Solid-liquid diffusion couple and method for simultaneously determining solid-liquid diffusion coefficient of alloy system

Abstract

The invention belongs to the technical field of liquid metal diffusion and advanced measurement, and particularly relates to a solid-liquid diffusion couple and a method for simultaneously measuring solid-liquid diffusion coefficients of an alloy system. The capillary tube is used for inhibiting melt convection, the balancing weight is used for ensuring solid-liquid interface attachment, and the gradient descent optimization algorithm is combined, so that the diffusion coefficients of the intermediate phase and the liquid phase of the alloy are synchronously measured in a single experiment. The device is simple in structure and suitable for high-melting-point metal, the relative calculation error is smaller than or equal to 5%, experiment efficiency and data consistency are remarkably improved, and the device can be widely applied to material processing and interface diffusion research.

Description

Technical Field

[0001] The invention belongs to the field of liquid metal diffusion and advanced measurement technology, and specifically relates to a solid-liquid diffusion couple and a method for simultaneously measuring the solid-liquid diffusion coefficient of an alloy system. Background Art

[0002] The information disclosed in this background technology section is only intended to enhance the understanding of the overall background of the invention, and should not necessarily be regarded as an admission or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art.

[0003] Diffusion is the main way for materials to transfer mass at the atomic scale. Recrystallization, grain growth, phase change, segregation, corrosion and other processes all involve the directional diffusion of atoms, which affects the composition distribution and microstructure of the material. Solid-liquid diffusion occurs at the interface between the solid and liquid phases. During the solid-liquid diffusion process between different metals, an obvious solid solution zone will appear at the interface or an intermetallic compound will be formed. The diffusion near the solid-liquid interface controls the microstructure and physical and chemical properties of the interface product. Liquid-solid diffusion between metals exists in many metal material processing processes, such as welding, hot-dip plating, and powder metallurgy. Different metals react at the liquid-solid interface to produce an IMC (intermetallic compound) layer. During the composite process of metal materials, atoms overcome energy barriers to diffuse, and the intermetallic compounds formed at the interface will affect the mechanical strength and physical and chemical properties of the material. The electrochemical properties of intermetallic compounds are different from those of the matrix. Generally, the open circuit potential of the intermediate phase is different from that of the matrix, which will cause local corrosion at the interface. Sravanth et al. obtained intermetallic compounds of different thicknesses in welding and found that the thicker the IMC layer, the more serious the corrosion. Understanding the growth characteristics of intermetallic compounds helps to regulate their growth process and improve the performance of the solid-liquid interface.

[0004] Commonly used test methods for determining the mutual diffusion coefficient of liquid alloy systems include the long capillary method, the capillary-molten pool method, the rotary cutting unit method, etc. Convection will affect the accuracy of the test. Keita studied the effect of convection caused by density difference on the measured diffusion coefficient and found that the measured diffusion coefficient will be significantly larger when convection exists in the diffusion couple. Therefore, the commonly used methods for determining the liquid diffusion coefficient will use capillaries to suppress melt convection.

[0005] At present, the commonly used solid-liquid diffusion couples are crucible diffusion couples and hot-dip diffusion couples. The research on solid-liquid diffusion mainly focuses on the solid-liquid interface, ignoring the influence of convection in the liquid phase on the diffusion process, which is not conducive to the quantitative determination of the diffusion coefficient in the solid-liquid diffusion couple. At the same time, the traditional diffusion coefficient determination test can only determine the diffusion coefficient in a single phase, which is inefficient and cannot guarantee data consistency.

[0006] Zhong Yunbo and others invented a diffusion couple device that can be used for solid-liquid diffusion. It also uses capillaries to suppress liquid phase convection. It has a simple structure and the two materials fit tightly under pressure. However, it also has some shortcomings when used for solid-liquid diffusion, such as some high-melting-point metals are not easy to process into filaments, and the liquid phase may flow into the gap between the solid phase and the capillary during the diffusion process. Therefore, those skilled in the art are in urgent need of a device and method with a simple structure that supports solid-liquid diffusion research of high-melting-point metals and can simultaneously measure multiphase diffusion coefficients in a single experiment to improve efficiency and reduce experimental errors. Summary of the invention

[0007] In view of the above-mentioned existing problems, the purpose of the present invention is to provide a solid-liquid diffusion couple and a method for simultaneously determining the solid-liquid diffusion coefficient of an alloy system. Based on the problem of large experimental workload for determining the diffusion coefficient, the present invention provides a solid-liquid diffusion couple and a test method that can simultaneously determine the diffusion coefficients of each intermediate phase and liquid phase in an alloy system, suppresses melt convection through a capillary, and ensures that the solid-liquid interface fits tightly with the combination of a counterweight block and a sleeve, and combines cellular automaton simulation and optimization algorithms to achieve a single experiment to simultaneously determine the diffusion coefficients of each intermediate phase and liquid phase in an alloy system, that is, to obtain multiple diffusion coefficients simultaneously in one experiment, thereby reducing the workload of the experiment and ensuring the consistency of the measurement results.

[0008] Specifically, the present invention provides the following technical solutions: The first aspect of the present invention provides a solid-liquid diffusion couple, which includes a crucible, a counterweight, a capillary, a sleeve, a metal wire and a metal block; the counterweight, capillary, sleeve, metal wire and metal block are all placed inside the crucible, and from the central axis of the crucible to the top, they are the counterweight, capillary, sleeve, metal wire and metal block respectively, wherein the sleeve is provided with a through hole to fix the position of the capillary; the capillary is provided with a blind hole to accommodate the metal wire; the counterweight applies vertical pressure to make the metal wire fit tightly against the metal block.

[0009] Preferably, the inner diameter of the crucible is 10~30 mm, and the height is 60~100 mm; the height of the counterweight block is 20~50 mm, and the diameter is 10~30 mm; the height of the sleeve is 20~40 mm, and the diameter is 10~30 mm; the length of the metal wire is 20~40 mm, and the diameter is 0.8~1.5 mm; the height of the metal block is 2~10 mm, and the diameter is 10~30 mm.

[0010] Preferably, the metal wire is Al, Zn or Sn, and the metal block is Cu, Fe or Ni.

[0011] Preferably, the melting point of the counterweight block is higher than the annealing temperature required for the experiment, so as to provide a constant contact pressure.

[0012] Preferably, the capillary is made of graphite, the inner diameter of which matches the diameter of the metal wire, and the depth of the blind hole is not less than 90% of the length of the metal wire.

[0013] Preferably, the crucible in the solid-liquid diffusion couple is annealed and a diffusion coefficient measurement experiment is performed.

[0014] A second aspect of the present invention provides a method for simultaneously measuring the solid-liquid diffusion coefficient of an alloy system using the above-mentioned solid-liquid diffusion couple, comprising the following steps: S1. First, place the metal wire into the capillary, then place the capillary into the sleeve, and then place the metal block, sleeve and counterweight block into the crucible in sequence to obtain a solid-liquid diffusion couple; S2. Under a protective atmosphere, the solid-liquid diffusion couple is annealed, and then the composition curve in the metal wire and the actual value of the thickness of each intermediate phase at the diffusion interface are measured; S3, setting an estimated value of the diffusion coefficient in each phase; using a cellular automaton to simulate the composition curve after a certain diffusion time and the estimated value of the thickness of each intermediate phase according to the physical model and mathematical model of the solid-liquid diffusion couple; S4, calculating the error between the estimated value and the measured value of the composition curve and the thickness of each intermediate phase; S5. If the error does not meet the accuracy requirement, use the modified diffusion coefficient estimate and repeat steps S3 and S4 until the error meets the accuracy requirement or reaches a given number of iterations.

[0015] Preferably, in step S2, the annealing treatment is specifically to first heat up to a set temperature of 665-900°C, keep the temperature for 1-5 hours and then cool rapidly.

[0016] Preferably, in step S3, the establishment of the physical model is based on the symmetry of the solid-liquid diffusion couple structure, a one-dimensional model is established in the axial direction of the diffusion couple, the spherical crown diffusion region is regarded as a one-dimensional diffusion with a change in cross-sectional area, and the cross-sectional area at the phase interface and the volume V enclosed by the phase interface and the initial solid-liquid interface are fitted to obtain the cross-sectional area at the phase interface and the volume enclosed by the phase interface and the initial solid-liquid interface during the diffusion process, and only the diffusion perpendicular to the interface is considered; Preferably, in step S3, the following assumptions are made in the mathematical model: 1) assuming that the interface mobility is large enough and the phase interface movement is controlled by diffusion; 2) assuming that the diffusion coefficient of each phase is a constant; The solute diffusion equation in the mathematical model is: (a) (b) (c) In the formula, i represents the i-th phase from the liquid phase to the solid phase, Ci is the solute concentration in the i-th phase, C i，min and C i，max are the minimum and maximum concentrations in the ith phase, D i is the diffusion coefficient of the ith phase, f i is the proportion of the i-th phase in the unit, 0< f i <1 is the interface unit; Initial conditions: At t = 0, C = C in the solid phase 1 , in the liquid phase C = C 0 ; The above equations are solved by finite difference. Equation (a) is used to calculate the diffusion flux in each phase and the diffusion flux at the interface respectively. Equation (b) calculates the evolution of the solute field over time based on the diffusion flux. Equation (c) is used to determine which phase or phase interface each unit belongs to and reflect the movement of the interface.

[0017] Preferably, in step S4, the error between the estimated value and the measured value is calculated according to formula (d): (d) In the formula, and They represent the estimated and measured values ​​of the solute concentration at the jth sampling point respectively.

[0018] Preferably, in step S5, the optimization algorithm includes a gradient descent method, and its optimization goal is to minimize the error function Er , the number of iterations is not less than 100 times.

[0019] Preferably, in step S5, the accuracy requirement is a relative error of ≤5%.

[0020] One or more embodiments of the present invention have at least the following beneficial effects: (1) The present invention suppresses melt convection through capillaries, and combines the counterweight block and sleeve structure to ensure close fit of the solid-liquid interface and avoid liquid seepage; the metal wire is in direct contact with the metal block, which simplifies the complexity of the device and reduces the difficulty of processing.

[0021] (2) The present invention can simultaneously obtain the intermediate phase (such as Cu) through the solid-liquid diffusion couple device 3 Al, Cu 9 Al 4 ) and liquid phase diffusion coefficient, the efficiency is improved by more than 50%.

[0022] (3) The present invention uses cellular automaton simulation and optimization algorithm iteration, combined with physical model dynamic error correction, to calculate the relative error between the thickness and the experimental value to be ≤5%.

[0023] (4) The present invention can simultaneously determine the solid / liquid diffusion coefficients through a single experiment, avoiding the cumbersome process of multiple experiments required by traditional methods, improving data consistency, and supporting the solid-liquid diffusion research of high-melting-point metals (such as the Cu-Al system). BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0025] Figure 1 This is a schematic diagram of the structure of the solid-liquid diffusion couple device of the present invention; Figure 2 It is a schematic diagram of the solid-liquid interface diffusion between the metal wire and the metal block of the present invention; Figure 3 The scanning electron microscope result at the diffusion couple solid-liquid interface of Example 1 of the present invention; Figure 4 The simulation results and experimental results of the solid-liquid diffusion couple device of Example 1 of the present invention after iteratively optimizing the diffusion coefficient by the gradient descent method; Figure 5 The scanning electron microscope result at the diffusion couple solid-liquid interface of Example 2 of the present invention; Figure 6 The simulation results and experimental results of the solid-liquid diffusion couple device of Example 2 of the present invention after iteratively optimizing the diffusion coefficient by the gradient descent method; In the figure, 1: crucible; 2: counterweight; 3: capillary; 4: sleeve; 5: metal wire; 6: metal block. DETAILED DESCRIPTION

[0026] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0027] The present invention will be further described in detail below in conjunction with specific embodiments. It should be noted that the specific embodiments are intended to explain the present invention rather than to limit it.

[0028] Example 1 : like Figure 1 As shown, this embodiment provides a solid-liquid diffusion couple device, including a crucible 1, a counterweight block 2, a capillary 3, a sleeve 4, a metal wire 5 and a metal block 6.

[0029] The sleeve 4 has a through hole for accommodating the capillary 3 ; the blind hole in the capillary 3 is used to accommodate the metal wire 5 ; the upper end surface of the metal block 6 contacts and fits tightly with the capillary 3 ; the counterweight 2 is placed on the top of the capillary 3 .

[0030] In this embodiment, the steps of assembling the diffusion couple are as follows: firstly, the metal wire is placed in the capillary, then the capillary is placed in the sleeve, and then the metal block, the sleeve and the counterweight are placed in the crucible in sequence to obtain a solid-liquid diffusion couple device.

[0031] In this embodiment, the metal wire 5 is set to Al; the metal block 6 is set to Cu; Heating temperature: 700℃; diffusion time (heat preservation): 5 h. The specific steps are as follows: (1) Place an Al wire with a diameter of 1 mm and a length of 30 mm into a graphite capillary with an inner diameter of 1 mm, and grind the end face of the Al wire with 2000 grit sandpaper; grind and polish the upper surface of a Φ30 mm × 5 mm cylindrical Cu block, and assemble the diffusion couple according to the operating steps.

[0032] (2) The diffusion couple was annealed in a protective atmosphere, kept at 700 °C for 5 h, and then rapidly cooled. The composition curve of the metal wire and the actual measured values ​​of the thickness of each intermediate phase at the diffusion interface were then determined.

[0033] (3) Setting the estimated value of the diffusion coefficient in each phase; using cellular automata to simulate the composition curve after a certain diffusion time and the estimated value of the thickness of each intermediate phase based on the physical model and mathematical model of the solid-liquid diffusion couple; In this embodiment, the physical model is established based on the symmetry of the solid-liquid diffusion couple structure. To simplify the calculation, a one-dimensional model is established in the axial direction of the diffusion couple. The length of the upper wire is 30 mm and the cross-sectional area is 0.785 mm. 2 The spherical crown diffusion area below is regarded as a one-dimensional diffusion with a change in cross-sectional area. According to the experimental results, the distance x between each phase interface and the initial solid-liquid interface, the cross-sectional area A (mm 2 ) and the volume V (mm) enclosed by the phase interface and the initial solid-liquid interface 3 )The cross-sectional area A(x) at the phase interface and the volume V(x) enclosed by the phase interface and the initial solid-liquid interface during the diffusion process are fitted, and only the diffusion perpendicular to the interface is considered; Where A(x) = 0.785 + 8.523 * x 2 (1); V(x) = 0.438 * x + 3.323 * x 3 (2).

[0034] like Figure 2As shown, in the physical model, the phase interface that migrates toward the solid phase in a spherical crown shape is regarded as an interface perpendicular to the axial direction, and it is ensured that S(x) and V(x) at the interface in the equivalent model are consistent with the actual values.

[0035] In this embodiment, the following assumptions are made in the mathematical model: 1. Assume that the interface mobility is large enough and the phase interface movement is controlled by diffusion; 2. Assume that the diffusion coefficient of each phase is a constant; Based on the above assumptions, the solute diffusion equation in the diffusion couple is: (3) (4) (5) In the formula, i represents the i-th phase from the liquid phase to the solid phase, C i is the solute concentration in the i-th phase, C i，min and C i，max are the minimum and maximum concentrations in the ith phase, D i is the diffusion coefficient of the ith phase, f i is the proportion of the i-th phase in the unit, 0< f i <1 is the interface unit; Initial conditions: At t = 0, C = C in the solid phase 1 , in the liquid phase C = C 0 ; The above equations are solved by finite difference. Equation (3) is used to calculate the diffusion flux in each phase and the diffusion flux at the interface respectively. Equation (4) calculates the evolution of the solute field with time based on the diffusion flux. Equation (5) is used to determine which phase or phase interface each unit belongs to and reflect the movement of the interface.

[0036] (4) Calculate the error between the estimated value and the measured value of the composition curve and the thickness of each intermediate phase; In this embodiment, the error between the estimated value and the measured value is calculated according to formula (6): (6) In the formula, and They represent the estimated and measured values ​​of the solute concentration at the jth sampling point respectively.

[0037] (5) If the error does not meet the accuracy requirement, the estimated diffusion coefficient is corrected using the gradient descent method, and steps S3 and S4 are repeated until the error meets the accuracy requirement or the given number of iterations is reached; like Figure 3As shown in the figure, the SEM results at the diffusion solid-liquid interface show that the phase interface after diffusion is spherical crown-shaped. The phases in the figure are Cu, Cu 3 Al, Cu 9 Al 4 , CuAl and liquid phase.

[0038] The diffusion coefficients obtained after 100 iterations of the gradient descent method are shown in Table 1: Table 1

[0039] like Figure 4 As shown in Figure 1, the iterative optimization based on the diffusion coefficient is constrained by the thickness of each phase and the liquid phase composition curve. Finally, the error of the thickness of each phase and the error of the composition curve are balanced. As shown in the data in Table 1, the relative error between the thickness of each intermediate phase and the actual value in the simulation results after iterative optimization is within 2%.

[0040] Embodiment 2: like Figure 1 As shown, this embodiment provides a solid-liquid diffusion couple device, including a crucible 1, a counterweight block 2, a capillary 3, a sleeve 4, a metal wire 5 and a metal block 6.

[0041] The sleeve 4 has a through hole for accommodating the capillary 3 ; the blind hole in the capillary 3 is used to accommodate the metal wire 5 ; the upper end surface of the metal block 6 contacts and fits tightly with the capillary 3 ; the counterweight 2 is placed on the top of the capillary 3 .

[0042] In this embodiment, the steps of assembling the diffusion couple are as follows: firstly, the metal wire is placed in the capillary, then the capillary is placed in the sleeve, and then the metal block, the sleeve and the counterweight are placed in the crucible in sequence to obtain a solid-liquid diffusion couple device.

[0043] In this embodiment, the metal wire 5 is set to Al; the metal block 6 is set to Ni; Heating temperature: 700℃; diffusion time (heat preservation): 5 h. The specific steps are as follows: (1) Place an Al wire with a diameter of 1 mm and a length of 30 mm into a graphite capillary with an inner diameter of 1 mm, and grind the end face of the Al wire with 2000 grit sandpaper; grind and polish the upper surface of a Φ30 mm × 5 mm cylindrical Cu block, and assemble the diffusion couple according to the operating steps.

[0044] (2) The diffusion couple is annealed in a protective atmosphere, kept at 700°C for 5 h, and then rapidly cooled. The composition curve in the metal wire and the actual measured values ​​of the thickness of each intermediate phase at the diffusion interface are then determined (composition curve determination).

[0045] (3) Setting the estimated value of the diffusion coefficient in each phase; using cellular automata to simulate the composition curve after a certain diffusion time and the estimated value of the thickness of each intermediate phase based on the physical model and mathematical model of the solid-liquid diffusion couple; In this embodiment, the physical model is established based on the symmetry of the solid-liquid diffusion couple structure. To simplify the calculation, a one-dimensional model is established in the axial direction of the diffusion couple. The length of the upper wire is 30 mm and the cross-sectional area is 0.785 mm. 2 The spherical crown diffusion area below is regarded as a one-dimensional diffusion with a change in cross-sectional area. According to the experimental results, the distance x between each phase interface and the initial solid-liquid interface, the cross-sectional area A (mm 2 ) and the volume V (mm) enclosed by the phase interface and the initial solid-liquid interface 3 )The cross-sectional area A(x) at the phase interface and the volume V(x) enclosed by the phase interface and the initial solid-liquid interface during the diffusion process are fitted, and only the diffusion perpendicular to the interface is considered; Where A(x) = 0.785 + 7.636 * x 2 (1); V(x) = 0.444 * x + 3.156 * x 3 (2).

[0046] In this embodiment, the following assumptions are made in the mathematical model: 1. Assume that the interface mobility is large enough and the phase interface movement is controlled by diffusion; 2. Assume that the diffusion coefficient of each phase is a constant. Based on the above assumptions, the solute diffusion equation in the diffusion couple is consistent with that in Embodiment 1.

[0047] (4) Calculate the error between the estimated value and the measured value of the composition curve and the thickness of each intermediate phase; In this embodiment, the error between the estimated value and the measured value is calculated according to formula (6): (6) In the formula, and They represent the estimated and measured values ​​of the solute concentration at the jth sampling point respectively.

[0048] (5) If the error does not meet the accuracy requirement, the estimated diffusion coefficient is corrected using the gradient descent method, and steps S3 and S4 are repeated until the error meets the accuracy requirement or the given number of iterations is reached; like Figure 5 As shown in the figure, the SEM results at the diffusion solid-liquid interface show that the phase interface after diffusion is spherical crown-shaped. The phases in the figure are Ni, Al, and Ni from top to bottom. 3 Ni 2 、Al 3 Ni and liquid phase.

[0049] The diffusion coefficients obtained after 100 iterations of the gradient descent method are shown in Table 2: Table 2

[0050] like Figure 6 As shown in Figure 2, the iterative optimization based on the diffusion coefficient is constrained by the thickness of each phase and the liquid phase composition curve. Finally, the error of the thickness of each phase and the error of the composition curve are balanced. As shown in the data in Table 2, the relative error between the thickness of each intermediate phase and the actual value in the simulation results after iterative optimization is within 5%.

[0051] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A solid-liquid diffusion couple, characterized in that: It includes a crucible, a counterweight, a capillary, a sleeve, a metal wire and a metal block; the counterweight, capillary, sleeve, metal wire and metal block are all placed inside the crucible, and from the central axis of the crucible to the bottom are the counterweight, capillary, sleeve, metal wire and metal block respectively, wherein the sleeve is provided with a through hole to fix the position of the capillary; the capillary is provided with a blind hole to accommodate the metal wire; the counterweight applies vertical pressure to make the metal wire fit tightly with the metal block.

2. The solid-liquid diffusion couple according to claim 1, characterized in that: The inner diameter of the crucible is 10~30 mm and the height is 60~100 mm; the height of the counterweight block is 20~50 mm and the diameter is 10~30 mm; the height of the sleeve is 20~40 mm and the diameter is 10~30 mm; the length of the metal wire is 20~40 mm and the diameter is 0.8~1.5 mm; the height of the metal block is 2~10 mm and the diameter is 10~30 mm.

3. The solid-liquid diffusion couple according to claim 1, characterized in that: The metal wire is Al, Zn or Sn, and the metal block is Cu, Fe or Ni; The melting point of the counterweight block is higher than the annealing temperature required for the experiment, and is used to provide a constant contact pressure; The capillary is made of graphite, the inner diameter of which matches the diameter of the metal wire, and the depth of the blind hole is not less than 90% of the length of the metal wire.

4. The solid-liquid diffusion couple according to claim 1, characterized in that: The crucible of the solid-liquid diffusion couple device was annealed and the diffusion coefficient measurement experiment was carried out.

5. The method for simultaneously measuring the solid-liquid diffusion coefficient of an alloy system by using a solid-liquid diffusion couple according to any one of claims 1 to 4, characterized in that: The steps include: S1. First, place the metal wire into the capillary, then place the capillary into the sleeve, and then place the metal block, sleeve and counterweight block into the crucible in sequence to obtain a solid-liquid diffusion couple; S2. Under a protective atmosphere, the solid-liquid diffusion couple is annealed, and then the composition curve in the metal wire and the actual value of the thickness of each intermediate phase at the diffusion interface are measured; S3, setting an estimated value of the diffusion coefficient in each phase; using a cellular automaton to simulate the composition curve after a certain diffusion time and the estimated value of the thickness of each intermediate phase according to the physical model and mathematical model of the solid-liquid diffusion couple; S4, calculating the error between the estimated value and the measured value of the composition curve and the thickness of each intermediate phase; S5. If the error does not meet the accuracy requirement, the diffusion coefficient estimate is corrected using an optimization algorithm, and steps S3 and S4 are repeated until the error meets the accuracy requirement or a given number of iterations is reached.

6. The method according to claim 5, characterized in that In step S2, the annealing treatment is specifically to first raise the temperature to a set temperature of 665-900°C, keep the temperature for 1-5 hours and then cool rapidly.

7. The method according to claim 6, characterized in that In step S3, the establishment of the physical model is based on the symmetry of the solid-liquid diffusion couple structure. A one-dimensional model is established in the axial direction of the diffusion couple. The spherical crown diffusion region is regarded as a one-dimensional diffusion with a change in cross-sectional area. The cross-sectional area at the phase interface and the volume V enclosed by the phase interface and the initial solid-liquid interface are fitted to obtain the cross-sectional area at the phase interface and the volume enclosed by the phase interface and the initial solid-liquid interface during the diffusion process, and only the diffusion perpendicular to the interface direction is considered.

8. The method according to claim 7, characterized in that In step S3, the following assumptions are made in the mathematical model: 1) the interface mobility is assumed to be large enough and the phase interface movement is controlled by diffusion; 2) the diffusion coefficient of each phase is assumed to be constant; The solute diffusion equation in the mathematical model is: （a） （b） （c） In the formula, i represents the i-th phase from the liquid phase to the solid phase, C i is the solute concentration in the i-th phase, C i，min and C i，max are the minimum and maximum concentrations in the ith phase, D i is the diffusion coefficient of the ith phase, f i is the proportion of the i-th phase in the unit, 0< f i <1 is the interface unit; Initial conditions: at t = 0, C = C1 in the solid phase and C = C0 in the liquid phase; The above equations are solved by finite difference. Equation (a) is used to calculate the diffusion flux in each phase and the diffusion flux at the interface respectively. Equation (b) calculates the evolution of the solute field over time based on the diffusion flux. Equation (c) is used to determine which phase or phase interface each unit belongs to and reflect the movement of the interface.

9. The method according to claim 7, characterized in that In step S4, the error between the estimated value and the measured value is calculated according to formula (d): （d） In the formula, and They represent the estimated and measured values ​​of the solute concentration at the jth sampling point respectively.

10. The method according to claim 7, characterized in that In step S5, the optimization algorithm includes a gradient descent method, and its optimization goal is to minimize the error function Er , the number of iterations is not less than 100; The accuracy requirement is a relative error of ≤5%.

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