Method and system for calculating oxygen diffusion coefficient of multiphase ceramic

Abstract

The invention discloses a calculation method and system for a multiphase ceramic oxygen diffusion coefficient. The method comprises the following steps: respectively establishing a basic crystal structure and an oxygen particle model of ceramic; constructing a multiphase ceramic oxygen diffusion model by adopting an amorphization-recrystallization strategy; the mean square displacement parameters of oxygen particles (including oxygen atoms, oxygen molecules and oxygen ions) in the multiphase ceramic at each temperature and at each moment are calculated through LAMMPS software. According to molecular dynamics, an Einstein relation and an Arrhenius diffusion equation, the change rule of the oxygen diffusion coefficient in the multiphase ceramic along with the temperature is systematically obtained, so that the accurate evaluation of the oxygen diffusion behavior of the multiphase ceramic is realized. The final prediction result is accurate and reliable, and scientific basis and theoretical guidance are provided for multiphase ceramic oxygen diffusion behavior research.

Description

Technical Field

[0001] The present invention relates to the technical field of ceramic thermal protection, and in particular to a method and system for calculating the oxygen diffusion coefficient of multiphase ceramics. Background Art

[0002] With the rapid development of technologies such as hypersonic vehicles and advanced gas turbines, the ability of materials to perform in extreme thermal environments has become a key bottleneck. Heat-resistant ceramic materials, with their high melting point, low thermal conductivity, excellent thermal stability, and high-temperature mechanical properties, are widely used in key areas of hypersonic vehicles, such as thermal barrier coatings, wing leading edges, turbine blades, and combustion chamber linings. In ultra-high-temperature oxidizing environments, ceramic materials need to operate stably in a thermal environment of thousands of degrees Celsius and withstand the multiple coupling effects of oxygen, thermal stress, and high-temperature corrosion. Therefore, the development of high-performance multiphase ceramic materials is of great strategic significance for ensuring the thermal structural integrity and flight safety of aircraft.

[0003] During the service life of multiphase ceramics, oxygen diffuses through the surface layer into the material at high temperatures, causing degradation of the ceramic's thermal protection. Oxygen diffusion behavior controls key processes such as interfacial reaction rates, oxide film growth dynamics, and internal microstructural evolution. Therefore, accurately calculating and predicting the oxygen diffusion coefficient in ceramic materials is crucial not only for evaluating their high-temperature oxidation resistance but also provides key parameters for material design, structural optimization, and service life prediction.

[0004] However, current research on oxygen diffusion in multiphase ceramics still faces numerous challenges. Experimental testing methods struggle to achieve in situ observations of oxygen diffusion in extreme environments such as high temperature and high pressure. The acquired data are subject to macroscopic averaging, making it difficult to reflect diffusion pathways and mechanisms at the microscopic scale. Furthermore, traditional empirical models cannot accurately describe the anisotropic characteristics and temperature dependence of the oxygen diffusion coefficient in different crystal phases, orientations, and interface states. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a high-precision, high-efficiency method and system for calculating the oxygen diffusion coefficient of multiphase ceramics. By systematically obtaining the diffusion coefficients of oxygen particles (oxygen atoms, oxygen molecules, oxygen ions) in multiphase ceramic materials based on their temperature-dependent structural characteristics, this method enables accurate assessment of the oxygen diffusion behavior of multiphase ceramics, providing a scientific basis and theoretical guidance for the oxidation resistance of multiphase ceramics.

[0006] Technical solution: The present invention provides a method for calculating the oxygen diffusion coefficient of multiphase ceramics, comprising the following steps:

[0007] Step 1: Obtain the basic crystal structure of each single-phase ceramic and establish the ceramic supercell structure according to the lattice matching criterion;

[0008] Step 2: Based on the amorphization-recrystallization strategy, a multiphase ceramic stable structure and oxygen particle region model is established according to each single-phase ceramic supercell structure to obtain a multiphase ceramic oxygen diffusion model;

[0009] Step 3: Based on the oxygen diffusion stability model of multiphase ceramics at different temperatures, the positions of oxygen particles in the oxygen diffusion model of multiphase ceramics at each temperature and at each moment are obtained using LAMMPS software;

[0010] Step 4: Based on the time-varying relationship of the oxygen particle position in the multiphase ceramic oxygen diffusion model at different temperatures, calculate the oxygen particle mean square displacement parameter, and use the Einstein relationship to obtain the oxygen diffusion coefficient of the multiphase ceramic at each temperature;

[0011] Step 5: Based on the oxygen diffusion coefficient of multiphase ceramics at various temperatures, the Arrhenius diffusion equation is used to evaluate the oxygen diffusion behavior in multiphase ceramics, including the relationship between the diffusion coefficient and temperature, the diffusion factor, and the diffusion activation energy.

[0012] Furthermore, in step 2, a stacking-type multiphase ceramic structure model is established based on the amorphization-recrystallization strategy, the multiphase ceramic structure model is relaxed to obtain a multiphase ceramic stable structure, and an oxygen particle region is set according to the size of the multiphase ceramic stable structure, and an oxygen particle region model is established. The oxygen particles are randomly dispersed in the oxygen particle region through the oxygen particle region model, and a multiphase ceramic oxygen diffusion model is constructed according to the stacking structure construction method.

[0013] Furthermore, in step 3, the multiphase ceramic oxygen diffusion model is fully relaxed at different temperatures using LAMMPS software to obtain a multiphase ceramic oxygen diffusion stability model at different temperatures. The position of oxygen particles outside the multiphase ceramic stable structure in the multiphase ceramic oxygen diffusion model is obtained based on the multiphase ceramic oxygen diffusion stability model, and the position of oxygen particles in the multiphase ceramic oxygen diffusion model at each temperature and at each moment is obtained.

[0014] Furthermore, in step 4, the oxygen particle mean square displacement parameter calculation formula is:

[0015]

[0016] Where MSD represents the mean square displacement of oxygen atoms in the multiphase ceramic oxygen diffusion model, N represents the total number of oxygen particles, and r i (t) represents the position of the i-th oxygen particle at time t, Δt represents the time change, and <> represents the ensemble average;

[0017] The calculation formula for the oxygen diffusion coefficient D of multiphase ceramics is:

[0018]

[0019] Furthermore, the relationship between the diffusion coefficient and temperature is expressed as:

[0020]

[0021] Where R is the gas constant, T is the temperature, D0 is the diffusion factor, and Q is the activation energy of oxygen diffusion.

[0022] The present invention also provides a calculation system for the oxygen diffusion coefficient of multiphase ceramics, comprising an oxygen diffusion model construction module, a molecular dynamics simulation module, and an oxygen diffusion coefficient calculation module;

[0023] The oxygen diffusion model construction module is used to obtain the basic crystal structure of each single-phase ceramic and establish the ceramic supercell structure based on the lattice matching criterion. Based on the amorphization-recrystallization strategy, the multiphase ceramic stable structure and oxygen particle region model are established according to each single-phase ceramic supercell structure to obtain the multiphase ceramic oxygen diffusion model.

[0024] The molecular dynamics simulation module is used to obtain the position of oxygen particles in the multiphase ceramic oxygen diffusion model at each temperature and at each moment based on the multiphase ceramic oxygen diffusion stability model at different temperatures using LAMMPS software;

[0025] The oxygen diffusion coefficient calculation module is used to calculate the oxygen particle mean square displacement parameter based on the time-varying relationship between the oxygen particle position in the multiphase ceramic oxygen diffusion model at different temperatures. The Einstein relationship is used to obtain the oxygen diffusion coefficient of multiphase ceramics at various temperatures. Based on the oxygen diffusion coefficient of multiphase ceramics at various temperatures, the Arrhenius diffusion equation is used to evaluate the oxygen diffusion behavior in multiphase ceramics, including the temperature-varying relationship of the diffusion coefficient, the diffusion factor, and the diffusion activation energy.

[0026] Furthermore, the oxygen diffusion model module includes a multiphase ceramic structure unit and an oxygen diffusion model unit;

[0027] The multiphase ceramic structure unit is used to establish the basic crystal structure of single-phase ceramics, expand the cell, and preliminarily establish a stacking multiphase ceramic structure. Based on the amorphization-recrystallization strategy, the stacking multiphase ceramic structure is heated to the highest melting point, then cooled to room temperature and fully relaxed to obtain a stable structure of the multiphase ceramic.

[0028] The oxygen diffusion model is used to set the oxygen particle area according to the stable structure size of multiphase ceramics and establish the multiphase ceramic oxygen diffusion model in the same stacking construction method.

[0029] Furthermore, the molecular dynamics calculation module includes a simulation environment setting unit, a parameter calculation unit, and a data recording unit;

[0030] The simulation environment setting unit is used to simulate environmental conditions, including setting the ambient temperature, boundary conditions, and ensemble, fully relaxing the multiphase ceramic oxygen diffusion model at a specific temperature, calculating the temperature of the system at different times, and obtaining a stable multiphase ceramic oxygen diffusion model at different temperatures;

[0031] The parameter calculation unit is used to obtain the position of oxygen particles in the multiphase ceramic oxygen diffusion model based on the stable multiphase ceramic oxygen diffusion model at a specific temperature, and calculate the mean square displacement parameters of oxygen particles in the multiphase ceramic oxygen diffusion system;

[0032] The data recording unit is used to record the calculation results of the mean square displacement of oxygen particles in the multiphase ceramic at each temperature and each moment under the ensemble of simulated environmental conditions.

[0033] Furthermore, the oxygen diffusion coefficient calculation module includes an oxygen diffusion coefficient calculation unit and an oxygen diffusion behavior evaluation unit;

[0034] The oxygen diffusion coefficient calculation unit is used to extract the mean square displacement parameters of oxygen particles in multiphase ceramics at different temperatures and time points based on the results of the data recording unit in the molecular dynamics calculation module, and calculate the oxygen diffusion coefficient of multiphase ceramics at different temperatures using the Einstein relationship;

[0035] The oxygen diffusion behavior evaluation unit is used to fit the relationship between the oxygen diffusion coefficient of multiphase ceramics and temperature according to the Arrhenius diffusion equation, obtain the oxygen diffusion factor and oxygen diffusion activation energy, and evaluate the oxygen diffusion behavior in multiphase ceramics.

[0036] Beneficial Effects: Compared with existing technologies, the present invention significantly enhances the calculation and data processing of the oxygen diffusion coefficient of multiphase ceramics. Based on molecular dynamics, this method calculates parameters of the multiphase ceramic oxygen diffusion system, such as temperature, oxygen particle position, and oxygen particle mean square displacement. Combined with the Einstein relation and the Arrhenius diffusion equation, this method systematically obtains temperature-dependent oxygen diffusion coefficients, oxygen diffusion factors, oxygen diffusion activation energies, and other oxygen diffusion parameters in multiphase ceramics. This allows for an accurate assessment of the oxygen diffusion behavior of multiphase ceramics, resulting in reliable and accurate predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic flow chart of the calculation method of the present invention;

[0038] Figure 2 Schematic diagram of the oxygen diffusion model structure of the zirconium dioxide-zirconium silicate (ZrO2-ZrSiO4) two-phase ceramic in the present invention;

[0039] Figure 3 This is a graph showing the relationship between the total mean square displacement of external oxygen atoms in the ZrO2-ZrSiO4 two-phase ceramic of the present invention and time;

[0040] Figure 4 is a graph showing the relationship between the mean square displacement of external oxygen atoms in the ZrO2-ZrSiO4 two-phase ceramic of the present invention and the time along the direction perpendicular to the interface (z direction);

[0041] Figure 5 This is a graph showing the relationship between the total diffusion coefficient of external oxygen atoms in the ZrO2-ZrSiO4 two-phase ceramic of the present invention and temperature;

[0042] Figure 6 1 is a graph showing the relationship between the diffusion coefficient of external oxygen atoms along the z direction and temperature in the ZrO2-ZrSiO4 two-phase ceramic of the present invention;

[0043] Figure 7 Schematic diagram of oxygen diffusion trajectory in the ZrO2-ZrSiO4 two-phase ceramic structure at 2000K in the present invention;

[0044] Figure 8 Schematic diagram of the oxygen diffusion model structure in the yttria-stabilized zirconium dioxide-ceria (YSZ-CeO2) multiphase ceramic structure of the present invention;

[0045] Figure 9 is a graph showing the relationship between the total mean square displacement of external oxygen atoms in the YSZ-CeO2 multiphase ceramic structure of the present invention and time;

[0046] Figure 10 is a graph showing the relationship between the mean square displacement of external oxygen atoms along the z direction and time in the YSZ-CeO2 multiphase ceramic structure of the present invention;

[0047] Figure 11 This is a graph showing the relationship between the total diffusion coefficient of external oxygen atoms in the YSZ-CeO2 multiphase ceramic structure of the present invention and temperature;

[0048] Figure 12 1 is a graph showing the relationship between the diffusion coefficient of external oxygen atoms along the z direction and temperature in the YSZ-CeO2 multiphase ceramic structure of the present invention;

[0049] Figure 13 Schematic diagram of oxygen diffusion trajectory in the YSZ-CeO2 multiphase ceramic structure at 2000K in the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Example 1

[0052] The present embodiment provides a method and system for calculating the oxygen diffusion coefficient of multiphase ceramics. The method involves using LAMMPS, an open source software package developed by Steve Plimpton's team at Sanford National Laboratory, for calculation. LAMMPS is a high-performance computing software based on the principles of classical molecular dynamics that uses Newton's equations of motion to simulate systems such as atoms, molecules, and coarse-grained models. It supports a variety of force fields (such as empirical potential, reaction force field, embedded atom method, etc.) and boundary conditions (such as periodic boundary conditions, fixed boundary conditions, etc.) to calculate various properties such as the structural evolution, thermodynamic properties, mechanical properties, transport properties, and phase change behavior of the material. The LAMMPS software package is used to calculate the relationship between the basic parameters of the multiphase ceramic oxygen diffusion system and the oxygen diffusion coefficient within a certain temperature range, and has the ability to predict and evaluate the oxygen diffusion behavior of multiphase ceramics.

[0053] like Figure 1 As shown, a method and system for calculating the oxygen diffusion coefficient of a multiphase ceramic in this embodiment, taking two-phase ceramics as an example, specifically includes the following steps:

[0054] Step 1: Establish the basic crystal structure of zirconium dioxide-zirconium silicate two-phase ceramics (ZrO2-ZrSiO4) and its oxygen diffusion model. In this embodiment, cubic zirconium dioxide (ZrO2) and tetragonal zirconium silicate (ZrSiO4) are selected as specific applications.

[0055] Step 1-1: Obtain cubic phase ZrO2 (lattice constant ) crystal structure.

[0056] Step 1-2: Obtain tetragonal ZrSiO4 (lattice constant ) crystal structure.

[0057] Step 1-3: Based on the lattice matching criterion, a 13×13×1 ZrO2 supercell structure and a 10×10×1 ZrSiO4 supercell structure are established respectively.

[0058] Step 2: Based on the amorphization-recrystallization strategy, the stable structure of stacking ZrO2-ZrSiO4 two-phase ceramics and its oxygen diffusion model are established, such as Figure 2 shown.

[0059] Step 2-1: Based on the supercell structure of ZrO2 and ZrSiO4 ceramics, a preliminary structural model of stacking ZrO2-ZrSiO4 two-phase ceramics is established.

[0060] Step 2-2: Based on the amorphous & recrystallization strategy, the stacking type ZrO2-ZrSiO4 two-phase ceramic structure is heated to 4000K, relaxed at 4000K for 50ps, and then cooled to room temperature within 500ps to obtain a stable ZrO2-ZrSiO4 two-phase ceramic structure.

[0061] Step 2-3: According to the size of the ZrO2-ZrSiO4 two-phase ceramic structure, set the oxygen atom area and build the oxygen atom model. The number of oxygen atoms is 20, which are randomly dispersed in the oxygen atom region.

[0062] Step 2-4: Based on the stacking structure construction method of step 2-1, establish ZrO2-ZrSiO4 two-phase ceramics in an oxygen environment, obtain the oxygen diffusion model of ZrO2-ZrSiO4 two-phase ceramics, and obtain the basic structural model of multiphase ceramics in an oxygen environment.

[0063] Step 3: Based on the established ZrO2-ZrSiO4 two-phase ceramic oxygen diffusion model, set the simulation environment to obtain the ZrO2-ZrSiO4 two-phase ceramic oxygen diffusion stability system at a specific temperature. Using the LAMMPS software package, obtain the positions of oxygen atoms outside the two-phase ceramic stable structure in the multiphase ceramic oxygen diffusion model at each temperature and at each time.

[0064] Step 3-1: Use the software package LAMMPS to set up the simulation environment, including periodic boundary conditions, ambient temperature, isothermal and isobaric NPT simulation ensemble, 1 fs time step, etc., and create an input file.

[0065] Step 3-2: Based on the established oxygen diffusion model of ZrO2-ZrSiO4 two-phase ceramics, run LAMMPS to obtain the oxygen diffusion stability model of ZrO2-ZrSiO4 two-phase ceramics at a specific temperature.

[0066] Step 3-3: Based on the oxygen diffusion stability model of ZrO2-ZrSiO4 two-phase ceramics, calculate and record the external oxygen atom positions in the oxygen diffusion model of ZrO2-ZrSiO4 two-phase ceramics at a specific temperature.

[0067] Step 3-4: Change and set different temperatures (1500-3000K) to obtain the external oxygen atom positions in the oxygen diffusion model of ZrO2-ZrSiO4 two-phase ceramics at different temperatures.

[0068] Step 4: Based on the time-varying relationship of the external oxygen atom position in the ZrO2-ZrSiO4 two-phase ceramic oxygen diffusion system at different temperatures, calculate the oxygen atom mean square displacement parameter, and use the Einstein relationship to obtain the oxygen diffusion coefficient of the multiphase ceramic at various temperatures.

[0069] Step 4-1: Based on the relationship between the position of oxygen atoms in the ZrO2-ZrSiO4 two-phase ceramic oxygen diffusion system and time at a specific temperature, the mean square displacement (MSD) of oxygen atoms in the multiphase ceramic oxygen diffusion model is calculated as follows:

[0070]

[0071] Where N represents the total number of oxygen atoms, r i (t) represents the position of the i-th oxygen atom at time t, Δt represents the time change, and <> represents the ensemble average. Figure 3 The relationship between the total mean square displacement of oxygen atoms in ZrO2-ZrSiO4 two-phase ceramics and time at different temperatures is shown. At different temperatures, the mean square displacement of oxygen atoms increases linearly with time. External oxygen atom diffusion is directional. For stacking ceramic structures, the oxygen atom diffusion coefficient perpendicular to the interface can reflect the interface's antioxidant capacity. Therefore, Figure 4 The time-dependent relationship between the mean square displacement of oxygen atoms in the ZrO2-ZrSiO4 two-phase ceramics along the direction perpendicular to the interface (z-direction) at different temperatures is shown. At the same time, the mean square displacement of the outer oxygen atoms along the z-direction is significantly lower than the total mean square displacement.

[0072] Step 4-2: Calculate the oxygen diffusion coefficient (D) of the ZrO2-ZrSiO4 two-phase ceramic at a specific temperature based on the relationship between the mean square displacement and time, which follows the Einstein relationship:

[0073]

[0074] Step 4-3: Change the temperature parameter settings and calculate and record the oxygen diffusion coefficient in ZrO2-ZrSiO4 two-phase ceramics at different temperatures based on the Einstein relationship.

[0075] Step 5: Based on the oxygen diffusion coefficient in ZrO2-ZrSiO4 two-phase ceramics at various temperatures, the Arrhenius diffusion equation is used to fit the external oxygen atom diffusion relationship in ZrO2-ZrSiO4 two-phase ceramics, including the relationship between the diffusion coefficient and temperature, the diffusion factor, and the diffusion activation energy.

[0076] Step 5-1: Based on the calculation results of the oxygen diffusion coefficient in ZrO2-ZrSiO4 two-phase ceramics in step 4, summarize the oxygen diffusion coefficient data at different temperatures. Figure 5 The relationship between the total diffusion coefficient of oxygen atoms in ZrO2-ZrSiO4 two-phase ceramics and temperature is shown. Figure 6 The relationship between the diffusion coefficient of oxygen atoms along the z direction in ZrO2-ZrSiO4 two-phase ceramics and temperature is shown.

[0077] Step 5-2: Based on the Arrhenius diffusion equation, the relationship between the oxygen ion diffusion coefficient of multiphase ceramics and temperature is expressed as:

[0078]

[0079] Where R represents the gas constant, T represents the temperature, D0 represents the diffusion factor, and Q represents the activation energy of oxygen diffusion. The total diffusion factor of external oxygen atoms is 4.30×10 -7 m 2 / s, the total diffusion activation energy is 158.21kJ / mol. The diffusion factor of external oxygen atoms along the z direction is 2.41×10 -7 m 2 / s, the diffusion activation energy along the z direction is 175.17kJ / mol. Figure 7 As shown in FIG, taking the temperature of 2000K as an example, the diffusion trajectory of external oxygen atoms in ZrO2-ZrSiO4 two-phase ceramics passes through the ZrO2-ZrSiO4 two-phase ceramic structure.

[0080] Example 2

[0081] Corresponding to Example 1, the present embodiment provides a method for calculating the oxygen diffusion coefficient of a multiphase ceramic. This method involves calculating using the open source software package LAMMPS developed by the Steve Plimpton team of Sanford National Laboratory. LAMMPS is a high-performance computing software based on the principle of classical molecular dynamics, which simulates systems such as atoms, molecules, and coarse-grained models using Newton's equations of motion. It supports a variety of force fields (such as empirical potential, reaction force field, embedded atom method, etc.) and boundary conditions (such as periodic boundary conditions, fixed boundary conditions, etc.), and calculates various properties such as the structural evolution, thermodynamic properties, mechanical properties, transport properties, and phase change behavior of the material. Using the LAMMPS software package, the basic parameters of the multiphase ceramic oxygen diffusion system are calculated as a function of temperature and the oxygen diffusion coefficient within a certain temperature range, and the ability to predict and evaluate the oxygen diffusion behavior of multiphase ceramics is possessed.

[0082] like Figure 1 As shown, a method for calculating the oxygen diffusion coefficient of a multiphase ceramic in this embodiment specifically includes the following steps:

[0083] Step 1: Establish the basic crystal structure and oxygen diffusion model of yttria-stabilized zirconium dioxide-ceria multiphase ceramics (Y2O3-ZrO2-CeO2, YSZ-CeO2). In this embodiment, cubic zirconium dioxide (ZrO2) and tetragonal ceria (CeO2) are selected as specific applications.

[0084] Step 1-1: Obtain the cubic ZrO2 crystal structure and set the grain orientation to (111) The lattice constant is a=7.20, Y was randomly substituted for Zr at a ratio of 8 mol %. To maintain electrical neutrality, the corresponding oxygen atoms in ZrO2 were deleted to establish yttria-stabilized zirconium dioxide (YSZ).

[0085] Step 1-2: Obtain tetragonal CeO2 (lattice constant a=7.73, ) crystal structure.

[0086] Step 1-3: Based on the lattice matching criterion, the lattice mismatch along the c-stacking is the lowest, and a 7×4×1 YSZ supercell structure and a 7×4×1 ZrSiO4 supercell structure are established.

[0087] Step 2: Based on the amorphization-recrystallization strategy, the stable structure of stacking YSZ-CeO2 multiphase ceramics and its oxygen diffusion model are established, such as Figure 8 shown.

[0088] Step 2-1: Based on the supercell structure of YSZ and CeO2 ceramics, a preliminary structural model of stacking YSZ-CeO2 multiphase ceramics is established.

[0089] Step 2-2: Based on the amorphization-recrystallization strategy, the stacked YSZ-CeO2 multiphase ceramic structure is heated to 3500K, relaxed at 3500K for 50ps, and then cooled to room temperature within 500ps to obtain a stable ZrO2-ZrSiO4 multiphase ceramic structure.

[0090] Step 2-3: According to the size of the YSZ-CeO2 multiphase ceramic structure, set the oxygen atom area and build the oxygen atom model. The number of oxygen atoms is 20, which are randomly dispersed in the oxygen atom region.

[0091] Step 2-4: Based on the stacking structure construction method in step 2-1, establish YSZ-CeO2 multiphase ceramics in an oxygen environment and obtain the oxygen diffusion model of YSZ-CeO2 multiphase ceramics.

[0092] Step 3: Based on the established YSZ-CeO2 multiphase ceramic oxygen diffusion model, set the simulation environment to obtain the YSZ-CeO2 multiphase ceramic oxygen diffusion stability system at a specific temperature. Use LAMMPS software to obtain the external oxygen atom positions in the multiphase ceramic oxygen diffusion model at each temperature and at each time.

[0093] Step 3-1: Use the software package LAMMPS to set up the simulation environment, including periodic boundary conditions, ambient temperature, isothermal and isobaric NPT simulation ensemble, 1 fs time step, etc., and create an input file.

[0094] Step 3-2: Based on the established YSZ-CeO2 multiphase ceramic oxygen diffusion model, obtain the YSZ-CeO2 multiphase ceramic oxygen diffusion stability model at a specific temperature.

[0095] Step 3-3: Based on the YSZ-CeO2 multiphase ceramic oxygen diffusion stability model, calculate and record the external oxygen atom positions in the YSZ-CeO2 multiphase ceramic oxygen diffusion model at a specific temperature.

[0096] Step 3-4: Change and set different temperatures (1500-3000K), run LAMMPS, and obtain the external oxygen atom positions in the YSZ-CeO2 multiphase ceramic oxygen diffusion model at different temperatures.

[0097] Step 4: Based on the relationship between the external oxygen atom position change and time in the YSZ-CeO2 multiphase ceramic oxygen diffusion system at different temperatures, calculate the mean square displacement of oxygen atoms, and use the Einstein relationship to obtain the oxygen diffusion coefficient of the multiphase ceramic at each temperature.

[0098] Step 4-1: Based on the relationship between the position of oxygen atoms in the YSZ-CeO2 multiphase ceramic oxygen diffusion system and time at a specific temperature, calculate the mean square displacement of oxygen atoms in the YSZ-CeO2 multiphase ceramic oxygen diffusion model. Figure 9 The relationship between the total mean square displacement of oxygen atoms in YSZ-CeO2 multiphase ceramics and time at different temperatures is shown. At different temperatures, the mean square displacement of oxygen atoms increases linearly with time. Figure 10 The time-dependent relationship between the mean square displacement of oxygen atoms in the YSZ-CeO2 multiphase ceramics along the direction perpendicular to the interface (z-direction) at different temperatures is shown. At the same time, the mean square displacement of the outer oxygen atoms along the z-direction is significantly lower than the total mean square displacement.

[0099] Step 4-2: Based on the relationship between the mean square displacement and time at different temperatures, use the Einstein relationship to calculate and record the external oxygen atomic diffusion coefficient in YSZ-CeO2 multiphase ceramics at different temperatures.

[0100] Step 5: Based on the oxygen diffusion coefficient in YSZ-CeO2 multiphase ceramics at various temperatures, the Arrhenius diffusion equation is used to evaluate the oxygen diffusion behavior in YSZ-CeO2 multiphase ceramics, including the relationship between the diffusion coefficient and temperature, the diffusion factor, and the diffusion activation energy.

[0101] Step 5-1: Based on the calculation results of the oxygen diffusion coefficient in YSZ-CeO2 multiphase ceramics in step 4, summarize the oxygen diffusion coefficient data at different temperatures. Figure 11 The relationship between the total diffusion coefficient of oxygen atoms in YSZ-CeO2 multiphase ceramics and temperature is shown. Figure 12The relationship between the diffusion coefficient of oxygen atoms along the z direction in YSZ-CeO2 multiphase ceramics and temperature is shown.

[0102] Step 5-2: Fitting by Arrhenius equation, the total diffusion factor of external oxygen atoms is 0.30×10 -9 m 2 / s, the total diffusion activation energy is 51.96 kJ / mol. The diffusion factor of external oxygen atoms along the z direction is 6.50×10 -9 m 2 / s, the diffusion activation energy along the z direction is 82.05kJ / mol. Figure 13 As shown in Figure 3, taking the temperature of 2000K as an example, the diffusion trajectory of external oxygen atoms in YSZ-CeO2 multiphase ceramics is only in the YSZ structure and fails to cross the interface.

[0103] Based on the above systematic calculations, parameters such as oxygen atomic positions, mean square displacement, and oxygen diffusion coefficients were obtained for the oxygen diffusion model of ZrO2-ZrSiO4 two-phase ceramics and YSZ-CeO2 multiphase ceramics over a wide temperature range (1500–3000K). Starting from the basic structure of the multiphase ceramic oxygen diffusion model, this experimental example systematically and comprehensively calculated the oxygen diffusion coefficients of ZrO2-ZrSiO4 two-phase ceramics and YSZ-CeO2 multiphase ceramics over a wide temperature range by combining molecular dynamics, Einstein relations, and the Arrhenius diffusion equation. This provides a complete indicator system for evaluating the oxidation resistance of multiphase ceramics in extreme environments. This method is also applicable to the calculation of oxygen diffusion coefficients of other multiphase ceramic materials, contributing to a deeper understanding of the high-temperature oxygen diffusion behavior of multiphase ceramics and providing theoretical guidance for the design and optimization of the oxidation resistance and thermal protection properties of multiphase ceramics.

Claims

1. A method for calculating the oxygen diffusion coefficient of multiphase ceramics, characterized in that: The following steps are involved: Step 1: Obtain the basic crystal structure of each single-phase ceramic and establish the ceramic supercell structure according to the lattice matching criterion; Step 2: Based on the amorphization-recrystallization strategy, a multiphase ceramic stable structure and oxygen particle region model is established according to each single-phase ceramic supercell structure to obtain a multiphase ceramic oxygen diffusion model; Step 3: Based on the oxygen diffusion stability model of multiphase ceramics at different temperatures, the positions of oxygen particles in the oxygen diffusion model of multiphase ceramics at each temperature and at each moment are obtained using LAMMPS software; Step 4: Based on the time-varying relationship of the oxygen particle position in the multiphase ceramic oxygen diffusion model at different temperatures, calculate the oxygen particle mean square displacement parameter, and use the Einstein relationship to obtain the oxygen diffusion coefficient of the multiphase ceramic at each temperature; Step 5: Based on the oxygen diffusion coefficient of multiphase ceramics at various temperatures, the Arrhenius diffusion equation is used to evaluate the oxygen diffusion behavior in multiphase ceramics, including the relationship between the diffusion coefficient and temperature, the diffusion factor, and the diffusion activation energy.

2. The method for calculating the oxygen diffusion coefficient of multiphase ceramics according to claim 1, wherein: In step 2, a stacking multiphase ceramic structure model is established based on the amorphization-recrystallization strategy, the multiphase ceramic structure model is relaxed to obtain a multiphase ceramic stable structure, an oxygen particle region is set according to the size of the multiphase ceramic stable structure, an oxygen particle region model is established, oxygen particles are randomly dispersed in the oxygen particle region through the oxygen particle region model, and a multiphase ceramic oxygen diffusion model is constructed according to the stacking structure construction method.

3. The method for calculating the oxygen diffusion coefficient of multiphase ceramics according to claim 1, wherein: In step 3, the multiphase ceramic oxygen diffusion model is fully relaxed at different temperatures using LAMMPS software to obtain a multiphase ceramic oxygen diffusion stability model at different temperatures. The position of oxygen particles outside the multiphase ceramic stable structure in the multiphase ceramic oxygen diffusion model is obtained based on the multiphase ceramic oxygen diffusion stability model, and the position of oxygen particles in the multiphase ceramic oxygen diffusion model at each temperature and at each moment is obtained.

4. The method for calculating the oxygen diffusion coefficient of multiphase ceramics according to claim 1, wherein: In step 4, the oxygen particle mean square displacement parameter calculation formula is: Where MSD represents the mean square displacement of oxygen atoms in the multiphase ceramic oxygen diffusion model, N represents the total number of oxygen particles, and r i (t) represents the position of the i-th oxygen particle at time t, Δt represents the time change, and <> represents the ensemble average; The calculation formula for the oxygen diffusion coefficient D of multiphase ceramics is:

5. The method for calculating the oxygen diffusion coefficient of multiphase ceramics according to claim 4, characterized in that: The relationship between the diffusion coefficient and temperature is expressed as: Where R is the gas constant, T is the temperature, D0 is the diffusion factor, and Q is the activation energy of oxygen diffusion.

6. A system for calculating the oxygen diffusion coefficient of multiphase ceramics, characterized in that: Contains oxygen diffusion model construction module, molecular dynamics simulation module, and oxygen diffusion coefficient calculation module; The oxygen diffusion model construction module is used to obtain the basic crystal structure of each single-phase ceramic and establish the ceramic supercell structure based on the lattice matching criterion. Based on the amorphization-recrystallization strategy, the multiphase ceramic stable structure and oxygen particle region model are established according to each single-phase ceramic supercell structure to obtain the multiphase ceramic oxygen diffusion model. The molecular dynamics simulation module is used to obtain the position of oxygen particles in the multiphase ceramic oxygen diffusion model at each temperature and at each moment based on the multiphase ceramic oxygen diffusion stability model at different temperatures using LAMMPS software; The oxygen diffusion coefficient calculation module is used to calculate the oxygen particle mean square displacement parameter based on the time-varying relationship between the oxygen particle position in the multiphase ceramic oxygen diffusion model at different temperatures. The Einstein relationship is used to obtain the oxygen diffusion coefficient of multiphase ceramics at various temperatures. Based on the oxygen diffusion coefficient of multiphase ceramics at various temperatures, the Arrhenius diffusion equation is used to evaluate the oxygen diffusion behavior in multiphase ceramics, including the temperature-varying relationship of the diffusion coefficient, the diffusion factor, and the diffusion activation energy.

7. The calculation system for oxygen diffusion coefficient of multiphase ceramics according to claim 6, characterized in that: The oxygen diffusion model module includes multiphase ceramic structure unit and oxygen diffusion model unit; The multiphase ceramic structure unit is used to establish the basic crystal structure of single-phase ceramics, expand the cell, and preliminarily establish a stacking multiphase ceramic structure. Based on the amorphization-recrystallization strategy, the stacking multiphase ceramic structure is heated to the highest melting point, then cooled to room temperature and fully relaxed to obtain a stable structure of the multiphase ceramic. The oxygen diffusion model is used to set the oxygen particle area according to the stable structure size of multiphase ceramics and establish the multiphase ceramic oxygen diffusion model in the same stacking construction method.

8. The calculation system for oxygen diffusion coefficient of multiphase ceramics according to claim 6, characterized in that: The molecular dynamics calculation module includes a simulation environment setting unit, a parameter calculation unit, and a data recording unit; The simulation environment setting unit is used to simulate environmental conditions, including setting the ambient temperature, boundary conditions, and ensemble, fully relaxing the multiphase ceramic oxygen diffusion model at a specific temperature, calculating the temperature of the system at different times, and obtaining a stable multiphase ceramic oxygen diffusion model at different temperatures; The parameter calculation unit is used to obtain the position of oxygen particles in the multiphase ceramic oxygen diffusion model based on the stable multiphase ceramic oxygen diffusion model at a specific temperature, and calculate the mean square displacement parameters of oxygen particles in the multiphase ceramic oxygen diffusion system; The data recording unit is used to record the calculation results of the mean square displacement of oxygen particles in the multiphase ceramic at each temperature and each moment under the ensemble of simulated environmental conditions.

9. The calculation system for oxygen diffusion coefficient of multiphase ceramics according to claim 8, characterized in that: The oxygen diffusion coefficient calculation module includes an oxygen diffusion coefficient calculation unit and an oxygen diffusion behavior evaluation unit; The oxygen diffusion coefficient calculation unit is used to extract the mean square displacement parameters of oxygen particles in multiphase ceramics at different temperatures and time points based on the results of the data recording unit in the molecular dynamics calculation module, and calculate the oxygen diffusion coefficient of multiphase ceramics at different temperatures using the Einstein relationship; The oxygen diffusion behavior evaluation unit is used to fit the relationship between the oxygen diffusion coefficient of multiphase ceramics and temperature according to the Arrhenius diffusion equation, obtain the oxygen diffusion factor and oxygen diffusion activation energy, and evaluate the oxygen diffusion behavior in multiphase ceramics.

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