A method for screening Cu-Ni-Mn spinodal decomposition alloy composition based on free energy second derivative criterion

Abstract

The application discloses a method for screening Cu-Ni-Mn amplitude modulation decomposition alloy components based on a free energy second derivative criterion, and belongs to the technical field of copper-nickel alloy component design and structure control. The application establishes or calls a free energy database of a Cu-Ni-Mn system, calculates a Gibbs free energy curve of a Cu-based FCC solid solution along a preset component scanning path, takes the second derivative of the free energy curve with respect to a component variable being less than 0 as a criterion of a thermodynamic unstable region of amplitude modulation decomposition, and screens to obtain an alloy component interval with amplitude modulation decomposition possibility. Further, a Cu-20Ni-20Mn alloy is selected for melting, homogenization, solid solution and aging treatment, so as to form a strip-shaped amplitude modulation decomposition structure in which a Cu-rich region and a Ni-Mn-rich region are alternately distributed. The application does not depend on specific commercial thermodynamic software, can reduce traditional trial and error experiments, and improves the component design efficiency of high-strength and high-toughness copper-nickel alloys used in liquid oxygen ultra-low temperature environments.

Description

Technical Field

[0001] This invention belongs to the field of copper-nickel alloy composition design and microstructure control technology, specifically involving a method for screening Cu-Ni-Mn amplitude-modulated decomposition alloy composition based on the second derivative criterion of free energy, and more particularly involving a method for calculating the Gibbs free energy curve of Cu-based FCC solid solution through a free energy database, and screening Cu-Ni-Mn alloy composition ranges that can undergo amplitude-modulated decomposition according to the second derivative criterion of free energy. Background Technology

[0002] Copper-nickel alloys possess excellent low-temperature toughness, corrosion resistance, machinability, and microstructural stability, making them valuable for applications in cryogenic equipment, engine seals, aerospace, marine engineering, and complex service environments. Especially in liquid oxygen cryogenic environments, specialized copper-nickel alloys not only need high strength but also good plasticity, impact toughness, and microstructural stability. Therefore, developing high-strength, high-toughness specialized copper-nickel alloys suitable for liquid oxygen cryogenic environments is an important direction in copper-based alloy material design.

[0003] Traditional Cu-Ni alloys primarily rely on solid solution strengthening to improve strength, but the strengthening ability of solid solution strengthening alone is limited. Increasing strength by adding large amounts of strengthening elements or introducing coarse second phases may lead to a decrease in the alloy's low-temperature toughness and increase the risk of crack initiation. In the cryogenic environment of liquid oxygen, coarse precipitates, continuous grain boundary precipitates, or significant compositional segregation within the material can all become sources of low-temperature damage. Therefore, how to improve the strength of copper-nickel alloys without introducing a large amount of coarse, brittle phases is a key issue in the design of special copper-nickel alloys.

[0004] Amplitude modulation (AM) decomposition is a continuous compositional fluctuation process occurring in supersaturated solid solutions within thermodynamically unstable regions. Unlike traditional nucleation-growth precipitates, AM decomposition typically does not require a significant nucleation barrier and can form a fine-scale, continuously distributed, and interface-dispersed compositional modulation microstructure. This type of microstructure can enhance alloy strength through compositional fluctuations, elastic strain fields, and fine-scale interface modulation effects, while avoiding the significant adverse effects of coarse second phases on low-temperature toughness.

[0005] From a thermodynamic perspective, whether amplitude modulation decomposition can occur depends on the response of the solid solution's free energy curve to minute compositional perturbations. When the solid solution is in the stable region, minute compositional fluctuations will cause the system's free energy to increase, and the compositional perturbation cannot spontaneously amplify. When the solid solution is in the thermodynamically unstable region of amplitude modulation decomposition, minute compositional fluctuations can reduce the system's free energy, and the compositional perturbation can spontaneously amplify, thus forming a continuous compositional modulation structure.

[0006] For the free energy curve of a solid solution under a set composition scanning path, its stability can be judged by the second derivative of the Gibbs free energy with respect to the composition variable. When the second derivative of the free energy curve is greater than 0, the system is in the composition perturbation stable region; when the second derivative of the free energy curve is less than 0, the system is in the amplitude-modulated decomposition thermodynamically unstable region, and the corresponding composition interval has the possibility of amplitude-modulated decomposition.

[0007] However, existing design methods for Cu-Ni-Mn amplitude-modulated decomposition alloys have the following technical drawbacks: First, existing technologies largely rely on trial and error and numerous heat treatment experiments. This typically requires preparing dozens of alloys across a wide compositional range, followed by screening for compositions and heat treatment regimes capable of amplitude modulation decomposition through microscopic observation and performance testing. This method involves long experimental cycles and high sample consumption, resulting in alloy development cycles lasting several months and persistently high research and development costs.

[0008] Second, existing technologies lack clear physical criteria to guide composition design, and are mostly based on specific alloy compositions or heat treatment processes. It is difficult to accurately quantify the start and end points of the unstable region of amplitude modulation decomposition, and it is also impossible to clearly distinguish between the stable and unstable regions, resulting in significant ambiguity and uncertainty in composition design.

[0009] Third, existing technologies are typically designed for specific temperatures or composition paths, lacking the flexibility to adapt to different heat treatment or service temperatures, and are also difficult to meet the design requirements of different composition scanning paths. Furthermore, existing technologies largely rely on specific commercial thermodynamic software, which has high technical barriers and limited scalability, making it difficult to extend to other copper-nickel based alloy systems.

[0010] Fourth, existing technologies have limited data sources and computational accuracy when establishing thermodynamic databases, and often require complex professional software support, making it difficult for ordinary R&D personnel to quickly master and implement them, thus making it difficult to popularize the technology.

[0011] Fifth, existing technologies lack a closed-loop design process that combines theoretical prediction and experimental verification. Typically, a large number of experiments are conducted first, followed by experience summarization. It is difficult to quickly determine whether the alloy has the thermodynamic conditions for amplitude modulation decomposition before experimental preparation, and the reliability of the prediction results lacks effective verification.

[0012] Sixth, although existing technologies disclose the composition and preparation methods of some Cu-Ni-Mn alloys, they fail to provide a systematically verified process parameter window that can directly guide production. For example, the influence of the aging temperature range on the ability to form amplitude-modulated decomposition structures lacks systematic research, making it difficult to meet the requirements of process operability for engineering applications.

[0013] Therefore, there is an urgent need to establish a Cu-Ni-Mn amplitude decomposition alloy composition screening method that has a short development cycle, low R&D cost, clear physical meaning of the criteria, quantifiable composition boundaries, flexible and universal methods, strong process adaptability, diverse data sources, low technical threshold, closed-loop verification of prediction and experiment, and specific and feasible process parameters, so as to guide the development of Cu-Ni-Mn and other Cu-Ni-X amplitude decomposition strengthened copper-nickel alloys. Summary of the Invention

[0014] A method for screening the composition of Cu-Ni-Mn amplitude-modulated decomposition alloys based on the second derivative criterion of free energy includes the following steps: Step 1: Establish or call up the Cu-Ni-Mn system free energy database Establish or access a database for calculating the Gibbs free energy of Cu-based FCC solid solutions under different Cu, Ni, and Mn contents. The free energy database includes one or more of the following parameters: Gibbs free energy parameters for pure Cu, Ni, and Mn components; Cu-Ni binary interaction parameters; Cu-Mn binary interaction parameters; Ni-Mn binary interaction parameters; and Cu-Ni-Mn ternary interaction parameters.

[0015] The free energy database is constructed or modified from one or more of the following data: experimental thermodynamic data, phase equilibrium data, thermal analysis data, first-principles calculation data, cluster expansion calculation data, and phonon vibrational free energy calculation data.

[0016] Based on the aforementioned free energy database, the Gibbs free energy of Cu-based FCC solid solutions is calculated according to equation (1): G FCC = X Cu *G CuFCC + X Ni *G NiFCC + X Mn *G MnFCC + R*T*[X Cu *ln(X Cu ) + X Ni *ln(X Ni ) +X Mn *ln(X Mn )] + G excess (1) Among them, X Cu X Ni and X Mn The mole fractions of Cu, Ni, and Mn, respectively, and G CuFCC G NiFCC and G MnFCCG represents the Gibbs free energy of pure components Cu, Ni, and Mn in the FCC structure, where R is the gas constant, T is the calculation temperature, and Gi is the gas constant. excess This refers to the excess Gibbs free energy.

[0017] Excess Gibbs free energy G excess Calculate according to formula (2): G excess = X Cu *X Ni *L Cu,Ni + X Cu *X Mn *L Cu,Mn + X Ni *X Mn *L Ni,Mn + X Cu * X Ni * X Mn *L Cu,Ni,Mn (2) In equation (2), L Cu,Ni L Cu,Mn L Ni,Mn and L Cu,Ni,Mn These are the binary interaction parameters of Cu-Ni, Cu-Mn, and Ni-Mn, and the ternary interaction parameters of Cu-Ni-Mn, respectively; each interaction parameter can be a temperature-dependent parameter or expressed in polynomial form.

[0018] Step 2: Set the calculation temperature and calculate the Gibbs free energy curve along the preset component scan path. The calculated temperature T (T is the thermodynamic temperature, unit: K) is set according to the target heat treatment temperature or target service temperature. The set temperature is determined based on the target heat treatment temperature or target service temperature, for example 450℃, but is not limited to 450℃.

[0019] At the set calculation temperature T, the Gibbs free energy of the Cu-based FCC solid solution is calculated along the preset Cu-Ni-Mn composition scanning path, and the free energy curve G=G(x,T) showing the change of Gibbs free energy with composition variables is obtained, where x is the composition variable on the preset composition scanning path.

[0020] The preset composition scanning path can be any of the following: scanning Ni content with a fixed Mn content; scanning Mn content with a fixed Ni content; scanning total alloy element content with a fixed Ni / Mn ratio; or any continuous composition path selected in the Cu-Ni-Mn ternary composition space.

[0021] Step 3: Calculate the second derivative of the free energy curve Calculate the second derivative d of the free energy curve G=G(x,T) obtained in step 2 with respect to the component variable x.2 G / dx 2 The second derivative can be calculated analytically or approximated using finite difference methods.

[0022] When using finite difference calculation, the calculation is performed according to equation (3): d 2 G / dx 2 ≈ [G(x+Δx,T) - 2G(x,T) + G(x-Δx,T)] / (Δx) 2 (3) In equation (3), Δx is the component step size on the preset component scanning path.

[0023] Step 4: Determine the thermodynamically unstable region of amplitude modulation decomposition based on the second derivative criterion. When the second derivative obtained in step 3 satisfies d 2 G / dx 2 When d < 0, the component point or adjacent component range is determined to be in the thermodynamically unstable region of amplitude modulation decomposition, and has the potential to undergo amplitude modulation decomposition; when d 2 G / dx 2 When the value is greater than 0, the component interval is determined to be in the component perturbation stable region.

[0024] Step 5: Screening to obtain the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloys. Based on the amplitude-modulated decomposition thermodynamically unstable region determined in step 4, Cu-Ni-Mn alloy composition ranges with the possibility of amplitude-modulated decomposition are screened out.

[0025] Preferably, the composition range of the Cu-Ni-Mn amplitude-modulated decomposition alloy includes, by mass percentage: Ni 18-22%, Mn 18-22%, with the balance being Cu and unavoidable impurities.

[0026] Step 6: Select candidate alloy compositions and verify their ability to form amplitude-modulated decomposition microstructures through experiments. Candidate alloy compositions were selected from the Cu-Ni-Mn amplitude decomposition alloy composition range obtained in step 5, and their ability to form amplitude decomposition structures was verified by smelting, solution treatment and aging treatment.

[0027] More preferably, the candidate alloy composition selected from the Cu-Ni-Mn amplitude-modulated decomposition alloy composition range is Cu-20Ni-20Mn, wherein the Ni content is 20wt.%, the Mn content is 20wt.%, and the balance is Cu and unavoidable impurities.

[0028] The melting method is any one of the following: vacuum induction melting, vacuum arc melting, protective atmosphere melting, or induction melting.

[0029] The solution treatment temperature is 550–700℃, the holding time is 1–5 hours, and water quenching is performed after the solution treatment.

[0030] The aging treatment temperature is 400-500℃, and the aging treatment is followed by air cooling.

[0031] The amplitude-modulated decomposition structure is a strip-shaped, wavy, or continuous component modulation structure with alternating distribution of Cu-rich and Ni-Mn-rich regions.

[0032] The ability to form amplitude-modulated decomposition tissues is verified using one or more of the following methods: scanning electron microscopy, transmission electron microscopy, energy dispersive spectroscopy, electron probe microanalysis, and atomic probe microanalysis.

[0033] Compared with the prior art, this patent application has the following advantages: 1. Development cycle significantly shortened, R&D costs significantly reduced. This invention eliminates the cumbersome process of traditional trial-and-error methods, which require preparing dozens of alloys across a wide composition range and conducting numerous heat treatment experiments. By using the second derivative criterion of free energy, it can quickly predict the amplitude-modulated decomposition composition range before the experiment, shortening the composition screening cycle from months to days. Simultaneously, this invention significantly reduces the consumption of high-purity metal raw materials and the costs of smelting, heat treatment, and other experimental processes. A single verification experiment on a Cu-20Ni-20Mn alloy successfully confirmed the accuracy of the predicted range, avoiding the duplication of numerous invalid experiments.

[0034] 2. The prediction criteria have clear physical meaning, and the composition boundaries can be quantified. This invention is based on the Cahn-Hilliard amplitude modulation decomposition theory, using the second derivative of the free energy with respect to composition being less than zero as the core criterion, with a clear and explicit physical meaning. This criterion can accurately and quantitatively determine the start and end composition points of the unstable region of amplitude modulation decomposition, specifically the range of 15 to 25% by weight Ni content at 450℃, and clearly distinguishes between the stable and unstable regions, eliminating the ambiguity in traditional empirical design and providing precise thermodynamic boundaries for alloy composition design.

[0035] 3. The method is flexible and versatile, with strong process adaptability. The calculation temperature of this invention can be flexibly set according to the actual heat treatment or service temperature. Example 2 verifies the predictive ability of this invention at 400℃, 450℃, 500℃, and 550℃. The results show that as the temperature increases, the unstable range of amplitude decomposition shifts towards lower nickel content. When the temperature rises to 550℃, amplitude decomposition no longer occurs. This method can effectively guide the design of process windows at different temperatures. Simultaneously, this invention supports multiple composition scanning paths, such as fixed element content and fixed element ratio. Regardless of whether a fixed manganese content, fixed nickel content, or fixed nickel-manganese ratio path is used, the prediction results are highly consistent, all pointing to a composition range where nickel and manganese are each 15 to 25 weight percentages, indicating that the method is robust to different design paths. Furthermore, this invention does not rely on specific commercial thermodynamic software; it only requires establishing or calling a free energy database for implementation, and can be easily extended to the design of amplitude decomposition-strengthened alloys in other copper-nickel based alloy systems.

[0036] 4. Diverse data sources and low technical barriers This invention establishes a free energy database through various methods, including experimental thermodynamic data, phase equilibrium data, first-principles calculations, and cluster expansion calculations, without relying on a single data source, effectively ensuring the accuracy and reliability of the calculations. In finite difference calculations, the difference step size can be flexibly adjusted according to accuracy requirements; for example, taking 0.5% of the weight can achieve a good balance between calculation accuracy and efficiency. All calculations can be performed using conventional programming tools such as Python or MATLAB, significantly reducing the technical threshold and implementation cost.

[0037] 5. Closed-loop verification of prediction and experiment ensures high reliability. This invention not only provides theoretical predictions but also performs closed-loop verification through the melting, solution treatment, aging, and microstructure characterization of specific candidate alloys. Scanning electron microscopy observation of the Cu-20Ni-20Mn alloy revealed the formation of strip-shaped microstructures with widths of approximately 50 to 150 nanometers. Energy dispersive spectroscopy (EDS) analysis confirmed the alternating distribution of copper-rich and nickel-manganese-rich regions. The experimental results perfectly match the predictions based on the second derivative criterion of free energy. This closed-loop approach, combining theoretical predictions with experimental verification, ensures the scientific validity and practicality of the method presented in this invention.

[0038] 6. The process parameters are specific and feasible, providing high guidance value. This invention provides specific process parameters that have been experimentally verified, including a solution treatment temperature of 600 degrees Celsius, water quenching after 3 hours, and an aging treatment temperature of 450 degrees Celsius, air cooling after 4 hours. These parameters can be directly used to guide production practice. Amplitude-modulated decomposition structures can be formed within an aging temperature window of 400 to 500 degrees Celsius, providing a clear operational space for adjusting microstructure dimensions and optimizing mechanical properties by controlling the aging temperature. Attached Figure Description

[0039] Figure 1 This is a diagram showing the possible component ranges of the Cu-Ni-Mn system obtained by amplitude modulation decomposition based on the second derivative criterion of free energy.

[0040] Figure 2 Scanning electron microscope image of the strip-shaped amplitude-modulated decomposition microstructure formed by solution treatment and aging of Cu-20Ni-20Mn alloy.

[0041] Figure 3 The results of energy dispersive spectroscopy (EDS) analysis of the strip-shaped amplitude-modulated decomposition structure of Cu-20Ni-20Mn alloy. Detailed Implementation

[0042] Example 1 In this embodiment, following the method described in steps 1 to 6 of the above-mentioned invention, a calculation temperature of 450°C is used, and a composition scanning path of scanning Ni content with fixed Mn content is used to screen the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloy, and experimental verification is performed using Cu-20Ni-20Mn alloy.

[0043] A method for screening the composition of Cu-Ni-Mn amplitude-modulated decomposition alloys based on the second derivative criterion of free energy includes the following steps: Step 1: Establish a free energy database for the Cu-Ni-Mn system This embodiment establishes a free energy database for the Cu-Ni-Mn system. The free energy database includes the Gibbs free energy parameters of pure Cu, Ni, and Mn components, Cu-Ni binary interaction parameters, Cu-Mn binary interaction parameters, Ni-Mn binary interaction parameters, and Cu-Ni-Mn ternary interaction parameters.

[0044] Specifically, the Gibbs free energy parameters for pure components are taken from the SGTE pure component database. The Cu-Ni binary interaction parameters are taken in the following Redlich-Kister polynomial form: L Cu,Ni = A0 + A1·(X Cu -X Ni ) + A2·(X Cu -X Ni ) 2 Among them, A0, A1, and A2 are temperature-related empirical parameters, and their specific values ​​are derived from the thermodynamic optimization results of the Cu-Ni binary phase diagram. The Cu-Mn, Ni-Mn binary interaction parameters and the Cu-Ni-Mn ternary interaction parameters adopt similar polynomial forms, and the parameters are derived from the thermodynamic evaluation literature data of the Cu-Mn-Ni ternary system.

[0045] Based on the aforementioned free energy database, the Gibbs free energy of Cu-based FCC solid solutions is calculated according to equation (1): G FCC = X Cu *G CuFCC + X Ni *G NiFCC + X Mn *G MnFCC + R*T*[X Cu *ln(X Cu ) + X Ni *ln(X Ni ) +X Mn *ln(X Mn )] + G excess (1) Among them, X Cu X Ni and X Mn The mole fractions of Cu, Ni, and Mn, respectively, and G CuFCC G NiFCC and G MnFCC G represents the Gibbs free energies of pure Cu, Ni, and Mn components in the FCC structure, R is the gas constant (8.314 J / (mol·K)), T is the calculation temperature, and G represents the free energies of pure Cu, Ni, and Mn components in the FCC structure. excess This refers to the excess Gibbs free energy.

[0046] Excess Gibbs free energy G excess Calculate according to formula (2): G excess = X Cu *X Ni *L Cu,Ni + X Cu *X Mn *L Cu,Mn + X Ni *X Mn *L Ni,Mn + X Cu * X Ni * X Mn *L Cu,Ni,Mn (2) In equation (2), L Cu,Ni L Cu,Mn L Ni,Mn and L Cu,Ni,Mn These are the binary interaction parameters of Cu-Ni, Cu-Mn, and Ni-Mn, and the ternary interaction parameters of Cu-Ni-Mn, respectively; each interaction parameter can be a temperature-dependent parameter or expressed in polynomial form.

[0047] Step 2: Set the calculation temperature and calculate the Gibbs free energy curve along the preset component scan path. In this embodiment, the calculation temperature is set to T = 450℃ (723.15K). This temperature corresponds to the temperature of the subsequent aging treatment.

[0048] The preset component scanning path used in this embodiment is as follows: the Mn content is fixed at 20 wt.%, and the Ni content is scanned from 0 wt.% to 40 wt.%, converting the ternary component change into a one-dimensional component variable x (x is the mass percentage of Ni) along this path. At the set calculation temperature, the Gibbs free energy of each component point is calculated to obtain the free energy curve G=G(x,723.15K).

[0049] Step 3: Calculate the second derivative of the free energy curve In this embodiment, the second derivative of the free energy curve is calculated using the finite difference method according to equation (3). The difference step size Δx is taken as 0.5 wt.%.

[0050] d 2 G / dx 2 ≈ [G(x+Δx,T) - 2G(x,T) + G(x-Δx,T)] / (Δx) 2 (3) For each component point x, at the set calculation temperature T = 723.15 K, calculate G(x + Δx, T), G(x, T) and G(x - Δx, T) respectively, and substitute them into equation (3) to obtain d. 2 G / dx 2 Approximate value.

[0051] Step 4: Determine the thermodynamically unstable region of amplitude modulation decomposition based on the second derivative criterion. In this embodiment, when the calculated d 2 G / dx 2 When d < 0, the component point is determined to be in the thermodynamically unstable region of amplitude modulation decomposition, and has the potential to undergo amplitude modulation decomposition; when d 2 G / dx 2 When the value is greater than 0, the component point is determined to be in the component perturbation stability region.

[0052] Calculation results show that at 450℃, when the Ni content is in the range of 15–25 wt.%, d 2 G / dx 2 <0, this component range is in the thermodynamically unstable region of amplitude modulation decomposition.

[0053] Step 5: Screening to obtain the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloys. Based on the determination results in step 4, the composition range of the Cu-Ni-Mn amplitude-modulated decomposition alloy obtained in this embodiment is: Ni content 15-25 wt.%, Mn content 20 wt.%, and balance Cu. Further considering multiple calculations and process windows, the preferred composition range is Ni 18-22 wt.%, Mn 18-22 wt.%, and balance Cu. Figure 1 This is a schematic diagram of the possible component ranges of amplitude modulation decomposition predicted in this embodiment.

[0054] Step 6: Select candidate alloy compositions and verify their ability to form amplitude-modulated decomposition microstructures through experiments. In this embodiment, Cu-20Ni-20Mn alloy (Ni content is 20wt.%, Mn content is 20wt.%, and the balance is Cu) was selected from the composition range obtained in step 5 as a candidate verification alloy, and experimental verification was carried out as follows.

[0055] 6.1: Smelting Weigh out the following high-purity raw materials according to the nominal composition of Cu-20Ni-20Mn: electrolytic copper (99.95 wt.%), electrolytic nickel (99.95 wt.%), and electrolytic manganese (99.8 wt.%). Considering that Mn is easily oxidized and lost during smelting, add an additional 0.8% by mass of manganese according to the nominal composition to compensate for smelting loss.

[0056] Place the weighed raw materials into a vacuum arc melting furnace. Evacuate the furnace to 5×10⁻⁶. -3 The pressure is below 0.06 MPa, then high-purity argon (99.999% purity) is introduced to create a protective atmosphere. The melting current is controlled between 250 and 350 A to ensure complete melting of the raw materials. Each alloy ingot is flipped and remelted four times to obtain a uniformly composed ingot. After melting, the molten material is poured into a water-cooled copper mold under a protective atmosphere to obtain a cylindrical ingot with a diameter of 20 mm × 50 mm.

[0057] 6.2: Homogenization Treatment The ingot is placed in a vacuum heat treatment furnace and evacuated to a vacuum level of 5×10⁻⁶. -3 Below Pa, the temperature is increased to 900℃ at a heating rate of 10℃ / min and held for 12 hours for homogenization treatment to reduce as-cast segregation. After homogenization treatment, the furnace is cooled to room temperature.

[0058] 6.3: Solution Treatment The homogenized alloy was cut into 10mm×10mm×5mm sample blocks using an electrical discharge wire cutter. The samples were placed in a box-type resistance furnace and heated to 600℃ at a heating rate of 15℃ / min, and held at that temperature for 3 hours for solution treatment. After solution treatment, the samples were quickly removed and water-quenched to room temperature (water temperature 20~25℃) to obtain a supersaturated solid solution.

[0059] 6.4: Timeliness Handling The solution-treated sample was placed in a heat treatment furnace and heated to 450℃ at a rate of 10℃ / min, and held at that temperature for 4 hours for aging treatment. After aging treatment, it was removed and air-cooled to room temperature. During the aging process, the supersaturated solid solution underwent continuous compositional fluctuations within the thermodynamically unstable region of amplitude modulation decomposition, forming amplitude modulation decomposition structures.

[0060] 6.5: Organizational Characterization and Validation After aging treatment, the samples were sequentially mechanically ground with 180#, 400#, 800#, 1200#, 2000#, and 3000# silicon carbide sandpaper, and then polished to a mirror finish with diamond polishing paste (2.5μm grit). The polished samples were then etched with an etching solution (5g FeCl3 + 10ml HCl + 90ml H2O) for 12–15 seconds, rinsed with deionized water, dehydrated with anhydrous ethanol, and dried with cold air.

[0061] The microstructure of the etched samples was observed using a scanning electron microscope (ZEISS Gemini 300) with an accelerating voltage of 15 kV. The observation results are as follows: Figure 2 As shown, the alloy forms a distinct strip-like structure with strip widths of approximately 50–150 nm and significant differences in contrast between the strips.

[0062] Energy dispersive spectroscopy (Oxford X-Max) was used 50 Elemental analysis was performed on regions with different contrast levels, using an accelerating voltage of 20 kV and a data acquisition time of 60 s. The analysis results are as follows: Figure 3 As shown: the light-colored areas contain an average of 72.5 wt.% Cu, 13.8 wt.% Ni, and 13.7 wt.% Mn; the dark-colored areas contain an average of 47.2 wt.% Cu, 27.5 wt.% Ni, and 25.3 wt.% Mn. The results indicate that the light-colored areas are relatively rich in Cu, while the dark-colored areas are relatively rich in Ni and Mn, forming a strip-shaped amplitude-modulated decomposition structure with alternating Cu-rich and Ni-Mn-rich regions.

[0063] The experimental results above are consistent with the amplitude modulation decomposition possible component ranges predicted by the second derivative criterion of free energy in steps 4 to 5, verifying the feasibility of the method of the present invention.

[0064] Example 2 This embodiment follows the method described in steps 1 to 6 of the above-described invention, using multiple different temperatures as calculation temperatures and scanning Ni content with a fixed Mn content as the composition scanning path, to screen the Cu-Ni-Mn amplitude-modulated decomposition alloy composition range at different temperatures, in order to verify the applicability of the method of the present invention to different target temperatures.

[0065] A method for screening the composition of Cu-Ni-Mn amplitude-modulated decomposition alloys based on the second derivative criterion of free energy includes the following steps: Step 1: Establish a free energy database for the Cu-Ni-Mn system This embodiment establishes a free energy database for the Cu-Ni-Mn system. The free energy database includes the Gibbs free energy parameters of pure Cu, Ni, and Mn components, Cu-Ni binary interaction parameters, Cu-Mn binary interaction parameters, Ni-Mn binary interaction parameters, and Cu-Ni-Mn ternary interaction parameters.

[0066] Specifically, the Gibbs free energy parameters for pure components are taken from the SGTE pure component database. The Cu-Ni binary interaction parameters are taken in the following Redlich-Kister polynomial form: L Cu,Ni = A0 + A1·(X Cu -X Ni ) + A2·(X Cu -X Ni ) 2 Among them, A0, A1, and A2 are temperature-related empirical parameters, and their specific values ​​are derived from the thermodynamic optimization results of the Cu-Ni binary phase diagram. The Cu-Mn, Ni-Mn binary interaction parameters and the Cu-Ni-Mn ternary interaction parameters adopt similar polynomial forms, and the parameters are derived from the thermodynamic evaluation literature data of the Cu-Mn-Ni ternary system.

[0067] Based on the aforementioned free energy database, the Gibbs free energy of Cu-based FCC solid solutions is calculated according to equation (1): G FCC = X Cu *G CuFCC + X Ni *G NiFCC + X Mn *G MnFCC + R*T*[X Cu *ln(X Cu ) + X Ni *ln(X Ni ) +X Mn *ln(X Mn )] + G excess (1) Among them, X Cu X Ni and X Mn The mole fractions of Cu, Ni, and Mn, respectively, and G CuFCC G NiFCC and G MnFCCG represents the Gibbs free energy of pure components Cu, Ni, and Mn in the FCC structure, where R is the gas constant, T is the calculation temperature, and Gi is the gas constant. excess This refers to the excess Gibbs free energy.

[0068] Excess Gibbs free energy G excess Calculate according to formula (2): G excess = X Cu *X Ni *L Cu,Ni + X Cu *X Mn *L Cu,Mn + X Ni *X Mn *L Ni,Mn + X Cu * X Ni * X Mn *L Cu,Ni,Mn (2) In equation (2), L Cu,Ni L Cu,Mn L Ni,Mn and L Cu,Ni,Mn These are the binary interaction parameters of Cu-Ni, Cu-Mn, and Ni-Mn, and the ternary interaction parameters of Cu-Ni-Mn, respectively; each interaction parameter can be a temperature-dependent parameter or expressed in polynomial form.

[0069] Step 2: Set the calculation temperature and calculate the Gibbs free energy curve along the preset component scan path. In this embodiment, three different calculation temperatures are set: T=400℃ (673.15K), T=500℃ (773.15K), and T=550℃ (823.15K). These temperatures correspond to different aging treatment temperatures or target service temperatures.

[0070] The preset component scanning path used in this embodiment is the same as in Embodiment 1: the Mn content is fixed at 20 wt.%, and the Ni content is scanned from 0 wt.% to 40 wt.%, converting the ternary component change into a one-dimensional component variable x (x is the mass percentage of Ni) along this path. At each set calculation temperature, the Gibbs free energy of each component point is calculated to obtain the free energy curve G=G(x,T) at each temperature.

[0071] Step 3: Calculate the second derivative of the free energy curve In this embodiment, the second derivative of the free energy curve is calculated using the finite difference method according to equation (3). The difference step size Δx is taken as 0.5 wt.%.

[0072] d 2 G / dx 2≈ [G(x+Δx,T) - 2G(x,T) + G(x-Δx,T)] / (Δx) 2 (3) For each component point x, calculate G(x+Δx,T), G(x,T) and G(x-Δx,T) respectively, and substitute them into equation (3) to obtain d. 2 G / dx 2 Approximate value.

[0073] Step 4: Determine the thermodynamically unstable region of amplitude modulation decomposition based on the second derivative criterion. In this embodiment, d is determined at each calculation temperature. 2 G / dx 2 The component range of <0.

[0074] The calculation results show that: At 400℃, when the Ni content is in the range of 17–27 wt.%, d 2 G / dx 2 <0; At 450°C (refer to Example 1), when the Ni content is in the range of 15–25 wt.%, d 2 G / dx 2 <0; At 500℃, when the Ni content is in the range of 10–20 wt.%, d 2 G / dx 2 <0; At 550℃, within the Ni content range of 0–40 wt.%, d 2 G / dx 2 All values ​​are greater than 0, indicating that no amplitude-modulated decomposition thermodynamic instability region has been observed.

[0075] Step 5: Screening to obtain the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloys. Based on the determination results of step 4, this embodiment obtains the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloys at various temperatures: The composition at 400℃ is: Ni content 17-27 wt.%, Mn content 20 wt.%, balance Cu; The composition at 450℃ is: Ni content 15-25 wt.%, Mn content 20 wt.%, balance Cu; The composition at 500℃ is: Ni content 10-20 wt.%, Mn content 20 wt.%, balance Cu; The possible component range for no amplitude-modulated decomposition at 550℃.

[0076] The above results indicate that as the calculation temperature increases, the range of the amplitude modulation decomposition instability region gradually shrinks and shifts towards lower Ni content; when the temperature rises to 550℃, the amplitude modulation decomposition thermodynamic instability region no longer exists under the condition of Mn content of 20wt.%.

[0077] Step 6: Select candidate alloy compositions and verify their ability to form amplitude-modulated decomposition microstructures through experiments. In this embodiment, candidate alloy compositions were selected from the temperature composition ranges obtained in step 5 for experimental verification. To ensure consistent initial microstructure, all candidate alloys underwent the same solution treatment process as in Example 1 (600℃ × 3h water quenching), except that they were held at their respective predicted temperatures (400℃, 450℃, 500℃, and 550℃) during the aging process. The specific selection and verification scheme is as follows: For the predicted range of 400℃, a Cu-22Ni-20Mn alloy (Ni 22wt.%, Mn 20wt.%, balance Cu) was selected and aged at 400℃. For the predicted range of 450℃, Cu-20Ni-20Mn alloy (same as in Example 1) was selected and aged at 450℃. For the 500℃ prediction range, a Cu-15Ni-20Mn alloy (Ni 15wt.%, Mn 20wt.%, balance Cu) was selected and aged at 500℃. For the 550℃ prediction range, Cu-20Ni-20Mn alloy was selected and aged at 550℃ as a control.

[0078] The melting, homogenization, solution treatment (600℃×3h water quenching) and microstructure characterization methods for each alloy are the same as step 6 of Example 1, except that the aging temperature is adjusted according to the above settings.

[0079] Experimental results show that: Cu-22Ni-20Mn alloy forms a strip-shaped amplitude modulation decomposition structure after aging at 400℃; Cu-20Ni-20Mn alloy forms a strip-shaped amplitude modulation decomposition structure after aging at 450℃ (as described in Example 1); Cu-15Ni-20Mn alloy forms a wavy amplitude modulation decomposition structure after aging at 500℃; while Cu-20Ni-20Mn alloy does not show obvious composition modulation structure after aging at 550℃, and only presents a uniform single-phase solid solution structure.

[0080] The above experimental results are in complete agreement with the conclusions predicted at various temperatures based on the second derivative criterion of free energy in steps 4 to 5, verifying the applicability of the method of the present invention to different target heat treatment temperatures or service temperatures.

[0081] Example 3 In this embodiment, following the method described in steps 1 to 6 of the above-described invention, the Cu-Ni-Mn amplitude-modulated decomposition alloy composition range is calculated and screened using 450°C as the calculation temperature and three different preset composition scanning paths. The Cu-20Ni-20Mn alloy is used for experimental verification to demonstrate the robustness of the method of the present invention to different composition scanning paths.

[0082] A method for screening the composition of Cu-Ni-Mn amplitude-modulated decomposition alloys based on the second derivative criterion of free energy includes the following steps: Step 1: Establish a free energy database for the Cu-Ni-Mn system This embodiment establishes a free energy database for the Cu-Ni-Mn system. The free energy database includes the Gibbs free energy parameters of pure Cu, Ni, and Mn components, Cu-Ni binary interaction parameters, Cu-Mn binary interaction parameters, Ni-Mn binary interaction parameters, and Cu-Ni-Mn ternary interaction parameters.

[0083] Specifically, the Gibbs free energy parameters for pure components are taken from the SGTE pure component database. The Cu-Ni binary interaction parameters are taken in the following Redlich-Kister polynomial form: L Cu,Ni = A0 + A1·(X Cu -X Ni ) + A2·(X Cu -X Ni ) 2 Among them, A0, A1, and A2 are temperature-related empirical parameters, and their specific values ​​are derived from the thermodynamic optimization results of the Cu-Ni binary phase diagram. The Cu-Mn, Ni-Mn binary interaction parameters and the Cu-Ni-Mn ternary interaction parameters adopt similar polynomial forms, and the parameters are derived from the thermodynamic evaluation literature data of the Cu-Mn-Ni ternary system.

[0084] Based on the aforementioned free energy database, the Gibbs free energy of Cu-based FCC solid solutions is calculated according to equation (1): G FCC = X Cu *G CuFCC + X Ni *G NiFCC + X Mn *G MnFCC + R*T*[X Cu *ln(X Cu ) + X Ni *ln(X Ni ) +X Mn *ln(X Mn)] + G excess (1) Among them, X Cu X Ni and X Mn The mole fractions of Cu, Ni, and Mn, respectively, and G CuFCC G NiFCC and G MnFCC Let G be the Gibbs free energies of Cu, Ni, and Mn pure components in the FCC structure, R be the gas constant, T be the calculation temperature, and G be the Gibbs free energies of pure components. excess This refers to the excess Gibbs free energy.

[0085] Excess Gibbs free energy G excess Calculate according to formula (2): G excess = X Cu *X Ni *L Cu,Ni + X Cu *X Mn *L Cu,Mn + X Ni *X Mn *L Ni,Mn + X Cu * X Ni * X Mn *L Cu,Ni,Mn (2) In equation (2), L Cu,Ni L Cu,Mn L Ni,Mn and L Cu,Ni,Mn These are the binary interaction parameters of Cu-Ni, Cu-Mn, and Ni-Mn, and the ternary interaction parameters of Cu-Ni-Mn, respectively; each interaction parameter can be a temperature-dependent parameter or expressed in polynomial form.

[0086] Step 2: Set the calculation temperature and calculate the Gibbs free energy curve along the preset component scan path. In this embodiment, the calculation temperature is set to T=450℃ (723.15K), which is the same as in Embodiment 1.

[0087] This embodiment employs the following three different preset component scanning paths: Path A (same as Example 1): With the Mn content fixed at 20 wt.%, the Ni content is scanned from 0 wt.% to 40 wt.%, and the ternary composition change is converted into a one-dimensional composition variable x_A along this path (x_A is the mass percentage of Ni). At the set calculation temperature, the Gibbs free energy of each composition point is calculated, and the free energy curve G_A=G_A(x_A,723.15K) is obtained.

[0088] Path B: With a fixed Ni content of 20 wt.%, the Mn content is scanned from 0 wt.% to 40 wt.%, and the ternary composition change is transformed into a one-dimensional composition variable x_B along this path (x_B is the mass percentage of Mn). At the set calculation temperature, the Gibbs free energy at each composition point is calculated, and the free energy curve G_B=G_B(x_B,723.15K) is obtained.

[0089] Path C: With a fixed Ni / Mn mass ratio of 1 (i.e., Ni and Mn contents are equal), the total alloy element content (Ni+Mn) is scanned from 10 wt.% to 60 wt.%, transforming the ternary composition change into a one-dimensional composition variable x_C along this path (x_C is the total mass percentage of Ni+Mn). At a set calculation temperature, the Gibbs free energy at each composition point is calculated, obtaining the free energy curve G_C=G_C(x_C,723.15K).

[0090] Step 3: Calculate the second derivative of the free energy curve In this embodiment, the second derivative of the free energy curve is calculated using the finite difference method according to equation (3).

[0091] d 2 G / dx 2 ≈ [G(x+Δx,T) - 2G(x,T) + G(x-Δx,T)] / (Δx) 2 (3) For each component point x, under the set difference step size Δx for each path, calculate G(x+Δx,723.15K), G(x,723.15K) and G(x-Δx,723.15K) respectively, and substitute them into equation (3) to obtain d. 2 G / dx 2 Approximate value.

[0092] The differential step size Δx for each path is set as follows: 0.5wt.% for path A, 0.5wt.% for path B, and 1.0wt.% for path C.

[0093] Step 4: Determine the thermodynamically unstable region of amplitude modulation decomposition based on the second derivative criterion. This embodiment determines d under each path. 2 G / dx 2 The component range of <0.

[0094] The calculation results show that: Along path A (with a fixed Mn content of 20 wt.%), when the Ni content is in the range of 15–25 wt.%, d 2 G / dx 2 <0; Along path B (with a fixed Ni content of 20 wt.%), when the Mn content is in the range of 15–25 wt.%, d 2 G / dx 2 <0; Along path C (with a fixed Ni / Mn=1), when the total Ni+Mn content is in the range of 30-50 wt.% (i.e., Ni and Mn are each about 15-25 wt.%), d 2 G / dx 2 <0.

[0095] Step 5: Screening to obtain the composition range of Cu-Ni-Mn amplitude-modulated decomposition alloys Based on the determination results of step 4, the Cu-Ni-Mn amplitude-modulated decomposition alloy composition ranges obtained from the three different paths in this embodiment are as follows: Pathway A: Ni content 15-25 wt.%, Mn content 20 wt.%, balance Cu; Pathway B: Ni content 20 wt.%, Mn content 15-25 wt.%, balance Cu; Pathway C: Ni content 15-25 wt.%, Mn content 15-25 wt.%, balance Cu (satisfying Ni / Mn=1).

[0096] The amplitude-modulated decomposition instability regions obtained from the three paths are projected into the Cu-Ni-Mn ternary composition space. The overlapping region of the three is: Ni content 15-25 wt.%, Mn content 15-25 wt.%, and the balance is Cu. Cu-20Ni-20Mn (Ni 20 wt.%, Mn 20 wt.%) is located at the center of this overlapping region.

[0097] Step 6: Select candidate alloy compositions and verify their ability to form amplitude-modulated decomposition microstructures through experiments. In this embodiment, a Cu-20Ni-20Mn alloy (Ni content 20 wt.%, Mn content 20 wt.%, balance Cu) was selected as a candidate verification alloy from the overlapping composition range obtained in step 5. The experimental verification process was exactly the same as step 6 of Example 1 (melting, homogenization, solution treatment, aging treatment at 450℃, and microstructure characterization).

[0098] Experimental results show that ( Figure 2 These are scanning electron microscope images. Figure 3 (Electronic spectroscopy analysis results): After solution treatment and aging, the Cu-20Ni-20Mn alloy exhibited a distinct strip-shaped amplitude-modulated decomposition structure, with alternating Cu-rich and Ni-Mn-rich regions. This result is consistent with the predictions obtained from three different composition scanning paths.

[0099] This embodiment illustrates that the method of the present invention is robust to different component scanning paths, and the prediction results do not depend on the selection of a specific path.

[0100] Although the above embodiments have provided a detailed description of the present invention, they are only some, not all, embodiments of the present invention. Other embodiments obtained by those skilled in the art based on these embodiments without inventive effort are all within the protection scope of the present invention.

Claims

1. A method for screening the composition of Cu-Ni-Mn amplitude-modulated decomposition alloys based on the second derivative criterion of free energy, characterized in that, Includes the following steps: Step 1: Establish or call up the Cu-Ni-Mn system free energy database; Step 2: Set the calculation temperature T, and calculate the Gibbs free energy curve G=G(x,T) of Cu-based FCC solid solution along the preset Cu-Ni-Mn composition scanning path, where x is the composition variable on the preset composition scanning path; Step 3: Calculate the second derivative d of the free energy curve G=G(x,T) obtained in Step 2 with respect to the component variable x. 2 G / dx 2 ; Step 4: When the second derivative calculated in step 3 satisfies d 2 G / dx 2 When <0, the component point or adjacent component range is determined to be in the thermodynamically unstable region of amplitude modulation decomposition, and there is a possibility of amplitude modulation decomposition. Step 5: Based on the amplitude-modulated decomposition thermodynamically unstable region determined in Step 4, screen out the Cu-Ni-Mn alloy composition ranges with the possibility of amplitude-modulated decomposition.

2. The method according to claim 1, characterized in that, The free energy database mentioned in step 1 includes the Gibbs free energy parameters, Cu-Ni binary interaction parameters, Cu-Mn binary interaction parameters, Ni-Mn binary interaction parameters, and Cu-Ni-Mn ternary interaction parameters of pure components Cu, Ni, and Mn. The free energy database is constructed or modified from one or more of the following data: experimental thermodynamic data, phase equilibrium data, thermal analysis data, first-principles calculation data, cluster expansion calculation data, and phonon vibrational free energy calculation data.

3. The method according to claim 1, characterized in that, The preset composition scanning path mentioned in step 2 is any of the following: scanning Ni content with a fixed Mn content, scanning Mn content with a fixed Ni content, scanning total alloy element content with a fixed Ni / Mn ratio, or any continuous composition path selected in the Cu-Ni-Mn ternary composition space.

4. The method according to claim 1, characterized in that, The second derivative mentioned in step 3 is approximately calculated using the finite difference method according to equation (3): d 2 G / dx 2 ≈ [G(x+Δx,T)-2G(x,T) + G(x-Δx,T)] / (Δx) 2 , where Δx is the component step size on the preset component scanning path.

5. The method according to claim 1, characterized in that, The Cu-Ni-Mn amplitude-modulated decomposition alloy composition range obtained in step 5 includes, by mass percentage: Ni 15-25%, Mn 15-25%, with the balance being Cu and unavoidable impurities.

6. The method according to claim 1, characterized in that, The method further includes step 6: selecting candidate alloy components from the Cu-Ni-Mn amplitude decomposition alloy composition range obtained in step 5, and verifying their amplitude decomposition microstructure formation ability through smelting, solution treatment and aging treatment.

7. The method according to claim 6, characterized in that, The preferred alloy composition is Cu-20Ni-20Mn, wherein the Ni content is 20wt.%, the Mn content is 20wt.%, and the balance is Cu and unavoidable impurities.

8. The method according to claim 6, characterized in that, The solution treatment temperature is 550–700℃, the holding time is 1–5 h, and water quenching is performed after the solution treatment; the aging treatment temperature is 400–500℃, the holding time is 1–5 h, and air cooling is performed after the aging treatment.

9. The method according to claim 1 or 6, characterized in that, The amplitude-modulated decomposition structure is a strip-shaped, wavy, or continuous component modulation structure with alternating distribution of Cu-rich and Ni-Mn-rich regions.

10. The method according to claim 6, characterized in that, The ability to form amplitude-modulated decomposition tissues is verified using one or more of the following methods: scanning electron microscopy, transmission electron microscopy, energy dispersive spectroscopy, electron probe microanalysis, and atomic probe microanalysis.

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