A Method for Predicting Composition Distribution in Suspension Zone Melting of Multi-Component Alloys Based on Thermodynamic Calculations

Abstract

This invention discloses a method for predicting the composition distribution of multi-element alloys in a suspended zone melting process based on thermodynamic calculations. It utilizes thermodynamic phase diagram calculations and a numerical model for non-equilibrium solidification. Based on the real-time melt zone composition, the distribution patterns of each alloying element in the solid and liquid phases are determined. Furthermore, by moving the melt zone, a quantitative prediction of the composition distribution of multi-element alloy bars after suspended zone melting is achieved. This method solves the problem of large prediction errors in the solidification composition of multi-element alloy systems caused by existing models using approximate simplified constant distribution coefficients. The calculation method of this invention is simple, avoiding the time-consuming and costly experimental process of multiple suspended zone meltings, reducing experimental workload, accelerating process optimization, and lowering the cost of repeated experiments.

Description

Technical Field

[0001] This invention belongs to the field of metal material purification and preparation technology, specifically involving a method for predicting the composition distribution in the smelting of multi-element alloys in a suspension region based on thermodynamic calculations. Background Technology

[0002] The rapid development of oil and gas chemicals, new energy and new materials, precision instruments, and aerospace has placed higher demands on the purity and orientation characteristics of high-end metallic materials. Zone melting technology, due to its high product purity and controllable crystal growth orientation, has a wide range of applications in the preparation of high-purity metallic materials and materials with excellent orientation. Suspension zone melting technology, employing a crucible-free melting approach, completely avoids impurity contamination introduced by the crucible during melting. It can be used for the purification of ultra-high purity metallic materials and the preparation of materials with specific alloy compositions and crystal orientations. Suspension zone melting equipment adopts a vertical structure, using electromagnetic induction coils to locally heat vertically loaded rod-shaped materials. After the heated zone melts, a controllable molten zone is formed locally on the rod due to surface tension and electromagnetic levitation. Simultaneously, the molten zone is moved by controlling the rod to slowly pass through the induction coil. Utilizing the principle of different solubilities of alloy components in the solid and liquid phases, the directional redistribution and purification of the rod's components are achieved by adjusting process parameters such as the size of the molten zone and the moving speed.

[0003] Numerous factors influence the alloy composition distribution of bars produced by zone melting, including the distribution coefficients of alloying elements, the length of the melting zone, the bar's moving speed, and the stability of the solid-liquid interface. Studying these factors solely through experimental methods is time-consuming and costly; therefore, numerical models are needed to predict the composition distribution of bars after zone melting. Current models typically use equilibrium phase diagrams of the alloy system to calculate the distribution coefficients of alloying elements, approximating them as constants. However, for multi-component alloy systems, due to the interactions between components, the distribution coefficients vary significantly with the melting zone composition, and simplified constant distribution coefficients cannot accurately predict the composition distribution of the solidified portion. Therefore, this invention combines thermodynamic calculations to obtain the corresponding distribution coefficients of each element based on the melting zone composition at different stages, establishing a numerical model to predict the composition distribution of bars after zone melting, thereby further optimizing the zone melting process. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the composition distribution of molten materials in the suspension region of multi-element alloys based on thermodynamic calculations, which solves the problem that existing models use approximate simplified constant allocation coefficients when calculating the composition distribution of molten materials in the suspension region of multi-element alloys, resulting in inaccurate prediction results.

[0005] The technical solution adopted in this invention is: a method for predicting the composition distribution in the smelting of multi-element alloys in a suspended region based on thermodynamic calculations, comprising the following steps:

[0006] Step 1: Establish a numerical model, determine the process parameters for smelting in the suspension zone, input the initial composition and dimensional parameters of the bar, and set the calculation step size;

[0007] Step 2: Set the composition of the melting zone. Based on thermodynamic calculations, call the thermodynamic database of the corresponding multi-element alloy system to calculate the alloy composition of the corresponding solidified part.

[0008] Step 3: Based on the principle of conservation of material in the molten zone and the solidification composition, calculate the change in composition of the molten zone after solidification;

[0009] Step 4: Update the composition of the molten zone and move the molten zone. Repeat steps 2 to 4 until the molten zone moves to the end of the bar and output the composition distribution of the molten bar after smelting.

[0010] The invention is further characterized in that,

[0011] The numerical model in step 1 was written in FORTRAN. The zone melting process parameters include the melting zone length z0, the melting zone movement speed v, and the vacuum degree P of the melting system. The input parameters include the initial concentration of alloying elements c0 and the length L of the melting bar. The starting position is set to z0. start =0, the calculation step size is dz, dz / L≤0.02.

[0012] In step 2, the initial melting zone composition is set according to the initial composition input in step 1. The thermodynamic calculation is performed using the TQ interface in Thermo-Calc software. Different thermodynamic databases are called according to the alloy system being calculated. The TCFE database is used for steel materials, the TCNI database is used for nickel-based alloys, the TCHEA database is used for high-entropy alloys, and the corresponding TC thermodynamic database is used for other alloy systems or the required thermodynamic database is constructed by yourself.

[0013] In step 3, the change in the composition of the molten zone is calculated using the following formula:

[0014] c L,z •z0 c S,z •dz+c0•dz=c L,z+dz •z0

[0015] Among them, c L,z The composition of the melting zone is given by z; z is the distance from the calculation position to the starting position. start The length of c is given by 0 ≤ z ≤ L - z0. S,z To calculate the composition after solidification at a specific location, c L,z+dz This is the composition of the melt zone in the next calculation step after the update.

[0016] In step 4, the criterion for determining whether the molten zone has reached the end of the bar is whether the sum of z and z0 reaches L. When the position of the molten zone satisfies z + z0 = L, the smelting enters the final solidification stage and the molten zone stops moving.

[0017] The bar composition distribution output in step 4 is a prediction of the composition distribution of the zone melting section.

[0018] If step 4 requires outputting the predicted composition distribution of the final solidification stage, the following steps are also included:

[0019] Step 5: Stop the movement of the molten zone, call the thermodynamic database, and calculate the composition of the solidified portion;

[0020] Step 6: Reduce the length of the molten zone, calculate and update the composition of the molten zone, and repeat steps 5-6 until the molten zone is completely solidified. Output the composition distribution of the bar after smelting in the region.

[0021] In step 6, after the molten zone stops moving as a whole, it is gradually reduced according to the calculated step size dz. The composition of the molten zone for the next step is calculated and updated according to the following formula until the molten zone is completely solidified when z=L:

[0022] c L,z •(Lz) c S,z •dz=c L,z+dz •(Lz-dz)

[0023] Among them, L-z0 <z≤L。

[0024] The beneficial effects of this invention are as follows: The method for predicting the composition distribution of multi-element alloys in a suspended zone based on thermodynamic calculations is constructed based on thermodynamic phase diagram calculations and a numerical model of non-equilibrium solidification. It determines the distribution law of each alloying element in the solid and liquid phases according to the real-time melt zone composition. Based on this, it achieves quantitative prediction of the composition distribution of multi-element alloy bars after suspended zone melting by moving the melt zone. This solves the problem of large prediction deviations in the solidification composition of multi-element alloy systems caused by existing models using approximate simplified constant distribution coefficients. The calculation method of this invention is simple, avoiding the time-consuming and costly experimental process of multiple suspended zone meltings, reducing experimental workload, accelerating the process optimization process, and lowering the cost of repeated experiments. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of the method for predicting the composition distribution in the smelting of multi-element alloys in a suspended region based on thermodynamic calculations, as described in this invention.

[0026] Figure 2 This is a schematic diagram of the principle of material conservation in the molten zone in the thermodynamic calculation-based method for predicting the composition distribution of multi-element alloy smelting in the suspension region of the present invention.

[0027] Figure 3 This is the prediction result of the bar composition distribution in Example 2 of the thermodynamic calculation-based method for predicting the composition distribution of multi-element alloy suspension zone melting, and the corresponding comparison diagram.

[0028] Figure 4 This is the prediction result of the bar composition distribution in Example 3 of the present invention, which is a prediction method for the composition distribution of multi-element alloy suspension zone melting based on thermodynamic calculations. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0030] Example 1

[0031] This invention provides a method for predicting the composition distribution during melting in the suspension region of multi-element alloys based on thermodynamic calculations, such as... Figure 1 As shown, the steps are as follows:

[0032] Step 1: Use FORTRAN to write a numerical model to determine the process parameters of the suspended zone melting, including the melting zone length z0, the melting zone movement speed v, and the vacuum degree P of the melting system. Input the initial composition and size parameters of the bar, including the initial concentration of alloying elements c0 and the length L of the melting bar. Set the starting position to z. start =0, the calculation step size is dz. To achieve high simulation accuracy, the step size dz should satisfy dz / L≤0.02.

[0033] Step 2: Set the initial melting zone composition based on the initial composition entered in Step 1. Based on thermodynamic calculations, use the TQ interface in Thermo-Calc software to call the corresponding thermodynamic database of the multi-element alloy system according to the calculated alloy system, and calculate the alloy composition of the corresponding solidified part. Among them, steel materials use the TCFE database, nickel-based alloys use the TCNI database, high-entropy alloys use the TCHEA database, and other alloy systems can use the corresponding TC thermodynamic database or construct the required thermodynamic database themselves.

[0034] Step 3: Combining the solidification composition with the principle of conservation of mass in the molten zone, calculate the change in composition of the molten zone after solidification. Since the length of the molten zone remains constant during zone melting, the law of conservation of mass should satisfy the following expression based on the calculated location:

[0035] c L,z •z0 c S,z •dz+c0•dz=c L,z+dz •z0(0≤z≤L-z0)

[0036] Where c L,z Here, z represents the composition of the melting zone, and z is the distance from the calculation position to the starting position. start The length, c S,z To calculate the composition after solidification at a specific location, c L,z+dz This is the composition of the melt zone in the next calculation step after the update.

[0037] Step 4: Update the composition of the molten zone and move the molten zone. Repeat Steps 2 - 4 until the molten zone moves to the end of the bar. The basis for determining whether the molten zone reaches the end of the bar is to calculate whether the sum of the length z from the starting position and the length z0 of the molten zone reaches the length L of the smelted bar. When the position satisfies z + z0 = L, the smelting enters the final solidification stage and the movement of the molten zone stops. start The length z of and the length z0 of the molten zone. When the position satisfies z + z0 = L, the smelting enters the final solidification stage and the movement of the molten zone stops.

[0038] Step 5: Stop the movement of the molten zone, call the thermodynamic database, and calculate the composition of the solidified part.

[0039] Step 6: After the entire molten zone stops moving, gradually reduce the length of the molten zone in calculation steps of dz. Calculate the composition of the next step of the molten zone after update according to the following formula. Repeat Steps 5 - 6 until the molten zone is completely solidified when z = L:

[0040] c L,z •(L - z) c S,z •dz = c L,z+dz •(L - z - dz) (L - z0 < z ≤ L)

[0041] Step 7: Output the composition distribution of the bar after zone melting. The output bar composition distribution can be divided into the zone melting section (0 ≤ z ≤ L - z0) and the final solidification section (L - z0 < z ≤ L). If only the composition distribution prediction of the zone melting section is required, Steps 5 and 6 above can be skipped, that is, when the position satisfies z + z0 = L, directly end the calculation and output the composition distribution result of the zone melting section.

[0042] Through the above method, the method for predicting the composition distribution of a multi - component alloy suspension zone melting based on thermodynamic calculation according to the present invention is based on the construction of a numerical model of thermodynamic phase diagram calculation and non - equilibrium solidification. The distribution law of each alloy element in the solid - liquid two - phase is determined according to the real - time composition of the molten zone. On this basis, the quantitative prediction of the composition distribution of the multi - component alloy bar after suspension zone melting is realized by moving the molten zone, solving the problem of large deviation in predicting the solidification composition of the multi - component alloy system caused by using an approximately simplified constant distribution coefficient in the existing model. The calculation method of the present invention is simple, avoiding the time - consuming and costly test process of multiple suspension zone meltings, reducing the test workload, accelerating the process optimization process, and reducing the cost of repeated tests.

[0043] Example 2

[0044] Step 1: Write a numerical model using FORTRAN language. The calculation program in the model is in accordance with the appendix Figure 1The process flow diagram is shown below. For the ternary boron-containing carbon steel Fe-BC system (0.231 wt.% C, 0.0029 wt.% B), the bar length is 11 cm, the melting zone length is 2 cm, the melting zone moving speed is 2 cm / h, the vacuum degree of the melting system is 1×10-4 Torr, and the calculation step size is set to 0.02 cm.

[0045] Step 2: For Fe-BC system iron-based alloy materials, use the TQ interface in Thermo-Calc thermodynamic calculation software, call the TCFE12 iron-based alloy thermodynamic database, input the initial alloy composition in Step 1 as the liquid phase composition of the molten zone, and calculate the alloy composition of the solidified part.

[0046] Step 3: Combining the solidified portion composition obtained in Step 2, calculate the melt zone composition for the next solidification step using the following formula. A schematic diagram illustrating the mass conservation principle is attached. Figure 2 :

[0047] c L,z •z0 c S,z •dz+c0•dz=c L,z+dz •z0(0≤z≤L-z0)

[0048] Step 4: Update the melt zone composition and move the melt zone to obtain the updated melt zone composition c. L,z+dz Repeat steps 2 to 4 until the molten zone moves to the end of the bar.

[0049] Step 5: When the melting zone moves to the end of the bar, i.e., z=9cm, the melting zone stops moving, and the composition calculation of the zone melting section is completed.

[0050] Step 6: Reduce the length of the molten zone in increments of 0.02 cm, and calculate the composition of the reduced molten zone using the following formula:

[0051] c L,z •(Lz) c S,z •dz=c L,z+dz •(Lz-dz)(L-z0 <z≤L)

[0052] Repeat steps 5-6 until the molten zone is completely solidified, i.e., z=11cm.

[0053] Step 7: Output the composition distribution of the bar stock after regional melting, as shown in the attached figure. Figure 3 As shown.

[0054] Comparing the data obtained by this calculation method with the component distribution calculated using the approximate simplified constant distribution coefficient and the experimental test results, it can be seen that the component distribution obtained by the prediction method combining thermodynamic calculation proposed in this invention has a high degree of agreement with the experimental results, and the prediction results are more accurate than the existing approximate simplified methods.

[0055] Example 3

[0056] The implementation method of this embodiment is basically the same as that of embodiment 2, except that:

[0057] The material system selected in step 1 is a nickel-based alloy, and its initial chemical composition of the bar is shown in Table 1 below:

[0058] Table 1 Initial Chemical Composition of Bars

[0059]

[0060] The bar length is 4cm, the melting zone length is 1cm, and the calculation step is set to 0.01cm.

[0061] In step 2, the TCNI11 nickel-based alloy thermodynamic database is used for nickel-based alloy materials.

[0062] This embodiment only performs composition prediction calculations for the zone melting section. When the melting zone moves to the end of the bar, i.e., z=3cm, steps 5 and 6 are skipped, the calculation ends, and the composition distribution of the bar in the zone melting section is output. The prediction results are shown in the attached figure. Figure 4 As shown, the prediction method proposed in this invention can be used in multi-element alloy systems with complex alloy compositions. Its application scenarios are not limited by the type of alloy, and there is no need to approximate and simplify the distribution coefficients of each element one by one, making the calculation process more convenient.

Claims

1. A method for predicting the composition distribution in the smelting region of a multi-element alloy based on thermodynamic calculations, characterized in that, Includes the following steps: Step 1: Establish a numerical model written in FORTRAN, determine the process parameters for smelting in the suspended zone, including the molten zone length z0, the molten zone movement speed v, and the vacuum degree P of the smelting system. Determine the initial composition and size parameters of the input bar, including the initial concentration c0 of alloying elements and the length L of the molten bar. Set the starting position as z. start =0, the calculation step size is dz, dz / L≤0.02; Step 2: Set the composition of the melting zone. Based on thermodynamic calculations, call the thermodynamic database of the corresponding multi-element alloy system to calculate the alloy composition of the corresponding solidified part. Step 3: Combining the solidification composition with the principle of conservation of mass in the molten zone, calculate the change in composition of the molten zone after solidification using the following formula: c L,z •z0 c S,z •dz+c0•dz=c L,z+dz •z0 Among them, c L,z The composition of the melting zone is given by z; z is the distance from the calculation position to the starting position. start The length of c is given by 0 ≤ z ≤ L - z0. S,z To calculate the composition after solidification at a given location, c L,z+dz To update the melt composition for the next calculation step; Step 4: Update the composition of the molten zone and move the molten zone. Repeat steps 2 to 4 until the molten zone moves to the end of the bar and output the composition distribution of the molten bar after smelting.

2. The method for predicting the composition distribution in the smelting of multi-element alloys in a suspended region based on thermodynamic calculations as described in claim 1, characterized in that, In step 2, the initial melting zone composition is set according to the initial composition input in step 1. The thermodynamic calculation is performed using the TQ interface in Thermo-Calc software. Different thermodynamic databases are called according to the alloy system being calculated. The TCFE database is used for steel materials, the TCNI database is used for nickel-based alloys, the TCHEA database is used for high-entropy alloys, and the corresponding TC thermodynamic database is used for other alloy systems or the required thermodynamic database is constructed by the user.

3. The method for predicting the composition distribution in the smelting of multi-element alloys in a suspended region based on thermodynamic calculations as described in claim 1, characterized in that, In step 4, the criterion for determining whether the melting zone has reached the end of the bar is whether the sum of z and z0 reaches L. When the position of the melting zone satisfies z + z0 = L, the smelting enters the final solidification stage and the melting zone stops moving.

4. The method for predicting the composition distribution in the smelting of multi-element alloys in a levitation region based on thermodynamic calculations as described in claim 1, characterized in that, The bar composition distribution output in step 4 is a prediction of the composition distribution of the zone melting section.

5. The method for predicting the composition distribution in the smelting of multi-element alloys in a suspended region based on thermodynamic calculations as described in claim 1, characterized in that, If step 4 requires outputting the predicted composition distribution of the final solidification stage, then the following steps are also included: Step 5: Stop the movement of the molten zone, call the thermodynamic database, and calculate the composition of the solidified portion; Step 6: Reduce the length of the molten zone, calculate and update the composition of the molten zone, and repeat steps 5-6 until the molten zone is completely solidified. Output the composition distribution of the bar after smelting in the region.

6. The method for predicting the composition distribution in the smelting of multi-element alloys in a levitation region based on thermodynamic calculations as described in claim 5, characterized in that, In step 6, after the molten zone stops moving as a whole, the molten zone is gradually reduced according to the calculated step size dz. The composition of the molten zone for the next step is calculated and updated according to the following formula until the molten zone is completely solidified when z=L: c L,z •(L-z) c S,z •dz=c L,z+dz •(L-z-dz) Among them, L-z0 <z≤L。

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