallization tendency during the cooling process, "freezing" the liquid structure to obtain a room-temperature glassy model.

[0087] Next, step S5 was executed, switching the ensemble to the NPT isothermal-isobaric ensemble, setting the target pressure to 0 GPa, and setting the cell volume and shape to be variable, to perform relaxation to eliminate internal stress. After approximately 6 ps of relaxation, the cell volume automatically adjusted and converged, and the final density stabilized at 2.96 g / cm³, which is in good agreement with the experimental value reported in the literature. Static geometry optimization was then performed using the conjugate gradient method for iterative optimization, with a convergence threshold set to... Finally, the CMAS glassy ground state model was obtained.

[0088] Finally, structural analysis was performed to verify the obtained CMAS glassy ground-state model. Figure 4 As shown, the final model exhibits typical amorphous structure characteristics, with atoms randomly distributed and without periodic repeating units. Silicon, aluminum, and oxygen atoms form a network structure, while calcium and magnesium ions are distributed in the interstices of the network. Atom pair radial distribution analysis results show that the first characteristic peak of the Si-O atom pair radial distribution function is located at... The first characteristic peak of the Al-O atom pair is located at All are within the range of glassy characteristic bond lengths, and the radial distribution function is within a distance greater than [missing information]. The time tends towards 1.0 without significant oscillation, consistent with the long-range disorder characteristics of the glassy state. Coordination number analysis shows that the average coordination number of Si atoms is 4.03, indicating that silicon atoms mainly exist in the form of [SiO4] tetrahedra. The above results verify that the model constructed in this embodiment successfully reproduces the core structural characteristics of the CMAS glassy state of "short-range order and long-range disorder," demonstrating the good agreement between the actual operation effect of the method of this invention and the data.

[0089] Example 7

[0090] This embodiment provides a computer device for executing the first-principles modeling method for CMAS glassy structures described in the above embodiments. Figure 6 As shown, the computer device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the first-principles modeling method for CMAS glassy structures as described in any of the above embodiments.

[0091] Specifically, the processor is the computational core of a computer device, responsible for executing complex calculations in first-principles molecular dynamics simulations. Because CMAS glass state modeling involves solving the Schrödinger equation for multi-electron systems, calculating interatomic interactions, and performing long-duration molecular dynamics evolution, the computational load is enormous. Therefore, processors typically employ high-performance multi-core central processing units (CPUs) or parallel computing clusters to meet the demands of high-load numerical computation. Memory stores the operating system, modeling software code, and a large amount of intermediate data generated during the calculation process, such as atomic coordinates, total system energy, and stress tensors at each time step. The bus serves as a common channel for data transmission, connecting the processor and memory to ensure high-speed and stable instruction calls and data read / write operations during long-term computations.

[0092] In addition, the computer device may also include non-volatile storage devices (such as hard disks), input interfaces, and output interfaces. The non-volatile storage devices are used to permanently store the final CMAS glassy ground-state model file and analysis data. The input interfaces connect to input devices such as keyboards and mice for users to input modeling parameters (such as chemical composition, melting temperature, quenching rate, etc.). The output interfaces connect to display devices for visualizing the modeling results, such as the final three-dimensional atomic model structure diagram and radial distribution function curve. Through the coordinated operation of the above hardware architecture, the high-precision, high-computational-load first-principles modeling method described in this invention can be effectively supported for successful implementation.

[0093] This embodiment also provides a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the first-principles modeling method for CMAS glassy structures as described in any of the above embodiments.

[0094] Specifically, a computer-readable storage medium, as the physical carrier of a computer program, essentially functions to store instruction code that can be recognized and executed by a computer system. The computer-readable storage medium described in this embodiment may include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices (such as DVDs), magnetic storage devices (such as magnetic tape), or any suitable combination thereof. It should be understood that although this embodiment lists various specific media forms, in practical applications, any tangible medium capable of containing or storing a program, as long as the program can be used by or in conjunction with an instruction execution system, device, or equipment, should fall within the protection scope of this embodiment.

[0095] In this embodiment, the computer program stored on the storage medium contains a series of instructions corresponding to the various logical steps in the method embodiment of the present invention. When the storage medium is connected to a computer device (such as the device described in Embodiment 7), the processor reads the program code in the storage medium through the bus interface and loads it into memory for execution. During execution, the processor automatically calls the underlying first-principles calculation software package according to the program instructions, and sequentially executes operations such as initial model construction, high-temperature melting relaxation, quenching and cooling, and final structure optimization. Through this storage medium, the technical solution of the present invention exists in the form of a software product, which facilitates distribution, installation, and backup between different computing platforms, greatly improving the portability of the method. This allows researchers without the ability to develop underlying algorithms to easily construct a high-quality CMAS glassy state model by loading the program.

[0096] In summary, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A first-principles modeling method of CMAS glassy structure, characterized in that, include: Based on the chemical composition of the CMAS to be modeled, the number of each atom in the system is determined, and an initial atomic model that satisfies the boundary conditions of electroneutrality and periodicity is constructed. Based on density functional theory, first-principles calculation parameters are set, including electron exchange correlation energy, pseudopotential type, plane wave basis set cutoff energy, and Brillouin zone sampling method. In the NVT canonical ensemble, the initial atomic model is heated to the melting temperature. Then, melt relaxation is performed until the system reaches thermodynamic equilibrium to obtain the molten state model; The molten state model is based on the melting temperature. Cool down to room temperature Quenching was performed to obtain a room temperature glassy model; The ensemble is switched to the NPT isothermal and isobaric ensemble, and the room temperature glassy state model is relaxed to eliminate internal stress and static geometric optimization is performed until the force on each atom converges to obtain the CMAS glassy ground state model.

2. The CMAS glassy structure first principles modeling method of claim 1, wherein: It also includes performing structural analysis on the CMAS glassy ground state model. If the structural analysis results conform to the glassy state characteristics, then the CMAS glassy ground state model is determined to be completed. The structural analysis includes radial distribution analysis of atomic pairs, coordination number analysis, and bond angle analysis.

3. The first-principles modeling method for CMAS glassy structures according to claim 2, characterized in that: The atomic pair radial distribution analysis includes Atomic pairs and The radial distribution of atomic pairs, if The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, The first characteristic peak of the radial distribution function of the atom pair is located at to Within the range, and the radial distribution function is greater than If the distance tends to 1.0 without obvious oscillation, it is determined to meet the long-range disorder characteristics of the glassy state.

4. The first-principles modeling method for CMAS glassy structures according to any one of claims 1-3, characterized in that: the melting temperature is set to 3000 K to 4500 K, the time of the melting relaxation is greater than or equal to 15 ps, and the time step is set to 1.0 fs to 2.0 fs; If the total energy of the system and the mean square displacements of silicon and aluminum atoms are detected, and the total energy of the system fluctuates within the mean, and the mean square displacements of silicon and aluminum atoms increase linearly with time, then the system is determined to have reached thermodynamic equilibrium.

5. The CMAS glassy structure first principles modeling method according to any one of claims 1-3, wherein: The molten state model uses a preset quenching rate. From melting temperature Continuous linear cooling to room temperature The quenching rate Set to 100K / ps to 500K / ps; Alternatively, the molten state model may employ a preset temperature interval. From melting temperature Cool down to room temperature in stages And isothermal relaxation of the NVT canonical ensemble is performed at each temperature node, the temperature interval Set it to 300K to 500K.

6. The CMAS glassy structure first principles modeling method according to any one of claims 1-3, wherein: In the NPT isothermal and isobaric ensemble, the target pressure is set to 0 GPa, and the cell volume and shape are set to be variable. The constant pressure control method is used to relax until the volume converges, thereby eliminating the internal stress.

7. The CMAS glassy structure first principles modeling method according to any one of claims 1-3, wherein, The static geometry optimization specifically includes the following steps: The last frame of the room-temperature glassy state model after eliminating internal stress was used as the starting point for optimization, and molecular dynamics thermal motion was stopped. Iterative optimization is performed using the conjugate gradient method or the quasi-Newton method, simultaneously optimizing the atomic positions and unit cell size until each atom is force-converged, thus obtaining the final CMAS glassy ground state model; Wherein, the residual force acting on the atom is less than a preset threshold, and it is determined that the atom is convergent under force, and the preset threshold is set to To .

8. The CMAS glassy structure first principles modeling method according to any one of claims 1-3, wherein: The electron exchange correlation energy adopts the PBE functional under the generalized gradient approximation, the plane wave basis set cutoff energy is greater than 400 eV, and the Brillouin zone sampling method adopts sampling at the Γ point in the Brillouin zone.

9. A computer device, comprising: include: The computer device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the first-principles modeling method for CMAS glassy structures as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the first-principles modeling method for CMAS glassy structures as described in any one of claims 1-8.

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