Note
Electrical-resistivity Measurements of Liquid Fe–C Alloys Using the Four-terminal Method
2016 Volume 56 Issue 11 Pages 2107-2109
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2016 Volume 56 Issue 11 Pages 2107-2109
Electrical-resistivity measurements of liquid Fe–C alloys were attempted using a new probe developed on the basis of the four-terminal method. The four graphite electrodes (except their ends) were covered with alumina tubing and were combined together with an outer alumina tube such that the sample diameter was determined by the outer tubing. The as-prepared probe was dipped into the liquid samples for measuring their resistivity. With the aim to confirm the reliability of the technique, the probes were firstly used to measure the electrical resistivity of liquid Ga and Sn samples. Subsequently, electrical-resistivity measurements were conducted for Fe-4.31mass%C and Fe-4.57%C samples at ca. 1585 K; these measurements yielded values of 1.48×10−6 and 1.58×10−6 Ω·m, respectively. A comparison with the reported data suggests that the electrical resistivity of liquid iron progressively increased with the carbon concentration up to 3 mass%, beyond which it showed a drastic increase. This resistivity change might have occured because of the structure of the liquid Fe–C alloy.
The electrical resistivities of iron and its alloys are essential to optimise the operation conditions in electromagnetic force technologies such as level magnetic field (LMF) and in-mold electromagnetic stirrer (EMS) techniques, which are employed in continuous casting of steel. The electric resistivities are also one of the fundamental properties required to understand the iron alloys. However, the electric resistivities of the Fe–C system have not been investigated thoroughly despite it being a typical Fe-based alloy. Thus, the reported values show considerable discrepancies. Using the direct measurement method, Arsent’ev et al.1) and Bornemann et al.2) reported that the electrical resistivity steeply increases with carbon concentration at low carbon contents, whereas, the values measured by Ono et al.3) using the rotating magnetic-field method (a type of the indirect method) showed a steep increase. These differences originated from the difficulty in measuring the electrical resistivity of a liquid metal at high temperatures. It is known that the direct method can measure the electrical resistivity with high accuracy. However, the reaction between the electrodes and the sample prevents proper measurements. For example, Arsent’ev et al. and Bornemann et al. used graphite electrodes installed into the sample cell in an attempt to cause a reaction between liquid iron and the electrodes.4) It is still desirable to develop such a method for measuring the electrical resistivity in which a reaction occurs between the liquid metals and the electrodes.
Endo et al.3) recently developed an L-shaped four-terminal probe (Fig. 1(a)) for measuring the electrical resistivities of Sb2Te3 and Ge2Sb2Te5 at temperature ranging from the respective melting temperatures of the samples to 1020 K. The electrical resistivity of the liquid metal in that study were measured with high accuracy by simply immersing the probe into the sample and considering the thermal expansions of the cell and the probe. This method can be applied to measure the electrical resistivity of molten steel after making some improvements that enable a reduction in the reaction degree between the sample and the lead wires. Consequently, this study aims to develop a new probe for the DC four-terminal method such that the electrical resistivity of the molten Fe–C system can be measured.
Probes used for the four terminal method: (a) developed by Endo et al.5) and (b) developed in this study.
The electrical resistivity of liquid Fe–C alloys was measured using the probe shown in Fig. 1(b). The electrode section was point-shaped to reduce the reaction area between the electrode and the sample. The electrodes were made of graphite, which is a common electrode material owing to its small thermal expansion, high thermal-shock resistance and chemical stability characteristics. The graphite rod (diameter: 3 mm) was insulated with an alumina tube (outer diameter: 6 mm). The distance between the inner electrodes was ca. 35 mm, and the distance between the inner and outer electrodes was ca. 10 mm. These electrodes were coated with an alumina tube with a 20-mm inner diameter. Once the probe was dipped into the liquid sample, a current (I) was supplied between the outer electrodes and a potential difference (ΔV) was measured between the inner electrodes.
The electrical resistance of the sample between the inner electrodes can be obtained using the Ohm’s law
| (1) |
| (2) |
| (3) |
In this study, the validity of the measurement technique was examined by measuring the electrical resistivity of molten Ga (99.99%) and Sn (99.9%). The experimental conditions are summarized in Table 1. The electrical resistivity measurements were carried out by supplying an electric current for ca. 12 s at intervals of 1 A.
| Crucible (i.d. in mm) | Atomosphere | Measurement temperature/K | Current /A | Thermometer | |
|---|---|---|---|---|---|
| Ga | Silica (27 mm) | air | 323–333 | 1–4 | Mercury thermometer |
| Sn | Alumina (34 mm) | Ar-3%H2 | 670–1071 | –4 –4 | R-type thermocouple |
| Factor of uncertainly | Type | Estimated value | Standard uncertainty | Sensitivity cofficirnt |
|---|---|---|---|---|
| Electric resistivity, ρ/Ω·m | 1.48×10−6 | |||
| Resistance, R/Ω | 2.16×10−4 | 4.89×10−6 | 6.94×10−3 | |
| Least square mathod/Ω | A | 1.335×10−7 | ||
| Repeatability/Ω | A | 9.203×10−7 | ||
| Accuracy from equipments/Ω | A | 4.80×10−6 | ||
| Inner diameter of container, d1/m | 1.97×10−2 | 4.7×10−5 | 1.88×10−4 | |
| Repeatability/m | A | 1.95×10−2 | 4.7×10−5 | |
| Gauging of calliper/m | B | 1.95×10−2 | 2.8×10−6 | |
| Liner coefficient of thermal/K−1 | B | 8.10×10−6 | 5.8×10−8 | |
| Temperature/K | B | 1582 | 5.8×10−1 | |
| Outer diameter of insulating tubes, d2/m | 6.103×10−3 | 9.4×10−7 | −1.15×10−4 | |
| Repeatability/m | A | 6.040×10−3 | 8.9×10−7 | |
| Gauging of micro-meter/m | B | 6.040×10−3 | 2.8×10−7 | |
| Linear coefficient of thermal expansion/K−1 | B | 8.10×10−6 | 5.8×10−8 | |
| Temperature/K | B | 1582 | 5.8×10−1 | |
| Distance between electrodes, l/m | 3.533×10−2 | 2.6×10−5 | −4.23×10−5 | |
| Repeatability/m | A | 3.649×10−2 | 2.5×10−5 | |
| Gauging of calliper/m | B | 3.649×10−2 | 2.8×10−6 | |
| Linear coefficient of thermal expansion/K−1 | B | 4.20×10−6 | 5.8×10−8 | |
| Temperature/K | B | 1582 | 5.8×10−1 |
The electrical-resistivity measurements for the molten Fe–C system were conducted as follows. The samples used were Fe-x mass%C (x = 4.33, 4.53, 4.57 and 4.71), which were made from electrolytic iron (99.9%) and carbon powder (99.7%). The alloy samples were put into an alumina Tammann tube (inner diameter: 34 mm) and were melted at 1582, 1587, 1679 or 1803 K in an electric furnace under a flow of 3% H2–Ar gas mixture. The temperature of the sample was measured using an R-type thermocouple beside the sample. When measuring the electrical resistivity of the Fe–C alloys, the temperature of the sample temporary decreased when the probe was inserted into the molten sample and became constant after 30 min. The measurements were then conducted every 10 min for 30 min as follows: electric currents were supplied for ca. 7 s in the −2–2 A range at intervals of 0.5 A. The measurement was conducted at a fixed temperature for each sample. The carbon concentration of the samples was measured via the combustion method using a LECO analyser for carbon and sulphur. The value of carbon concentration was the average of those obtained before and after the measurement.
Molten Ga showed an electrical resistivity of 25.8 × 10−8 Ω·m at 323 K; this value is smaller than the tabulated value6) by 1.5%. This discrepancy remained for the measurements performed at other temperatures. The electrical resistivity of Sn was measured to be 51.2 × 10−8 Ω·m at 670 K, which is 1.7% smaller than the tabulated value;6) however, it is within the range of previously reported values.7,8,9,10) The temperature dependence of the sample was in good agreement with the tabulated and reported values. The uncertainties of the preliminary experimental results will be discussed later with the results obtained for the molten Fe–C system.
Figure 2 shows the relationship between the supplied current and voltage during the electrical-resistivity measurements for the molten Fe–C system. These results were obtained 30 min after the probes were immersed into the molten sample. The results at 1582 and 1587 K showed good linearity, with correlation coefficients higher than 0.99995. On the basis of these results, it is considered that the Ohm’s law applies to these results and thereby the electrical resistances can be derived from the slopes of the linear plots (Fig. 2) using the least-square method. The electrical resistivities were calculated accordingly. The measured values at 1582 K for molten Fe-4.33 mass%C and at 1587 K for Fe-4.57 mass%C were 1.48 × 10−6 and 1.58 × 10−6 Ω·m, respectively. However, as shown in Fig. 2, the results at 1679 K and 1803 K did not show good linearity (correlation coefficients of 0.9969 and 0.9953, respectively, which are lower than those obtained at 1582 and 1587 K). In these cases, the electric current was unstable and the measured current was significantly lower than that tried to be supplied. There were no changes in the appearance of the electrode ends (i.e. the electrode ends were in contact with the molten sample during the measurements) after the experiments at 1582 K and 1587 K. However, the measurements at 1679 K and 1803 K resulted in shorter graphite electrodes. This suggests that the graphite electrodes were dissolved into the sample at these temperatures such that the precision of the measurements was negatively affected.
Relationship between the supplied current (I) and the voltage (ΔV) during the electrical-resistivity measurements for the molten Fe–C system calculated 30 min after the probes were immersed into the melted sample.
The uncertainties in the measured values were determined herein using the guide to the expression of uncertainty in measurement11) (GUM). The major sources of uncertainty in the measurements were as follows: (i) the resistance of the sample, (ii) d1, (iii) d2 and (iv) L. Moreover, ρ values were expressed with their expanded uncertainties (coverage factor k = 2) as follows:
Ga: ρ = (25.8±7.0) × 10−8 Ω·m at 323 K
Sn: ρ = (51.2±6.8) × 10−8 Ω·m at 670 K
Fe – 4.31%C: ρ = (148±7) × 10−8 Ω·m at 1582 K
Fe – 4.57%C: ρ = (158±7) × 10−8 Ω·m at 1587 K
The uncertainties were nearly identical for all the measurements. The main factor for the combined standard uncertainty was the sensitivity coefficient for resistivity, which was determined by π (d12 − 2d22)/(4L). In order to reduce the uncertainty, decreasing the value of (d12 – 2d22) and increasing the value of L would be effective. Thus, d1 and d2 would become half of their original values, resulting in a combined standard uncertainty of 1×10−8 Ω·m for the Fe-4.31 mass%C alloy.
Figure 3 shows the carbon concentration dependence of electrical resistivity for the molten Fe–C alloys compared with the reported values.1,2,3,4) The values measured herein at ca. 1585 K were close to those reported by Ono et al. at 1573 K. The electrical resistivity measured herein showed a drastic increase with carbon concentration; this dependence was also observed by Ono et al. for carbon concentrations larger than 3%. Carbon concentration dependence of electrical resistivity was discussed from the viewpoint of the structure of the molten Fe–C system. Waseda et al.12) analysed the structure of a molten Fe–C alloy via X-ray diffraction and discussed the characteristics of the atomic distribution as follows.
The atomic arrangement of the molten Fe–C system at relatively low carbon concentrations was the same as in the solid system. Thus, the carbon atoms occupy the interstitial sites. A large number of voids are created in the liquid state and carbon atoms can be placed at these voids for concentrations up to 3%C. However, no interstitial sites are created for carbon concentrations higher than 3%. At these loadings, the carbon atoms occupy both the interstitial and substitutional sites. At these carbon concentrations, electrical resistivity showed a drastic increase. This finding suggests a correlation between atomic arrangement and electrical resistivity. Thus, the mean free path of free electrons decreases drastically with carbon concentration at high carbon loadings (i.e. [C] > 3%).
In this study, a new probe was developed on the basis of the DC four-terminal method for measuring the electrical resistivity of the molten Fe–C system using graphite electrodes. The measured values of molten Fe-4.33 mass%C and Fe-4.57 mass%C samples were expressed with expanded uncertainties (coverage factor k = 2) as follows:
Fe-4.31 mass%C: ρ = (148±7) × 10−8 Ω·m (1582 K)
Fe-4.57 mass%C: ρ = (158±7) × 10−8 Ω·m (1587 K)
The electrical resistivity of the molten Fe–C system drastically increased for concentrations larger than 3 mass%C at ca. 1585 K. This can be explained by the atomic arrangement of carbon in the molten iron structure.
This research was supported by JFE 21st Century Foundation. The authors express great gratitude for their support.
