METHOD FOR DETERMINING THE PHASE TRANSITION TEMPERATURE OF MOLTEN SALTS

Abstract

The present invention relates to a method for determining a phase transition temperature using electrical conductivity.More specifically, the invention relates to a method for determining a phase transition temperature using electrical conductivity, the method comprising preparing a graph of the change in electrical conductivity of molten salts as a function of temperature, and carrying out at least one mathematical analysis consisting of (i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph; and (iii) determining the number (n) of data and the resolution (ΔT) on the basis of the graph to derive Tn by equation (1) below and performing a linear regression analysis on a linear section to detect an outlier on the basis of a distance with respect to the linear regression equation, Tn = Tmax – ΔT xn Equation (1) where n denotes the number of data, and ΔT denotes a measurement temperature range and indicates the resolution.

Description

Title of the invention: METHOD FOR DETERMINING A TEMPERATURE OF PHASE TRANSITION OF MOLTEN SALTS

[0001] The present application claims the benefit of the priorities of Korean Patent Application No. 10-2023-0119841 filed on September 8, 2023 and Korean Patent Application No. 10-2024-0039332 filed on March 21, 2024 with the Korean Intellectual Property Office. Technical field of the invention

[0002] The present disclosure relates to a method for determining a phase transition temperature using electrical conductivity, as well as a method capable of rapidly and accurately determining the phase transition temperature of a solid solution without using expensive equipment specially designed for this purpose. Technical background

[0003] Materials exhibit a phase change at a single temperature. A temperature at which liquefied materials solidify is called the solidification temperature, and a temperature at which solid materials are melted is called the melting temperature. A temperature at which liquefied materials begin to solidify is called the liquidus temperature, and a temperature at which solid materials begin to melt is called the solidus temperature.

[0004] When materials are pure without impurities, the temperature does not change during the phase change, so the four phase change temperatures are the same. As long as a solid turns into a liquid and a liquid turns into a solid, the same temperature is maintained without any temperature change. However, all materials contain impurities, which can cause differences in the four phase change temperature values. However, since the starting point remains unchanged even if the temperature changes, the liquidus temperature is a value that does not change. Accordingly, international temperature standards use the liquidus temperature of a specific material as the most ideal reference point.

[0005] Furthermore, a molten salt reactor (MSR) uses a liquid fuel in the form of a molten salt mixture and is attractive because of its inherent safety characteristics. The molten salt mixture must remain liquid within the desired temperature range and must have a relatively low melting point for efficient heat transfer and fluid dynamics in the reactor. Since the selection of the molten salt mixture with a melting point appropriate affects the safety, efficiency and overall performance of the reactor, understanding the phase transition behavior of various molten salt mixtures can be essential for the development of a molten salt reactor design.

[0006] In order to evaluate the safety and corrosiveness of materials in fuel salts of a molten salt reactor, it is essential to obtain a phase equilibrium diagram of the fuel salt according to the compositions, and the experimentally determined phase transition temperature value in high-temperature molten salts can be very important for use as reference data for a fuel salt phase equilibrium diagram based on computational thermodynamics. In this regard, a differential scanning calorimetry (DSC) method, a representative method for experimental determination of the phase transition temperature, has the problem that expensive special reactor cells must be used and bulky equipment in a small glove box must be installed in order to analyze molten salts which are very sensitive to moisture and oxygen in the atmosphere.

[0007] Furthermore, Korean Patent No. 10 1412594 B1 discloses a method for measuring the electrical conductivity of a solution. Therefore, it is expected that Korean Patent Record No. 10 1412594 B1 can be widely applied in related fields when it is possible to determine a phase transition temperature using an electrical conductivity that is suitable for use in actual processing sites. Summary of the invention

[0008] One aspect of the present disclosure may provide a method of determining an electrical conductivity and determining a phase transition temperature based on the determined electrical conductivity.

[0009] According to one aspect of the present disclosure, a method of determining a phase transition temperature using electrical conductivity may comprise preparing a graph of change in electrical conductivity of molten salts as a function of temperature; and

[0010] performing at least one mathematical analysis consisting of (i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph; and (iii) determining the number n of data and the resolution AT based on the graph to derive Tn by equation (1) below and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation,

[0011] Tn = Tn = Tmax - AT xn Equation (1)

[0012] where n denotes the number of data, and AT denotes a measurement temperature interval and indicates the resolution. Brief description of the figures

[0013] The above and other aspects, features and advantages of the present disclosure will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

[0014] [Fig-1] - [Fig.l] is a diagram illustrating an algorithm flowchart schematic for determining a phase transition temperature using electrical conductivity data;

[0015] [Fig.2] - [Fig.2] is a diagram illustrating the definitions of the elements described in the algorithm flowchart of [Fig.l];

[0016] [Fig.3] - [Fig.3] is a diagram illustrating results graphs first-order differentials (part 3A of [Fig.3]) and second-order differentials for measuring an electrical conductivity-temperature curve and a phase transition temperature determined in molten salts (0.56LiCl-0.44KCl)-NdCl3(30% by weight) (part 3B of [Fig.3]);

[0017] [Fig.4] - [Fig.4] is a diagram illustrating results graphs first-order differentials (part 4A of [Fig.4]) and second-order differentials for measuring an electrical conductivity-temperature curve and a phase transition temperature determined in molten salts (0.56LiCl-0.44KCl)-NdC13 (15 wt%) (part 4B of [Fig.4]). Detailed description of the invention

[0018] Hereinafter, exemplary embodiments of the present disclosure will be described with reference to the accompanying drawings. However, the exemplary embodiments of the present disclosure may be modified into various other forms, and the scope of the present disclosure is not limited to the exemplary embodiments which will be described below.

[0019] The phase transition behavior of the molten salt mixture is one of the basic characteristics that is essential to understand in determining an operating temperature affecting the safety, efficiency and overall performance of the molten salt reactor. According to the present disclosure, a novel method for determining a phase transition temperature using electrical conductivity data is provided.

[0020] In the method for determining a phase transition temperature using electrical conductivity of the present disclosure, any material whose electrical conductivity is measured can be used without limitations. particular, and may be a solid solution or molten salts having electrical conductivity, etc., and examples of molten salts may include one or more selected from the group consisting of LiPF6, LiF, KF, NaF, RbF, CsF, CaF2, MgF2, SrF2, BaF2, A1F3, UF3, UF4, PuF3, ThF3, ZrF4, NdF3, CeF3, LaF3, LiCl, KC1, NaCl, RbCl, CsCl, CaCl2, MgCl2, SrCl2, BaCl2, A1C13, UC13, UC14, PuCl3, ThCl3, ZrCL NdCl3, CeCl3, LaCl3, LiBr, KCBr, NaBr, RbBr, CsBr, CaBr2, MgBr2, SrBr2, BaBr2, AlBr3, UBr3, UBr4, PuBr3, ThBr3, ZrBr4, NdBr3, CeBr3, LaBr3, Lil, Kl, Nal, Rbl, Csl, Cal2, Mgl2, Srl2, Bal2, A1I3, UI3, UI4, Pul3, Thl3, Zrl4, Ndl3, Cel3, Lal3, Lil, Kl, Nal, LiNO3, KNO3, NaNO3, RbNO3 and CsNO3, and preferably may comprise one or more selected from the group consisting of LiCl-KCl, NaCl-KCl, NaCl-MgCl2, LiCl-NaCl-CaCl2-BaCl2, NaCl-KCl-BaCl2, Csl, UC13, UC14, NdCl3, CeCl3, and LaC.

[0021] In more detail, the method of determining a phase transition temperature using electrical conductivity of the present disclosure comprises preparing a graph of the change in electrical conductivity of molten salts as a function of a change in temperature; and performing at least one mathematical analysis.

[0022] Carrying out the mathematical analysis that can be applied to the present disclosure consists of (i) carrying out a first-order differential on the graph of the change in the electrical conductivity of molten salts, (ii) carrying out a second-order differential on the graph of the change in the electrical conductivity of molten salts, and (iii) determining the number (n) of data and the resolution (AT) based on the graph of the change in the electrical conductivity of molten salts to derive Tn by equation (1) below and carrying out a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation.

[0023] Tn= Tmax - AT xn Equation (1)

[0024] (In equation (1) above, n denotes the amount of data, and AT denotes a measurement temperature interval and indicates the resolution.)

[0025] As a result of performing the mathematical analysis, in case (i), a point where a value is the highest when processing the first-order differential, in case (ii), an inflection point where the value becomes 0 when processing the second-order differential, and in case (iii), the temperature corresponding to the outlier can be determined as the phase transition temperature.

[0026] The phase transition temperature to be measured in the present disclosure is not particularly limited as long as it is the temperature at which the phase of the material changes, but may be, for example, the liquidus temperature TL.

[0027] Furthermore, when the difference between the liquidus temperature TL and the solidus temperature Ts is 25°C or less, i.e., the closer the difference, the more difficult it may be to distinguish between the liquidus and solidus temperatures. In this case, when (iii) performing the mathematical analysis is included, a relatively accurate liquidus temperature TL can be determined.

[0028] According to the present disclosure, the preparation of the graph of the change of the electrical conductivity of molten salts as a function of the change of temperature is first carried out. In this case, the device or method for determining the electrical conductivity is not limited and any known device or method for determining electrical conductivity can be used.

[0029] Furthermore, when preparing the graph of the change in electrical conductivity of molten salts as a function of temperature change, the temperature change may be both the increase and decrease in temperature. For example, when measuring electrical conductivity while lowering the temperature, a maximum temperature Tm greater than or equal to the melting point of the molten salts may be selected and the measurement may start at the maximum temperature. In this case, the maximum temperature is not particularly limited and may be, for example, a maximum temperature that a high-temperature furnace can withstand, but taking into account the economic aspects of the method, the temperature may be decreased from the melting temperature of the molten salts to be analyzed and from a temperature of 50 to 500°C above the melting temperature to room temperature.Alternatively, the electrical conductivity can be measured by starting from the solid salt and increasing the temperature to the melting temperature or higher. However, taking into account the accuracy of the data, when raising the temperature and preparing the graph of the change in electrical conductivity of molten salts versus the change in temperature, it is preferable that the temperature increase rate be slow at 20 °C / h or lower. In this way, taking into account the time required for analysis and the accuracy of the analysis, it is preferable to prepare the graph by decreasing the temperature from the melting temperature of molten salts or the temperature 50 to 500 °C higher than the melting temperature to room temperature.

[0030] In equation (1) of (iii) above, n is the number of data, and the range of n is not particularly limited. Taking into account the reliability of the data, the range of n is preferably 10 or more, and may be an integer equal to 100 or less, for example 50 or less, or 30 or less. Furthermore, AT may refer to the resolution at the interval of the measurement temperature, and this is also not particularly limited and can be adjusted if necessary, but taking into account data reliability and time required, AT is preferably 2 to 10 °C.

[0031] Furthermore, when detecting the outlier based on the distance from the linear regression equation of (iii) above, when the absolute value of the distance constant representing the distance from the linear regression equation is greater than or equal to the discrimination reference value in Table 1, it can be detected as an outlier. However, the discrimination reference value can also be adjusted if necessary.

[0032] For example, when detecting the outlier based on the distance from the linear regression equation, at least one of the following equations A to E may be applied. That is, the distance from the linear regression equation may be detected by selecting at least one of the above equations. (Equation A) (Equation Bj (Equation C) (Equation D) (Equation E) ŸV

[0033] In more detail, the algorithm proceeds based on the discrimination reference value disclosed in Table 1 below.

[0034] [Tables 1] Formula for derivation of the distance constant Reference value of discrimination Equation A 2 Equation B The smaller value of 6 / n and 0.99 Equation C 2 Equation D 1 Equation E When n is less than 30, it is 1, and when n is greater than or equal to 30, it is 2 / n0'5.

[0035] For example, when applying both equations A to E, if the absolute value of the distance constant is less than the discrimination reference value in Table 1 when applying the selected equation, the algorithm proceeds to re-execute the linear regression analysis, adding n as n+1, re-executing the linear regression analysis and adding 1 to n again, i.e., n+2. In this case, it is not necessary to satisfy all equations A to E and independently confirm whether it is less than the discrimination reference value according to each equation. When the absolute value of the distance constant according to equations A to E is greater than or equal to the discrimination reference value, the determination of the point as an outlier and the determination of the temperature of the point as the liquidus temperature TL can be performed.

[0036] Furthermore, the outlier detection based on the distance from the linear regression equation in (iii) above ends when the liquidus temperature TL becomes equal to the solidus temperature Ts.

[0037] For example, the present disclosure may include: increasing the temperature of the solid molten salts and preparing a graph of the change in electrical conductivity of the molten salts as a function of the increase in temperature; determining the solidus temperature Ts by performing the first-order differential or the second-order differential on the graph of the change in electrical conductivity of the molten salts as a function of the increase in temperature; melting the molten salts by raising the temperature to a temperature of 50 to 500°C higher than the melting temperature of the molten salts; preparing the graph of the change in electrical conductivity of the molten salts as the temperature decreases while decreasing the temperature of the molten salts to room temperature;and determining the number n of data and the resolution AT based on the graph of the change in electrical conductivity of molten salts versus temperature drop to derive Tn using equation (1) and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, wherein detecting the outlier includes applying one or more equations selected from equations A to E and, based on the distance constant confirmed based on the equation(s), performing the linear regression analysis again and adding n as n+1, if an absolute value of a distance constant is less than a discrimination reference value, and determining as an outlier when the absolute value of the distance constant is greater than or equal to one; discrimination reference value, and determining the temperature at this point as the liquidus temperature TL.

[0038] Hereinafter, the present disclosure will be described in more detail by means of specific examples. The following examples are merely illustrative to aid in understanding the present disclosure, and the scope of the present disclosure is not limited thereto. EXAMPLES Materials and equipment

[0039] To perform an electrical conductivity measurement, a custom glass capillary cell (1.5 mm inner diameter, 3 cm capillary length) was used. In this case, a Pt line (1 mm diameter) was used to establish electrical contact between the capillary cell and a highly conductive liquid. Electrical conductivity values ​​were obtained by measuring a step voltage in units of microseconds using a potentiometer.

[0040] Furthermore, a cell constant is a coefficient used to convert a measured resistance (or the inverse of resistance) into conductivity, and the capillary cell is selected to have a cell constant within an appropriate range. In general, for highly conductive liquids, cells with values ​​greater than or equal to 300 cm-1 are recommended. The cell constant was measured in a constant temperature water bath at 291 K by placing a standard KCl solution of known conductivity into the capillary cell, which was determined using the equation below.

[0041] C = kxR

[0042] Here, C represents the cell constant (cm1), k represents the electrical conductivity (S cm1) of the solution, R represents the resistance of the solution, and the value R was determined from a slope of a current-voltage curve obtained from a method of measuring a step voltage in units of microseconds.

[0043] Method for determining the phase transition temperature of molten salts

[0044] According to the present disclosure, in the molten salt mixture, by using the electrical conductivity measuring system described above in Material and Equipment of 1 above, it is possible to measure an electrical conductivity value at regular intervals while lowering the temperature and, by applying a series of mathematical algorithms to the measured value, it is possible to objectively and accurately determine the phase transition temperature. 1. Measurement of electrical conductivity

[0045] To measure the electrical conductivity of the high-temperature molten salt, the molten salt mixture was inserted into a quartz container and then inserted into a high-temperature furnace in a glove box (99.999% argon, both humidity and oxygen < 1 ppm). The temperature of the high-temperature furnace was regulated and monitored by means of a thermocouple, and the thermocouple was placed as close as possible to the end of the capillary cell to measure the accurate temperature. To determine the phase transition of the molten salt mixture, the electrical conductivity was measured at regular intervals while lowering the temperature in the range of 300 to 600 °C

[0046] (2) Determination of the phase transition temperature on the basis of a mathematical algorithm

[0047] 1) Second-order differential method

[0048] The measured electrical conductivity-temperature curve can be subjected to a first-order and / or second-order differential, and a point where the result of the first-order differential is the highest and the value at which an inflection point becomes 0 in the result of the second-order differential can be determined as the phase transition temperature. This method can distinguish transition points that are difficult to determine as the intersection of a simple linear regression equation, and can determine a more accurate temperature by appropriately adjusting a temperature interval corresponding to a resolution.

[0049] However, for example, in a molten salt system of a composition having two phase transition temperatures, which are the solidus temperature Ts and the liquidus temperature TL, when the temperature interval between Ts and TL is narrow, calculations based on a differential may lead to inaccuracy in some cases. The phase transition temperature may be determined by using a phase transition temperature determination method based on a mathematical algorithm such as that presented below, or by additionally implementing this method.

[0050] 2) Analysis algorithm using linear regression and statistical analysis of data

[0051] As shown in the flowchart of the algorithm in [Fig. 1], the phase transition temperature can be determined by a systematic method of determining a value according to various statistical evaluation criteria of equations A, B, C, D and E.

[0052] In this case, the definitions of each description in the above algorithm are as follows.

[0053] To = Tmax: highest temperature at which the measurement of the conductivity value begins.

[0054] Tn = minimum temperature in the linear section

[0055] Tmax = maximum temperature

[0056] Tl = liquidus temperature

[0057] AT = resolution

[0058] n = minimum number of data

[0059] R2 = coefficient of determination

[0060] Z = distance constant

[0061] IZI = Absolute value of the distance constant

[0062] Zdet = Discrimination reference value

[0063] Furthermore, equations A, B, C, D and E are examples of statistical equations which can assess how far the data value is from the linear regression equation, which is as follows: [Equation AJ Z ( to) » [BJ Equation « [Equation C] ^(0 « [DJ Equation s [Equation E) ® ,

[0064] In this case, the definitions of the elements described in each equation are as follows.

[0065] n: number of data

[0066] k: number of independent terms in the regression model (e.g., for a linear model, y = ax + b, so two as a and b) : i-th y value yî'f i-th predicted y-value -¾ * i-same value x 1; average of value x sæ <; — — 1

[0067] Experimental example: Determination of the phase transition temperature

[0068] LiCl-KCl molten salts were the measurement targets, which are chloride-based molten salts used for the thermochemical reprocessing of spent nuclear fuels. Various physical properties of the corresponding molten salts have been studied by several researchers. The melting temperature as a function of the KCl (or LiCl) composition has been measured in several studies using a thermal analysis method, for example.

[0069] To demonstrate the validity of the phase transition temperature determination method based on electrical conductivity, the electrical conductivity-temperature curve was obtained from a LiCl-KCl based molten salt mixture, and the solidus temperature (Ts: solidus temperature) and liquidus temperature (TL: liquidus temperature) were determined, respectively.

[0070] Accordingly, all measured temperature values ​​were compared with previously reported reliable results.

[0071] [Fig.3] (part 3A of [Fig.3]) illustrates the electrical conductivity-temperature curve measured in LiCl-KCl-NdCl3 (30 wt%) molten salts and [Fig.3] (part 3B of [Fig.3]) illustrates the first differential and second differential result graphs for determining the phase transition temperature, and [Fig.4] (part 4A of [Fig.4]) illustrates the electrical conductivity-temperature curve measured in LiCl-KCl-NdCl3 (15 wt%) molten salts and [Fig.4] (part 4B of [Fig.4]) the first differential and second differential result graphs for determining the temperature phase transition. In this case, the wt% is expressed as a percentage of a mass of NdCl3 relative to the mass of the total solution, using the eutectic mixture LiCl-KCl as solvent.

[0072] In experimental example 1 (type I) of [Fig. 3], when a gap between Ts and TL was sufficiently large, an accurate transition temperature could be determined based on the first-order and / or second-order differential of the corresponding curve. It was confirmed that the Ts measured in this way was 353 °C (first-order differential), 352 °C (second-order differential), and that the Tl was 420 °C (first-order differential) and 417 °C (second-order differential), respectively, which were found to be very similar to the values ​​presented in the literature (TS: 355 °C and TL: 424 °C).

[0073] Furthermore, as in experimental example 2 (type II) of [Fig. 4], when the deviation between Ts and TL is less than 25°C, it may be difficult to clearly determine the inflection point corresponding to TL. Therefore, additional TL,cal values ​​that meet the statistical evaluation criteria presented in the present disclosure were calculated as in Table 1 and compared in Table 2.

[0074] Table 2 shows the results obtained from statistical equations A to E that evaluate the extent to which the data values ​​deviate from the linear regression equation. In Table 2 below, column 1 represents n, columns 2 and 3 represent T (absolute temperature, a value obtained by adding 273 to the temperature in degrees Celsius) and the x value (1 / T, the inverse of the absolute temperature), respectively, and column 4 represents the y value (In k). Column 5 represents the predicted value from the linear regression equation. A, B, C, D, and E shown in columns 6 to 10 show the values ​​calculated by substituting each of the above equations.

[0075] [Tables2] n T / KX(l / T) Y(lnK) Y pred Residual Leverage St udent's R Co ok's DFFITS 1 873 0.00115 0.7941 6 0.7974 2 -0.003 26 0.1138 6 -0.050 90 0.00017 -0.0182 5 2 863 0.00116 0.7716 2 0.7748 3 -0.002 21 0.1050 5 -0.034 28 0.00007 -0.0117 4 3 853 0.00117 0.7499 8 0.7517 1 -0.001 73 0.0965 6 -0.026 70 0.00004 -0.0087 3 4 843 0,00119 0,7281 0 0,7280 4 0,0000 7 0,0884 3 0,0010 2 0,00000 0,00032 5 833 0,00120 0,7062 4 0,7038 0 0,0024 3 0,0806 8 0,0372 9 0,00006 0,01105 6 823 0,00122 0,6797 4 0,6789 8 0,0007 6 0,0733 5 0,0116 6 0,00001 0,00328 7 813 0,00123 0,6562 1 0,6533 4 0,0026 7 0,0664 8 0,0406 3 0,00006 0,01084 8 803 0,00125 0,6314 5 0,6274 7 0,0039 8 0,0601 1 0,0603 3 0,00012 0,01526 9 793 0,00126 0,6036 5 0,6007 5 0,0029 0 0,0542 8 0,0438 6 0,00006 0,01051 10 783 0,00122 0,5752 8 0,5733 4 0,0019 5 0,0490 5 0,0293 3 0,00002 0,00666 11 773 0,00129 0,5451 7 6,5452 2 -0,000 05 0,0444 6 -0,000 71 0,00000 -0,0001 5 12 763 0,00131 0,5134 7 0,5163 6 -0,002 89 0,0405 7 -0,043 33 0,00004 -0,0089 1 13 753 0,00133 0,4821 3 0,4867 4 -0,004 61 0,0374 5 -0,069 02 0,00010 -0,0136 1 14 743 0,00135 0,4443 4 0,4563 2 -0,011 99 0,0351 5 -0,179 44 0,00061 -0,0342 5 15 733 0,00136 0,4087 7 0,4250 7 -0,016 30 0,0337 6 -0,243 95 0,00108 -0,0456 0 16 728 0,00137 0,3953 2 0,4091 3 -0,013 80 0,0334 2 -0,206 48 0,00076 -0,0383 9 17 723 0,00138 0,3730 5 0,3929 6 -0,019 91 0,0333 4 -0,298 06 0,00158 -0,0553 5 18 718 0,00139 0,3526 2 0,3765 7 -0,023 95 0,0335 2 -0,358 84 0,00230 -0,0668 3 19 713 0,00140 0,3362 4 0,3599 4 -0,023 70 0,0339 8 -0,355 23 0,00229 -0,0666 3 , 20 708 0,00141 0,3126 0 0,3430 9 -0,030 49 0,0347 3 -0,457 84 0,00388 -0,0868 5 21 703 0,00142 0,2888 2 0,3259 9 -0,037 17 0,0357 8 -0,559 54 0,00596 -0,1077 9 22 698 0,00143 0,2692 5 0,3086 5 -0,039 39 0,0371 5 -0,593 89 0,00697 -0,1166 5 23 693 0,00144 0,2434 3 0,2910 6 -0,047 63 0,0382 4 -0,720 84 0,01068 -0,1449 0 24 683 0,00146 0,1992 3 0,2551 0 -0,055 87 0,0432 6 -0,850 64 0,01652 -0,1808 8 25 673 0,00149 0,1471 0 0,2180 7 -0,070 97 0,0491 6 -1,093 11 0,03067 -0,2485 5 26 663 0,00151 0,0993 9 0,1799 3 -0,080 55 0,0566 7 -1,253 82 0,04627 -0,3073 1 27 653 0,00153 0,0606 5 0,1406 2 -0,079 97 0,0659 3 -1,250 90 0,05413 -0,3323 4 28 643 0,00156 -0,062 98 0,1000 9 -0,163 07 0,0721 0 -2,844 03 0,26961 -0,8220 3 29 638 0,00157 -0,137 20 0,0793 5 -0,216 54 0,0834 5 -4,325 37 0,52174 -1,3051 6 30 633 0,00158 -0,205 82 0,0582 7 -0,264 10 0,0903 4 0,85292 -2,0627 8 31 623 0,00161 -1,227 81 0,0151 2 -1,242 92 0,1058 4 22,906 59 32 613 0,00163 -6,447 02 -0,029 45 -6,417 58 0,1238 0 743,882 73 33 603 0.00166 -9.391 46 -0.075 49 -9.315 97 0.1444 4 ,

[0076] For the electrical conductivity-temperature curve measured in salt (0.56LiCl-0.44KCl)-NdCl3 (15 wt%), the TL values ​​obtained from the analysis algorithm using linear regression and statistical analysis of the data have been summarized in Table 3 below.

[0077] [Tables3] TL,cal % difference Value presented in the literature [J.Mol.Liq.382 (2023) 121869] 382 A 350 8.4 B 330 13.6 C 380 0.5 D 360 5.8 E 370 3.1

[0078] Accordingly, as can be seen in Table 3, in the case of the electrical conductivity-temperature curve of [Fig.4], the % difference value calculated from the value reported in the literature showed a difference of about 10%, which was confirmed in the order C <E<D<A<B.

[0079] Furthermore, in order to confirm the objectivity and relevance according to the evaluation method for equations A to E, for the electrical conductivity-temperature curve with different result values ​​using 0.70LiCl-0.30KCl salts with different compositions, the TL values ​​obtained from the analysis algorithm using linear regression and statistical data analysis have been summarized in Table 4 below.

[0080] [Tables4] TL,cal % difference Value presented in the literature [Russ. J.Inorg.Chema. 53 (2008) 1509] 452 A 360 20.4 B 350 22.6 C 450 0.4 D 445 1.5 E 450 0.4

[0081] Accordingly, as can be seen in Table 4 above, the % difference values ​​from the literature values ​​showed differences in the order C, E < D < A < B. In general, it can be seen that methods C and E showed small differences from the literature values, and methods A and B showed relatively large differences.

[0082] As such, it can be expected that the method of integrating values ​​according to various statistical evaluation criteria based on the present disclosure can provide a level of objectivity, rationality and sensitivity control to achieve a desired level of uncertainty.

[0083] In other words, the system for determining a phase transition temperature using an electrical conductivity measurement according to the present disclosure is very promising as a new methodology for measuring the phase transition temperature of various multi-component molten salt systems, and this technology presents a much simpler and faster measurement system compared to existing thermal analysis techniques. Furthermore, this analysis algorithm allows for consistent determination of the transition temperature under all conditions and environments.

[0084] According to the method for determining a phase transition temperature using electrical conductivity, by measuring the electrical conductivity of a target and adopting a series of mathematical algorithms using the measured electrical conductivity to determine the phase transition temperature, it is possible to simply and quickly calculate accurate phase transition temperature values. Therefore, according to the present disclosure, it is expected that the phase transition temperature values ​​experimentally determined in high-temperature molten salts, etc. can be used as reference data for phase equilibrium diagrams based on computational thermodynamics.

[0085] Although exemplary embodiments have been illustrated and described above, it will be apparent to those skilled in the art that modifications and variations may be made without departing from the scope of the present disclosure as defined by the appended claims.

Claims

Claims

1. A method for measuring a phase transition temperature using electrical conductivity, comprising: preparing a graph of change in electrical conductivity of molten salts as a function of temperature;and performing at least one mathematical analysis of (i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph, and (iii) determining the number (n) of data and the resolution (AT) based on the graph to derive Tn by equation (1) below and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, Tn = Tmax - AT xn Equation (1) where Tn denotes the minimum temperature in the linear section, Tmax denotes the maximum temperature, n is an integer from 10 to 100, and AT denotes a measurement temperature interval and indicates the resolution.;

2. The method of claim 1, wherein in the mathematical realization according to case (i), a point where a value is the largest when processing the first-order differential, in the mathematical realization according to case (ii), an inflection point where the value becomes 0 when processing the second-order differential, and in the mathematical realization according to case (iii), the temperature corresponding to the outlier are determined as the phase transition temperature.

3. The method of claim 1, wherein the preparation of the graph of the change in electrical conductivity of molten salts as a function of temperature change is first carried out and when a difference between the liquidus temperature (TL) and the solidus temperature (Ts) is 25°C or less based on the graph of the change in electrical conductivity of molten salts versus temperature change, the mathematical analysis of (iii) is carried out.

4. The method of claim 1, wherein the temperature change refers to increasing the temperature from the solid molten salts to be analyzed to the melting temperature or decreasing the temperature from the melting temperature of the molten salts to room temperature.

5. The method of claim 1, wherein the molten salts comprise at least one component selected from the group consisting of LiCl-KCl, NaCl-KCl, CsCl-KCl, LiCl-NaCl-CaCl2-BaCl2, NaCl-KCl-BaCl2, CaF2, NdCl3, CeCl3, and LaCl3.

6. The method of claim 1, wherein the phase transition temperature is the liquidus temperature (TL).

7. The method of claim 1, wherein in equation (1) of (iii) above, n is an integer from 10 to 100, and AT is from 2 to 10 or

8. c. The method of claim 1, further comprising performing the linear regression analysis again and adding n as n+1 if an absolute value of a distance constant representing the distance from the linear regression equation is less than a discrimination reference value, and determining as an outlier if the absolute value of the distance constant below is greater than or equal to a discrimination reference value, and determining the temperature at that point as the liquidus temperature (TL), when applying one or more of equations A to E below: (Equation AJ (Equation B) " (Equation Cj (Equation D) (k 4- 1 (Equation E) (in this case, the definitions of the elements described in each equation are as follows: n: number of data k: number of independent terms in the regression model i-eme value y : ï-th predicted y-value bth value x mean of value x

9. Or x denotes 1 / T, inverse of absolute temperature, and y denotes In k. The method of claim 8, wherein, when detecting the outlier based on the distance from the linear regression equation in the mathematical analysis (iii) above, when the absolute value of the distance constant representing the distance from the linear regression equation is greater or equal to each of the following discrimination reference values in each distance constant derivation equation A to E, it is detected as the outlier. Equation A: 2 Equation B: smaller value of 6 / n and 0.99 Equation C: 2 Equation D: 1 Equation E: when n is less than 30, it is 1, and when n is greater than or equal to 30, it is 2 / n0.

5.

10. The method of claim 8, wherein the detection of the outlier based on the distance from the linear regression equation in the above mathematical analysis (iii) ends when the liquidus temperature (TL) becomes equal to the solidus temperature (Ts).

11. The method of claim 1, further comprising: increasing the temperature of the solid molten salts and preparing a graph of the change in electrical conductivity of the molten salts as a function of the increase in temperature; determining the solidus temperature (Ts) by performing the first-order differential or the second-order differential on the graph of the change in electrical conductivity of the molten salts as a function of the increase in temperature; melting the molten salts by increasing the temperature to a temperature of 50 to 500°C above the melting temperature of the molten salts; preparing the graph of the change in electrical conductivity of the molten salts as the temperature decreases while decreasing the temperature to room temperature;and determining the number (n) of data and the resolution (AT) based on the graph of the change in electrical conductivity of molten salts versus temperature drop to derive Tnen using equation (1) above and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, wherein detecting the outlier includes,; performing the linear regression analysis again and adding n as n+1, if an absolute value of a distance constant representing the distance from the linear regression equation is less than a discrimination reference value, and determining as an outlier if the absolute value of the distance constant below is greater than or equal to a discrimination reference value, and determining the temperature at that point to be the liquidus temperature (TL), when applying one or more of equations A to E below. (Equation A) (Equation Bj (Equation C) (Equation D) (Equation E) (in this case, the definitions of the elements described in each equation are as follows: n: number of data k: number of independent terms in the regression model ' i-th value yy: i-th predicted y-value x< ' t-th value xx > mean of value x Or x denotes 1 / T, inverse of the absolute temperature, and y denotes In k. wherein each discrimination reference value in each of the distance constant derivation equations A to E is: Equation A: 2 Equation B: smaller value of 6 / n and 0.99 Equation C: 2 Equation D: 1 Equation E: when n is less than 30, it is 1, and when n is greater than or equal to 30, it is 2 / n0.5).

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