A method for predicting thermal expansion coefficient of Pt-based superalloys based on multi-scale integrated calculation

Abstract

The present invention relates to the technical field of high-temperature alloy materials and discloses a method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated computing. The method comprises the following steps: S1: establishing a Pt-based high-temperature alloy crystal structure model using high-throughput modeling technology; S2: calculating a first thermal expansion coefficient and a second thermal expansion coefficient using high-throughput first-principles methods, and calculating a first thermal expansion rate of change and a second thermal expansion rate of change using the first thermal expansion coefficient and the second thermal expansion coefficient, respectively; S3: obtaining a thermodynamic database using AutoCalphad software; S4: calculating a third thermal expansion coefficient based on the first thermal expansion rate of change and thermodynamic data; calculating a fourth thermal expansion coefficient based on the second thermal expansion rate of change and thermodynamic data; and establishing a multiphase mixing model based on the third thermal expansion coefficient and the fourth thermal expansion coefficient to obtain the thermal expansion coefficient of the Pt-based high-temperature alloy. The present invention can reduce the number of experimental characterizations of thermal expansion and shorten the R&D cycle of Pt-based high-temperature alloys.

Description

Technical Field

[0001] The present invention relates to the technical field of high-temperature alloy materials, and in particular to a method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculation. Background Art

[0002] The precious metal platinum (Pt) exhibits excellent high-temperature oxidation and corrosion resistance, enabling stable service under complex and extreme conditions. This makes it an indispensable material for many specialized applications, such as rocket propulsion engine nozzles, satellite attitude control engine nozzles, and high-temperature thermal barrier coating bond coats. Pt-based superalloys with γ- and γ'-phase structures exhibit excellent oxidation resistance. However, when used as bond coats for high-temperature thermal barrier coatings, the thermal expansion of the aluminum oxide in the adjacent thermally grown oxide layer is smaller than that of the bond coat. This resulting thermal expansion mismatch reduces adhesion between the aluminum oxide and the bond coat during thermal cycling, ultimately shortening the life of the thermal barrier coating system. The smaller the thermal expansion mismatch, the longer the life of the thermal barrier coating system. Therefore, studying the thermal expansion coefficient of Pt-based superalloys and developing new Pt-based superalloys with matched thermal expansion coefficients is crucial for long-life thermal barrier coatings.

[0003] However, the thermal expansion coefficient of Pt-based superalloys is currently primarily characterized through experimental testing. This requires the preparation of numerous precious metal specimens, and the cost of a single high-temperature thermal expansion test can exceed several thousand yuan, resulting in significant raw material and experimental costs. Therefore, a method for predicting the thermal expansion coefficient of Pt-based superalloys is urgently needed that can reduce the number of experimental characterizations required, shorten the R&D cycle for Pt-based superalloys, and reduce R&D costs, thereby accelerating the application of new Pt-based superalloys. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide a method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation, which can reduce the number of experimental characterizations of thermal expansion, shorten the R&D cycle of Pt-based high-temperature alloys and reduce R&D costs, thereby accelerating the application of new Pt-based high-temperature alloys.

[0005] The technical solution adopted by the present invention is as follows: a method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculation, comprising the following steps:

[0006] S1: Establish the crystal structure model of γ-phase solid solution Pt-based binary superalloy and the crystal structure model of γ'-phase solid solution Pt-based ternary superalloy using high-throughput modeling technology;

[0007] S2: Calculate the first thermal expansion coefficient of the γ-phase solid solution Pt-based binary superalloy using high-throughput first-principles calculations, and calculate the first thermal expansion change rate of the γ-phase solid solution Pt-based binary superalloy corresponding to different alloying elements using the first thermal expansion coefficient. Calculate the second thermal expansion coefficient of the γ'-phase solid solution Pt-based ternary superalloy, and calculate the second thermal expansion change rate of the γ'-phase solid solution Pt-based ternary superalloy corresponding to different alloying elements using the second thermal expansion coefficient.

[0008] S3: The thermodynamic database was obtained using AutoCalphad software, and the corresponding phase fraction, element mole fraction, and site-occupancy thermodynamic data for the γ-phase solid solution Pt-based binary superalloy and the γ'-phase Pt-based ternary superalloy were obtained.

[0009] S4: Calculate the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy based on the first thermal expansion change rate and the phase fraction, element mole fraction, and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy;

[0010] The fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary superalloy is calculated based on the second thermal expansion change rate and the corresponding phase fraction, element mole fraction and occupancy fraction thermodynamic data of the γ' phase solid solution Pt-based ternary superalloy;

[0011] A multiphase mixed model of thermal expansion is established according to the third thermal expansion coefficient and the fourth thermal expansion coefficient, and the thermal expansion coefficient of the Pt-based high-temperature alloy having the γ phase and the γ' phase is obtained.

[0012] As a preferred embodiment of the present invention, S1 includes the following steps:

[0013] S11: Obtain the crystal structure of γ-phase Pt and γ'-phase Pt3Al based on the Materials Project database;

[0014] S12: Using Phonopy software, the crystal structure of γ-phase Pt was expanded from a single-cell Pt containing 4 atoms to a 2×2×2 supercell Pt containing 32 Pt atoms. 32 The crystal structure of γ'-phase Pt3Al is expanded from a single-cell Pt3Al containing 4 atoms to a 2×2×2 supercell Pt3Al containing 24 Pt atoms and 8 Al atoms. 24 Al 18 ;

[0015] S13: supercell Pt 32 One Pt atom in the Pt is replaced by the alloying element X to establish a γ-phase solid solution Pt 31 X high temperature alloy crystal structure model;

[0016] Pt 24 Al 18 One Pt atom is replaced by alloying element X to establish a γ' phase solid solution Pt 23 Al 18 X high temperature alloy crystal structure model;

[0017] Pt 24 Al 18 One Al atom is replaced by alloying element X to establish a γ' phase solid solution Pt 24 Al 17 X high-temperature alloy crystal structure model.

[0018] As a preferred embodiment of the present invention, S2 includes the following steps:

[0019] S211: High-throughput first-principles calculation of γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy;

[0020] S212: Calculate the γ-phase solid solution Pt corresponding to different alloying elements X by the first thermal expansion coefficient 31 The first thermal expansion rate of X high temperature alloy is shown in formula (1):

[0021]

[0022] In formula (1), K X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion rate of X high temperature alloy, α X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy, α Pt represents the thermal expansion coefficient of γ-phase Pt, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X high-temperature alloy.

[0023] As a preferred embodiment of the present invention, S2 includes the following steps:

[0024] S221: Through high-throughput first-principles calculations, the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 The crystal structure of X high temperature alloy is relaxed with high precision to obtain the γ' phase solid solution Pt corresponding to different alloy elements X. 23 Al 18 X, Pt 24 Al 17 X static total energy of high temperature alloy;

[0025] S222: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to screen out the effective alloying element X;

[0026] S223: Calculation of the γ' phase solid solution Pt corresponding to the effective alloying element X by high-throughput first-principles calculation 23 Al 18 X, Pt 24 Al 17 The second expansion coefficient of X high temperature alloy;

[0027] S224: Calculate the γ' phase solid solution Pt corresponding to the effective alloying element X by the second thermal expansion coefficient 23 Al 18 X, Pt 24 Al 17 The second thermal expansion rate of X high temperature alloy is shown in formulas (2) and (3).

[0028]

[0029] In formula (2), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The occupancy fraction of X atoms in X high-temperature alloy;

[0030] In formula (3), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 24 Al 17The site occupancy fraction of X atoms in X high-temperature alloy.

[0031] As a preferred embodiment of the present invention, high-throughput first-principles calculations are performed on the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 When performing high-precision structural relaxation on the crystal structure of X high-temperature alloy, the energy convergence standard is 10 - 6 eV / atom, the force convergence criterion is

[0032] As a preferred embodiment of the present invention, S222 includes the following steps:

[0033] S222-11: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to calculate the transfer energy, as shown in formula (4):

[0034]

[0035] In formula (4), Pt 23 Al 18 X, Pt 25 Al 17 , Pt 24 Al 17 The static total energy of X and Pt3Al, It represents the transfer energy required for the alloying element X to shift from the Al site to the Pt site in Pt3Al;

[0036] S222-12: Determine the content of different alloying elements X in Pt based on transfer energy 24 Al 18 The occupancy tendency of the γ' phase solid solution Pt corresponding to different alloying elements X is determined. 23 Al 18 X, Pt 24 Al 17 X Crystal structure of high temperature alloy;

[0037] S222-13: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The crystal structure of X high temperature alloy is evaluated by calculating the phonon spectrum using Phonopy software. 23 Al18 X, Pt 24 Al 17 The dynamic stability of X high temperature alloy is determined to determine the effective alloying element X.

[0038] As a preferred embodiment of the present invention, S222 includes the following steps:

[0039] S222-21: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is calculated by calculating the different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 Mixing enthalpy in X high temperature alloy, evaluation of different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 Solid solubility of X in high temperature alloy, thereby screening out effective alloying element X;

[0040] As a preferred embodiment of the present invention, S4 includes the following steps:

[0041] S41: Based on the first thermal expansion change rate and the phase fraction, element mole fraction and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy, the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy is calculated, as shown in formula (5).

[0042]

[0043] In formula (5), α γ The third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, α Pt Indicates the thermal expansion coefficient of γ-phase Pt, K X represents the first thermal expansion rate of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X superalloy;

[0044] S42: Based on the second thermal expansion change rate and the phase fraction, element mole fraction and occupancy fraction thermodynamic data corresponding to the γ' phase solid solution Pt-based ternary high-temperature alloy, the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy is calculated, as shown in formula (6),

[0045]

[0046] In formula (6), α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates γ' phase solid solution Pt 24 Al 17 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion rate of X high temperature alloy;

[0047] S43: A multiphase mixed model of thermal expansion is established based on the third thermal expansion coefficient and the fourth thermal expansion coefficient to obtain the thermal expansion coefficient of the Pt-based high-temperature alloy having the γ phase and the γ' phase, as shown in formula (7).

[0048] α alloy =f γ α γ +f γ' α γ' (7),

[0049] In formula (7), α alloy represents the thermal expansion coefficient of the Pt-based superalloy with γ phase and γ' phase, α γ represents the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, f γ represents the phase fraction of γ-phase solid solution Pt-based binary high-temperature alloy, α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, f γ' Represents the phase fraction of γ' phase solid solution Pt-based ternary high-temperature alloy.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention uses high-throughput first-principles calculations coupled with phase diagram thermodynamics and other multi-scale integrated calculation methods to evaluate the thermal expansion coefficient of Pt-based high-temperature alloys. It can quickly predict the thermal expansion coefficient of a Pt-based alloy with a specific composition, and can predict the influence of 33 alloying elements on the thermal expansion coefficient of Pt-based high-temperature alloys. The prediction capability covers all possible Pt-based alloy composition ranges, can reduce the number of experimental tests on high-temperature thermal expansion coefficients during the research and development of precious metal alloys, can reduce the raw material cost and experimental characterization cost of developing Pt-based high-temperature alloys by more than 10 times, shorten the research and development cycle and research and development cost of Pt-based high-temperature alloys, and thus accelerate the application of new Pt-based high-temperature alloys. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of the method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculations of the present invention;

[0053] Figure 2 It is a thermal expansion coefficient-temperature curve diagram of the γ-phase solid solution of the Pt-based high-temperature alloy thermal expansion coefficient prediction method based on multi-scale integrated calculation of the present invention;

[0054] Figure 3 It is a thermal expansion change rate-temperature curve diagram of the γ-phase solid solution of the Pt-based high-temperature alloy thermal expansion coefficient prediction method based on multi-scale integrated calculation of the present invention;

[0055] Figure 4 The γ' phase Pt is the γ' phase of the Pt-based high temperature alloy thermal expansion coefficient prediction method based on multi-scale integrated calculation of the present invention. 24 Al 18 and the anti-γ' phase Pt 24 Al 18 Thermal expansion coefficient-temperature curve and thermal expansion rate-temperature curve;

[0056] Figure 5 The present invention is based on the multi-scale integrated calculation of the thermal expansion coefficient prediction method of Pt-based high-temperature alloys containing alloy elements γ' phase Pt 24 Al 18 Thermal expansion coefficient-temperature curve;

[0057] Figure 6 The present invention is based on the multi-scale integrated calculation of the thermal expansion coefficient prediction method of Pt-based high-temperature alloys containing alloy elements γ' phase Pt 24 Al 18 Thermal expansion rate-temperature curve;

[0058] Figure 7 This is a curve diagram of the thermal expansion coefficient of a Pt-Al binary alloy varying with temperature, according to the method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculations of the present invention;

[0059] Figure 8 This is a curve diagram of the change of the thermal expansion coefficient of a Pt-Al-Cr alloy with the Al content according to the method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculation of the present invention;

[0060] Figure 9 This is a curve diagram of the change of the thermal expansion coefficient of Pt-Al-Cr alloy with the Cr content in the thermal expansion coefficient prediction method of Pt-based high-temperature alloy based on multi-scale integrated calculation of the present invention. DETAILED DESCRIPTION

[0061] Typical embodiments that embody the features and advantages of the present invention are described in detail in the following description. It should be understood that the present invention is capable of various variations in different embodiments without departing from the scope of the present invention, and that the descriptions and illustrations are intended to be illustrative rather than limiting.

[0062] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0063] Explanation: Pt-based high-temperature alloys include Pt-based binary high-temperature alloys with γ phase and Pt-based ternary high-temperature alloys with γ' phase. Pt-based binary high-temperature alloys are represented by Pt 31 X high temperature alloy, Pt-based ternary high temperature alloy is expressed as Pt 23 Al 18 X high temperature alloy or Pt 24 Al 17 X high temperature alloys, Indicates the magnitude and units of thermal expansion.

[0064] Example 1

[0065] The prediction method of thermal expansion coefficient of Pt-based superalloy based on multi-scale integrated calculation, such as Figure 1 As shown, the following steps are included:

[0066] S1: Establish the crystal structure model of γ-phase solid solution Pt-based binary superalloy and the crystal structure model of γ'-phase solid solution Pt-based ternary superalloy using high-throughput modeling technology;

[0067] In this embodiment, S1 includes the following steps:

[0068] S11: Obtain the crystal structure of γ-phase Pt and γ'-phase Pt3Al based on the Materials Project database;

[0069] S12: Using Phonopy software, the crystal structure of γ-phase Pt was expanded from a single-cell Pt containing 4 atoms to a 2×2×2 supercell Pt containing 32 Pt atoms.32 The crystal structure of γ'-phase Pt3Al is expanded from a single-cell Pt3Al containing 4 atoms to a 2×2×2 supercell Pt3Al containing 24 Pt atoms and 8 Al atoms. 24 Al 18 ;

[0070] S13: supercell Pt 32 One Pt atom in the Pt is replaced by the alloying element X to establish a γ-phase solid solution Pt 31 X high temperature alloy crystal structure model;

[0071] Pt 24 Al 18 One Pt atom is replaced by alloying element X to establish a γ' phase solid solution Pt 23 Al 18 X high temperature alloy crystal structure model;

[0072] Pt 24 Al 18 One Al atom is replaced by alloying element X to establish a γ' phase solid solution Pt 24 Al 17 X high-temperature alloy crystal structure model.

[0073] In this embodiment, the alloy elements X are Al, Si, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, La, Ce, Hf, Ta, W, Re, Os, Ir, Au, and Th, totaling 33 elements.

[0074] In this embodiment, the γ-phase solid solution Pt 31 There are 33 X high-temperature alloy crystal structure models, and 66 γ' phase solid solution Pt-based ternary high-temperature alloy crystal structure models. Specifically, Pt 24 Al 18 One Pt atom is replaced by alloying element X to establish a γ' phase solid solution Pt 23 Al 18 X high temperature alloy crystal structure model, a total of 33 types, Pt 24 Al 18 One Al atom is replaced by alloying element X to establish a γ' phase solid solution Pt 24 Al 17 X high temperature alloy crystal structure model, a total of 33 types, of which Pt 24 Al 18 One Pt atom in the Pt structure is replaced by Al, and Al occupies the Pt position. 23 Al 19 Inverse crystal structure model, Pt24 Al 18 One Al atom is replaced by Pt element, and Pt occupies Al 25 Al 17 Inverse crystal structure model.

[0075] S2: Calculate the first thermal expansion coefficient of the γ-phase solid solution Pt-based binary superalloy using high-throughput first-principles calculations, and calculate the first thermal expansion change rate of the γ-phase solid solution Pt-based binary superalloy corresponding to different alloying elements using the first thermal expansion coefficient. Calculate the second thermal expansion coefficient of the γ'-phase solid solution Pt-based ternary superalloy, and calculate the second thermal expansion change rate of the γ'-phase solid solution Pt-based ternary superalloy corresponding to different alloying elements using the second thermal expansion coefficient.

[0076] In this embodiment, S2 includes the following steps:

[0077] S211: High-throughput first-principles calculation of γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy, such as Figure 2 As shown;

[0078] S212: Calculate the γ-phase solid solution Pt corresponding to different alloying elements X by the first thermal expansion coefficient 31 The first thermal expansion rate of X high temperature alloy, such as Figure 3 As shown in formula (1),

[0079]

[0080] In formula (1), K X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion rate of X high temperature alloy, α X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy, α Pt represents the thermal expansion coefficient of γ-phase Pt, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X superalloy;

[0081] S221: Through high-throughput first-principles calculations, the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 The crystal structure of X high temperature alloy is relaxed with high precision to obtain the γ' phase solid solution Pt corresponding to different alloy elements X. 23 Al 18 X, Pt 24 Al17 X static total energy of high temperature alloy;

[0082] S222: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to screen out the effective alloying element X;

[0083] In this embodiment, S222 includes the following steps:

[0084] S222-11: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to calculate the transfer energy, as shown in formula (4):

[0085]

[0086] In formula (4), Pt 23 Al 18 X, Pt 25 Al 17 , Pt 24 Al 17 The static total energy of X and Pt3Al, It represents the transfer energy required for the alloying element X to shift from the Al site to the Pt site in Pt3Al;

[0087] S222-12: According to the transfer energy Determine the content of different alloying elements X in Pt 24 Al 18 The occupancy tendency of the γ' phase solid solution Pt corresponding to different alloying elements X is determined. 23 Al 18 X, Pt 24 Al 17 X Crystal structure of high temperature alloy;

[0088] In this embodiment, when When it is negative, the alloying element Y tends to occupy the Pt site; when When it is positive, the alloying element Y tends to occupy the Al site.

[0089] S222-13: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17The crystal structure of X high temperature alloy is evaluated by calculating the phonon spectrum using Phonopy software. 23 Al 18 X, Pt 24 Al 17 The dynamic stability of X high temperature alloy is determined to determine the effective alloying element X.

[0090] In this embodiment, when the calculated phonon spectrum has no imaginary frequency, it means that the γ' phase solid solution Pt corresponding to the alloy element X 23 Al 18 X, Pt 24 Al 17 The X high-temperature alloy is kinetically stable, and the alloying element X can exist in the γ' phase solid solution Pt-based ternary high-temperature alloy, thereby determining the effective alloying element X.

[0091] S223: High-throughput first-principles calculation of the γ' phase solid solution Pt corresponding to the effective alloying element X 23 Al 18 X, Pt 24 Al 17 The second expansion coefficient of X high temperature alloy, such as Figure 4-7 As shown;

[0092] S224: Calculate the γ' phase solid solution Pt corresponding to the effective alloying element X by the second thermal expansion coefficient 23 Al 18 X, Pt 24 Al 17 The second thermal expansion rate of X high temperature alloy, such as Figure 4-7 As shown in formulas (2) and (3),

[0093]

[0094] In formula (2), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The mole fraction of X atoms in the X superalloy;

[0095] In formula (3), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X24 Al 17 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 24 Al 17 The mole fraction of X atoms in the X high-temperature alloy.

[0096] In this example, high-throughput first-principles calculations were performed to investigate the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 When performing high-precision structural relaxation on the crystal structure of X high-temperature alloy, the energy convergence standard is 10 -6 eV / atom, the force convergence criterion is Set the parameters "IBRION=8,NSW=1" in the first-principles calculation software vasp.

[0097] S3: The thermodynamic database was obtained using AutoCalphad software, and the corresponding phase fraction, element mole fraction, and site-occupancy thermodynamic data for the γ-phase solid solution Pt-based binary superalloy and the γ'-phase Pt-based ternary superalloy were obtained.

[0098] S4: Calculate the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy based on the first thermal expansion change rate and the phase fraction, element mole fraction, and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy;

[0099] The fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary superalloy is calculated based on the second thermal expansion change rate and the corresponding phase fraction, element mole fraction and occupancy fraction thermodynamic data of the γ' phase solid solution Pt-based ternary superalloy;

[0100] A multiphase mixed model of thermal expansion is established based on the third thermal expansion coefficient and the fourth thermal expansion coefficient to obtain the thermal expansion coefficient of the Pt-based high-temperature alloy having a γ phase and a γ' phase;

[0101] In this embodiment, S4 includes the following steps:

[0102] S41: Calculate the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy based on the first thermal expansion change rate and the phase fraction, element mole fraction, and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy, such as Figure 7As shown in formula (5),

[0103]

[0104] In formula (5), α γ The third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, α Pt Indicates the thermal expansion coefficient of γ-phase Pt, K X represents the first thermal expansion rate of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X superalloy;

[0105] S42: Based on the second thermal expansion change rate and the phase fraction, element mole fraction and occupancy fraction thermodynamic data corresponding to the γ' phase solid solution Pt-based ternary high-temperature alloy, the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy is calculated, such as Figure 8 、 9 As shown in formula (6),

[0106]

[0107] In formula (6), α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates γ' phase solid solution Pt 24 Al 17 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion rate of X high temperature alloy;

[0108] S43: A multiphase mixed model of thermal expansion is established based on the third thermal expansion coefficient and the fourth thermal expansion coefficient to obtain the thermal expansion coefficient of the Pt-based high-temperature alloy having the γ phase and the γ' phase, as shown in formula (7).

[0109] α alloy =f γ αγ +f γ' α γ' (7),

[0110] In formula (7), α alloy represents the thermal expansion coefficient of the Pt-based superalloy with γ phase and γ' phase, α γ represents the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, f γ represents the phase fraction of γ-phase solid solution Pt-based binary high-temperature alloy, α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, f γ' Represents the phase fraction of γ' phase solid solution Pt-based ternary high-temperature alloy.

[0111] Example 2

[0112] This embodiment is basically the same as the embodiment 1, except that S222 includes the following steps:

[0113] S222-21: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is calculated by calculating the different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 Mixing enthalpy in X high temperature alloy, evaluation of different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 The solid solubility of X in high-temperature alloys is used to screen out the effective alloying element X.

[0114] In this embodiment, when the mixing enthalpy is ≤ 0.01 eV, it means that the alloying element X can be dissolved into the γ' phase solid solution Pt-based ternary high-temperature alloy. When calculating the mixing enthalpy, the energy convergence standard is 10 -6 eV / atom.

[0115] The above embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and replacements made by technicians in this field on the basis of the present invention fall within the scope of protection required by the present invention.

Claims

1. A method for predicting the thermal expansion coefficient of Pt-based superalloys based on multi-scale integrated calculation, characterized by: The following steps are involved: S1: Establish the crystal structure model of γ-phase solid solution Pt-based binary superalloy and the crystal structure model of γ'-phase solid solution Pt-based ternary superalloy using high-throughput modeling technology; S2: Calculate the first thermal expansion coefficient of the γ-phase solid solution Pt-based binary superalloy using high-throughput first-principles calculations, and calculate the first thermal expansion change rate of the γ-phase solid solution Pt-based binary superalloy corresponding to different alloying elements using the first thermal expansion coefficient. Calculate the second thermal expansion coefficient of the γ'-phase solid solution Pt-based ternary superalloy, and calculate the second thermal expansion change rate of the γ'-phase solid solution Pt-based ternary superalloy corresponding to different alloying elements using the second thermal expansion coefficient. S3: The thermodynamic database was obtained using AutoCalphad software, and the corresponding phase fraction, element mole fraction, and site-occupancy thermodynamic data for the γ-phase solid solution Pt-based binary superalloy and the γ'-phase Pt-based ternary superalloy were obtained. S4: Calculate the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy based on the first thermal expansion change rate and the phase fraction, element mole fraction, and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy; The fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary superalloy is calculated based on the second thermal expansion change rate and the corresponding phase fraction, element mole fraction and occupancy fraction thermodynamic data of the γ' phase solid solution Pt-based ternary superalloy; A multiphase mixed model of thermal expansion is established according to the third thermal expansion coefficient and the fourth thermal expansion coefficient, and the thermal expansion coefficient of the Pt-based high-temperature alloy having the γ phase and the γ' phase is obtained.

2. The method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation according to claim 1, characterized in that: S1 includes the following steps: S11: Obtain the crystal structure of γ-phase Pt and γ'-phase Pt3Al based on the Materials Project database; S12: Using Phonopy software, the crystal structure of γ-phase Pt was expanded from a single-cell Pt containing 4 atoms to a 2×2×2 supercell Pt containing 32 Pt atoms. 32 The crystal structure of γ'-phase Pt3Al is expanded from a single-cell Pt3Al containing 4 atoms to a 2×2×2 supercell Pt3Al containing 24 Pt atoms and 8 Al atoms. 24 Al 18 ; S13: supercell Pt 32 One Pt atom in the Pt is replaced by the alloying element X to establish a γ-phase solid solution Pt 31 X high temperature alloy crystal structure model; Pt 24 Al 18 One Pt atom is replaced by alloying element X to establish a γ' phase solid solution Pt 23 Al 18 X high temperature alloy crystal structure model; Pt 24 Al 18 One Al atom is replaced by alloying element X to establish a γ' phase solid solution Pt 24 Al 17 X high-temperature alloy crystal structure model.

3. The method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation according to claim 1, characterized in that: S2 includes the following steps: S211: High-throughput first-principles calculation of γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy; S212: Calculate the γ-phase solid solution Pt corresponding to different alloying elements X by the first thermal expansion coefficient 31 The first thermal expansion rate of X high temperature alloy is shown in formula (1): In formula (1), K X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion rate of X high temperature alloy, α X Indicates the γ-phase solid solution Pt corresponding to different alloying elements X 31 The first thermal expansion coefficient of X high temperature alloy, α Pt represents the thermal expansion coefficient of γ-phase Pt, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X high-temperature alloy.

4. The method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation according to claim 1, characterized in that: S2 includes the following steps: S221: Through high-throughput first-principles calculations, the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 The crystal structure of X high temperature alloy is relaxed with high precision to obtain the γ' phase solid solution Pt corresponding to different alloy elements X. 23 Al 18 X, Pt 24 Al 17 X static total energy of high temperature alloy; S222: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to screen out the effective alloying element X; S223: Calculation of the γ' phase solid solution Pt corresponding to the effective alloying element X by high-throughput first-principles calculation 23 Al 18 X, Pt 24 Al 17 The second expansion coefficient of X high temperature alloy; S224: Calculate the γ' phase solid solution Pt corresponding to the effective alloying element X by the second thermal expansion coefficient 23 Al 18 X, Pt 24 Al 17 The second thermal expansion rate of X high temperature alloy is shown in formulas (2) and (3). In formula (2), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The occupancy fraction of X atoms in X high-temperature alloy; In formula (3), Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion rate of X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion coefficient of X high temperature alloy, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 24 Al 17 The site occupancy fraction of X atoms in X high-temperature alloy.

5. The method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculation according to claim 4, characterized in that: Through high-throughput first-principles calculations, the γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 When performing high-precision structural relaxation on the crystal structure of X high-temperature alloy, the energy convergence standard is 10 -6 eV / atom, the force convergence criterion is 6. The method for predicting the thermal expansion coefficient of a Pt-based high-temperature alloy based on multi-scale integrated calculation according to claim 4, characterized in that: S222 includes the following steps: S222-11: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is used to calculate the transfer energy, as shown in formula (4): In formula (4), Pt 23 Al 18 X, Pt 25 Al 17 , Pt 24 Al 17 The static total energy of X and Pt3Al, It represents the transfer energy required for the alloying element X to shift from the Al site to the Pt site in Pt3Al; S222-12: Determine the content of different alloying elements X in Pt based on transfer energy 24 Al 18 The occupancy tendency of the γ' phase solid solution Pt corresponding to different alloying elements X is determined. 23 Al 18 X, Pt 24 Al 17 X Crystal structure of high temperature alloy; S222-13: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The crystal structure of X high temperature alloy is evaluated by calculating the phonon spectrum using Phonopy software. 23 Al 18 X, Pt 24 Al 17 The dynamic stability of X high temperature alloy is determined to determine the effective alloying element X.

7. The method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation according to claim 4, characterized in that: S222 includes the following steps: S222-21: γ' phase solid solution Pt based on different alloying elements X 23 Al 18 X, Pt 24 Al 17 The static total energy of X high temperature alloy is calculated by calculating the different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 Mixing enthalpy in X high temperature alloy, evaluation of different alloying elements X in the corresponding γ' phase solid solution Pt 23 Al 18 X, Pt 24 Al 17 The solid solubility of X in high-temperature alloys is used to screen out the effective alloying element X.

8. The method for predicting the thermal expansion coefficient of Pt-based high-temperature alloys based on multi-scale integrated calculation according to claim 1, characterized in that: S4 includes the following steps: S41: Based on the first thermal expansion change rate and the phase fraction, element mole fraction and occupancy fraction thermodynamic data corresponding to the γ-phase solid solution Pt-based binary high-temperature alloy, the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy is calculated, as shown in formula (5). In formula (5), α γ The third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, α Pt Indicates the thermal expansion coefficient of γ-phase Pt, K X represents the first thermal expansion rate of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, x X Represents γ-phase solid solution Pt 31 The mole fraction of X atoms in the X superalloy; S42: Based on the second thermal expansion change rate and the phase fraction, element mole fraction and occupancy fraction thermodynamic data corresponding to the γ' phase solid solution Pt-based ternary high-temperature alloy, the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy is calculated, as shown in formula (6), In formula (6), α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, represents the thermal expansion coefficient of γ' phase Pt3Al, Indicates γ' phase solid solution Pt 23 Al 18 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 23 Al 18 The second thermal expansion rate of X high temperature alloy, Indicates γ' phase solid solution Pt 24 Al 17 The occupancy fraction of X atoms in X high temperature alloy, Indicates the γ' phase solid solution Pt corresponding to different alloying elements X 24 Al 17 The second thermal expansion rate of X high temperature alloy; S43: A multiphase mixed model of thermal expansion is established based on the third thermal expansion coefficient and the fourth thermal expansion coefficient to obtain the thermal expansion coefficient of the Pt-based high-temperature alloy having the γ phase and the γ' phase, as shown in formula (7). a alloy =f γ a γ +f γ' a γ' (7), In formula (7), α alloy represents the thermal expansion coefficient of the Pt-based superalloy with γ phase and γ' phase, α γ represents the third thermal expansion coefficient of the γ-phase solid solution Pt-based binary high-temperature alloy corresponding to different alloying elements X, f γ represents the phase fraction of γ-phase solid solution Pt-based binary high-temperature alloy, α γ' represents the fourth thermal expansion coefficient of the γ' phase solid solution Pt-based ternary high-temperature alloy corresponding to different alloying elements X, f γ' Represents the phase fraction of γ' phase solid solution Pt-based ternary high-temperature alloy.

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