Introduction

The loss of copper in the slag during copper smelting has long been a significant problem,[1] and it is essential to improve the process efficiency by minimizing this loss. Many efforts have been made to fundamentally understand the origin and characteristics of this phenomenon.[2,3]

Generally, the copper loss in the slag can be of two types: chemical loss and mechanical loss. The chemical loss is inherently related to the pyrometallurgical process and can be evaluated by the thermodynamic equilibrium.[4,5,6,7] The major factors determining the change in the solubility of copper in the slag are the oxygen partial pressure, temperature, composition of the slag and matte, and activity of the metal oxide and sulfide.[8,9,10] The mechanical loss of copper in the slag is attributable to the floating particles or unsettled droplets of either metallic copper or sulfide, and their sizes vary widely from a few microns to a few millimeters.[11] The mechanical loss can further be categorized into five types, based on its origin. The first is related to the formation of copper in the slag owing to the temperature or oxygen partial pressure.[12] The second is related to the entrapment of the matte when the SO2 or other gases formed in the matte cross the matte/slag interface.[12,13,14] The third is related to slag tapping in the settler area of the copper flash furnace. Mechanical entrainment can occur owing to the rising of the underlying dense liquid phase during the tapping process.[15] The fourth occurs when the metallic copper penetrates the refractory.[16] Finally, the fifth is related to the attachment of the matte/metal droplets to the solid particles (Fe3O4 and MgAl2O4) in the slag. This interrupts the sedimentation of the droplets. However, the literature on the copper loss attributable to the solid particles is limited.[17,18,19] During flash smelting, the loss of copper because of the attachment of the copper droplets to the solid magnetite phase is a significant industrial problem. It has been reported that magnetite is produced during the combustion of ores using an oxygen-enriched injection gas during the oxygen sprinkle, Noranda, and Outokumpu flash smelting processes,[20,21,22] The generated magnetite forms a mushy zone between the matte and slag layers,[23,24] resulting in the formation of SO2 gas because of the reaction with the matte, which is followed by the flotation of the matte or copper droplets in the slag.[24] In addition, the presence of magnetite increases the viscosity of the slag. This significantly decreases the rate of settling of the droplets.[5] However, there have only been a few studies on the reaction rates between the magnetite phase and the matte.[25,26] Kaiura and Toguri[25] investigated the dissolution rate of magnetite pellets immersed in Fe-S-O and Cu-Fe-S melts at 1523 K. They found that the dissolution of the magnetite is governed by the mass transfer of oxygen in the Fe-S-O and Cu-Fe-S melts. The rate of mass transfer decreased as the oxygen concentration was increased in the Fe-S-O melt. The increase in the Cu concentration in the Cu-Fe-S melt also decreased the dissolution rate of the magnetite because the solubility of oxygen is lower at higher Cu concentrations. They suggested that SO2 gas was not produced under any of the conditions because weight loss of the melting matte did not happen. Asaki et al.[26] evaluated the dissolution rate of rotating magnetite rods in Fe-S-O melts at 1493 K. They confirmed that their experiments were in the absence of SO2 formation and also concluded that the mass transfer of oxygen in the melt is the rate-determining step. Thus, the effect of SO2 gas formation on the dissolution rate of magnetite remains unknown because of a lack of experimental studies, even though it has been suggested that gas formation does occur during industrial smelting processes.

Therefore, we aimed to investigate the effects of the generated SO2 gas on the decrease in the dissolution rate of magnetite by using Cu2S, which ensures gas formation because of its extremely low oxygen solubility. The high-temperature phenomena occurring at the interface between magnetite and Cu2S were directly observed using a novel in-situ observation system.[27] The reaction interface was observed through the magnetite thin film by utilizing the slight transparency of the magnetite phase under visible light. The rate of the reaction between magnetite and Cu2S was evaluated based on the time dependence of the decrease in the magnetite thickness, which was analyzed based on the changes in its brightness during the in-situ observations. The reaction behavior was also analyzed while using FeS instead of Cu2S. Finally, by combining the results of the analyses of the sample quenched during the reaction, the effect of gas formation on the dissolution behavior is discussed.

Experimental

Sample Preparation

Direct-current sputtering was performed on C-plane sapphire substrates (0.85 mm in thickness) to fabricate magnetite thin films at 523 K using a 4-inch (101.6 mm) Fe3O4 target. The sputtering conditions are listed in Table I. Circular magnetite thin films 3 mm in diameter were fabricated using a stainless-steel (SUS) mask (0.3 mm in thickness). The morphologies and phases of the obtained thin films were characterized by field-emission scanning electron microscopy (FE-SEM, JSM-7800F, JEOL Ltd., Japan) and X-ray diffraction (XRD) analysis (Smartlab, Rigaku Ltd., Japan), and spectrophotometer (U-4100, Hitachi High-Tech Corporation, Japan).

Table I Sputtering Conditions for Deposition of Magnetite Film on Sapphire Substrate
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In order to ensure that the reaction state between the magnetite thin films and Cu2S was the same for several trials of the observation, the Cu2S sample (4 mm in diameter and 1.3 mm in thickness) was prepared through the following two steps. First, copper wire (> 99.99 pct) and sulfur lumps (99.9995 pct) were placed in a closed-end quartz tube (internal diameter of 14 mm), which was placed in a closed-end SUS tube (internal diameter of 18 mm) and sealed using a Swagelok® cap in a glove box filled with pure Ar. This assembly was then heated at 673 K for 30 min, 873 K for 30 min, 1273 K for 30 min, and 1473 K for 1 h. The assembly was then removed from the furnace and allowed to cool to room temperature. Second, the obtained homogeneous sulfides were crushed and placed in an alumina tube (internal diameter of 4 mm), which was sealed in a SUS tube in the glove box and then heated at 1473 K for 30 min. The obtained sulfides in the alumina tube were cut into pieces 1.3 mm in thickness. To prepare FeS, iron powder (> 99.9 pct) was used instead of the copper wire. The phases of the fabricated samples were confirmed by XRD analysis, while the sulfur concentrations were determined by the combustion-IR absorption method (carbon/sulfur analysis, EMIA-920, HORIBA, Japan) and determined to be 21 and 38 wt pct for Cu2S and FeS, respectively.

In-Situ Observations

Figure 1(a) shows a schematic diagram of the experimental apparatus used for the in-situ observations of the interface between the magnetite and matte phases at high temperatures. The system consists of an inverted optical microscope and a SUS chamber with a Ta wire heater. A short-pass filter (< 550 nm) was inserted in front of the CMOS camera. The temperature was controlled by measuring the temperature of the graphite just above the sample using a single-color pyrometer from the top of the chamber. The temperature calibration was carried out using the melting point of pure Cu and Si, which was judged by monitoring with the camera. The accuracy of the temperature was ± 1 K. Figure 1(b) shows a magnified image of the sample assembly. Either Cu2S or FeS matte was placed on the magnetite film (1.3-μm-thick) on the sapphire substrate. The surrounding alumina tube helped keep the diameter and thickness of the matte constant during the experiments, as this was important for determining the reaction rate. The inside of the chamber was evacuated (< 6 × 10–3 Pa) and then filled with Ar gas at an oxygen partial pressure of 9 × 10-7 atm, which was measured with an oxygen sensor. The test sample was heated to 1473 K at 200 K/min and held at this temperature for 30 minutes, and the behavior of the interface between the matte and magnetite phases was observed by the bright field observation with a white light (metal halide lamp, 60 W). The recorded movies were analyzed using the image processing software Image J 1.53. It should be noted that the in-plane resolution of the images was 4 μm. A quenched sample was also prepared after holding the Cu2S melt at 1473 K for 60 seconds to evaluate the initial reaction behavior, by turning off the heater to solidify the melt within 15 seconds with a cooling rate of 480 K/min. The quenched sample was physically separated into Cu2S and the substrate parts, and the fractured surface was analyzed using an electron probe microanalyzer (EPMA, JFA-8530F, JEOL Ltd., Japan) and a violet-laser 3D profile microscope (VK-9510, KEYENCE Ltd., Japan).

Fig. 1
figure 1

Schematics of in-situ observation system: (a) entire system and (b) magnified image of sample

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Results and Discussion

Fabrication of Magnetite Thin Film

Figures 2(a) and (b) show SEM images of the surface and cross-section, respectively, of the magnetite thin film fabricated on the sapphire substrate. Figure 2(c) shows the XRD pattern of the thin film along with the diffraction pattern of magnetite (ICSD #35001) and the pattern of the sapphire substrate. The thin film was confirmed to consist of a single phase of magnetite whose (111) plane was exposed. The magnetite thin film consisted of grains several hundred nanometers in size (Figure 2(a)). Further, as can be seen from Figure 2(b), a uniform magnetite film with a thickness of 2.5 μm was obtained, and the growth rate was 0.8 μm/h.

Fig. 2
figure 2

SEM images of (a) surface and (b) cross-section of magnetite thin film and (c) XRD pattern of magnetite thin film fabricated on sapphire substrate

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Figure 3 shows the transmittance characteristic of the magnetite film (2.5 μm in thickness). Although it exhibited strong absorption affected by the d-electrons of Fe[28], the film showed transmittance of maximum 15 pct at 850 nm and several pct even at less than 550 nm. In previous studies, the fabrication of magnetite thin films was performed by either reactive sputtering using an Fe target in conjunction with O2 gas[29] or the post-deposition annealing of FeO films,[30] which is often accompanied by the impurity phases such as FeO and Fe2O3. However, the present direct fabrication is a simpler process and resulted only in a homogeneous magnetite phase. Thus, the approach can be used for the fabrication of uniform magnetite thin films. To be able to exploit the transmittance of the magnetite film and to exclude the radiant light at high temperatures, visible light with a wavelength of less than 550 nm was used for the in-situ observations.

Fig. 3
figure 3

Transmission spectrum of magnetite thin film on sapphire substrate as a function of wavelength

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Results of In-Situ Observations

Interfacial reaction between magnetite and FeS

Figures 4(a)–(c) show snapshots of the interface between magnetite and FeS at 0, 60, and 300 seconds, respectively, after the temperature had reached 1473 K. The captured movie is included as supplementary Movie S-1 (refer to electronic supplementary material). The brightness of the images increased rapidly. This was due to the increase in the transmittance of the magnetite film owing to a decrease in its thickness. All of the magnetite was consumed within 60 seconds, and no gas was formed, as evident from the constant brightness over the entire area. It should be noted that the observed bubbles (dashed circle in Figure 4(b)) were formed because of the entrapment of the atmospheric Ar when the FeS melted on the substrate, as a comparable number of bubbles were observed even in the absence of magnetite. The SO2 bubbles were not observed at the magnetite/FeS interface. It can be explained from the phase equilibration of the FeS-O system reported by Asaki et al.[26] after Stofko et al.[31] As far as the magnetite is dissolved into FeS melt, the total gas pressure (≈ \(P_{\text{SO}_2}+P_{\text{S}_2}\)) is lower than atmospheric pressure. Therefore, the magnetite dissolved quickly into the FeS at the interface without SO2 being formed.

Fig. 4
figure 4

Interfacial morphology during reaction between FeS and magnetite at (a) 0, (b) 60, and (c) 300 s after temperature had reached 1473 K (see Supplementary Movie S-1)

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Interfacial reaction between magnetite and Cu2S

Figure 5 shows snapshots of the interface between magnetite and Cu2S at 0, 60, 300, 600, 900, and 1800 seconds after the temperature had reached 1473 K. The corresponding movie is included as supplementary Movie S-2(a). In contrast to the case for FeS, numerous bubbles were observed at the magnetite/Cu2S interface. This was because SO2 gas was generated by the reaction of magnetite and Cu2S at the interface, as given in Eq. [1]:

Fig. 5
figure 5

Behavior of bubbles at interface between Cu2S and magnetite near Points A and B at (a) 0, (b) 60, (c) 300, (d) 600, (e) 900, and (f) 1800 s after temperature had reached 1473 K (see Supplementary Movie S-2)

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$${\text{Fe}}_{{3}} {\text{O}}_{{4}} ( {\text{s}} )+ {{ 2{\underline {\text{S}}} }}( {\text{in matte}} ) \to 2{\text{SO}}_{{2}} ( {\text{g}} ) \, + { 3}{\underline{{{\text{Fe}}}}} ( {\text{in matte}} )$$
(1)

After 60 seconds, the formation of a small number of bubbles a few tens of microns to a hundred microns in size was observed, as shown in Figure 5(b). The number of small bubbles (10–50 μm) increased significantly at 300 seconds (Figure 5(c)), and larger bubbles formed by the coalescence of the smaller ones. The size of the bubbles increased continuously until 600 seconds (Figure 5(d)). However, no changes were observed after 600 seconds, suggesting that all the magnetite had been consumed. To evaluate the changes in the thickness of the magnetite film, the changes in the brightness at Points A and B, which were arbitrarily selected from the area of the interface without any bubbles, were measured, as shown in Figure 6(a). The intensity increased gradually and became constant after 600 seconds, although continuous bubble formation and aggregation made it difficult to observe the magnetite/matte interface. Thus, a slight deviation in the intensity was inevitable.

Fig. 6
figure 6

Measured changes in brightness (a) at Points A and B and (b) calculated changes in film thickness as functions of holding time

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Because part of the irradiating light is absorbed by the magnetite, the detected intensity (I) is comparable to the transmittance after reflection at the interface. Therefore, the magnetite film thickness was estimated using the Lambert–Beer law, as given by Eq. [2]:

$$d\cdot\alpha =-\text{log}\left(\frac{I}{{I}_{0}}\right)$$
(2)

Here, d is the thickness of the magnetite film and I0 is the intensity of the irradiating light, which corresponds to the intensity in the absence of magnetite (constant intensity in Figure 6(a)). Further, α represents the absorption coefficient of the film. It should be noted that the self-luminescence at the high temperature interface could be ignored because its intensity was negligibly small compared with the intensity of the irradiating light. Because the absorption coefficient of the magnetite film was not constant for wavelengths of less than 550 nm (see Figure 3(a)), an initial thickness of 1.3 μm was used for the evaluation. Figure 6(b) shows the changes in the thickness of the magnetite film at points A and B as functions of the holding time. The thickness change of the whole area is also shown as a color map movie as supplementary Movie S-2(b). The changes in the thickness of the magnetite film at points A and B exhibit a similar trend. The magnetite film thickness decreased constantly, indicating that its reaction with Cu2S progressed and was accompanied by the generation of SO2 gas, as shown in Figures 5(a) and (b). Although the regions with bubbles were avoided during the thickness analyses, since the intensity in these regions was lower owing to the degree of reflection at the interface being lower, the slight deviation in the thickness change was probably attributable to the small bubbles. The magnetite film finally disappeared at 780 seconds, as evidenced by the fact that morphological and brightness changes were not observed (see Figures 5(e) and (f), and Supplementary Movie S-2). Throughout the observations, the formation, coalescence, and expansion of SO2 gas bubbles were observed. In addition, the gas bubbles did not detach from the interface. Thus, the bubbles remaining at the interface probably significantly interfered with the dissolution of the magnetite, because of which its dissolution took much longer as compared with that of FeS.

The reduction in the interfacial area because of the SO2 bubbles would directly affect the time needed for the consumption of the magnetite film. Therefore, the interfacial area was measured from the interfacial morphology (Figures 5(a) through (f)). The changes in the morphology over time are shown in Figure 7. Here, the interfacial area was calculated by subtracting the area of the attached SO2 gas bubbles from that of the entire liquid interface and was normalized with respect to the initial area. In the beginning (0–60 seconds), no significant change in the interfacial area was observed. However, a large decrease was seen after 60 seconds because of the increase in the number of SO2 gas bubbles formed and their coalescence at the interface. After 600 seconds, the area ratio of interface between magnetite and matte remained almost constant at approximately 0.6. The interfacial area continued to decrease until the entire magnetite film had been consumed, implying that a similar decrease may occur during the actual process. If the gas bubbles were to accumulate at the interface, they would significantly inhibit the reaction.

Fig. 7
figure 7

Ratio of reaction area at magnetite/matte interface to total interfacial area as a function of time

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Results of Ex-Situ Analysis

To understand the reaction behavior in the initial stage, the bubble distribution around the interface between Cu2S and magnetite was evaluated by quenching the sample after holding it at 1473 K for 60 seconds. Figure 8(a) shows a laser microscopy image of the fractured surface of the substrate part. It is also represented schematically by the dashed line in Figure 8(b). Numerous bubbles of various sizes (ranging from a few microns to a hundred microns) were observed, and their numbers were much higher than those of the bubbles detected during the in-situ observations. Figures 8(c) and (d) show the height profiles of the typical bubbles along Lines 1 (A-A′) and 2 (B-B′) in Figure 8(a). The bubble bottoms were flat in the case of the large bubbles (∼100 μm) while the small bubbles (1–40 μm) were spherical. This suggests that only the large bubbles became attached to the interface and thus could be detected during the in-situ observations, as shown schematically in left side of Figure 8(b). Therefore, while only a few bubbles were observed at approximately 60 seconds during the in-situ observations (Figure 5(a)), the reaction did occur at the interface, and smaller bubbles were accumulated a little away from the interface. This also suggests that the large number of small bubbles generated at the interface interfered with the dissolution of the magnetite film right from the beginning of the reaction.

Fig. 8
figure 8

(a) Surface image of substrate part obtained using laser microscope and (b) schematic diagram of quenched sample. (c) Shape and height of bubble along Line 1 and (d) that along Line 2 in laser microscopy image. Red curves in (c) and (d) are indicators of the shape of the bubbles (Color figure online)

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Figure 9 shows the elemental mapping results for the sample shown in Figure 8. Although the evaluation was a qualitative analysis because of the rough surface of the sample, most of the regions were confirmed to consist of Cu2S, as Cu and S were detected in these regions. The flat bottoms of the bubbles larger than 100 μm were confirmed as magnetite and sapphire was not exposed. Thus, the remaining bubbles were present on the magnetite film and were not affected by the sapphire substrate. Such bubbles may also be present between the magnetite and matte phases within industrial flash furnaces.

Fig. 9
figure 9

SEM image and elemental mapping results by EPMA for quenched sample (reaction time is 60 s) (Color figure online)

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Quantitative Analysis of Rate of Reaction Between Cu2S and Magnetite

The in-situ observations indicated that the dissolution rate of magnetite was extremely low and that the reaction between Cu2S and magnetite at 1473 K was accompanied by the formation of SO2 gas, which accumulated at the interface. Kaiura and Toguri[25] and Asaki et al.[26] reported that, in the absence of gas formation, the dissolution of magnetite into the matte phase is controlled by the mass transfer of oxygen in the matte phase. In contrast, in the present study, the formation of SO2 gas began immediately as per Eq. [1] because the solubility of oxygen in Cu2S is negligibly low.[32] In such a case, the concentration gradient of Fe in the matte would contribute more to the dissolution rate than would oxygen. Therefore, the mass transfer of Fe in the matte was assumed to be the rate-determining step. The decrease in the interfacial area because of the remaining SO2 gas bubbles (Figure 7) was also considered during the evaluation.

When the dissolution process is controlled by mass transfer in the steady state, the flux of Fe, N, can be expressed by Eq. [3] using the effective reaction rate constant, K:

$$N=K({\left[\text{Fe}\right]}_{\text{s}}-{\left[\text{Fe}\right]}_{\text{b}})$$
(3)

Here, [Fe]s and [Fe]b represent the iron concentration in molten Cu2S at the magnetite/matte interface and that in the bulk, respectively. Further, N (= V/A·d[Fe]b/dt) is the flux, where V and A are the volume of Cu2S and the area of the magnetite/Cu2S interface, respectively. By considering the gradual decrease in the interfacial area, A (Figure 7), the following equation could be obtained:

$$\frac{V}{A(t)}\cdot\frac{{d[\text{Fe}]}_{\text{b}}}{dt}=K({\left[\text{Fe}\right]}_{\text{s}}-{\left[\text{Fe}\right]}_{\text{b}})$$
(4)

If V is constant, then the integration of Eq. [4] from 0 to t yields

$$V\cdot\text{ln}\left(\frac{{[\text{Fe}]}_{\text{s}}-{[\text{Fe}]}_{\text{b0}}}{{[\text{Fe}]}_{\text{s}}-{[\text{Fe}]}_{\text{b}}}\right)=K\cdot{\int }_{0}^{t}A\left(t\right)dt$$
(5)

Here, [Fe]b0 represents the initial Fe content in Cu2S (= 0 in this study). The relationship between the left-hand side of Eq. [5] and \({\int }_{0}^{t}A\left(t\right)dt\) at Points A and B is shown in Figure 10. Note that [Fe]b was estimated from the amount of magnetite dissolved as determined from the change in its thickness (Figure 6(b)). [Fe]s was assumed to be the Fe concentration in the matte under equilibration with the gas, magnetite, and metallic copper. The thermodynamic data reported by Shishin et al.[33] were used to determine [Fe]s, and the calculations were performed using the thermodynamic analysis software FactSage 7.3.

Fig. 10
figure 10

Relationship between \({\int }_{0}^{t}A\left(t\right)dt\) and V·ln([Fe]s-[Fe]b0/[Fe]s-[Fe]b) during dissolution of Fe into molten Cu2S at 1473 K at Points A and B (The line in the figure was obtained from 0 to 600 seconds)

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The relationship was a linear one for both points between 0 and 600 seconds, although a slight deviation caused by the difficulty in determining the thickness was inevitable. The gradients, which represent K, had similar values for the entire interface. After 600 seconds, the gradient was almost zero because most of magnetite had been consumed. The obtained K values for Points A and B for t = 0 to 600 seconds are listed in Table II along with the results for FeS. The mass transfer coefficients for the dissolution of magnetite into molten FeS reported by Kaiura et al.[25] and Asaki et al.[26] are also listed in Table II. The K values for Points A and B were 6.1 × 10–7 and 4.9 × 10–7 m/s, respectively and much smaller than the reported mass transfer coefficients in the case of FeS, which can be as high as 2.3 to 5.9 × 10–5 m/s. In the abovementioned studies, after the magnetite had dissolved in the molten FeS, gas formation did not occur.[25,26] This was also the case during the present study. Thus, it can be concluded that gas formation at the magnetite/Cu2S interface significantly affects the rate of dissolution of magnetite, even though the effect of the decrease in the reaction area because of the accumulation of the gas bubbles (Figure 7) was considered in this study.

Table II Calculated Reaction Rate Constant, K, During Dissolution of Fe Into Molten Cu2S at 1473 K for Points A and B and Reported Mass Transfer Coefficient, k, for Ddissolution of Fe Into FeS
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Mechanism Responsible for Inhibition of Reaction Between Cu2S and Magnetite

Figure 11 shows schematic images of the reaction between Cu2S and magnetite. To begin with, although only bubbles 50–100 μm in size were observed during the in-situ observations, fine bubbles formed continuously and accumulated at and around the interface by the dissolution of the magnetite film (see Figures 5(a) and 11(a)). These small bubbles gradually aggregated, as confirmed during the in-situ observations (see Figures 5(c) and 11(b)). The generated bubbles remained at the interface throughout the holding period (Figure 11(c)). As a result, the dissolution of a 1.3-μm-thick magnetite film took more than 600 seconds. Thus, the K values were extremely small. This delay in the mass transfer of Fe is related to the phenomenon of gas formation owing to following two effects: (1) a decrease in the effective reaction area because of the fine bubbles at the interface, including the bubbles smaller than the in-plane resolution during the in-situ observations (4 μm) and (2) the narrowing of the flow path for Fe diffusion by the bubbles that accumulated around the interface. In contrast, the dissolution rate of magnetite in FeS in the absence of gas formation was much higher. Therefore, preventing gas formation and ensuring that the bubbles formed do not accumulate at the interface is essential for increasing the reaction rate. Based on the fact that the generated bubbles became attached to the magnetite film, it can be assumed that the surface tension of Cu2S is less than the sum of the magnetite/Cu2S interfacial tension and the surface energy of magnetite, even though a detailed evaluation was not possible because of a lack of physical data. Therefore, it would be difficult to remove the bubbles from the matte-magnetite interface spontaneously, and hence the design of the process to prevent the gas formation at the interface is key to reduce copper loss. It would be also effective to add forced convection into the melt to easily detach the bubbles formed at the matte-magnetite interfere.

Fig. 11
figure 11

Schematic diagram of reaction mechanism between Cu2S and magnetite over time. (a) Initial bubble formation at 0 to 120 s, (b) agglomeration of bubbles at 120 to 600 s, and (c) the final state at 600 to 1800 s

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Summary

In this study, the interfacial reactions between magnetite (Fe3O4) and matte (Cu2S, FeS) at 1473 K were analyzed using a novel in-situ observation method. The results obtained can be summarized as follows:

  1. 1.

    By exploiting the slight transparency of magnetite to visible light, in-situ observations were performed on a magnetite thin film fabricated by sputtering. The morphological changes in the film could be observed clearly, and the decrease in its thickness could be evaluated quantitatively based on the change in the brightness at the interface.

  2. 2.

    During the reaction between FeS and magnetite, no gas was observed at the interface, and the magnetite dissolved immediately into the FeS.

  3. 3.

    The reaction between Cu2S and magnetite was accompanied by the formation of SO2 gas at the interface. The SO2 bubbles agglomerated and accumulated around the interface, and the time required for the dissolution of a 1.3-μm-thick magnetite film was more than 600 seconds. The effective reaction rate coefficient was determined to be 4.9 to 6.1 × 10–7 m/s based on the assumption that the dissolution process is controlled by the mass transfer of Fe into the molten Cu2S. The strong inhibition of the reaction by the formation of SO2 gas can be attributed to the following factors: (1) the reduction in the effective reaction area by the fine bubbles at the interface and (2) the narrowing of the flow path for Fe diffusion by the bubbles that accumulated around the interface.