Method of measuring equilibrium distribution coefficient of alloy with component that undergoes peritectic reaction during solidification

Abstract

To enable determination of an equilibrium distribution coefficient of an alloy with a component that undergoes a peritectic reaction during solidification.SOLUTION: A method of determining an equilibrium distribution coefficient is provided, comprising melting an alloy that undergoes a peritectic reaction during solidification, unidirectionally solidifying the alloy into the state with a solid phase region, liquid phase region, and a region being solidified, cooling the alloy to fix its structure, and deriving the equilibrium distribution coefficient corresponding to a solid phase ratio for each of a solidified structure before the peritectic reaction and a solidified structure after the peritectic reaction in the fixed structure.SELECTED DRAWING: Figure 12

Description

[Technical field]

[0001] The present invention relates to a method for measuring the equilibrium distribution coefficient of an alloy having a component system that exhibits a peritectic reaction during solidification, particularly for a steel material. [Background technology]

[0002] In the manufacturing of alloys such as large steel ingots, macrosegregation, which causes non-uniformity of components throughout the product, affects the material properties of the final product, so the accuracy of its prediction is important. Macrosegregation occurs when the local solute-enriched liquid phase caused by microsegregation moves due to thermal convection, so the accuracy of predicting microsegregation directly leads to improved accuracy of predicting macrosegregation. There are several parameters that affect microsegregation, but one of the most dominant parameters is the equilibrium distribution coefficient (or distribution coefficient) between the solid and liquid phases. The equilibrium distribution coefficient between the solid and liquid phases (hereinafter simply referred to as the equilibrium distribution coefficient) is defined as the solute concentration on the solid phase side at the interface (solid-liquid interface) when the solid and liquid phases are in equilibrium, divided by the solute concentration on the liquid phase side.

[0003] The equilibrium distribution coefficient differs for each element, and also depends on temperature and other component elements (solute concentration). Therefore, there are no reported values ​​that can be used universally for all alloys. In calculating microsegregation, it is necessary to obtain an appropriate equilibrium distribution coefficient for each alloy component. The simplest method for obtaining the equilibrium distribution coefficient is the solidification-water cooling experiment (for example, Non-Patent Document 1). After melting the alloy sample to be measured at high temperature, the temperature is lowered and held in a temperature range where the liquid phase and solid phase coexist. After holding, the measurement sample is quenched and the cross section of the sample is observed to identify the solid and liquid phase regions, and their average concentrations are measured using EDS (Energy Dispersive X-ray Spectroscopy) or EPMA (Electron Probe Micro Analyzer), and the equilibrium distribution coefficient is calculated from the ratio. However, it is known that the equilibrium distribution coefficient changes successively during solidification because it depends on temperature and components. In the above-mentioned solidification-water cooling experiment, only one condition of alloy components can be measured in one test, and when measuring continuous changes in the equilibrium distribution coefficient using this method, multiple experiments must be performed while adjusting the alloy components.

[0004] On the other hand, there is a method for continuously measuring the equilibrium distribution coefficient from the solute concentration distribution of the alloy sample after solidification. For example, there is a method in which a sample solidifying in one direction is quenched midway, the structure at each stage of solidification is extracted from multiple points on the cross section of the sample, and the equilibrium distribution coefficient at each stage of solidification is measured by fitting an analytical equation for microsegregation to each solute concentration distribution (Non-Patent Document 2). There is also a method in which the solute concentration distribution during solidification is measured and estimated from the solidified sample, and the balance of solute mass in the solid phase and liquid phase during solidification is calculated from the change in the distribution (Non-Patent Document 3). These methods have in common that they assume that solute elements distributed to the solid phase during solidification do not move after distribution, and they infer the distribution behavior during solidification from the solute concentration distribution of the solidified sample and calculate the equilibrium distribution coefficient. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] "Iron and Steel", vol. 103 (2017), published by the Iron and Steel Institute of Japan, p. 703 [Non-Patent Document 2] ISIJ Int., 61(2021), published by the Iron and Steel Institute of Japan, 1879 pages [Non-Patent Document 3] Met. Mater. Trans. A, 51A (2020), ASM International and The Minerals, Metals & Materials Society, 5771 pages Summary of the Invention [Problem to be solved by the invention]

[0006] Although the above method can be used to measure the change in equilibrium distribution coefficient during solidification, the above method cannot be applied to some alloy components, specifically, component systems that include peritectic reactions. Peritectic reaction is one of the solidification reactions in which the type of solidified solid phase changes during solidification. For example, the solid phase at the beginning of solidification is ferrite, but below a certain temperature during solidification, the solid phase that crystallizes during solidification changes to austenite, and further, the ferrite phase that has already solidified transforms into austenite. The latter phenomenon is problematic in the measurement of continuous equilibrium distribution coefficients, because there is a difference in solubility between ferrite and austenite depending on the element (equilibrium distribution coefficient between ferrite and austenite). For example, in the case of Mo, since its solid solubility limit in austenite is low, it is known that when the ferrite phase transforms into austenite by the peritectic reaction, the Mo element moves to the ferrite phase that has not yet transformed at the interface between the ferrite and austenite phases (solute redistribution). In other words, in alloy components in which the peritectic reaction occurs, the solute concentration distribution in the solid phase changes after the peritectic reaction, so there is a problem that it cannot be measured by existing methods that require the assumption that the solute distributed to the solid phase during solidification does not move thereafter.

[0007] The present disclosure has been made in light of the above circumstances, and aims to provide a method for continuously measuring equilibrium distribution coefficients even when the solid phase solute concentration distribution changes during solidification due to a peritectic reaction. [Means for solving the problem]

[0008] In the present disclosure, an alloy that undergoes a peritectic reaction during the solidification process is melted, a temperature gradient is generated to cause unidirectional solidification in the upward direction, and the alloy is cooled before the entire alloy has completely solidified to fix the structure, and the change in equilibrium distribution coefficient before the peritectic reaction and the equilibrium distribution coefficient after the peritectic reaction are obtained from the structure before and after the peritectic reaction. Effect of the Invention

[0009] In the present disclosure, for an alloy that undergoes a peritectic reaction during solidification, the change in equilibrium distribution coefficient before and after the peritectic reaction can be continuously measured. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram showing a structural change accompanying a peritectic reaction in a sample used in one embodiment. [Diagram 2] 1 is a graph showing the change in solute concentration before and after the peritectic reaction. [Diagram 3] FIG. 2 is a schematic diagram showing a resistance heating furnace used in one embodiment. [Figure 4] FIG. 13 is a diagram showing state changes in unidirectional solidification. [Diagram 5] FIG. 4 is a diagram for explaining the operation of the resistance heating furnace. [Figure 6] FIG. 13 is a diagram for explaining the solidified state of a sample that has been unidirectionally solidified. [Figure 7] FIG. 13 is a diagram for explaining the MBA method. [Figure 8] FIG. 13 is a diagram for explaining random sampling. [Figure 9] FIG. 2 is a diagram showing a solidified structure obtained by unidirectional solidification in an example. [Figure 10] FIG. 13 is a graph showing the relationship between the solid fraction and the solute concentration, which is arranged by random sampling, before and after the peritectic reaction. [Figure 11] 1 is a graph showing the relationship between the solid fraction and the equilibrium distribution coefficient before and after the peritectic reaction. [Figure 12] Similarly, this is a graph summarizing the relationship between the solid fraction and the equilibrium distribution coefficient before and after the peritectic reaction. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] In one embodiment of the present disclosure, a peritectic steel material will be described as an example of an alloy that undergoes a peritectic reaction during solidification. An example of the structural change of this alloy is shown in a schematic diagram in Figure 1. It is believed that in this material, the solidifying solid phase changes from the δ-ferrite phase to the austenite phase during solidification, and the ferrite phase that has already solidified transforms into the austenite phase in turn. Since there is a difference in the solid solubility of elements in the ferrite phase and the austenite phase (= equilibrium distribution coefficient between ferrite and austenite), solutes move in areas where ferrite transforms into austenite (solute redistribution).

[0012] Figure 2 shows a conceptual diagram of the change in solute concentration distribution (solute redistribution) before and after the peritectic reaction. For example, in the case of Mo, the solid solubility limit of the austenite phase is smaller than that of the ferrite phase, so the solute migrates to the ferrite phase at the ferrite / austenite interface. As such, the solute concentration distribution in the solid phase after the peritectic reaction changes significantly from the solute concentration distribution before the peritectic reaction, so a measurement method that assumes that the solute concentration distribution in the solid phase does not change from the time of solidification cannot be applied.

[0013] In this embodiment, a sample having solidification structures both before and after the peritectic reaction is prepared, the solute concentration distribution of each solidification structure before and after the peritectic reaction is measured, and the solute mass balance of the solid and liquid phases during solidification is calculated (hereinafter, the MBA method) to obtain the equilibrium distribution coefficient.

[0014] The sample 10 is made of a steel material in which a peritectic reaction occurs, and the sample 10 is prepared in the shape of a rod. As shown in FIG. 3, the resistance heating furnace 1 has a crucible 2 for loading a sample 10, a base 3 for placing the crucible 2, and a cylindrical, heat-resistant holding tube 4 for supporting the crucible 2 from the periphery and above. A cylindrical furnace body 5 that is vertically movable is disposed around the holding tube 4. A heating element 6 is provided on the inner periphery of the furnace body 5. The configuration of the heating element 6 is not particularly limited, but it is necessary that the heating element 6 has a mechanism that can sufficiently heat the upper part of the sample 10. The resistance heating furnace 1 may be provided with a mechanism in which the furnace body 5 is fixed and the base 3 is vertically movable.

[0015] For the evaluation, the furnace body 5 is moved so that the heating element 6 is positioned on the outer periphery of the sample 10, the heating element 6 heats the sample 10 to melt the entire sample 10 (FIG. 4A), and then the furnace body 5 is gradually moved upward to solidify the lower side of the sample 10 and make the upper side completely liquid (FIG. 4B). Next, the entire sample 10 is cooled, for example with water, to fix the structure (FIG. 4C). As a result, the structure of the sample 10 is fixed in a liquid phase on the upper side and in a completely solid phase on the lower side, with the structure in the middle of solidifying being fixed between them. Furthermore, the structure in the middle of solidifying is divided into structures before and after the peritectic reaction. In other words, from the top (high temperature part) to the bottom (low temperature part) of the sample, a measurement sample is obtained that has solidification structures of a completely liquid phase, a structure before the peritectic reaction, a structure after the peritectic reaction, and a completely solid phase.

[0016] Prior to the test, the liquidus temperature, peritectic reaction temperature, and solidus temperature of the sample 10 are measured using differential thermal analysis, differential scanning calorimetry, or the like. The specific operation of the resistance heating furnace 1 will be explained with reference to Figure 5. In order to measure the equilibrium distribution coefficients from the structures before and after the peritectic reaction, it is necessary to identify the positions of the solidified structures before and after the peritectic reaction in the measurement sample. The simplest method for identifying the structures is to measure the temperature distribution in the sample and distinguish between the area above the peritectic reaction temperature as before the reaction and the area below as after the reaction. Therefore, a preliminary test is performed to measure the temperature gradient (temperature distribution) in the sample during unidirectional solidification. The method is as follows. A thermocouple 7 is placed in the crucible 2, and the cooling rate in the sample 10 is measured while unidirectional solidification is being performed. The temperature measurement position of the thermocouple 7 is set in the solid-liquid coexistence region or in the area that becomes completely solid during unidirectional solidification. Here, the temperature gradient may be measured by observing the structure of the sample 10 after water cooling. For example, the temperature gradient can be found by dividing the cooling rate by the solidification rate. It is known that there is a correlation between the morphology of the solidified structure and the cooling rate during solidification, and it is possible to estimate the cooling rate from the morphology of the solidified structure. The solidification rate can be measured by a method of determining the solid and liquid phase portions by observing the sample 10 after water cooling, or from the temperature measurement results while solidifying in one direction as described above.

[0017] Specifically, the sample 10 is placed in the crucible 2 and completely melted by the heating element 6 (A in FIG. 5), and then the furnace body 5 is raised to solidify the sample 10 (B in FIG. 5). Thereafter, the furnace body 5 is returned to its initial position to melt the sample 10 again (C in FIG. 5). At this time, the temperature of the sample 10 is measured by the thermocouple 7, and the temperature change of the sample 10 during solidification is obtained.

[0018] Next, to perform a unidirectional solidification / water-cooling test, the sample 10 is melted by the heating element 6 (D in FIG. 5), the furnace body 5 is raised to obtain a part of the sample 10 that is completely solid, a part that is completely liquid, and a part that is in the process of solidifying (E in FIG. 5), and the sample 10 is immediately water-cooled to fix the structure. In this embodiment, the cooling is performed by water cooling, but the type of cooling medium is not particularly limited as long as the structure can be fixed. In addition, in this embodiment, the preliminary test for measuring the temperature distribution and the unidirectional solidification and water cooling test are performed consecutively, but as long as the same alloy samples and test conditions are prepared and the temperature distributions in both tests can be made exactly the same, these tests do not have to be performed consecutively.

[0019] The longitudinal section of a unidirectionally solidified sample is observed. A schematic diagram is shown in Figure 6. The tip of the solidification structure (dendrite structure) is at the liquidus temperature T L corresponds to the solid fraction f S is 0. The solidus temperature T S At the position corresponding to the solid fraction f S is 1. Here, the liquidus temperature is the temperature at which solidification begins from a molten state, the solidus temperature is the temperature at which solidification ends, and the solid fraction is the ratio of the solid and liquid phases during solidification (0 to 1). Between the liquidus temperature and the solidus temperature there exists a temperature (peritectic reaction temperature) at which a peritectic reaction occurs. The high temperature area above this temperature is the region where the peritectic reaction has not yet occurred, while the low temperature area below this temperature can be said to be the region where the peritectic reaction has already occurred. The location where the peritectic reaction occurs is identified, and the equilibrium distribution coefficients of ferrite / liquid phase and austenite / liquid phase are simultaneously determined.

[0020] The longitudinal section of the solidified sample is polished and then corroded with chemicals to reveal the solidified structure (dendrite structure). The tip of the dendritic structure is set as the liquidus temperature, and the temperature distribution immediately before the sample is water-cooled is calculated from the temperature change at an arbitrary position within the sample measured in the preliminary test and the time required for water cooling from the start of the test. The location where the peritectic reaction occurred can be roughly determined from the temperature distribution of the sample and the peritectic reaction temperature measured by differential thermal analysis. Therefore, one location above that point can be selected as the solidification structure before the peritectic reaction, and one location below that can be selected as the solidification structure after the peritectic reaction, and the solute concentration distribution can be measured using EDS or EPMA.

[0021] In order to measure the equilibrium distribution coefficient from the start to the end of solidification, a position just before the peritectic reaction occurs is selected from the region before the peritectic reaction, and a position just above the solidus temperature is selected from the region after the peritectic reaction. The accuracy of the measured value improves if three or more measurement points are used, but measurement is possible with at least the above two points. In this example, the position where the peritectic reaction occurred was estimated based on the temperature, but since the position may be slightly shifted due to supercooling during solidification or calculation errors in temperature, it is desirable to confirm the peritectic reaction start position (presence or absence of austenite phase, etc.) by other methods, such as corroding the sample with a chemical after solidification.

[0022] The MBA method is applied to the solute concentration distribution before the peritectic reaction measured from the solidified sample to obtain the equilibrium distribution coefficient of ferrite / liquid phase, and the MBA method is applied to the solute concentration distribution after the peritectic reaction to obtain the equilibrium distribution coefficient of austenite / liquid phase. The details of the MBA method will be explained with reference to Fig. 7. Note that, in the following, the explanation of the peritectic reaction will be omitted. For any solute element, when the transition of the solute concentration distributed to the solid phase at each stage of solidification (each solid fraction) from the beginning to the end of solidification is known, the solid fraction f S Solute concentration C on the solid phase side at the solid-liquid interface when S(fS) can be read from the transition. And the solid fraction f S The solute concentration C on the liquid side at the solid-liquid interface when L(fS) can be calculated using the transition of the solute concentration distributed to the solid phase side and the following formula 1. Here, C0 in the formula is the initial concentration of the solute. The following formula 1 is the solid fraction f S The mass of solute in the liquid phase at this time can be calculated by subtracting the mass of solute in the solid phase from the mass of solute in the entire system. And the solid fraction f S The equilibrium distribution coefficient k (fS) is the solid fraction f S Solute concentration C on the solid phase side at the solid-liquid interface when S(fS) and the solute concentration in the liquid phase, C L(fS) It can be calculated from:

[0023]

number

[0024] The random sampling method will now be described in detail. Calculations using the MBA method require data on the transition of solute concentration distributed to the solid phase side at each solid fraction from the start to the end of solidification. This data is obtained by observing the solidified structure after water cooling, identifying the solid-liquid interface at each solid fraction during solidification, and performing point analysis using EDS or EPMA at the corresponding locations, but it is difficult to accurately identify the solid-liquid interface at each solid fraction experimentally. The random sampling method is a technique that can obtain the transition of solute concentration distributed to the solid phase side at each solid fraction from the start to the end of solidification without identifying the solid-liquid interface from the structure after solidification. When a sample solidifies, solutes are distributed between the solid and liquid phases. It is assumed that the solutes distributed to the solid phase do not move in the solid phase after distribution, and that the concentration of the solute distributed to the solid phase increases or decreases monotonically as solidification progresses (increase in solid fraction). In this case, the solidification structure of the solidified sample is randomly analyzed at multiple points using EDS or EPMA, the measurement results (solute concentration) obtained are sorted in ascending or descending order, and numbers are assigned to the measurement points in the sorted order. The numbers are divided by the total number of measurement points to obtain the solid fraction at that measurement point, and the data of the solute concentration distribution to the solid phase at each solid fraction from the start to the end of solidification can be reproduced. The solid fraction at this time is called the apparent solid fraction or two-dimensional solid fraction. There are several methods for sorting in the random sampling method, but the simplest method is to select solute elements whose solute concentration distributed to the solid phase increases or decreases monotonically, and sort the elements based on those elements. An example of random sampling is shown in Figure 8.

[0025] The mechanism by which the equilibrium distribution coefficients before and after the peritectic reaction can be measured simultaneously by combining a measurement sample that has solidification structures both before and after the peritectic reaction with the MBA method is described below. Regarding the solute concentration distribution after the peritectic reaction, the distribution changes due to the redistribution of the solute, but the area where the change occurs is limited to the area that was ferrite phase before the peritectic reaction, and the impact of the redistribution of the solute on the part that solidified after the peritectic reaction (austenite phase solidification) is minor, and it is considered that the solidified structure after the peritectic reaction retains the solute concentration when it was distributed to the solid phase side. In other words, in the relationship between the solid fraction obtained by the random sampling method and the solute concentration distribution, if we limit it to the measured values ​​after the peritectic reaction, the solid fraction f S Solute concentration C on the solid phase side at the solid-liquid interface when S(fS) can be read as is.

[0026] In addition, even if the solute is redistributed in the ferrite phase and the concentration distribution changes within that range, the total amount of solute does not change within the range. Therefore, if we limit it to the structure that solidified after the peritectic reaction, the solid fraction f S The solute concentration C on the liquid side at the solid-liquid interface when L(fS)It is possible to calculate In other words, since the solute concentration distribution in the range that was solidified before the reaction changes in the solidified structure after the peritectic reaction, it is not possible to calculate the equilibrium distribution coefficient before the peritectic reaction using the MBA method and random sampling method, but it is possible to calculate the equilibrium distribution coefficient after the peritectic reaction. And since the solidified structure before the peritectic reaction is not affected by solute redistribution, it is possible to calculate the equilibrium distribution coefficient before the peritectic reaction as it is using the MBA method and random sampling method. The equilibrium distribution coefficient obtained in this way can be used to predict micro- and macro-segregation and improve product quality. EXAMPLES

[0027] Approximately 100 g of a measurement sample (low alloy steel) was placed in a high-purity alumina crucible (outer diameter 17 mm × inner diameter 13 mm × height 150 mm) shown in Figure 3, which was then placed in an electric resistance heating furnace 1 and heated to above the liquidus temperature in an Ar atmosphere until it was completely melted. The composition of the low alloy used in this example (the balance being Fe and unavoidable impurities) is shown below.

[0028] [Table 1]

[0029] Since the temperature gradient within the sample during unidirectional solidification is required, the temperature measurement described below is carried out. The tip of an R-type thermocouple covered with a high-purity alumina protective tube (outer diameter 5 mm x inner diameter 3 mm x length 600 mm) is placed in the molten metal at an arbitrary position (preferably in the lower half of the sample, for example, 30 mm above the bottom of the sample). At the same time that temperature measurement with the temperature recorder begins, the furnace body equipped with a heat source is raised at a speed of 5 mm / min to obtain the temperature history of a specific position during unidirectional solidification.

[0030] After confirming that the temperature at the temperature measurement position has dropped sufficiently, stop measuring the temperature, return the furnace to its original position, and melt the sample again. If a more accurate temperature gradient is desired, it is desirable to repeat this temperature measurement at a different position. Once temperature measurement is complete, remove the protective tube (thermocouple). Then, solidify unidirectionally under the same conditions as when the temperature was measured (furnace rising speed 5mm / min), and water-cool the measurement sample before it completely solidifies. At this point, record the time from the start of the test to water-cooling. The timing of water-cooling can be determined approximately by measuring the temperature at any position on the upper half of the measurement sample during the temperature gradient measurement.

[0031] The water-cooled sample is cross-sectioned longitudinally through its central axis, polished, and then corroded with a chemical (e.g., a mixture of an aqueous solution of copper ammonium chloride and hydrochloric acid) to observe the dendritic structure. At this time, the tip of the dendritic structure corresponds to the solidification start temperature, that is, the liquidus temperature. Figure 9 shows a longitudinal section of the solidification structure of the measurement sample. In addition, the temperature at a specific position (e.g., 30 mm above the bottom of the sample) within the sample during unidirectional solidification can be determined from the measured temperature change over time at that position and the time required from the start of the test to water cooling. The temperature gradient and temperature distribution within the sample immediately before water cooling can then be estimated from the temperatures at two different heights immediately before water cooling.

[0032] The locations of the structures before and after the peritectic reaction of the sample during solidification can be identified from the temperature distribution in the measurement sample and the peritectic reaction temperature measured by differential thermal analysis. However, in actual unidirectional solidification, the location where the peritectic reaction starts may shift to the low temperature side due to undercooling or measurement errors. To obtain a more accurate equilibrium distribution coefficient, it is desirable to confirm the presence of the austenite phase not only by temperature distribution but also by further corrosion or other methods.

[0033] By using the above-mentioned method, the solidification structure before and after the peritectic reaction of a sample during unidirectional solidification can be obtained. Next, samples for EPMA are obtained from two locations on the cross section of the sample: one location above the peritectic reaction temperature of 1475°C (1477°C in this embodiment) and one location above the solidus temperature of 1450°C (1454°C in this embodiment).

[0034] After cooling in water, the solidification structure of the sample was observed. Line analysis of the dendritic structure (secondary dendrite arm) was performed using EPMA, and the results showed that the solute concentration distribution of Mn monotonically increased from the start to the end of solidification in both the solidification structure before the peritectic reaction and the solidification structure after the peritectic reaction. Therefore, since the effect of the change in concentration distribution of Mn due to solute redistribution is considered to be small, Mn was used as the sorting criterion for the random sampling method. Mn was sorted in ascending order, and other elements at the same measurement point were also sorted based on Mn. After that, numbers were assigned from 1 in order from the measurement point with the lowest Mn concentration, and the number was divided by the number of all measurement points to treat it as the solid phase ratio (apparent solid phase ratio).

[0035] In this example, the measured values ​​are averaged at certain solid fractions during random sampling. This is to suppress the variation in data, but is not necessarily required. The equilibrium distribution coefficient is calculated by applying the MBA method to the relationship between the solid fraction and solute concentration before and after the peritectic reaction organized by the random sampling method.

[0036] Figure 10 shows the relationship between the solid fraction after conversion to the apparent solid fraction and the solute concentration. The relationship between the solid fraction and the equilibrium distribution coefficient was calculated using the MBA method from the relationship between the solid fraction and the solute concentration obtained by random sampling. The results are shown in Figure 11.

[0037] Since the measurement was performed at a location in the sample that was in the middle of solidifying, it is believed that some of the calculated values ​​on the high solid fraction side of the results shown in Figure 11 were calculated from the area that was liquid just before water cooling. The area that was liquid just before water cooling was an area that rapidly solidified during water cooling, and is not the solidification behavior that we are actually interested in measuring, so it is necessary to identify the area that was liquid just before water cooling and exclude the calculated values ​​in that range. In addition, the solute concentration distribution after the peritectic reaction changes on the low solid fraction side (the area that was solidified before the reaction) due to the redistribution of solutes. In other words, it is also necessary to identify the solid fraction where the peritectic reaction occurred in the calculation results of the equilibrium distribution coefficient after the peritectic reaction and exclude the data on the low solid fraction side.

[0038] Since the temperature distribution within the sample during unidirectional solidification is known, if the relationship between temperature and solid fraction is known, it is possible to estimate the solid fraction to which solidification has progressed at the measured position. One method for determining the relationship between temperature and solid fraction is to use an empirical formula for estimating the liquidus temperature. The liquidus temperature of an alloy is determined by the alloy's components, and empirical formulas have been reported that use the solute concentration as an explanatory variable (for example, Solidification of Steel, edited by Solidification Process Research Group, 19th Committee on Steelmaking, Japan Society for the Promotion of Science, Shokado Shoten, Kyoto, (2015), Appendix 13). For example, the liquidus temperature T of some iron-based alloys is L It has been reported that it can be calculated using the following empirical formula:

[0039]

number

[0040] During solidification, the liquid phase becomes concentrated due to microsegregation, and the freezing point (liquidus temperature) drops. It is assumed that the liquidus temperature at this time coincides with the liquidus temperature calculated by the above empirical formula, that the temperature in the liquid phase is uniform, and that the temperature of the solid phase in contact with the liquid phase is equal to the temperature of the liquid phase. Since the MBA method can calculate the solute concentration in the liquid phase at each solid phase ratio, the liquid phase temperature at each solid phase ratio can be calculated by substituting these into the empirical formula for the liquidus temperature. However, carbon C diffuses quickly, and the solute concentration is not maintained when it is distributed to the solid phase during solidification, so the random sampling method cannot be adopted. Therefore, in this embodiment, the equilibrium distribution coefficient of carbon C cited from existing literature and the analytical formula for microsegregation in the equilibrium solidification model are used to calculate the solute concentration in the liquid phase at each solid phase ratio, C L(fS) was calculated. By matching the temperature distribution within the sample to the liquid phase temperature at each solid fraction thus determined, it is possible to determine to what solid fraction the solidification had progressed at the measured position immediately before water cooling.

[0041] The measurement positions of the solidification structure before the peritectic reaction (55 mm from the bottom of the sample) and after the peritectic reaction (37 mm from the bottom of the sample) are known to be 1477°C and 1454°C, respectively, from the temperature distribution.S The solute concentration C on the liquid side at the solid-liquid interface when L(fS) By substituting this into the empirical formula for the liquidus temperature, the solid fraction corresponding to 1477°C and 1454°C was estimated to be approximately 0.5 for the solidified structure before the peritectic reaction and approximately 0.81 for the solidified structure after the peritectic reaction. In addition, the solid fraction corresponding to the peritectic reaction temperature of 1475°C in the structure after the peritectic reaction was estimated to be approximately 0.51.

[0042] As shown in Figure 12, the solidification structure before the peritectic reaction corresponds to a solid fraction of approximately 0.5, so the data for the solid fraction after that was judged to be liquid and was excluded. The solidification structure after the peritectic reaction corresponds to a solid fraction of approximately 0.81, so the calculated values ​​after that were excluded. In addition, in the calculated value of the solidification structure after the peritectic reaction, the solid fraction corresponding to the peritectic reaction temperature of 1475°C was approximately 0.51, and the calculated values ​​on the low solid fraction side were excluded because the concentration distribution changed due to the peritectic reaction. Then, by combining these two calculated values, it was possible to calculate the equilibrium distribution coefficient from the start to the end of solidification even for alloy systems in which the peritectic reaction occurs. [Explanation of symbols]

[0043] 1 Resistance heating furnace 2. Crucible 3 Pedestal 4 Holding tube 5 Furnace body 6 Heating element 7 Thermocouples 10 Samples

Claims

1. A method for measuring the equilibrium distribution coefficient of an alloy that undergoes a peritectic reaction during solidification, comprising melting the alloy that undergoes a peritectic reaction during solidification, unidirectionally solidifying it into a state having a solid phase region, a liquid phase region, and a region in the process of solidifying, cooling the alloy to fix the structure, and determining, in the fixed structure, the equilibrium distribution coefficients corresponding to the solid phase ratio for the solidified structure before the peritectic reaction and for the solidified structure after the peritectic reaction.

2. 2. The method for measuring the equilibrium distribution coefficient of an alloy which undergoes a peritectic reaction during solidification according to claim 1, wherein the position of the peritectic reaction is determined by measuring the temperature of the molten alloy.

3. 3. The method for measuring the equilibrium distribution coefficient of an alloy which undergoes a peritectic reaction during solidification according to claim 1 or 2, wherein the solidified structure is measured to obtain a solute concentration distribution, which is then converted into a relationship between the solid phase ratio and the solute concentration distribution.

4. 4. The method for measuring the equilibrium distribution coefficient of an alloy which undergoes a peritectic reaction during solidification according to claim 3, wherein the equilibrium distribution coefficient is determined from said relationship by an MBA method.

5. 5. The method for measuring the equilibrium distribution coefficient of an alloy which undergoes a peritectic reaction during solidification according to claim 4, wherein the change in solid phase concentration is determined by random sampling from the concentration distribution of the solidified structure.

6. 3. The method for measuring the equilibrium distribution coefficient of an alloy which undergoes a peritectic reaction during solidification according to claim 1 or 2, wherein the alloy is preliminarily solidified in one direction, and a temperature gradient is obtained by measuring the temperature.

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