A method for predicting high-temperature oxidation film stability of an alloy based on theoretical calculation

Abstract

The present application relates to the technical field of material performance prediction, and discloses a method for predicting high-temperature oxidation film stability of an alloy based on theoretical calculation, comprising the following steps: S1: obtaining stable oxides actually formed on the surface of the alloy, corresponding molar mass, metal atom number, density of the alloy, and average atomic weight of the alloy for the alloy composition and a preset high-temperature oxidation environment; S2: obtaining the theoretical density of the oxides according to the initial crystal structure of the oxides; S3: obtaining key parameters for evaluating the protection performance of metal oxides; S4: when the key parameters are less than or equal to a first preset value, the high-temperature oxidation film stability of the alloy is poor; when the key parameters are greater than the first preset value and less than a second preset value, the high-temperature oxidation film stability of the alloy is good; and when the key parameters are greater than or equal to the second preset value, the high-temperature oxidation film stability of the alloy is poor. The present application can efficiently, at low cost, and in advance, screen high-performance oxidation-resistant alloys.

Description

Technical Field

[0001] This invention relates to the field of material property prediction technology, and specifically to a method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations. Background Technology

[0002] The oxidation resistance of high-temperature alloys is one of the core factors determining their long-term service reliability in hot-end components such as aero-engines and gas turbines. The Pilling-Bedworth Ratio (PBR) theory is a classic criterion for evaluating the protective properties of metal oxide films. However, in traditional applications of this theory, key parameters usually rely on handbook data or experimental measurements of known properties, and significant simplification assumptions are often introduced during the analysis, resulting in limited predictive power, especially for novel multi-component alloy systems.

[0003] In the design and development of novel alloys, directly measuring their behavior under high-temperature, long-term oxidation conditions (e.g., hundreds of hours at 1300°C) through experiments presents challenges due to its long development cycle and high cost. Current technologies lack a systematic method based entirely on theoretical calculations to accurately obtain all key parameters of the PBR criterion and reliably predict oxide film stability. Particularly in determining the actually formed oxide phase, calculating the accurate density of multiphase alloys, and obtaining the intrinsic theoretical density of specific oxides, traditional methods struggle to break free from their reliance on empirical data and cannot effectively address unknown or complex alloy systems. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the present invention aims to provide a method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations. This method eliminates the need for traditional, time-consuming high-temperature oxidation experiments. Instead, it provides accurate parameter inputs for the PBR formula through systematic theoretical calculations, thereby enabling effective pre-screening and evaluation of the alloy's oxidation resistance before alloy preparation and experimental testing.

[0005] The technical solution adopted in this invention is as follows: A method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations, comprising the following steps:

[0006] S1: Based on the alloy composition and the preset high-temperature oxidation environment, obtain the stable oxide actually formed on the alloy surface, and obtain the corresponding molar mass and number of metal atoms based on the stable oxide actually formed on the alloy surface;

[0007] Based on the alloy composition, the equilibrium phase composition and mass fraction of each phase of the alloy at the high-temperature oxidation environment temperature are determined by phase diagram calculation. Combined with the theoretical density of each phase, the density of the alloy is calculated by the mixing rule.

[0008] The average atomic weight of the alloy is calculated by weighted averaging based on the alloy's composition and atomic fraction.

[0009] S2: Obtain the initial crystal structure of the stable oxide actually formed on the alloy surface from the database, perform structure optimization and energy minimization through first-principles calculations to obtain the equilibrium unit cell volume of the stable oxide, and calculate the theoretical density of the oxide through the equilibrium unit cell volume of the stable oxide.

[0010] S3: The key parameters for evaluating the protective performance of metal oxides are obtained by using the molar mass of the stable oxide, the number of metal atoms, the theoretical density, the alloy density, and the average atomic weight of the alloy, as shown in formula (1).

[0011] (1),

[0012] In formula (1), As a key parameter for evaluating the protective performance of metal oxides, The molar mass of the oxide is The density of the alloy, The number of metal atoms in the oxide molecule. The average atomic weight of the alloy. This is the theoretical density of the oxide;

[0013] S4: When the key parameter is less than or equal to the first preset value, the stability of the high-temperature oxide film of the alloy is poor; when the key parameter is greater than the first preset value and less than the second preset value, the stability of the high-temperature oxide film of the alloy is good; when the key parameter is greater than or equal to the second preset value, the stability of the high-temperature oxide film of the alloy is poor.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] This invention eliminates the need for traditional, time-consuming high-temperature oxidation experiments. Instead, it shortens the cycle and reduces costs through systematic theoretical calculations. Specifically, by integrating thermodynamic calculations, phase diagram calculations, and first-principles calculations, it obtains all parameters in the Pilling-Bedworth Ratio (PBR) formula, thereby predicting the stability (i.e., density and protective properties) of the oxide film.

[0016] By applying the above prediction method to calculate the PBR value of the target alloy, and based on the criterion that the PBR value is between 1 and 2.5, alloy components with the potential to form a dense oxide film can be quickly screened out, thereby significantly narrowing the scope of experimental verification and improving R&D efficiency. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations, as described in this invention.

[0018] Figure 2 This is a flowchart of the alloy density calculation in the method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations in this invention;

[0019] Figure 3 This is a flowchart of the oxide density calculation in the method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations in this invention. Detailed Implementation

[0020] Typical embodiments embodying the features and advantages of the present invention will be specifically described in the following description. It should be understood that the present invention can have various variations in different embodiments without departing from the scope of the present invention, and the descriptions and illustrations herein are for illustrative purposes only and not intended to limit the present invention.

[0021] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] This embodiment discloses a method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations, including the following steps:

[0023] S1: Based on the alloy composition and the preset high-temperature oxidation environment, obtain the stable oxide actually formed on the alloy surface, and obtain the corresponding molar mass based on the stable oxide actually formed on the alloy surface. Number of metal atoms ;

[0024] Based on the alloy composition, the equilibrium phase composition and mass fraction of each phase at the high-temperature oxidation environment temperature were determined by phase diagram calculations. Combined with the theoretical density of each phase, the density of the alloy was calculated using the mixing principle. ;

[0025] The average atomic weight of the alloy is calculated by weighted averaging based on the alloy's composition and atomic fraction. ;

[0026] In S1, obtaining the stable oxide actually formed on the alloy surface includes the following steps:

[0027] S111: Based on the alloy's constituent elements, list all elements in the alloy that may be oxidized, query professional databases (such as Materials Project), and identify oxides that meet the quantitative index of oxide thermodynamic stability as zero and the high symmetry structure condition in the description of oxide crystal structure as all possible stable oxides that may be formed under high temperature oxidation environment.

[0028] S112: Obtain the decomposition temperature of each oxide from the thermodynamic database, retain the oxides that are stable under the preset high-temperature oxidation environment, and use the first-principles calculation software (such as VASP, CASTEP) debye model to calculate the standard molar enthalpy of formation or thermal expansion coefficient thermodynamic data of the retained stable oxides, or query relevant data from reliable thermodynamic databases (such as FactSage, Materials Project).

[0029] S113: Under a preset high-temperature oxidation environment, retain the stable oxides with a more negative standard molar enthalpy of formation (i.e., more negative), and then use first-principles calculations to determine the standard molar enthalpy of formation of different phases of the retained stable oxides at high temperatures, and retain the stable oxides of the corresponding phases with a more negative standard molar enthalpy of formation.

[0030] Alternatively, compare the thermal expansion coefficient of the stable oxide with that of the alloy matrix, and retain the corresponding stable oxide with the smaller difference.

[0031] In S1, the molar mass of the stable oxide is determined based on the stable oxide of the corresponding phase. and the number of metal atoms in oxide molecules ;

[0032] In S1, the density of the alloy is calculated. This includes the following steps:

[0033] S121: Based on the alloy composition, determine the corresponding phase diagram in a material phase diagram database (such as Springer Materials, Pandat software) or calculate the alloy composition phase diagram using the CALPHAD method;

[0034] S122: On the phase diagram, locate the composition point of the alloy and determine its phase region at a set temperature;

[0035] S123: If it is in the two-phase region, the mass fraction of the two equilibrium phases is calculated using the lever rule; if it is in the three-phase region, the mass fraction of each equilibrium phase is calculated using the center of gravity rule.

[0036] S124: Obtain the theoretical density of each equilibrium phase at a preset temperature;

[0037] In this embodiment, theoretical density = (total mass of atoms in unit cell) / (unit cell volume).

[0038] S125: Calculate the overall theoretical density of the alloy using the mixing rule formula based on the mass fraction and theoretical density of each phase. .

[0039] S2: Obtain the initial crystal structure of the stable oxide actually formed on the alloy surface from the database, perform structure optimization and energy minimization through first-principles calculations to obtain the equilibrium unit cell volume of the stable oxide, and calculate the theoretical density of the oxide from the equilibrium unit cell volume of the stable oxide. ;

[0040] Specifically, S2 also includes the following steps:

[0041] S21: Based on the determined stable oxides actually formed on the alloy surface, obtain the initial crystal structure of the stable oxides actually formed on the alloy surface from the database;

[0042] S22: Using first-principles calculation software (such as VASP), the initial crystal structure of the stable oxide is optimized and its energy minimized under a selected exchange-correlation functional to obtain the unit cell volume of the stable oxide in equilibrium. ;

[0043] S23: The theoretical density of oxides is calculated using the unit cell volume of oxides with stable crystal structures, as shown in equation (2).

[0044] (2),

[0045] In formula (2), The theoretical density of the oxide, The number of chemical formula units in a single unit cell. The molar mass of a chemical formula unit For the optimized unit cell volume, It is Avogadro's constant;

[0046] In S23, based on the optimized crystal structure, the phonon spectrum is calculated using the phonopy model. If there is no acoustic imaginary frequency in the entire Brillouin zone, the stable oxide crystal structure is determined to be stable.

[0047] If imaginary frequencies exist, first adjust the settings of the first-principles calculation software, then re-obtain the optimized crystal structure using S22. Adjusting the settings of the first-principles calculation software includes the following: If there are small imaginary frequencies (<20cm) in the acoustic branch near the Gamma point (q=0). -1 To improve the accuracy of calculation parameters, such as by setting a denser k-point grid, a higher plane wave cutoff energy, and a more stringent SCF convergence criterion; and to improve the accuracy of force constant calculation, such as by reducing displacement and increasing the size of the supercell.

[0048] If a significant imaginary frequency (>20cm) appears at the q-point of the finite wave vector or on the optical branch... -1), the geometric structure is re-optimized, such as setting a strict ion relaxation convergence criterion; symmetry breaking is considered, such as breaking the symmetry of the original space group and re-optimizing the structure;

[0049] In this embodiment, phonon spectrum calculation is the key to verifying whether the optimized structure is in a stable equilibrium state (the minimum point of the potential energy surface).

[0050] S3: Key parameters for evaluating the protective performance of metal oxides are obtained from the molar mass of the stable oxide, the number of metal atoms, the theoretical density, as well as the alloy density and the average atomic weight of the alloy, as shown in formula (1).

[0051] (1),

[0052] In formula (1), is the key parameter for evaluating the protective performance of metal oxides. is the molar mass of the oxide. is the density of the alloy. is the number of metal atoms in the oxide molecule. is the average atomic weight of the alloy. is the density of the oxide;

[0053] In this embodiment, the Pilling-Bedworth Ratio (PBR) is a key parameter for evaluating the protective performance of metal oxides in the field of metal corrosion, and it is defined as the ratio of the volume of the metal oxide to the volume of the metal consumed to form the oxide.

[0054] S4: When the key parameter is less than or equal to the first preset value, the volume contraction of the oxide causes the oxide film layer to be porous and loose, losing its barrier function, and the stability of the alloy high-temperature oxide film is poor; when the key parameter is greater than the first preset value and less than the second preset value, the volume expansion of the oxidation product induces a moderate growth compressive stress in the film, thereby promoting the formation of a continuous, dense and well-bonded protective oxide layer with the substrate, and the stability of the alloy high-temperature oxide film is good; when the key parameter is greater than or equal to the second preset value, the excessive volume expansion generates a severe growth stress, resulting in the oxide film being prone to cracking or peeling off from the substrate, and its protective performance is significantly deteriorated, and the stability of the alloy high-temperature oxide film is poor.

[0055] Specifically, when PBR ≤ 1, the volume contraction of the oxide causes the film layer to be porous and loose, losing its barrier function; when 1 < PBR < 2.5, the volume expansion of the oxidation product induces a moderate growth compressive stress in the film, thereby promoting the formation of a continuous, dense and well-bonded protective oxide layer with the substrate; when PBR ≥ 2.5, the excessive volume expansion generates a severe growth stress, resulting in the oxide film being prone to cracking or peeling off from the substrate, and its protective performance is significantly deteriorated.

[0056] Specifically, taking alloy Pt 79 Ir3Al 12 Cr6 is oxidized at 1300℃ in air or under a specific oxygen partial pressure for 100 hours, and its alloy WRe... 25 The following will be further explained using the example of oxidation at 1000℃ under air or a specific oxygen partial pressure for 100 hours.

[0057] Case 1

[0058] This case study involves alloy Pt. 79 Ir3Al 12 Cr6 is oxidized at 1300℃ in air or under a specific oxygen partial pressure for 100 hours.

[0059] List all elements in the alloy that may be oxidized (Pt, Ir, Al, Cr). Based on the alloy composition and the preset high-temperature oxidation environment, consult professional databases (such as Materials Project) and identify oxides that meet the quantitative index of oxide thermodynamic stability of zero and the high symmetry structure condition in the symmetry description of oxide crystal structure as all possible stable oxides that may be formed under high-temperature oxidation environment, such as PtO2, IrO2, Al2O3, Cr2O3, etc., as well as complex composite oxides.

[0060] The decomposition temperatures of each oxide were obtained from a thermodynamic database. In this case, the decomposition temperatures were: PtO2 (570℃), IrO2 (800℃), Al2O3 (1800℃), and Cr2O3 (2200℃). It can be concluded that under the target service environment (i.e., the corresponding preset high-temperature oxidation environment), the stable oxides are Al2O3 and Cr2O3. The standard molar enthalpy of formation thermodynamic data of the above stable oxides were calculated using first-principles calculation software (such as VASP and CASTEP).

[0061] At a given temperature (1300℃), assuming all considered phases are thermodynamically stable (i.e., Energy Abovehull is 0), thermodynamic stability is determined based on the standard molar enthalpy of formation of each oxide. The standard molar enthalpy of formation (ΔH) f More negative (i.e., more negative) oxides are thermodynamically preferentially formed and are more stable. Al₂O₃: ΔH f =-1653.27 kJ·mol -1 Cr2O3: ΔH f =-1141 kJ·mol -1 According to the comparison of standard molar enthalpy of formation, Al2O3 is preferentially formed than Cr2O3. At 1300℃ and with high Al content, Al2O3 is more stable.

[0062] The standard molar enthalpy of formation of different phases of alumina (such as γ-Al2O3 and α-Al2O3) at high temperature was calculated using first-principles calculations. The alumina phase with the more negative standard molar enthalpy of formation was retained. α-Al2O3 (corundum structure) is the most stable phase at high temperature.

[0063] Based on the above, it is determined that under these conditions, a continuous and stable α-Al₂O₃ oxide film is most likely to form, with a very small amount of non-dense Cr₂O₃ film coexisting. Therefore, the stable oxide is determined to be α-Al₂O₃. Furthermore, M(Al₂O₃) = 2 * 26.98(Al) + 3 * 15.999(O) ≈ 101.96 g / mol; n = 2 (one Al₂O₃ molecule contains 2 Al atoms).

[0064] The phase diagram of the Pt-Ir-Al-Cr quaternary system in the relevant region was obtained using professional phase diagram databases (such as Springer Materials and Pandat software), or the equilibrium phase diagram section of this composition was calculated using thermodynamic calculation software (such as Pycalphad and Thermo-Calc). On the isothermal section at 1300℃, the composition point Pt-3Ir-12Al-6Cr (at.%) was located. Calculations revealed that at high temperatures, this composition point lies in the two-phase region, namely the equilibrium region of the γ phase (Pt-rich solid solution) and the β phase (Al-rich intermetallic compound, such as PtAl). A tie-line was drawn through the alloy composition point, showing the γ phase composition as Pt-2Ir-5Al-1Cr (at.%) and the β phase composition as Pt-1Ir-30Al-2Cr (at.%). The mass fraction (or mole fraction) of the two phases was calculated using the lever rule. Specifically, the atomic fraction was first converted to a mass fraction, and then the mass fraction of the γ phase was calculated using the lever rule. =65%, the mass fraction of the β phase is =35%( + = 1);

[0065] Find the crystal structures and theoretical lattice constants of the γ-phase (face-centered cubic Pt-based solid solution) and β-phase (such as B2 structure PtAl) from literature or crystallography databases (such as ICSD, Materials Project). Calculate the density of each phase using the crystallographic formula (density = (total atomic mass in unit cell) / (unit cell volume)). =19.5g / cm³ and =15.2g / cm³;

[0066] Applying the mixing principle, the theoretical density of the alloy ,

[0067] Right now =0.65*19.5+0.35*15.2≈17.74g / cm 3 ;

[0068] List the components and atomic weights: Pt: 195.08 g / mol, atomic fraction 79%; Ir: 192.22 g / mol, atomic fraction 3%; Al: 26.98 g / mol, atomic fraction 12%; Cr: 52.00 g / mol, atomic fraction 6%. Weighted average calculation: A = 0.79 * 195.08 + 0.03 * 192.22 + 0.12 * 26.98 + 0.06 * 52.00 ≈ 166.24 g / mol;

[0069] Note: Here, A is the average atomic weight of the alloy, which, when used in the PBR formula, approximates the atomic weight of the metallic element forming the oxide. When the oxide is pure Al₂O₃, strictly speaking, A should be the atomic weight of Al (26.98). However, in the selective oxidation of the alloy to form Al₂O₃, it is the Al in the alloy that is consumed, and the average atomic weight A of the alloy reflects the average molar mass of the matrix, serving as a bridge between the volume of alloy consumed and the volume of oxide formed. Therefore, using the average atomic weight of the alloy is a reasonable engineering approximation. In more accurate models, equivalent atomic weights can be used.

[0070] The initial crystal structure of α-Al₂O₃ was obtained from the database. The rhombohedral unit cell (space group R-3c) of α-Al₂O₃ contains 6 Al₂O₃ chemical formula units. Initial lattice parameters (a≈4.81 Å, b≈4.81 Å, c≈13.12 Å) and atomic coordinates were determined. First-principles calculation software (such as VASP) was used, setting the calculation parameters (plane wave cutoff energy, k-point grid, exchange-correlated functional (such as PBE-sol or SCAN, which provides more accurate predictions of solid lattice constants)). Ion relaxation and cell shape / volume relaxation were performed to converge the total energy and atomic forces of the system to the set thresholds. After optimization, the final equilibrium lattice constant was output, and the cell volume was calculated. ;

[0071] The optimized structure is used as input for phonon spectrum calculation. The force constant matrix is ​​calculated using the finite displacement method or the more efficient density functional perturbation theory (DFPT). Phonon dispersion relation is plotted, and all phonon mode frequencies in the entire Brillouin zone are checked. If all frequencies are real (>0), especially the optical branch has no imaginary frequencies (no negative frequencies), then the α-Al2O3 structure is proven to be dynamically stable. If imaginary frequencies appear, the calculation settings need to be checked, the supercell expanded, or other possible structures need to be considered until a stable structure is obtained.

[0072] For stable oxides with stable structures, their theoretical density Calculated by the formula: .

[0073] ① For an α-Al2O3 rhombohedral unit cell, there are Z=6 Al2O3 units.

[0074] ②M is the molar mass of Al2O3 (atomic weight of Al: 26.98 g / mol, atomic weight of O: 16.00 g / mol; M(Al2O3) = 2*26.98 + 3*16.00 = 101.96 g / mol).

[0075] ③V represents the optimized unit cell volume. The formula for calculating the volume of a hexagonal unit cell is: (Needs to be converted to cm³, 1 ų = 10) -24 cm³);

[0076] V= / 2*(4.81Å) 2 *(13.12Å)≈262.96ų, V=262.96ų×(10 −24 cm 3 / ų)=2.6296×10 −22 cm 3 ).

[0077] ④N A This is Avogadro's constant (approximately 6.022 × 10²³ mol). -1 ).

[0078] In summary, the calculation yields... The predicted value, i.e. =(6*101.96) / (2.6296×10 −22 *6.022×10²³mol -1 (≈3.86 g / cm³, close to the experimental value).

[0079] The calculated density of 3.86 g / cm³ is lower than the experimental value of 3.98 g / cm³ at room temperature, which is in line with the physical law that "thermal expansion leads to an increase in volume and a decrease in density", thus verifying the rationality of the calculation.

[0080] To calculate the PBR value, substitute the parameters obtained from the above steps into the PBR formula:

[0081] Given M≈101.96 g / mol, ρ1≈17.74 g / cm³, n = 2, A≈166.24 g / mol, and ρ2≈3.86 g / cm³, we can calculate PBR≈(101.96*17.74) / (2*166.24*3.86)≈1.41.

[0082] When evaluating the oxidation resistance of alloys at high temperatures, this should be used. ≈3.86g / cm³ is used in the formula The temperature density value is very high. This will make the PBR calculation results closer to the actual physical state of high-temperature service, thus making the evaluation conclusion of oxide film protection (dense, loose or crack-prone) more accurate and reliable.

[0083] The calculated PBR value is approximately 1.41, falling within the ideal range of 1 to 2.5. Based on PBR theory, it can be predicted that Pt... 79 Ir3Al 12 When Cr6 alloy is oxidized at 1300℃, it tends to form a continuous α-Al2O3 oxide film. The PBR value of this oxide film is moderate, indicating that the volume of Al2O3 generated is slightly larger than the volume of alloy consumed. This may generate moderate compressive stress in the oxide film, which is conducive to the formation of a dense, complete protective oxide film that is well bonded to the matrix. This indicates that the alloy has good oxidation resistance.

[0084] Case 2

[0085] This case study uses WRe alloy. 25 Oxidize at 1000℃ in air or under a specific oxygen partial pressure for 100 hours.

[0086] List all elements (W, Re) that may be oxidized in the alloy. Based on the alloy composition and the preset high-temperature oxidation environment, consult professional databases (such as Materials Project) and identify oxides that meet the quantitative index of oxide thermodynamic stability of zero and the high symmetry structure condition in the symmetry description of oxide crystal structure as all possible stable oxides WO3 and complex composite oxides that may be formed under high-temperature oxidation environment.

[0087] The decomposition temperatures of each oxide were obtained from thermodynamic databases. In this case, ReO3 (400℃), Re2O7 (360℃), WO3 (1200℃), and WO2 (which is rapidly oxidized to WO3). It can be concluded that WO3 is the stable oxide under the target service environment. The thermodynamic data of the thermal expansion coefficient of the above stable oxides were calculated using first-principles calculation software (such as VASP or CASTEP), or relevant data were retrieved from reliable thermodynamic databases (such as FactSage or Materials Project).

[0088] At a given temperature (1000℃), the coefficient of thermal expansion of the stable oxide is compared with that of the alloy matrix, and the stable oxide with the smaller difference is retained.

[0089] In this case, CET(WO3) is 4-9 (10) when the K level is between 573K and 1273K. -6 / K); the matrix W-Re is 5 to 11 (10) at 573K-1273K. -6 / K), the oxide layer has good compatibility with the substrate.

[0090] Based on the above, the stable oxide is determined to be WO3. Therefore, M(WO3) = 183.84(W) + 3 * 16.00(O) = 231.84 g / mol; n = 1 (one WO3 molecule contains one W atom).

[0091] W-Re binary phase diagrams can be obtained from professional phase diagram databases (such as Springer Materials, Pandat software) or calculated using thermodynamic calculation software (such as Pycalphad, Thermo-Calc).

[0092] W-Re alloys typically form continuous solid solutions (single phase) at high temperatures because tungsten and rhenium have similar atomic sizes and identical crystal structures (body-centered cubic, BCC), making them completely miscible across the entire composition range. At typical high service temperatures, WRe... 25 The alloy is located in a single BCC solid solution phase region;

[0093] The alloy composition is WRe 25 (Mass fraction), that is, the mass fraction of tungsten is w w =75%, rhenium mass fraction is w Re =25%. Search literature or crystallography databases (such as ICSD, Materials Project) for tungsten (W): atomic weight A W =183.84 g / mol, room temperature density ρ W,RT ≈19.25g / cm 3 Rhenium (Re): Atomic weight A Re =186.21 g / mol, room temperature density ρ Re,RT ≈21.02g / cm 3 High-temperature density correction: Density decreases with increasing temperature. This requires correction using the coefficient of thermal expansion. The linear coefficients of thermal expansion for tungsten and rhenium at high temperatures (e.g., 1000°C) are approximately 4.6 × 10⁻⁶. −6 K −1 and 6.5×10 −6 K −1 (Average value). High-temperature density It can be estimated using the following formula: , ρ W (T)=19.25 / (1+3*4.6×10−6*(1273K-298 K))≈18.99g / cm 3 , ρ Re(T)=21.02 / (1+3* 6.5×10−6*(1273K-298K))≈20.63g / cm 3 ;

[0094] In this embodiment, Let T be the density of the substance at temperature T. This is the density of a substance at a reference temperature (typically room temperature). The density temperature coefficient of a substance. For the current temperature value under consideration, This is a reference temperature.

[0095] Applying the mixing principle, the theoretical density of the alloy is ρ1 = w w *ρ W (T)+w Re *ρ Re (T). That is, ρ1 = 0.75*18.99 + 0.25*20.63 ≈ 19.38 g / cm³. 3 ;

[0096] List the alloy composition and atomic weights: W: 183.84 g / mol, atomic fraction 75%; Re: 186.21 g / mol, atomic fraction 25%. Calculate the weighted average: A = 0.754 × 183.84 + 0.246 × 186.21 = 138.61 + 45.78 ≈ 184.39 g / mol.

[0097] Note: Here, A is the average atomic weight of the alloy. When used in the PBR formula, it is an approximation of the atomic weight of the metallic element that forms the oxide.

[0098] The initial crystal structure of WO3 was obtained from the database. The tetragonal unit cell of WO3 (space group P4 / nmm) contains two WO3 chemical formula units, and the initial lattice parameters (a≈5.32 Å, b≈5.32 Å, c≈3.94 Å) and atomic coordinates are as follows:

[0099] Use first-principles calculation software (such as VASP). Set the calculation parameters (plane wave cutoff energy, k-point grid, exchange-correlated functional (such as PBE-sol or SCAN, which predicts solid lattice constants more accurately)). Perform ion relaxation and cell shape / volume relaxation to bring the total energy and atomic forces of the system to converge to the set thresholds. After optimization, output the final equilibrium lattice constant and calculate the cell volume. .

[0100] The optimized structure is used as input for phonon spectrum calculation. The force constant matrix is ​​calculated using the finite displacement method or the more efficient density functional perturbation theory (DFPT). Phonon dispersion relation is plotted, and all phonon mode frequencies across the entire Brillouin zone are checked. If all frequencies are real (>0), especially if the optical branch has no imaginary frequencies (no negative frequencies), then the WO3 structure is dynamically stable. If imaginary frequencies appear, the computational settings need to be checked, the supercell expanded, or other possible structures considered until a stable structure is obtained.

[0101] For stable structures, their theoretical density Calculated by the formula: .

[0102] ① For a tetragonal unit cell of WO3, there are Z = 2 WO3 units.

[0103] ②M is the molar mass of WO3 (atomic weight of W: 183.84 g / mol, atomic weight of O: 16.00 g / mol);

[0104] M(WO3)=1*183.84+3*16.00=231.84g / mol).

[0105] ③V represents the optimized unit cell volume. The formula for the unit cell volume of the tetragonal crystal system is: ;

[0106] V=(5.32) 2 ×3.94=28.3024×3.94≈111.51 ų; 1 ų=10 −24 cm 3 That is, V = 1.1151 × 10 −22 cm 3;

[0107] ④N A This is Avogadro's constant (approximately 6.022 × 10²³ mol). -1 ).

[0108] Calculated The predicted value, i.e. =(2*231.84) / (1.1151×10 −22 *6.022×10²³mol -1 (≈6.91 g / cm³, close to the experimental value).

[0109] The calculated density of 6.91 g / cm³ is lower than the experimental value of 7.16 g / cm³ at room temperature, which is in line with the physical law that "thermal expansion leads to an increase in volume and a decrease in density", thus verifying the rationality of the calculation.

[0110] Calculate the PBR value by substituting the parameters obtained from the above steps into the PBR formula:

[0111] Given M≈231.84g / mol, ρ1≈19.38g / cm³, n=1, A≈184.39g / mol, and ρ2≈6.91g / cm³, we can calculate PBR≈(231.84*19.38) / (1*184.39*6.91)≈3.53;

[0112] The calculated PBR value is approximately 3.53, which is greater than 2.5. Based on PBR theory, it can be predicted that this indicates WRe 25 The alloy forms a WO3 oxide film, but its internal stress is too high, making it prone to cracking and unable to provide effective antioxidant protection.

[0113] When evaluating the oxidation resistance of alloys at high temperatures, ρ²(T) ≈ 6.91 g / cm³ should be used as the formula. The temperature density value is very high. This will make the PBR calculation results closer to the actual physical state of high-temperature service, thus making the evaluation conclusion of oxide film protection (dense, loose or crack-prone) more accurate and reliable.

[0114] In the design of novel high-temperature alloys, designers can first calculate a preliminary series of compositions using thermodynamic phase diagrams. Then, for each candidate composition, the method described in this invention is applied to quickly calculate its predicted primary oxide film type and corresponding PBR value. Compositions predicted to form protective oxides such as Al₂O₃ or Cr₂O₃ with PBR values ​​between 1.0 and 2.5 are selected. Finally, only these preferred compositions are verified through experimental melting and actual high-temperature oxidation tests. This method can significantly reduce the blind spots and workload of experiments, accelerating the development process of high-performance oxidation-resistant alloys.

[0115] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations, characterized in that: Includes the following steps: S1: Based on the alloy composition and the preset high-temperature oxidation environment, obtain the stable oxide actually formed on the alloy surface, and obtain the corresponding molar mass and number of metal atoms based on the stable oxide actually formed on the alloy surface; Based on the alloy composition, the equilibrium phase composition and mass fraction of each phase of the alloy at the high-temperature oxidation environment temperature are determined by phase diagram calculation. Combined with the theoretical density of each phase, the density of the alloy is calculated by the mixing rule. The average atomic weight of the alloy is calculated by weighted averaging based on the alloy's composition and atomic fraction. S2: Obtain the initial crystal structure of the stable oxide actually formed on the alloy surface from the database, optimize the structure and minimize the energy through first-principles calculations to obtain the equilibrium unit cell volume of the stable oxide, and calculate the theoretical density of the oxide through the equilibrium unit cell volume of the stable oxide. S3: The key parameters for evaluating the protective performance of metal oxides are obtained by using the molar mass of the stable oxide, the number of metal atoms, the theoretical density, the alloy density, and the average atomic weight of the alloy, as shown in formula (1). （1）， In formula (1), As a key parameter for evaluating the protective performance of metal oxides, The molar mass of the oxide is The density of the alloy, The number of metal atoms in the oxide molecule. The average atomic weight of the alloy. This is the theoretical density of the oxide; S4: When the key parameter is less than or equal to the first preset value, the stability of the high-temperature oxide film of the alloy is poor; when the key parameter is greater than the first preset value and less than the second preset value, the stability of the high-temperature oxide film of the alloy is good; when the key parameter is greater than or equal to the second preset value, the stability of the high-temperature oxide film of the alloy is poor.

2. The method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations according to claim 1, characterized in that: In S1, obtaining the stable oxide actually formed on the alloy surface includes the following steps: S111: Based on the alloy's constituent elements, list all elements in the alloy that may be oxidized, and consider oxides that satisfy the quantitative index of oxide thermodynamic stability as zero and the high symmetry structure condition in the description of oxide crystal structure as all stable oxides that may be formed under high temperature oxidation environment. S112: Obtain the decomposition temperature of each oxide from the thermodynamic database, retain the oxides that are stable under the preset high-temperature oxidation environment, and use first-principles calculation software to calculate the standard molar enthalpy of formation or thermodynamic data of the coefficient of thermal expansion of the retained stable oxides. S113: Under a preset high-temperature oxidation environment, retain the stable oxide with a more negative standard molar enthalpy of formation, and then use first-principles calculations to determine the standard molar enthalpy of formation of different phases of the retained stable oxide at high temperature, and retain the stable oxide of the corresponding phase with a more negative standard molar enthalpy of formation. Alternatively, compare the thermal expansion coefficient of the stable oxide with that of the alloy matrix, and retain the corresponding stable oxide with the smaller difference.

3. The method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations according to claim 1, characterized in that: In S1, the density of the alloy is calculated, including the following steps: S121: Determine the corresponding phase diagram in the material phase diagram database based on the alloy composition; S122: On the phase diagram, locate the composition point of the alloy and determine its phase region at a set temperature; S123: If it is in the two-phase region, the mass fraction of the two equilibrium phases is calculated using the lever rule; if it is in the three-phase region, the mass fraction of each equilibrium phase is calculated using the center of gravity rule. S124: Obtain the theoretical density of each equilibrium phase at the corresponding temperature; S125: The theoretical density of the alloy is calculated using the mixing rule formula based on the mass fraction and theoretical density of each phase.

4. The method for predicting the stability of high-temperature oxide films on alloys based on theoretical calculations according to claim 1, characterized in that: S2 also includes the following steps: S21: Based on the stable oxide actually formed on the alloy surface determined, obtain the initial crystal structure of the stable oxide actually formed on the alloy surface from the database; S22: Using first-principles calculation software, the initial crystal structure of the stable oxide is optimized and its energy minimized under the selected exchange-correlation functional to obtain the unit cell volume of the stable oxide in equilibrium. ; S23: Calculate the theoretical density of the oxide through the unit cell volume of the oxide with a stable crystal structure, and the formula is as shown in Equation (2). （2）， In formula (2), The theoretical density of the oxide, The number of chemical formula units in a single unit cell. The molar mass of a chemical formula unit For the optimized unit cell volume, is Avogadro's constant.

5. The method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations according to claim 4, characterized in that: In S23, based on the optimized crystal structure, use the phonopy model to calculate the phonon spectrum. If there is no imaginary frequency in the acoustic branch within the entire Brillouin zone, it is determined that the crystal structure of the stable oxide is stable; If there is an imaginary frequency, first adjust the setting parameters of the first-principles calculation software, and then re-obtain the crystal structure with optimized structure through S22.

6. The method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations according to claim 5, characterized in that: Adjusting the setting parameters of the first-principles calculation software includes the following contents: If there is a small imaginary frequency on the acoustic branch near the Gamma point, improve the calculation parameter accuracy or the force constant calculation accuracy; If there is a significant imaginary frequency at a finite wave vector q point or on the optical branch, re-optimize the geometric structure or consider symmetry breaking.

7. The method for predicting the stability of high-temperature oxide films of alloys based on theoretical calculations according to claim 1, characterized in that: In S4, when PBR ≤ 1, the volume contraction of the oxide results in a porous and loose film layer, losing the barrier function, and the stability of the alloy high-temperature oxidation film is poor; when 1 < PBR < 2.5, the volume expansion of the oxidation product induces a moderate growth compressive stress stress stress in the film, thus promoting the formation of a continuous, dense and well-bonded protective oxide layer with the substrate, and the stability of the alloy high-temperature oxidation film is good; when PBR ≥ 2.5, the excessive volume expansion generates a severe growth stress, causing the oxidation film to crack or peel off from the substrate easily, and its protection performance deteriorates significantly, and the stability of the alloy high-temperature oxidation film is poor.

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