Gibbs free energy prediction method for high-entropy spinel synthesis temperature

Abstract

The application discloses a Gibbs free energy prediction method for high-entropy spinel synthesis temperature, and belongs to the technical field of computational materials science and high-temperature ceramic preparation. The method comprises the following steps: determining the composition of high-entropy spinel and a precursor, and constructing an atomic model of all related phases; calculating the ground state energy by using VASP software, and obtaining the mixing enthalpy of the synthesis reaction; adopting a unified configuration entropy calculation formula which simultaneously considers the contribution of ion occupation disorder and the inherent octahedral vacancy of spinel, so as to realize fair calculation of the configuration entropy of high-entropy and single-component spinel; based on the mixing enthalpy and the configuration entropy, the change curve of the Gibbs free energy with temperature is calculated; by comparing the Gibbs free energy-temperature curves of the high-entropy spinel and each competitive single-component spinel, the temperature corresponding to the intersection point of the curves is determined as the reference temperature for synthesizing the high-entropy spinel. The application solves the problem that the entropy value calculation of high-entropy spinel is not unified, and can provide clear thermodynamic guidance for experiments.

Description

Technical Field

[0001] This invention belongs to the field of computational materials science and high-temperature ceramic preparation technology, specifically relating to a method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature. Background Technology

[0002] Spinel-structured oxide ceramics are widely used functional materials. In recent years, researchers have introduced the design concept of high-entropy alloys into the ceramics field, developing high-entropy spinel ceramics by dissolving various metallic elements in similar proportions within the spinel lattice. These materials often exhibit superior or novel physicochemical properties compared to traditional single-component spinels, such as higher structural stability, better radiation resistance, and tunable electromagnetic properties, showing potential applications in catalysis, thermal barrier coatings, and infrared radiation materials.

[0003] The preparation of high-entropy spinels often employs a high-temperature solid-state method, which involves mixing corresponding binary oxide precursor powders and then calcining them at high temperatures for an extended period. The synthesis temperature is a crucial process parameter determining whether a single pure phase can be obtained, as well as the final microstructure and properties of the material. Currently, the determination of the synthesis temperature for high-entropy spinels with specific compositions relies primarily on experimental experience. Researchers need to repeatedly experiment with sintering at different temperature points, combined with phase analysis methods such as X-ray diffraction, to determine a rough temperature range where the target phase can be obtained. This method lacks theoretical foresight, resulting in long material development cycles, high costs, and difficulty in systematically guiding the exploration of new materials.

[0004] From a thermodynamic perspective, the occurrence and tendency of a chemical reaction can be determined by its Gibbs free energy change (ΔG). For the reaction of synthesizing spinel from binary oxides, ΔG is determined by both the enthalpy change of mixing (ΔH) and the entropy change of mixing (ΔS), with the relationship ΔG = ΔH – TΔS. If we can theoretically calculate and compare the changes in ΔG with temperature (T) for high-entropy spinel and its possible single-component competing phases (such as ZnAl2O4, MgAl2O4, etc.), we can thermodynamically predict the temperature range in which the tendency to form the high-entropy phase will exceed the tendency to form other competing phases, thus providing a theoretical reference for setting the initial synthesis temperature in experiments.

[0005] First-principles calculation software based on density functional theory (such as VASP) can accurately obtain the ground-state energy of materials at absolute zero (0K), thus reliably calculating the enthalpy of mixing (ΔH) of the reaction. However, calculating the entropy (ΔS) presents challenges. For high-entropy materials, their high mixing entropy is considered one of the main driving forces for material stability, but the complete calculation of mixing entropy involves multiple components, including configurational entropy, vibrational entropy, magnetic entropy, and electronic entropy, making the calculation extremely complex. Existing studies typically only approximate the dominant configurational entropy. A more prominent problem is the inconsistency between the formula for calculating the configurational entropy of high-entropy spinel and the entropy treatment of conventional single-component spinel. The configurational entropy of single-component spinel is often ignored or simplified, while the entropy formula for high-entropy spinel focuses on the mixing effect brought about by multiple principal components. This inconsistency in calculation benchmarks makes it impossible to place the thermodynamic data of both on the same platform for fair comparison, thus making it difficult to reliably analyze phase competition relationships and predict synthesis temperatures by calculating ΔG-T curves. Currently, there is no systematic method to solve this problem, thereby providing direct computational guidance for the synthesis experiments of high-entropy spinel. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the Gibbs free energy of the synthesis temperature of high-entropy spinel.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature includes the following steps: S1. Determine the constituent elements and their proportions of the target high-entropy spinel, determine the corresponding binary oxide precursors, and perform physical modeling on the high-entropy spinel, all corresponding single-component spinels, and all binary oxide precursors to obtain their respective atomic structure models as input models for density functional theory calculations. S2. Based on density functional theory, calculate the ground state energy of all atomic structure models in step S1 at 0K using VASP software; S3. Based on the ground state energy obtained in step S2, calculate the enthalpy of mixing for the synthesis of the high-entropy spinel and the reactions of each single-component spinel using the enthalpy of mixing calculation formula; the enthalpy of mixing calculation formula is: , in, It's spinel DFT energy. Let be the DFT energy of the k-th binary oxide precursor. The molar number of the k-th binary oxide precursor. This represents the sum of the molar numbers of all binary oxide precursors. It should be noted that the energy unit calculated from VASP is electron volt (eV), which is commonly converted to the enthalpy of mixture in kJ·mol⁻¹. -1 At that time, the conversion factor used was: 1 eV / atom = 96.485 kJ•mol. -1 Ensure consistent unit conversions.

[0008] S4, For complex oxides A x B y O z According to the unified formula for calculating configuration entropy, the configuration entropy of the high-entropy spinel and each single-component spinel are calculated respectively; the unified formula for calculating configuration entropy is: , Where x, y, and z represent the total number of ions at the A, B, and O sites of spinel, respectively. and The mole fractions of each element at the A-site, B-site, and anionic site of spinel are respectively; M, N, and P are the number of different ion types occupying the A-site, B-site, and anionic site in spinel, including octahedral intrinsic vacancies; R is the gas constant; the total number of intrinsic octahedral vacancies is determined based on the standard spinel structure, and the number of 16c vacancies in a unit cell is 16, so the unit chemical formula is considered to be AB4O4, where the number of B-site cations and 16c vacancies are equal; S5. Based on the enthalpy of mixing obtained in step S3 and the configuration entropy obtained in step S4, calculate the change of Gibbs free energy with temperature for the synthesis reactions of the high-entropy spinel and each single-component spinel using the Gibbs free energy calculation formula; the Gibbs free energy calculation formula is as follows: , in the formula It is the Gibbs free energy of chemical reaction (n). It is the enthalpy of mixture of chemical reaction (n). It is the entropy of the mixture of the products of chemical reaction (n); and = Compositional entropy of products - Compositional entropy of reactants, where the reactant binary oxide is an ordered compound with a compositional entropy of 0. Equal to the configurational entropy of the product spinel; T is the absolute temperature, in Kelvin (K); S6. Compare the curves of Gibbs free energy of the high-entropy spinel and each single-component spinel as a function of temperature obtained in step S5, and determine the intersection point of the curves; if, after the intersection point, the Gibbs free energy of the high-entropy spinel is more negative than the Gibbs free energy of all single-component spinels corresponding to the constituent elements of the target high-entropy spinel, then the temperature corresponding to the intersection point is taken as the reference temperature for synthesizing the target high-entropy spinel.

[0009] Furthermore, in step S1, the physical modeling of high-entropy spinel specifically involves: based on the standard structure of spinel AB2O4, constructing a 2×2×2 supercell model containing multiple elements randomly occupying positions according to its chemical formula, wherein the A site corresponds to the 8aWyckoff position, the B site corresponds to the 16dWyckoff position, and the O site corresponds to the 32eWyckoff position, and multiple elements randomly occupy the A site or the B site according to their stoichiometric ratio.

[0010] Furthermore, the configuration entropy Sconf calculated in step S4 is used to replace the mixing entropy, since the mixing entropy is mainly contributed by the configuration entropy, and the vibrational entropy, magnetic dipole entropy and electronic randomness entropy can be ignored.

[0011] Furthermore, in this method, the mixing entropy is mainly contributed by the configuration entropy, while the vibrational entropy, magnetic dipole entropy, and electronic randomness entropy have negligible influence. Therefore, the configuration entropy is used instead of the mixing entropy for calculation.

[0012] Furthermore, in step S5, when calculating the Gibbs free energy, the configurational entropy of the reactant binary oxide is 0.

[0013] Furthermore, in step S6, the determination of the curve intersection point specifically refers to determining the intersection point between the Gibbs free energy-temperature curve of the high-entropy spinel and the curve corresponding to the single-component spinel with the most negative Gibbs free energy.

[0014] Furthermore, in step S6, the reference temperature refers to the initial temperature at which the thermodynamic driving force for synthesizing the high-entropy spinel begins to exceed the thermodynamic driving force for synthesizing all single-component spinels under conventional synthesis reaction conditions in an atmospheric air atmosphere. Beneficial effects

[0015] 1. The configuration entropy calculation formula proposed in this invention not only includes the entropy contributions of A-sites, B-sites, and anionic sites due to the random occupation of multiple ions, but also, for the first time, explicitly considers the contribution of the inherent octahedral vacancies (16c sites) in the spinel crystal structure to the configuration entropy. This model is universal and can handle the configuration entropy calculation of spinels ranging from simple single-component spinels to complex high-entropy spinels using the same physical basis and calculation rules. It solves the problem of the fragmented entropy calculation standards for the two types of systems in the prior art, laying the foundation for subsequent accurate thermodynamic comparisons.

[0016] 2. This method integrates first-principles energy calculations (via VASP) with the aforementioned unified entropy calculation model. First, precise energy parameters are obtained at the atomic level to calculate the enthalpy of mixing. Then, combined with the calculated configuration entropy, the functional relationship between the reaction Gibbs free energy and temperature is finally calculated. This process constructs a complete computational path from the initial atomic model design of the material to the prediction of its macroscopic synthesis reaction thermodynamic behavior.

[0017] 3. By plotting and comparing the ΔG-T curves of the synthesis reactions of high-entropy spinel and all related single-component spinels, the thermodynamic competition between them can be intuitively revealed. This method defines a clear criterion: when the ΔG-T curve of high-entropy spinel intersects with the ΔG-T curve of its most stable competing phase (i.e., the single-component spinel with the most negative ΔG), and the ΔG value of the high-entropy phase is lower after the intersection point, the temperature corresponding to this intersection point is determined as the reference temperature for synthesizing the high-entropy spinel. This temperature point has a clear physical significance, indicating that above this temperature, the thermodynamic driving force for the formation of the high-entropy phase begins to exceed the formation of all single-component phases.

[0018] 4. By applying the method of this invention, the ease of synthesizing a specific high-entropy spinel can be theoretically assessed in advance before conducting actual high-temperature sintering experiments, and a rough range of initial reaction temperatures can be predicted. This changes the experimental model that relies entirely on "trial and error," helping researchers focus on experimental conditions, reduce unnecessary repetitive experiments, thereby saving time, energy, and raw material consumption, and improving the efficiency of materials research and development.

[0019] 5. The calculation steps and judgment logic described in this invention do not depend on specific element types. For novel high-entropy spinel systems designed with different element combinations or different site ratios, only the element settings during modeling need to be changed accordingly to follow the same process for calculation and prediction. This makes this method a fundamental tool for high-throughput computational screening, assisting in the discovery of promising novel high-entropy spinel material combinations that possess thermodynamic formation advantages at relatively low temperatures. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of a unit cell ball-and-stick model of spinel with 56 atoms. This is for the A-site high-entropy spinel (Zn) used in this invention. 0.25 Mn 0.25 Ca 0.25 Mg 0.25 In Al2O4, Zn, Mn, Ca, Mg, etc. are randomly placed at site A, Al is at site B, and O is the anion. For single-component spinel ZnAl2O4, MnAl2O4, and MgAl2O4, Zn, Mn, and Mg are placed at site A, respectively, Al is at site B, and O is the anion.

[0021] Figure 2 for Figure 1 The curves showing the relationship between the Gibbs free energy and temperature for all materials in the diagram are shown, where the horizontal axis corresponding to the dashed line is the reference temperature for synthesizing the high-entropy spinel. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. It should be understood that the following embodiments are for illustrative purposes only and not for limiting the scope of this invention. Example

[0023] This embodiment uses A-site quaternary high-entropy spinel (Zn) 0.25 Mn 0.25 Ca 0.25 Mg 0.25 Using Al2O4 as the target material, this demonstration illustrates the entire process of theoretically predicting its reference synthesis temperature. Those skilled in the art should understand that this method remains applicable even with different element types or proportions.

[0024] S1: Determining Composition and Physical Modeling The chemical formula of the target high-entropy spinel is (Zn) 0.25 Mn 0.25 Ca 0.25 Mg 0.25 Al2O4. Its corresponding precursor binary oxides are ZnO, MnO, CaO, MgO, and Al2O3. The single-component spinels to be compared are ZnAl2O4, MnAl2O4, and MgAl2O4.

[0025] Use materials modeling software (such as Materials Studio) to construct the following initial crystal structure model: 1. High-entropy spinel model: Based on the standard spinel MgAl₂O₄ unit cell (space group Fd-3m), a 2×2×2 supercell (containing 56 atoms) is constructed. At the 8 A-sites (8aWyckoff sites) of this supercell, 2 Zn atoms, 2 Mn atoms, 2 Ca atoms, and 2 Mg atoms are randomly allocated according to stoichiometry to simulate the high-entropy solid solution state at the A-sites; all 16 B-sites (16d sites) are occupied by Al atoms; and all 32 O-sites (32e sites) are occupied by O atoms. This model corresponds to... Figure 1 part.

[0026] 2. Single-component spinel models: Standard unit cell models (14 atoms in total) of ZnAl2O4, MnAl2O4, and MgAl2O4 were constructed respectively. In these models, the A site (8a) is completely occupied by Zn, Mn, or Mg atoms, respectively, and the B site (16d) is completely occupied by Al atoms.

[0027] 3. Precursor oxide models: Construct unit cell models for ZnO (wurtzite structure), MnO (rock salt structure), CaO (rock salt structure), MgO (rock salt structure), and α-Al2O3 (corundum structure).

[0028] After performing preliminary geometric optimization on all the constructed models, they are exported in the POSCAR file format required for VASP software calculations.

[0029] S2: Ground state energy calculation based on DFT First-principles calculations were performed using the VASP software package. The main parameter settings are as follows: the exchange-correlation functional was the PBE functional under the generalized gradient approximation; the plane wave cutoff energy was set to 520 eV; the Gamma center method was used to generate a k-point grid to ensure that the total energy of all systems converged to within 1 meV / atom; the convergence criterion for the electronic self-consistent cycle was an energy change of less than 1 × 10⁻⁶ eV. -6 eV; the convergence criterion for ion relaxation is a residual force on each atom of less than 0.01 eV / Å.

[0030] Perform a complete geometric relaxation calculation on all POSCAR files prepared in step S1 until both atomic forces and unit cell stresses meet the convergence criteria. Extract the final relaxed ground state total energy (E0) from the calculated output OUTCAR or vasprun.xml file. DFT ), which serves as the input for subsequent thermodynamic calculations.

[0031] S3: Calculate the enthalpy of mixture of the synthesis reaction ( ) Based on the formula for calculating the enthalpy of mixing, the reactions for synthesizing high-entropy spinel and each individual spinel component were calculated separately. .

[0032] For high-entropy spinel (Zn 0.25 Mn 0.25 Ca 0.25 Mg 0.25 Al2O4, its reaction formula is: 0.25ZnO+0.25MnO+0.25CaO+0.25MgO+Al2O3→(Zn 0.25 Mn 0.25 Ca 0.25 Mg 0.25 Al2O4; Its enthalpy of mixing is: =[E HE-Spinel -(0.25E ZnO +0.25E MnO +0.25E CaO +0.25E MgO +EAl2O3 )] / (0.25+0.25+0.25+0.25+1), Among them, E HE-Spinel E represents the DFT energy of the high-entropy spinel model. ZnO E MnO、 E CaO、 E Al2O3 Here, represents the DFT energy of each oxide precursor. The calculated value is -6.468 kJ·mol⁻¹. -1 .

[0033] Similarly, calculate the enthalpy of mixture of single-component spinels, for example, for MgAl2O4: MgO + Al₂O₃ → MgAl₂O₄ ΔH mix(MgAl2O4) =[E MgAl2O4 -(E MgO +E Al2O3 )] / (1+1) The calculation yields: ΔH mix(ZnAl2O4) = -16.143 kJ·mol -1 ΔH mix(MnAl2O4) = -15.734 kJ·mol -1 ΔH mix(MgAl2O4) =-19.628kJ·mol⁻¹.

[0034] S4: Calculate the configuration entropy of spinel (S conf ) The calculation was performed using the unified formula for configuration entropy, with the gas constant R taken as 8.314 J·mol⁻¹. -1 ·K -1 .

[0035] 1. High-entropy spinel (Zn 0.25 Mn 0.25 Ca 0.25 Mg 0.25 Al2O4: A site: Occupying ion species M=4 (Zn, Mn, Ca, Mg), mole fraction of each x a =0.25.

[0036] B site: Occupying ion species N=1 (Al), mole fraction y b =1.

[0037] O site: Occupying ion type P=1 (O), mole fraction z o =1.

[0038] Vacancy contribution: In the spinel AB2O4 structure, there are 8 A sites, 16 B sites, and 16 unoccupied octahedral vacancies (16c sites) per unit cell.Therefore, the mole fraction of vacancy x vac =Number of 16c loci / (Number of B loci + Number of 16c loci) = 16 / (16+16)=0.5。

[0039] Substitute into the formula: S conf(HE) =-R[(0.25ln0.25+0.25ln0.25+0.25ln0.25+0.25ln0.25)+ (4×0.5ln0.5+ (4×0.5ln0.5)+(4×1×ln1) ] =-R[4×(0.25×ln0.25)+4×ln0.5] ≈4.159R 2. Single-component spinel (taking MgAl2O4 as an example): Position A: M=1 (Mg), x a =1.

[0040] Position B: N=1 (Al), y b =1.

[0041] O position: P=1(O), z o =1.

[0042] Vacancy contribution: Same as high-entropy spinel structure.

[0043] Substitute into the formula: S conf(MgAl2O4) =-R[(1×ln1)+( 4×0.5ln0.5+4×0.5ln0.5 )+( 4×1×ln1 )] =-R[0+4×0.5ln0.5+0] ≈2.773R Similarly, the configuration entropy of ZnAl2O4 and MnAl2O4 is calculated to be 2.773R.

[0044] In the calculation of this method, this S is used. conf The value is taken as ΔS mix Approximate value.

[0045] S5: Calculate the change in Gibbs free energy with temperature (ΔG(T)) According to the Gibbs free energy formula ΔG(T) = ΔH mix -T·S conf Calculations are performed. Since the precursor oxide is an ordered compound with a configuration entropy of 0, S... conf This is the average configuration entropy of the product spinel.

[0046] Calculate the ΔG values ​​for each reaction at different temperatures (e.g., 0-2000K, in 100K intervals): ΔG HE (T)= -6.468-T×(4.159R / 1000)kJ·mol -1 (R is substituted with the value 8.314) ΔG Mg (T)= -19.628 -T×(2.773R / 1000)kJ·mol -1 ΔG Zn (T)= -16.143 -T×(2.773R / 1000)kJ·mol -1 ΔG Mn (T)= -15.734 -T×(2.773R / 1000)kJ·mol -1 The calculation results are plotted as a curve of ΔG versus temperature T, as follows: Figure 2 As shown.

[0047] S6: Determine the reference synthesis temperature by analyzing the curve. observe Figure 2 The ΔG-T curve shown: 1. The ΔG of all reactions decreased linearly with increasing temperature, indicating that increasing the temperature is beneficial to the synthesis reaction.

[0048] 2. In the low-temperature range, the ΔG curve of the single-component spinel MgAl2O4 is the lowest (most negative), indicating that from a thermodynamic point of view, MgAl2O4 is most easily formed at low temperatures, and it is the most important competing phase.

[0049] 3. High-entropy spinel (Zn 0.25 Mn 0.25 Ca 0.25 Mg 0.25 The slope of the ΔG curve of Al2O4 (-S) conf (It) is larger, therefore it falls faster.

[0050] 4. The ΔG curve of high-entropy spinel intersects with that of MgAl2O4 at a temperature of approximately 1000 K.

[0051] 5. After the intersection point (~1000K), the ΔG value of high-entropy spinel is lower than that of all single-component spinels (ZnAl2O4, MnAl2O4, MgAl2O4).

[0052] Based on the judgment criteria, 1000K (approximately 727°C) was determined to be the optimal temperature for synthesizing this high-entropy spinel (Zn). 0.25 Mn 0.25 Ca 0.25 Mg 0.25The reference temperature for Al2O4. This temperature means that, above this temperature, the thermodynamic driving force for solid-state reactions to produce high-entropy single-phase products will exceed the driving force for the formation of any single-component spinel.

[0053] Comparative Example 1 Instead of employing the theoretical prediction method provided in this invention, a mixed powder of ZnO, MnO, CaO, MgO, and Al2O3 was directly calcined based on the commonly used empirical temperature for spinel preparation (e.g., 1300℃). Specific experimental parameters included: mixed powder particle size ≤ 5 μm; ball milling for 24 h using a planetary ball mill (ball-to-powder ratio 10:1, rotation speed 300 r / min); heating to 1300℃ at a rate of 5℃ / min under normal atmospheric pressure; holding at this temperature for 4 h; and then cooling with the furnace. X-ray diffraction analysis showed that, in addition to the main phase being high-entropy spinel, the product also contained significant impurity phases such as MgAl2O4 and ZnAl2O4. This indicates that although the high-entropy phase can be generated at 1300℃, the reaction is incomplete, competing phases still exist, and a pure high-entropy spinel material was not obtained. This result also indirectly confirms that at 1300℃ (about 1573K), although the driving force of the high-entropy phase may be greater, kinetic factors may lead to the residue of the competing phase, and the ~1000K (727℃) predicted in this invention is a starting reference point for the reversal of thermodynamic driving force. The above comparative examples demonstrate that the unified entropy calculation method provided by this invention, which includes vacancy contributions, can provide more accurate thermodynamic predictions that better reflect the nature of spinel structures, thus providing a reliable basis for determining reasonable synthesis initiation temperatures. The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature, characterized in that, Includes the following steps: S1. Determine the constituent elements and their proportions of the target high-entropy spinel, determine the corresponding binary oxide precursors, and perform physical modeling on the high-entropy spinel, all corresponding single-component spinels, and all binary oxide precursors to obtain their respective atomic structure models as input models for density functional theory calculations. S2. Based on density functional theory, calculate the ground state energy of all atomic structure models in step S1 at 0K using VASP software; S3. Based on the ground state energy obtained in step S2, calculate the enthalpy of mixing for the synthesis of the high-entropy spinel and the reactions of each single-component spinel using the enthalpy of mixing calculation formula; the enthalpy of mixing calculation formula is: ， in, It's spinel DFT energy. Let be the DFT energy of the k-th binary oxide precursor. The molar number of the k-th binary oxide precursor. It is the sum of the molar numbers of all binary oxide precursors; S4, For complex oxides A x B y O z According to the unified formula for calculating configuration entropy, the configuration entropy of the high-entropy spinel and each single-component spinel are calculated respectively; the unified formula for calculating configuration entropy is: ， Where x, y, and z represent the total number of ions at the A, B, and O sites of spinel, respectively. , and The mole fractions of each element at the A-site, B-site, and anionic site of spinel are respectively; M, N, and P are the number of different ion types occupying the A-site, B-site, and anionic site in spinel, including octahedral intrinsic vacancies; R is the gas constant; the total number of intrinsic octahedral vacancies is determined based on the standard spinel structure, and the number of 16c vacancies in a unit cell is 16, so the unit chemical formula is considered to be AB4O4, where the number of B-site cations and 16c vacancies are equal; S5. Based on the enthalpy of mixing obtained in step S3 and the configuration entropy obtained in step S4, calculate the change of Gibbs free energy with temperature for the synthesis reactions of the high-entropy spinel and each single-component spinel using the Gibbs free energy calculation formula; the Gibbs free energy calculation formula is as follows: ， in the formula It is the Gibbs free energy of chemical reaction (n). It is the enthalpy of mixture of chemical reaction (n). It is the entropy of the mixture of products of chemical reaction (n); and = Compositional entropy of products - Compositional entropy of reactants, where the reactant binary oxide is an ordered compound with a compositional entropy of 0. Equal to the configurational entropy of the product spinel; T is the absolute temperature, in Kelvin (K); S6. Compare the curves of Gibbs free energy of the high-entropy spinel and each single-component spinel as a function of temperature obtained in step S5, and determine the intersection point of the curves; if, after the intersection point, the Gibbs free energy of the high-entropy spinel is more negative than the Gibbs free energy of all single-component spinels corresponding to the constituent elements of the target high-entropy spinel, then the temperature corresponding to the intersection point is taken as the reference temperature for synthesizing the target high-entropy spinel.

2. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1, characterized in that, In step S1, a physical model of high-entropy spinel is performed. Specifically, based on the standard structure of spinel AB2O4, a 2×2×2 supercell model containing multiple elements randomly occupying positions is constructed according to its chemical formula. The A site corresponds to the 8aWyckoff position, the B site corresponds to the 16dWyckoff position, and the O site corresponds to the 32eWyckoff position. Multiple elements randomly occupy the A site or the B site according to their stoichiometric ratio.

3. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1, characterized in that, The configuration entropy Sconf calculated in step S4 is used to replace the mixing entropy, since the mixing entropy is contributed by the configuration entropy, while the vibrational entropy, magnetic dipole entropy, and electronic randomness entropy are ignored.

4. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1 or 3, characterized in that, The mixing entropy is contributed by the configuration entropy. The vibrational entropy, magnetic dipole entropy, and electronic randomness entropy have negligible effects, so the configuration entropy is used instead of the mixing entropy for calculation.

5. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1, characterized in that, In step S5, when calculating the Gibbs free energy, the configurational entropy of the reactant binary oxide is 0.

6. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1, characterized in that, In step S6, the determination of the curve intersection point specifically refers to determining the intersection point between the Gibbs free energy-temperature curve of the high-entropy spinel and the curve corresponding to the single-component spinel with the most negative Gibbs free energy.

7. The method for predicting the Gibbs free energy of high-entropy spinel synthesis temperature according to claim 1, characterized in that, In step S6, the reference temperature refers to the initial temperature at which the thermodynamic driving force for synthesizing the high-entropy spinel begins to exceed the thermodynamic driving force for synthesizing all single-component spinels under conventional synthesis reaction conditions in an atmospheric air atmosphere.

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