Thermal Diffusivity and Conductivity of Fe₃O₄ Scale Provided by Oxidation of Iron

Abstract

The thermal diffusivity and conductivity of Fe₃O₄ scale have been determined with the laser flash method. Fe₃O₄ scale was provided by oxidation of iron plates at 823 K in Ar containing 0.84%H₂ and 15.6%H₂O. The scale was characterized by scanning electron microscopy and X-ray diffraction analysis for high temperature use to identify the phase of the scale. The thermal diffusivity and conductivity derived for the Fe₃O₄ scale decrease from 1.1 × 10⁻⁶ m²s⁻¹ to 4.1 × 10⁻⁷ m²s⁻¹ and from 3.5 Wm⁻¹K⁻¹ to 1.7 Wm⁻¹K⁻¹, respectively, with increasing temperature from room temperature to 676 K. The effective thermal conductivity of iron oxide scale with Fe₃O₄ has been evaluated assuming that Fe₃O₄ occupies 30% of the total scale thickness, suggesting the impact of the presence of Fe₃O₄ is about ten percent.

1. Introduction

In the water spray cooling process after hot rolling, it is essential to extract heat from the hot steel to the cooling water via the iron oxide scale tens of micrometers thick that is produced on the steel surface during hot rolling, and the actual scale formed on the commercial heavy steel plates during hot rolling consists of 70%FeO and 30%Fe₃O₄ in volume, for example.¹⁾ The cooling process is also analyzed by computer-aided simulation, which requires thermal diffusivity and conductivity values of the component phases as input data. There have been a few reports regarding the thermal diffusivity and conductivity of FeO scale provided by oxidation of iron.^2,3,4,5) For Fe₃O₄, there are some extant data only for sintered samples.^6,7) However, the authors’ previous experience says that sintered FeO is not an alternative to FeO scale.^2,3) Similarly, hence it would be required to measure the properties of Fe₃O₄ scale provided by oxidation of iron as well to simulate heat extraction via the scale more accurately. Consequently, the present work aims to determine the thermal diffusivity and conductivity of Fe₃O₄ scale as a function of temperature with the laser flash method, and to confirm whether the presence of Fe₃O₄ should be considered for computer-aided simulation via the effective thermal conductivity of the scale.

2. Experimental

2.1. Sample Preparation

Iron plates (99.99% purity, 1.0 mm thick) were used as substrates. These iron substrates were oxidized at 823 K for 604.8 ks in Ar containing 0.84%H₂ and 15.6%H₂O, of which the oxygen partial pressure is 7.1× 10⁻¹⁹ Pa where Fe₃O₄ is thermodynamically stable, but FeO cannot be formed.⁸⁾ In the present work, six samples (A–F) with Fe₃O₄ scale were prepared: Samples A–D were used for laser flash thermal diffusivity measurements. Sample E was subject to scanning electron microscopy (SEM) analysis along with samples A–D. Sample F was prepared for X-ray diffraction (XRD) analysis, which was conducted in the range from room temperature to 1173 K. The thickness of the Fe₃O₄ scale was evaluated from the SEM images. The density of the Fe₃O₄ scale was estimated by the lattice constant from the XRD results.

2.2. Laser Flash Measurement

The laser flash method was applied to measure the thermal diffusivity. Before measurements, graphite coating was applied onto the sample surface to increase the laser absorption. In measurements, one surface of the sample was heated by a laser pulse, and the resulting temperature rise at the other surface was recorded by an infrared radiometer. The temperature rises always smaller than 1 K, for example it is only about 0.2 K for the measurement of sample A at room temperature. In the same manner as the previous reports,^2,3) this temperature rise curve was analyzed with curve-fitting (CF) method⁹⁾ to obtain the thermal diffusivity of Fe₃O₄ scale on iron substrate with the thickness data, being converted to the thermal conductivity with the product of density and specific heat capacity (637.7 J kg⁻¹ K⁻¹, 715.0 J kg⁻¹ K⁻¹, 786.6 J kg⁻¹ K⁻¹, 840.7 J kg⁻¹ K⁻¹, 871.8 J kg⁻¹ K⁻¹ and 893.0 J kg⁻¹ K⁻¹ at room temperature, 476 K, 676 K, 872 K, 1025 K and 1177 K¹⁰⁾). The thicknesses at each temperature were revised with the consideration of linear expansion of Fe₃O₄ and Fe^7,11) from the values obtained at room temperature.

To avoid the α–γ transformation of Fe at 1184 K,¹²⁾ measurements were conducted in the range from room temperature to 1177 K for sample A, 1025 K for sample B, 872 K for sample C and 676 K for sample D. In these measurements, the samples were placed in a vacuum of 1.2 Pa to avoid further oxidation. The heating rate was on the whole 4 K min⁻¹ while 15 K min⁻¹ was employed in the temperature range (473 K–873 K) where FeO may decompose.¹³⁾ All the measurements were done about 10 min after thermal equilibrium was established at desired temperatures. The thermal diffusivity was also measured during the cooling cycle for reference.

3. Results and Discussion

3.1. Sample Details

The thicknesses of Fe₃O₄ scale and Fe substrate were 38 μm and 0.99 mm at room temperature, respectively. Then density of Fe₃O₄ scale was estimated by the lattice constant (a=8.40 Å) from the XRD results as 5.19 g cm⁻³.

Figures 1(a)–1(d) show SEM cross-sectional images of Fe₃O₄ scale for samples A, C and D after laser flash measurements with heating and for sample E as-grown, in which images Fe has brighter contrast and Fe₃O₄ has darker contrast. It can be seen that sample E has Fe₃O₄ scale only. This sample had no thermal history due to laser flash measurement. Thus, all the samples before the measurements had Fe₃O₄ scale only. Sample D also has Fe₃O₄ scale only although it was heated up to 676 K. On the contrary, there is FeO phase near the scale/Fe interface in sample C heated up to 872 K. This FeO would be generated by reaction between Fe₃O₄ and Fe at high temperature. For sample A heated up to 1177 K, almost all Fe₃O₄ was reduced to FeO. In addition, the image of sample B has been similar to that of sample A.

Fig. 1.

SEM cross-sectional images of samples measured up to (a) 1177 K (Sample A); (b) 872 K (Sample C); (c) 676 K (Sample D); along with (d) Sample E.

These observation results are in consistency with the XRD profiles on sample F, as shown in Fig. 2. There are only Fe₃O₄ peaks detected below 873 K, whereas there are only FeO peaks above 1023 K. Figure 1(b) shows that there is FeO phase near the scale/Fe interface at 873 K; however, there are no FeO peaks in Fig. 2. This would be due to the penetration depth of X-ray.

Fig. 2.

High-temperature XRD profiles. (Online vesion in color.)

3.2. Thermal Diffusivity and Conductivity of Fe₃O₄ Scale

Figures 3(a) and 3(b) show values of thermal diffusivity and conductivity of Fe₃O₄ scale (α_Fe3O4 and k_Fe3O4) for samples A and D as a function of temperature. First, focus on sample A. The values of α_Fe3O4 and k_Fe3O4 at room temperature are 1.1 × 10⁻⁶ m² s⁻¹ and 3.5 W m⁻¹ K⁻¹, respectively. With increasing temperature, the respective values decrease to 4.1 × 10⁻⁷ m² s⁻¹ and 1.7 W m⁻¹ K⁻¹ at 676 K, above which they increase until 872 K and then decrease again. With decreasing temperature, both values slightly increase; however, they do not go back to the initial values but are rather closer to the values of FeO before the correction of interfacial heat resistance.^2,3) This is because Fe₃O₄ was reduced to FeO at temperatures higher than 873 K.

Fig. 3.

(a) Thermal diffusivity and (b) conductivity of Fe₃O₄ scale plotted against temperature.

In sample D, in contrast, the values of α_Fe3O4 and k_Fe3O4 during the heating cycle are in good agreement with those during the cooling cycle and also with those during the heating cycle in sample A. The values of α_Fe3O4 and k_Fe3O4 for samples B and C during the heating cycle have almost followed those for samples A and D. Thus, it is suggested that the thermal diffusivity and conductivity for Fe₃O₄ scale decrease from 1.1 × 10⁻⁶ m² s⁻¹ to 4.1 × 10⁻⁷ m² s⁻¹ and from 3.5 W m⁻¹ K⁻¹ to 1.7 W m⁻¹ K⁻¹, respectively, with increasing temperature from room temperature to 676 K.

Figure 4 shows the values of k_Fe3O4 compared with reported values.^6,7) All these data show negative temperature dependence but there is discrepancy in the values. The thermal conductivities are affected by porosities, however they are almost in the same order of magnitude. The thermal conductivities measured by Akiyama⁶⁾ are much larger than others, which reason is considered to be the effect of the coatings. It is considered that the present data are reliable as for Fe₃O₄ scale provided by oxidation. However, there is an interface between Fe₃O₄ scale and iron substrate in the present samples, which may affect the thermal conductivity values should be discussed in the future work.

Fig. 4.

Thermal conductivity of Fe₃O₄ scale in comparison with those of sintered Fe₃O₄.

3.3. Effective Thermal Conductivity of Iron Oxide Scale with Fe₃O₄

As mentioned in Introduction, the main component of the actual scale is FeO; however, there is also Fe₃O₄ near the scale surface.¹⁾ Hence, the effective thermal conductivity (k_scale) of iron oxide scale with Fe₃O₄ is estimated by the following predictive equation:   

$$\frac{d_{\text{scale}}}{k_{\text{scale}}}=\frac{f_{\text{FeO}}{d}_{\text{scale}}}{k_{\text{FeO}}}+\frac{f_{\text{Fe}3\text{O}4}{d}_{\text{scale}}}{k_{\text{Fe}3\text{O}4}}$$(1)

where d_scale is the total thickness of the scale and f is the volume fraction. f_Fe3O4 is assumed as 30%, because Endo et al.¹⁾ suggest that actual scale consists of 70%FeO and 30%Fe₃O₄. Figure 5 shows the effective k_scale estimated as above, compared with measured values of FeO³⁾ and oxide scale.¹⁾ The differences between effective k_scale and k_FeO are 11.2%, −7.1% and −11.6% from room temperature to 676 K. Thus, it is considered that the presence of Fe₃O₄ has little effect in computer-aided simulation for heat extraction in the actual water spray cooling process.

Fig. 5.

Effective thermal conductivity of iron oxide scale with Fe₃O₄.

4. Conclusions

• The thermal diffusivity and conductivity derived for Fe₃O₄ scale decrease from 1.1 × 10⁻⁶ m² s⁻¹ to 4.1 × 10⁻⁷ m² s⁻¹ and from 3.5 W m⁻¹ K⁻¹ to 1.7 W m⁻¹ K⁻¹, respectively, with increasing temperature from room temperature to 676 K.

• Assuming that Fe₃O₄ occupies 30% of the scale thickness, the effective thermal conductivity of iron oxide scale is about ten percent different from FeO.

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