Dynamic Surface Tension Behavior of Liquid Iron during Carburization and Decarburization Processes

Abstract

A new technique to study the kinetics of the carburization and decarburization processes of liquid iron is proposed. A liquid iron droplet was electromagnetically levitated in a CO–CO₂ gas mixture during carburization and decarburization, and its surface oscillation was continuously recorded using a high-speed camera. The surface tension varied depending on each elementary step in the carburization and decarburization processes. This behavior was caused by transient adsorption and desorption of oxygen on the surface of the liquid iron accompanied by CO and CO₂ gases. The kinetics of the carburization process were discussed and the conclusion was drawn that the desorption rate of oxygen adatoms in the form of CO₂ was predominantly controlled by the gas-phase mass transfer.

1. Introduction

Carburization and decarburization reactions of liquid iron are the most important reactions in the production of iron and steel. Many researchers^{1,2,3,4,5,6,7,8)} have measured the reaction rates of carburization and decarburization, and investigated the rate-determining step under various conditions. Ito et al.²⁾ measured the reaction rate of carburization using an electromagnetic levitation technique with CO–CO₂ gas mixtures. They reported that the concentrations of carbon and oxygen in liquid iron rapidly increased when the CO partial pressure in the gas phase was increased during carburization. Subsequently, the carbon and oxygen concentrations gradually reached constant values. Thus, the carburization and decarburization behavior was studied based on concentration changes in the liquid iron. In the studies cited above, the samples were quenched after a certain time and chemical analysis was conducted for the quenched samples. Consequently, using this approach, it is not possible to study the rapid adsorption and desorption processes at the liquid iron surface.

Previously, we used the oscillating droplet method combined with a gas–liquid equilibrium method to demonstrate that oxygen acts as a strong surfactant in liquid iron, whereas carbon has a negligible effect on the surface tension.^9,10) The equilibrium constant of the oxygen adsorption reaction at the liquid iron surface and surface excess of oxygen have been determined in previous studies.^9,10) In the present study, based on surface adsorption data, we propose a continuous technique for studying the carburization and decarburization processes by measuring the surface tension using the oscillating droplet method.

2. Experimental

2.1. Gas–liquid Equilibrium Method

Oxygen and carbon activities were controlled using Ar–He–CO–CO₂ gas mixtures based on the following equilibrium reactions:   

$$\text{2CO(g)}+{\text{O}}_{\text{2}}\text{(g)}={\text{2CO}}_{\text{2}}\text{(g),}$$(1)

  

$$\text{C(s)}+{\text{CO}}_{\text{2}}\text{(g)}=\text{2CO(g)}\text{.}$$(2)

The activity of the gaseous components (a_i: i = CO, CO₂ and O₂) is defined as a standardized partial pressure relative to 10⁵ Pa and the carbon activity (a_C) is relative to graphite at 10⁵ Pa. The values of a_O2 and a_C were calculated using the equilibrium constants determined from the thermochemical data in the literature,¹¹⁾ and were confirmed by the quantitative chemical analysis of oxygen and carbon dissolved in the iron sample after quenching.

2.2. Experimental Procedure

The experimental apparatus and technique used were similar to those described in detail elsewhere.^9,10) High-purity (99.9972 mass%) iron prepared using an ion-exchange method¹²⁾ was used as the sample. The iron sample of about 0.9 g was placed on a quartz sample holder and positioned in a levitation coil. The quartz tube (inner diameter: 18 mm) was evacuated to a pressure of the order of 10⁻² Pa using a diaphragm pump and a turbo molecular pump, and then filled with high-purity Ar gas (99.9999 vol.%). The iron sample was initially levitated in an Ar gas atmosphere using the electromagnetic levitation (EML) facility, and an Ar–He–CO–CO₂ gas mixture was introduced into the quartz tube to control the oxygen and carbon activities. Ar and He gases were purified using an Mg-deoxidizer kept at 873 K before introduction into the quartz tube. The liquid iron was carburized and decarburized by changing the CO and CO₂ activities in the gas phase. The total gas flow rate was 2 L·min⁻¹ at 273 K and 101.325 kPa, and it was estimated that the gas reached the sample after approximately 3 s based on the volume of gas tube.

The temperature of the sample was measured using a single-color pyrometer (wavelength: 0.9 μm; temperature resolution: 1 K; sampling rate: 2 Hz). The pyrometer was calibrated at the melting temperature of iron (1808 K). The temperature of the sample was controlled by changing the flow rates of Ar and He gases in the gas mixture and kept at 1873 ± 15 K. Images of the oscillating liquid iron droplet were recorded by a high-speed camera with a resolution of 256 × 256 pixels at a frame rate of 250 fps from the top of the sample.

Figure 1 shows the experimental conditions presented in the form of a log a_O2 vs log a_C plot at 1873 K. The initial condition (i) was controlled at log a_O2 = −12 and log a_C = −3 using a CO/CO₂ gas mixture with a_CO = 5 × 10⁻² and a_CO2 = 1 × 10⁻⁴. The sample was kept under this condition for 30 min to achieve equilibrium between the liquid iron and the gas phase. The surface tension was measured and the initial activities of CO and CO₂ gases were then changed to a_CO = 2 × 10⁻¹ and a_CO2 = 4 × 10⁻⁴ to obtain condition (ii) as indicated in the figure. Thus, the change from condition (i) to (ii) corresponds to a carburization process with constant a_O2. The reverse process from condition (ii) to (i) is a decarburization process.

Fig. 1.

Experimental conditions for carburization from condition (i) to (ii) and the decarburization from condition (ii) to (i) at 1873 K presented as a log a_O2 vs log a_C plot.

In addition to the continuous experiments, some samples were quenched during carburization and decarburization and quantitative chemical analysis of oxygen and carbon was carried out to determine the time dependence of the composition, and also to assure the gas–liquid equilibrium. The carbon and oxygen contents were analyzed using an infrared-absorption method with a LECO CS-444 LS Carbon/ Sulfur Determinator and a LECO TC-436 Oxygen-Nitrogen Analyzer, respectively.

2.3. Determination of Surface Tension

The surface tension of liquid iron was calculated from the modified Rayleigh equation proposed by Cummings and Blackburn.^13,14) The surface oscillation frequency and translational frequency of the center of gravity were determined through fast Fourier transform using sequential images of the oscillating droplet. The details of the frequency analysis were explained with consideration of sample rotation in our previous work.⁹⁾ The sample radius was calculated using the density of liquid iron reported by Nishizuka et al.,¹⁵⁾ which is given as:   

$$\rho /\mathrm{k}\mathrm{g}·{\mathrm{m}}^{-3}=7\mathrm{\hspace{0.17em} }041.0-0.9316\times \left(T-1\mathrm{\hspace{0.17em} }808\right),$$(3)

where T is the absolute temperature.

3. Results

3.1. Carburization Process

Figure 2 shows the time dependence of the surface tension of liquid iron during carburization, corresponding to a change from condition (i) to (ii) as indicated in Fig. 1. The oxygen activity in the gas phase was kept at log a_O2 = −12. Here, the gas composition was changed at 0 s. The temperature variation caused by changing the gas composition was within 15 K. Although the oxygen activity in the gas phase was kept constant during carburization, the surface tension decreased significantly to 1675 mN·m⁻¹ within 10 s of changing the gas composition [designated by (A) in Fig. 2]. Following this, the surface tension gradually increased and became constant within 300 s [designated by (B)].

Fig. 2.

Surface tension behavior of liquid iron during carburization from condition (i) to (ii) at 1873 K (solid circles). The surface tension was also estimated from the oxygen contents obtained from the quenching experiments (triangles).

3.2. Decarburization Process

After the carburization process described in the preceding section, decarburization from condition (ii) to (i) was conducted. The result is shown in Fig. 3. The temperature variation caused by changing the gas composition at 0 s was within 15 K. Although the oxygen activity in the gas phase was held constant at log a_O2 = −12 during the decarburization process, the surface tension rapidly increased to 1870 mN·m⁻¹ within 10 s of changing the gas composition [designated by (C) in Fig. 3]. Subsequently, the surface tension gradually decreased and became constant after 150 s [designated by (D)].

Fig. 3.

Surface tension behavior of liquid iron during decarburization from condition (ii) to (i) at 1873 K (solid circles). The surface tension was also estimated from the oxygen contents obtained from the quenching experiments (triangles).

3.3. Compositional Change during Carburization and Decarburization

Table 1 shows the oxygen and carbon contents in mass (w_O and w_C) obtained from the chemical analysis of samples quenched during carburization and decarburization. The values of a_O2 and a_C were calculated from w_O and w_C using the following thermodynamic relationships and data from the literature:^11,16)   

$$\frac{\text{1}}{\text{2}}{\text{O}}_{\text{2}}\left(\text{g}\right)=\underset{\_}{\text{O}}\text{ (in Fe)},$$(4)

  

$$log{a}_{{\text{O}}_2}=\text{2}\times \left(log{f}_{\text{O}}+log{w}_{\text{O}}-log{K}_{(4)}\right),$$(5)

  

$$log{f}_{\text{O}}=e_{\text{O}}^{\text{O}}{w}_{\text{O}}+e_{\text{O}}^{\text{C}}{w}_{\text{C}},$$(6)

  

$$\text{C(s)}=\underset{\_}{\text{C}}\text{ (in Fe)},$$(7)

  

$$log{a}_{\text{C}}=log{f}_C+log{w}_{\text{C}}-log{K}_{(8)},$$(8)

  

$$log{f}_{\text{C}}=e_{\text{C}}^{\text{C}}{w}_{\text{C}}+e_{\text{C}}^{\text{O}}{w}_{\text{O}},$$(9)

where O and C represent oxygen and carbon dissolved in liquid iron, K_(i) is the equilibrium constant of reaction (i), f_O and f_C are the activity coefficients of oxygen and carbon, respectively, relative to 1 mass% of oxygen and carbon in liquid iron, and e_i^j is an interaction parameter of j for i.¹⁶⁾

Table 1. Chemical contents of oxygen and carbon, w_O and w_C, obtained from chemical analysis and the oxygen and carbon activities.

Process	Time	Results of chemical analysis		Calculated aO2 and aC using wO and wC		Estimated σ from aO2
	t/s	wO/mass%	wC/mass%	log aO2	log aC	σ/mN·m–1
Carburization	0	0.0029	0.028	–12.0	–3.2	1813
	10	0.0120	0.024	–10.8	–3.2	1653
	60	0.0054	0.044	–11.5	–3.0	1762
	200	0.0043	0.065	–11.7	–2.8	1785
	350	0.0036	0.074	–11.9	–2.7	1805
Decarburization	0	0.0030	0.101	–12.0	–2.6	1813
	10	0.0008	0.095	–13.2	–2.6	1873
	60	0.0015	0.110	–12.7	–2.6	1856
	120	0.0022	0.097	–12.3	–2.6	1835
	400	0.0033	0.082	–12.0	–2.7	1813

Figure 4 displays the time dependence of a_O2 and a_C during the carburization and decarburization processes. Panels (A)–(D) correspond to the surface tension behavior presented in Figs. 2 and 3. The values of a_O2 and a_C calculated from w_O and w_C agree well with the values calculated from the CO/CO₂ gas compositions used in the experiments at 0 s, which means that a_O2 and a_C were well-controlled using the gas–liquid equilibrium method. During carburization, a_O2 in the liquid iron rapidly increased for 10 s after changing the gas composition, which is designated as process A. Subsequently, a_O2 in the liquid iron gradually decreased with time and approached the equilibrium value (process B). During carburization, a_O2 in the liquid iron rapidly decreased for 10 s after changing the gas composition (process C). Finally, a_O2 in the liquid iron gradually increased with time and approached its initial value (process D).

Fig. 4.

Time dependence of activities of carbon and oxygen during carburization (solid circle) and decarburization (open squares) at 1873 K presented as a plot of log a_O2 vs log a_C.

4. Discussion

4.1. Surface Tension Behavior during Carburization and Decarburization

The surface tension behavior during carburization and decarburization presented in Figs. 2 and 3 is discussed in this section. The overall carburization reaction is expressed by:   

$$\text{2CO(g)}\to \underset{\_}{\text{C}}\text{(in Fe)}+{\text{CO}}_2(\mathrm{g}),$$(10)

which consists of the following five elementary reactions:   

$$\text{CO(g)}\to \text{CO(ad)},$$(11)

  

$$\text{CO(ad)}\to \text{C(ad)}+\text{O(ad)},$$(12)

  

$$\text{C(ad)}\to \underset{\_}{\text{C}}\text{(in Fe)}\hspace{0.17em}\hspace{0.17em}\text{and}\hspace{0.17em}\hspace{0.17em}\text{O(ad)}\to \underset{\_}{\text{O}}\text{(in Fe),}$$(13)

  

$$\text{O(ad)}+\text{CO(g)}\to {\text{CO}}_{\text{2}}\text{(ad)},$$(14)

  

$${\text{CO}}_{\text{2}}\text{(ad)}\to {\text{CO}}_{\text{2}}\text{(g)}$$(15)

where (ad) represents adsorption at the iron surface. The rapid decrease in the surface tension during process A in Fig. 2 is caused by reactions (11) and (12). The number of oxygen atoms adsorbed at the iron surface increases because of the occurrence these reactions. This is supported by the experimental observation of the increase in a_O2 in the liquid iron for 10 s after changing the gas composition (process A in Fig. 4). Thus, when liquid iron is carburized by increasing the CO activity from 5 × 10⁻² to 2 × 10⁻¹ in the gas phase, oxygen and carbon atoms adsorbed and dissolved into the iron melt (reactions (12) and (13)), and their activities approached to the line presenting a_CO = 2 × 10⁻¹ in the gas phase. This led to the rapid decrease in the surface tension. The similar behavior was also reported by Ito et al.²⁾ They conducted the carburization experiments for levitated liquid iron droplets using CO–CO₂ gas mixtures, and concluded that the rate was controlled by the mass transfer in the melt during the initial stage, which is consistent with the present result.

The adsorbed carbon atoms then dissolve into the iron melt, which is expressed by reaction (13). Conversely, the accumulated excess oxygen adatoms on the iron surface react with CO gas, and desorb as CO₂ gas, which is expressed by reactions (14) and (15). During the desorption process, the surface tension gradually increases as shown in Fig. 2 (process B). This behavior can also be explained by the slower decrease in a_O2 in the liquid iron from 10 to 350 s along the line presenting a_CO = 2 × 10⁻¹ in the gas phase (process B in Fig. 4). Thus, during process B, the liquid iron is not in equilibrium with the gas phase, but is in a transition state from the initial condition (i) to (ii). The kinetics in the process B is discussed later in the section 4. 3.

The surface tension behavior during the decarburization process shown in Fig. 3 can be also explained by the change in the number of adsorbed oxygen atoms. When the CO activity was decreased from 2 × 10⁻¹ to 5 × 10⁻² by changing the gas composition, the number of adsorbed oxygen atoms decreased, which was caused by the reverse reactions of (11) and (12). This decrease in the number of adsorbed oxygen atoms results in the rapid increase in the surface tension (process C in Fig. 3). This is supported by the experimental observation of a decrease in a_O2 in the liquid iron for 10 s after changing the gas composition (process C in Fig. 4).

Subsequently, the transient deficiency of adsorbed oxygen atoms is recovered by supplying oxygen atoms from CO₂ gas, as expressed by the reverse reactions of (14) and (15). As a result, the surface tension gradually decreases because of increasing oxygen adatoms (process D in Fig. 3). This behavior is also consistent with the slower increase in a_O2 in the liquid iron from 10 to 400 s (process D in Fig. 4).

4.2. Changes in Fractional Surface Coverage and Oxygen Surface Excess during Carburization and Decarburization

The equilibrium constant of the oxygen adsorption reaction on the liquid iron surface, K_ad, is expressed in the form of a Langmuir isotherm:   

$$K_{\text{ad}}=\frac{{\theta }_{\text{O}}}{a_{{\text{O}}_{\text{2}}}{\hspace{0.17em}}^{1/2}(1-{\theta }_{\text{O}})}$$(16)

where θ_O is the fractional surface coverage. The value of K_ad was determined as a function of temperature in our previous study as:⁹⁾   

$$\begin{array}{r}ln{K}_{\text{ad}}=\frac{\left(4.27\pm 0.04\right)\times {10}^4}{T}-\left(10.1\pm 0.3\right)\\ \left(1\mathrm{\hspace{0.17em} }773–2\mathrm{\hspace{0.17em} }073K\right).\end{array}$$(17)

From these relationships, the value of θ_O was estimated and presented as a function of a_O2 in Fig. 5. The change in θ_O during the carburization and decarburization processes is also plotted in this figure. The θ_O value was initially 0.25 at log a_O2 = −12 and then increased to 0.57 at 10 s after changing the gas composition for carburization. Subsequently, θ_O gradually returned to its initial value. For the decarburization process, the θ_O decreased from 0.25 to 0.08 at 10 s after changing the gas composition before returning to its initial value.

Fig. 5.

Relationship between the fractional surface coverage of oxygen adatoms on the liquid iron for carburization (solid circles) and decarburization (open squares), and oxygen activity (solid line) at 1873 K.

The surface excess of oxygen, Γ_O, can be obtained from the fractional coverage using the following relationship:   

$${\Gamma }_O={\theta }_O·{\Gamma }_O{\hspace{0.17em}}^{\mathrm{s}\mathrm{a}\mathrm{t}},$$(18)

where Γ_O^sat is the surface excess of oxygen at saturation. The value of Γ_O^sat is taken to be 18.6 × 10⁻⁶ mol·m⁻². as determined in our previous study.⁹⁾ Figure 6 shows the relationship between Γ_O and log a_O2 together with the change in Γ_O during carburization and decarburization. Thus, from monitoring the oscillation of the liquid iron droplet, we can gain information about the rapid transient change in the adsorption behavior of oxygen at high temperatures.

Fig. 6.

Relationship between the surface excess of oxygen on the liquid iron for carburization (solid circles) and decarburization (open squares), and oxygen activity (solid line) at 1873 K.

4.3. Kinetics in the Carburization Process

The rate-determining step during carburization is discussed in this section. There are three steps for the carburization process:

1. Mass transfer in the gas phase

2. Chemical reactions on the liquid iron surface

3. Mass transfer in the liquid iron

The carburization process is divided into two processes: processes A and B, as indicated in Figs. 2, 4, 5 and 6. Process A was rapid and was complete within 10 s. This means that both gas-phase mass transfer and the chemical reactions taking place on the surface were fast. This was followed by process B, which took place slowly, over the course of 350 s. Considering the mass transfer in the liquid iron during process B, the surface tension values were estimated using the oxygen contents in the liquid iron obtained from the quenching experiments. The oxygen activities were calculated from the oxygen contents as presented in Table 1. The surface tension was previously determined as a function of oxygen activity as:^9,10)   

$$\begin{array}{l}\begin{array}{l}\sigma /\text{mN}\cdot {\text{m}}^{-1}\\ =\left(1\mathrm{\hspace{0.17em} }925\pm 65\right)-\left(0.455\pm 0.034\right)\times \left(T-1\mathrm{\hspace{0.17em} }808\right)\end{array}\\ -0.155Tln\left(1+exp\left(\frac{\left(4.27\pm 0.04\right)\times {10}^4}{T}-\left(10.1\pm 0.3\right)\right)a_{{\text{O}}_2}^{1/2}\right)\end{array}$$(19)

The surface tension was estimated using Eq. (19) with the obtained oxygen activities, and is presented in Table 1 and in Fig. 2. The estimated values are in good agreement with the data obtained by the continuous surface tension measurements, which indicates that there is no significant chemical potential gradient of oxygen between the surface and the inside of the liquid iron during process B. A similar observation was also made for the decarburization process (process D), and the estimated values are presented in Table 1 and Fig. 3; these results support the above conclusion.

The dissolved oxygen atoms transferred from the iron melt to the gas phase in the form of CO₂ during the process B, which is expressed as:   

$$\frac{\mathrm{d}{n}_{\text{O}}}{A\mathrm{d}t}=\frac{k_{\text{g}}}{RT}(P_{{\text{CO}}_{\text{2}}}^{\text{b}}-P_{{\text{CO}}_{\text{2}}}^{\text{s}})$$(20)

Here, n_O is the amount of O atoms in the melt in mole, A [m²] is the surface area of the melt and t [s] is the time. The term on the left-hand side corresponds to the change in the oxygen atoms in units of mole per unit area and time. This is calculated from Table 1 during process B from 10 to 60 s. k_g [m·s⁻¹] is the gas film mass transfer coefficient and R is the gas constant (8.314 J·mol·K). P_CO2^s and P_CO2^b are the partial pressures of CO₂ in Pa on the surface and in the bulk gas phase. P_CO2^s is calculated from the equilibrium relationship between CO₂, O₂ and C using a_O2 and a_C given in Table 1. P_CO2 in the bulk gas phase is 4.0 × 10 Pa (a_CO2 = 4.0 × 10⁻⁴). T is the absolute temperature in the boundary film in the gas phase, which is given by the average of the temperatures on the surface and in the bulk gas phase [T = 0.5 × (1873 + 300) = 1086.5 K]. Thus, k_g was estimated to be 7.1 × 10⁻² m·s⁻¹ for process B from the experimental data.

Ito et al. also conducted the carburization experiments for levitated liquid iron droplets using CO–CO₂ gas mixtures [2]. They concluded that the rate was initially controlled by the mass transfer in the melt, and after that, the rate was controlled by the counter diffusion of CO and CO₂ in the gas phase. This well explains the behaviors found in the processes A and B obtained in the present study.

Finally, the following modeling using the Ranz–Marshall correlation is attempted for further discussion. The Sherwood number (Sh) is expressed in terms of the Reynolds number (Re) and the Schmidt number (Sc) according to the Ranz–Marshall correlation for mass transfer for a sphere under forced convection:^17,18)   

$$Sh=2.0+0.6R{e}^{1/2}S{c}^{1/3}.$$(21)

The dimensionless numbers are defined by the following functions as:   

$$Sh=\frac{k_{\text{g}}d}{D_{{\text{CO}}_{\text{2}}}},$$(22)

  

$$Re=\frac{{\rho }_{\text{g}}{v}_{\text{g}}d}{{\mu }_{\text{g}}},$$(23)

  

$$Sc=\frac{{\mu }_{\text{g}}}{{\rho }_{\text{g}}{D}_{{\text{CO}}_{\text{2}}}}.$$(24)

Here, d is the diameter of the droplet [m], which was estimated to be 6.3 × 10⁻³ m from the sample mass and density given in Eq. (3), D_CO2 is the diffusion coefficient of CO₂ in He gas [m²·s⁻¹], ρ_g is the density of the gas [kg·m⁻³], v_g is the velocity of the gas [m·s⁻¹] and μ_g is the viscosity of the gas [Pa·s].

The following assumptions were made to evaluate k_g using the Ranz–Marshall correlation.

1. Oxygen adatoms desorbed in the form of CO₂ gas, which diffused from the liquid iron surface to the bulk gas phase through the boundary film.

2. The temperature of the boundary film in the gas phase is given by the average of the temperatures on the surface and in the bulk gas phase. D_CO2 ρ_g v_g μ_g are estimated at the average temperature (1086.5 K).

3. Helium is the dominant gas species during process B (P_He = 0.8 × 10⁵ Pa).

The viscosity and diffusion coefficients for the He–CO₂ system were estimated using the Chapman–Enskog equation.¹⁹⁾ The values of Re and Sc were estimated to be 3.2 and 2.1, respectively. Using these values, Sh and k_g were determined to be 3.4 and 2.7 × 10⁻¹ m·s⁻¹, respectively for process B. Thus, the estimated value is four times as large as the experimental one. However, it greatly depends on the temperature of the boundary film in the gas phase. Considering the uncertainty in the gas film temperature, they roughly agree with each other.

5. Summary

The surface tension of liquid iron was measured continuously during carburization and decarburization. The surface tension rapidly decreased in the initial stages of carburization and then gradually returned to its initial value. This behavior was caused by the transient adsorption and desorption of oxygen at the liquid iron surface accompanied by CO and CO₂ gases. From the results obtained, the kinetics of the carburization process were studied, leading to the conclusion that the desorption rate of oxygen adatoms was predominantly controlled by the gas-phase mass transfer. Thus, we have proposed a new technique to study the kinetics of carburization and decarburization processes of liquid iron in a noncontact manner.

Acknowledgement

The authors thank Prof. T. Tsukada (Tohoku University), Prof. T. Hibiya (Keio University) and Assoc. Prof. S. Ozawa (Chiba Institute of Technology) for their helpful comments and discussion. This work was financially supported by SENTAN, Japan Science and Technology Agency (JST) and ISIJ Research Promotion Grant. One of the authors (KM) acknowledges support of the Grant-in-Aid for JSPS Fellows.

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