High-Temperature Oxidation of Steel under Linear Flow Rates of Air and Water Vapor—An Experimental Determined Set of Data

Abstract

High-temperature oxidation phenomena play a crucial role in steel production and processing. The development of new alloying concepts, the modification of production routes due to the decarbonization of steelmaking, and increasing quality demands will additionally stimulate research activities on high-temperature oxidation. Within the scope of this publication, the oxidation behavior of an unalloyed steel was investigated by means of thermogravimetric (TG) and metallographic analysis. The TG measurements were performed with a simultaneous thermal analyzer in combination with a water vapor generator and a mass spectrometer for quality control. Experiments were conducted in a temperature range from 900 to 1200 °C under various oxidation atmospheres, containing synthetic air and water vapor, with different linear flow rates of the oxidizing medium. According to the thermogravimetric data, an evaluation method is introduced to obtain direct kinetic data for linear and parabolic scale growth. The influence of the experimental parameters on high-temperature oxidation is discussed in detail.

1. Introduction

Over recent decades, high-temperature oxidation of iron and steel has been a widely studied topic to establish an improved knowledge of the underlying mechanisms [1,2,3,4,5]. During steel production and processing, the product surface is exposed to temperatures up to 1250 °C and a wide variation of oxidizing atmospheres. Generally, high-temperature oxidation phenomena may be divided into external and internal. Various internal oxidation mechanisms can be observed, especially in alloyed steels or steels contaminated by trace elements, which may lead to essential quality losses of the product [6,7,8,9,10,11,12,13,14]. Current trends in the steel industry, such as the increased use of obsolete scrap, the corresponding increase of the content of residuals and tramp elements, or the replacement of natural gas with hydrogen for industrial burners, just to name a few, will raise new oxidation issues. The present paper introduces an experimental setup, designed to investigate the influence of widely varying thermal cycles and atmospheres on high-temperature oxidation. Combining the gas supply, water vapor generator, simultaneous thermal analysis, and mass spectrometer provides the precise adjustment of experimental conditions and delivers highly reproducible measurement results. A wide variety of industrial processes for steel production may thus be simulated in the future, including continuous casting, reheating, hot rolling, and annealing.

The first Investigations mainly address external oxidation, the calculation of growth rates for linear and parabolic scale growth, the influence of temperature on scale formation, and the impact of increasing water vapor contents on growth rates. The results also indicate that experimental parameters, such as gas flow rate, significantly affect high-temperature oxidation rates and, therefore, need to be adjusted carefully. The present work provides an excellent basis for extending future research activities toward simulating internal oxidation phenomena, such as grain boundary oxidation or liquid metal embrittlement.

1.1. Oxidation Kinetics and Influencing Factors

The progression of scale layer thickness, “x”, can be described in a simplified way by the linear and parabolic rate law in Equations (1) and (2). In 1 and 2, k_l denotes the linear and k_p the parabolic rate constant, t is the time in seconds, and C_l and C_p are constant values. Tammann was the first to derive the parabolic growth law from Fick’s first law in 1920 [15,16]. For applications to industrial processes, oxidation is often described similarly by referring to weight gain per area, “W.” Pilling and Bedworth initially described the parabolic relationship in Equation (3) in 1923 [17]. The integration constants are omitted under the boundary condition that the scale layer thickness or the mass gain are zero at time t = 0.

Table 1. SI units of x, W, k_l, and k_p.

$\mathit{x}$	${\mathit{k}}_{{\mathit{l}}_{\mathit{x}}}$	${\mathit{k}}_{{\mathit{p}}_{\mathit{x}}}$	$\mathit{W}$	${\mathit{k}}_{{\mathit{p}}_{\mathit{W}}}$
m	m·s−1	m2·s−1	kg·m−2	kg2·m−4·s−1

summarizes the SI units of x, W, k_l, and k_p. Values for k_l and k_p are usually determined via thermogravimetric methods, where changes in mass due to the reaction of the base material with oxygen are recorded [18,19,20,21,22,23,24,25]. The layer and mass-related scaling constants can be converted into each other.

$$\frac{dx}{dt}=k_{l_x} \to x=k_{l_x}t+C_{l_x}$$

(1)

$$\frac{dx}{dt} ~ J=-D \frac{\mathsf{\Delta }c}{x} or \frac{dx}{dt}=\frac{k_{p_x}}{x} \to x^2=2k_{p_x}t+C_{p_x}$$

(2)

$$\frac{dW}{dt}=\frac{k_{p_W}}{W} \to W^2=2k_{p_W}t+C_{p_W}$$

(3)

A linear, uniform increase in scale layer thickness can be observed mainly at the beginning of the oxidation. Only a thin oxide layer is present, through which iron ions are transported quickly. The scaling rate is controlled by the transfer and adsorption/dissociation of oxygen from the oxidation medium to the scale surface and the oxidation reaction itself. As the oxidation time becomes longer, the scale layer thickness increases, which increases the transport path of iron ions and subsequently reduces the quantity available for the oxidation reaction. As a result, the diffusion-controlled transport of iron ions for the oxidation reaction becomes the limiting factor, and the scaling follows a parabolic rate law [23,24,26,27,28].

The oxidation rate is influenced significantly by the chemical composition of steel, especially by the elements chromium and silicon [19,29,30,31,32,33,34,35,36,37,38,39], and experimental parameters, such as temperature [5,19,21,22,23,24,25,40,41,42,43], surface condition [44], type of gas, and gas quantity. The influence of water vapor and the gas flow rates are explained in more detail.

1.1.1. Water Vapor

In steel processing, water vapor is part of most oxidizing atmospheres, such as in continuous casting resulting from the air–mist–cooling of the strand surface, in reheating furnaces from combustion, and in rolling from cooling water, just to name a few examples. The presence of water vapor in an oxidation atmosphere significantly increases the scaling rate [21,38,41,45,46,47,48,49]. A detailed explanation of the underlying mechanism was performed by Rahmel and Tobolski [45]. As the scale grows, the plasticity decreases and local fissures form at the interface between the metal and oxide due to flow obstructions, similar to the “edge effect” reported by Engell [50]. A supporting effect of the colliding oxide layers occurs at the corners, which impedes the flow of the scale layer and causes it to detach from the metal surface. Thus, the gap between the metal surface and the scale layer inhibits further diffusion of iron ions and decreases the oxidation rate. Water vapor can penetrate the gaps formed in this way and react with the metal surface to metal oxide and hydrogen, which diffuses to the oxide layer and reduces it. The resulting water vapor can diffuse back to the metal surface while the iron ions and electrons migrate outwards through the oxide layer. This process repeats until oxide bridges, which span the resulting gaps, are formed. The resulting pores in the oxide layer show that the water vapor/hydrogen mixture has degraded through reduction. Tuck et al. [47] found that the formation of pores in the scale does not have to occur in an oxidation atmosphere containing water vapor, but scaling is nevertheless increased compared to pure oxygen. The increased plasticity of the scale explains this behavior due to a better movement of dislocations, preventing an early loss of contact between the scale and steel.

1.1.2. Flow Rate

The amount of the oxidation medium supplied per unit of time is crucial for the oxidation progress. As already mentioned, iron diffuses fast during the phase of linear oxidation. A higher gas velocity at the interface accelerates the transport from the gas medium to the scale, the adsorption and dissociation, and finally, the oxidation rate. If the quantity of oxidation medium provided at the interface is equal to or greater than the quantity of iron ions transported by diffusion, the oxidation speed becomes independent of the further increased quantity and velocity of the oxidation gas. This is referred to as a critical gas velocity [24,28].

2. Materials and Methods

2.1. Equipment and Methods

All thermogravimetric oxidation experiments were conducted using a Netzsch STA 449 F3 Jupiter (STA, Simultaneous Thermal Analysis, Netzsch GmbH & Co. Holding KG, Selb, Germany) with a DTA-TG (Differential thermal analysis—Thermogravimetric analysis) sample carrier for freely suspended samples. The complete setup includes various precision pressure controllers and mass flow controllers (MFCs, Bronkhorst High-Tech B.V., Ruurlo, The Netherlands), a water vapor generator aSteam DV-2 (aDROP Feuchtemeßtechnik GmbH, Fürth, Germany), a quadrupole mass spectrometer QMS 403 C Aëolos (Netzsch GmbH & Co. Holding KG, Selb, Germany), several thermostats (Netzsch GmbH & Co. Holding KG, Selb, Germany), and various control valves (Netzsch GmbH & Co. Holding KG, Selb, Germany). Figure 1 shows a schematic flow chart of the gases and the system components and Figure 2 is a schematic illustration of the experimental setup. The gases arrive first at the top side of the sample and a shielding gas (argon) is supplied on the bottom of the furnace, which is permanently switched on to protect the balance system. The balance system has an accuracy of 0.1 µg and continuously records the mass change during experiments. Temperature control is performed by two type S thermocouples located in the sample holder and beside the sample with an accuracy of +/−2 °C.

At the gas outlet, a partial gas flow is continuously analyzed by the mass spectrometer, so the adjusted gas atmosphere can be controlled; see Figure 3. Only impeccable experiments are evaluated regarding the gas supply, and misinterpretations due to a delayed gas can be avoided, as shown in Figure 3b, where the water vapor was delayed for approximately 5 min.

The amount of gas supplied by the MFCs is up to 500 mL·min⁻¹ and their linear precision and repeatability precision is ±1% F.S. (percentage of Full Scale) and ±0.2% F.S., respectively. Contrary to the gases provided by the MFCs, water vapor is directly supplied from the water vapor generator. The operating principle can be summarized as follows: distilled water from the integrated water tank is fed into an electrically heated evaporator unit. The following chamber mixes the resulting water vapor with an added carrier gas. An additional heater ensures a preheating of the carrier gas and that the temperature in the mixing chamber does not fall below the dew point of the resulting gas mixture. Without a carrier gas, it is possible to perform oxidation experiments with 100% saturated steam. The maximum gas amount of H₂O corresponds to a value of approximately 415 mL·min⁻¹. Thermostats with a temperature of 200 °C are used at the transfer lines to avoid condensation in the system after the water vapor generator. The uniformity of the water vapor flow rate is controlled by the mass spectrometer, so constancy can be ensured over a complete experiment; see Figure 3.

In the experimental case, an isobaric system can be assumed, whereby Gay-Lussac’s law can be applied to calculate the supplied gas volume at each oxidation temperature under the assumption that thermal expansion for each oxidation gas is equal. For a given gas volume, the gas velocity in the furnace tube (inner diameter 26.5 mm) can be calculated from the cross-sectional area reduced by the space requirement of the sample and sample holder. For simplicity, a homogeneous speed distribution is assumed in the furnace. The flow rate of shielding gas, which arrives from the balance system, is not considered in those calculations because it never reaches the sample.

2.2. Oxidation Program and Parameters

In the framework of the research presented, pure (technical) iron was investigated. The chemical composition is shown in

Table 2. Chemical composition analyzed via optical emission spectroscopy.

C [wt.%]	Mn [wt.%]	Si [wt.%]	P [wt.%]	S [wt.%]
0.0127	0.0167	<0.001	0.0045	0.0038

.

This raw material was cut with the wet abrasive cutting machine ATM Brilliant 220 (ATM Qness GmbH, Mammelzen, Germany) to prepare samples measuring 13 mm × 12.2 mm × 2 mm. To suspend the specimen, a hole measuring 2.5 mm in diameter was drilled in the upper part of the sample. No additional grinding or polishing took place after cutting and the surface roughness corresponded to a Sa value of approximately 1 µm. In contrast to the Ra value, the Sa value represents the (3D) areal average roughness. For subsequent examinations, the exact dimensions of each sample were measured. To avoid contamination of the sample, a cleaning step with ethanol and acetone was performed right before each experiment. Preceding an experiment, the furnace chamber, balance system, and gas supply lines were evacuated three times and purged with argon. This ensured identical initial conditions for each test and eliminates the risk of pre-oxidation during the inert heating process. Prior to the experiment, a baseline compensation with the same time–temperature–gas program was performed with an inert Al₂O₃ sample to eliminate the influence of the incident gas flow and the thermal buoyancy on the weight signal.

Figure 4 shows the time–temperature–gas program for the oxidation tests performed. All samples were slowly heated to the target temperature (900−1000−1100−1200 °C) at 15 °C·min⁻¹, followed by a homogenization for 5 min, ensuring uniform conditions at the sample surface. Heating and homogenization were performed under argon 5.0 purging at a constant purging rate. Immediately afterwards, the oxidation gas, either synthetic air (80 vol.-%N₂ and 20 vol.-%O₂) or a synthetic air/water vapor mixture, was injected into the furnace and the oxidation was started for a period of 60 min. The parameters for the oxidation experiments are summarized in

Table 3. Experimental parameters.

Experiment	Temperature [°C]	Atmosphere	Time [min]	Flow Rate [mL·min−1]	Gas Velocity b [cm·s−1]
1	900	synthetic air	60	10	0.15
2	900	synthetic air	60	25	0.37
3	900	synthetic air	60	100	1.49
4 (I; II)	900	synthetic air	60	200	2.98
5	900	synthetic air	60	300	4.47
6	900	synthetic air	60	400	5.96
7	1000	synthetic air	60	200	3.23
8	1100	synthetic air	60	200	3.48
9	1200	synthetic air	60	25	0.47
10	1200	synthetic air	60	100	1.87
11 (I, II)	1200	synthetic air	60	200	3.74
12	1200	synthetic air	60	400	7.48
13	1200	synthetic air	60	500	9.35
14	1200	synthetic air with 9.4 vol.-%water vapor	60	302 a	4.13
15	1200	synthetic air with 20.6 vol.-%water vapor	60	344 a	4.71
16	1200	synthetic air with 30.6 vol.-%water vapor	60	392 a	5.37
17	1200	synthetic air with 40.3 vol.-%water vapor	60	458 a	6.27
18(I, II)	1200	synthetic air with 50.1 vol.-%water vapor	60	548 a	7.51

^a flow rate at 100 °C; ^b gas velocity at oxidation temperature; (I; II) experiment performed twice.

. After the oxidation time, the gas supply was switched back to inert to preserve the state of high-temperature oxidation and avoid post-oxidation. The furnace tube was flushed simultaneously with argon 5.0 and nitrogen, and the sample was cooled with a cooling rate of −60 °C·min⁻¹.

The structure of the final scale layer was investigated by metallographic methods. The samples were cold embedded before cutting to ensure that the scale and steel/scale interface was protected. After the cutting operation, another cold embedding was carried out for easier handling during grinding (grit 180−320−600−1200) and polishing (9 µm and 3 µm). The samples were analyzed using an optical light microscope (Polyvar Reichert-Jung MEF 2 and Keyence VHX7000, KEYENCE International, Mechelen, Belgium).

3. Results and Discussion

Table 3 summarizes all relevant parameters for the oxidation experiments. Unless otherwise stated, the flow rate refers to the calibration temperature of the MFC. Depending on the gas quantity and oxidation temperature, the gas velocity in the furnace tube ranged from 0.15 to 9.35 cm·s⁻¹. The Reynolds number was determined with respect to the temperature and gas velocity. A maximum value of approximately 8 indicates a completely laminar gas flow; therefore, laminar conditions can be assumed for all experiments.

The first step to a uniform evaluation of all experimental results is to define the onset of the mass gain curve, determined by the intersection of two tangents [51]. The first tangent is applied in the time range of the inert atmosphere and corresponds to a horizontal straight line. The second tangent is applied in the initial mass gain range, whereby smaller discontinuities of the measurement curve are not considered. The defined onset point represents the starting point for the standardized generation of mass gain curves. A mathematical description based on the results of the oxidation experiments is performed by using a regression model. As mentioned, the scaling of steel is described by a combination of linear and parabolic oxidation.

To obtain the linear oxidation constant, k_l, the initial part of the measured mass gain curve is fitted by linear regression (Equation (4)) using the data points of the first 100 s. If a transition from linear to parabolic oxidation takes place before 100 s, the range of the measuring points considered must be adjusted. Afterwards, the time, t_t, where a transition to diffusion-controlled growth occurs can be determined precisely by analyzing the deviation squares from the mass gain curve and the linear regression at each measuring point. The time that exceeds a deviation higher than a pre-defined factor represents the start of diffusion-controlled oxidation. The pre-defined boundary factor is usually set to 0.1, but if required, it is adjusted individually to achieve the best-fitting results. To compensate discontinuities in the measurement curve, especially in the initial phase, the deviation squares are averaged over a range of 25 s.

$$W=k_l\ast t$$

(4)

The mathematical description of the diffusion-controlled part is performed via a parabolic function. Due to dividing the regression curve into two areas, an additional coefficient “a” is needed to ensure a continuous function; see Equation (5). The slopes of the linear and parabolic oxidation regime must be identical at the transition time, t_t, and it can be described mathematically by the first derivative of the two functions at this point; see Equation (6). By using a starting value for k_p, a first value for a can be determined. The exact evaluation of k_p and a is performed iteratively by minimizing the deviation squares between the measured mass gain curve and the parabolic regression. The evaluation is entirely automatic and usually does not require any manual correction. Thus, uncertainties that would arise from a human evaluation are avoidable. The complete evaluation procedure is shown schematically in Figure 5.

$$W^2=k_p\ast t+a \to W=\sqrt{k_p\ast t+a}$$

(5)

$$k_l=\frac{k_p}{2\ast \sqrt{k_p\ast t_t+a}}\to a={\left(\frac{k_p}{2k_l}\right)}^2-k_p\ast t_t$$

(6)

Figure 6a shows the results of the weight increase for the test series from 900 to 1200 °C. The dashed lines for the oxidation temperatures 900 and 1200 °C indicate an experiment repetition to ensure reproducibility. For better comparability, the mass gain is related to the sample surface. The flow rate of synthetic air is 200 mL·min⁻¹. Based on the investigated steel grade and the experimental temperatures, a scale that mainly consists of wustite is expected but in the area of the scale/gas interface, magnetite and hematite may also form [5,52,53]. An increase in temperature leads to an enhancement of oxidation due to increased diffusion. The mass increase for 900 °C is approximately 28 mg·cm⁻² after 60 min. For 1000 °C, it is 49 mg·cm⁻², and for 1100 °C, 81 mg·cm⁻². The mass gain at 1200 °C is approximately 110 mg·cm⁻². The slope of the linear oxidation segment is only slightly influenced by the temperature, indicating that the transfer from the gas and adsorption/dissociation of oxygen is also a rather fast process at 900 °C. However, a lower temperature leads to a significantly faster transition from linear to parabolic oxidation due to the limited diffusion of iron ions. The scale thickness quickly reaches a level at which diffusion is not sufficient for a constant mass gain. The values obtained for k_l, k_p, and t_t are summarized in

Table 4. Values for k_l, k_p, and t_t in 200 mL·min⁻¹ synthetic air for different temperatures.

Temperature [°C]	Gas Medium	kl [mg·cm−2·s−1]	tt [s]	kp [mg2·cm−4·s−1]
900	synthetic air	0.12	29	0.17
1000		0.15	85	0.43
1100		0.16	126	1.10
1200		0.17	169	2.56

and Figure 6b.

In order to ensure that the results are independent of the gas velocity in the furnace tube, the purging rate of air was varied for 900 and 1200 °C. The results for 1200 °C are shown in Figure 7a,b. In addition to the 200 mL·min⁻¹ purging rate, as commonly used (3.74 cm·s⁻¹ at 1200 °C), tests were carried out for 25, 100, 400, and 500 mL·min⁻¹. This corresponds to a gas velocity in the furnace tube of 0.47, 1.87, 7.48, and 9.35 cm·s⁻¹, respectively.

For the lowest gas velocity, the linear and parabolic oxidation segments are significantly influenced by the purging rate, whereby a linear mass gain is observed for almost the whole experiment. The total mass gain is approximately 80 mg·cm⁻². An increase in gas velocity intensifies oxidation drastically in the early oxidation stage, and an earlier transition from a linear growth characteristic to a parabolic one occurs. The transition time, t_t, ranges from 84 to 2468 s and increases significantly with decreasing gas velocity. In the parabolic range, oxidation is hardly influenced by gas velocity and the parabolic rate constant stays approximately the same. Thus, the mass gain curves equalize, and the final mass gain does not depend on the gas purging rate. Consequently, if the oxidation time exceeds 30 min, a gas velocity in the furnace tube of around 1.87 cm·s⁻¹ is sufficient to achieve results irrespective of the gas quantity, resulting in a final mass gain of roughly 110 mg·cm⁻² after 60 min. In the linear oxidation segment, the differences in the mass gain become smaller for a gas velocity higher than 7.48 cm·s⁻¹. For the experiments at 1200 °C with a gas velocity higher than 3.74 cm·s⁻¹, a discontinuity in the mass gain curve becomes visible after about 2000 s. At this time, the “edge effect” due to flow obstruction of the scale causes the scale layer on one side to lift off completely. The oxidation rate decreases later during the experiment because of the interrupted iron ion diffusion path, as the mass gain on this site is limited to the oxygen uptake during wustite transformation to magnetite and hematite.

Figure 8a,b show the mass gain at 900 °C for a gas velocity from 0.15 up to 5.96 cm·s⁻¹ and correspond to a flow rate of 10 up to 400 mL·min⁻¹. As in the experiments at 1200 °C, an increase in gas velocity intensifies oxidation, especially in the early (linear) stage. The mass gain is notably influenced at the lowest investigated gas velocity of 0.15 cm·s⁻¹. For a gas velocity higher than 0.37 cm·s⁻¹, a similar mass gain is achieved after 60 min and the parabolic rate constant stays approximately the same. The final mass gain is around 28 mg·cm⁻². In the linear range, the differences in the mass gain get smaller for a gas velocity higher than 4.47 cm·s⁻¹. The transition time, t_t, decreases from 1247 s for the lowest gas velocity to 19 s for the highest gas velocity.

Table 5. Values for k_l, k_p, and t_t at 900 and 1200 °C for different gas velocities.

900 °C
Gas velocity [cm·s−1]	0.15	0.37		1.49		2.98		4.47		5.96
kl [mg·cm−2·s−1]	0.009	0.02		0.08		0.12		0.15		0.17
tt [s]	1247	335		54		29		23		19
kp [mg2·cm−4·s−1]	0.05	0.17		0.16		0.17		0.17		0.18
1200 °C
Gas velocity [cm·s−1]	0.47		1.87		3.74		7.48		9.35
kl [mg·cm−2·s−1]	0.03		0.10		0.17		0.26		0.31
tt [s]	2468		310		169		96		84
kp [mg2·cm−4·s−1]	1.32		2.44		2.56		2.48		2.41

and Figure 9 summarize the values for the oxidation constants, k_l and k_p, and the transition time, t_t.

According to the literature section, the results of the gas variation experiments at 900 and 1200 °C can be explained as follows (see Table 5 and Figure 9). A higher gas velocity at the sample surface favors mass transfer and adsorption/dissociation of oxygen. Thus, a high gas velocity results in initially faster oxidation (higher k_l). However, oxidation cannot be increased to infinity because areas where adsorption/dissociation can take place are limited, so linear oxidation becomes more similar for higher gas velocities; see Figure 7 and Figure 8. Related to k_l, the transition time, t_t, at high gas velocities is far less affected compared to at low gas velocities. The necessary mass gain for a transition from linear to parabolic oxidation increases slightly with decreasing gas velocity due to the fact that the amount of iron ions required for linear growth can be maintained longer since mass transfer and adsorption/dissociation of oxygen are lower; see Figure 7 and Figure 8. During parabolic oxidation, the diffusion of iron ions controls the growth rate of the oxide layer. The thicker the layer, the slower the growth rate and vice versa. Hence, the different oxide layer thicknesses balance after a while and k_p is approximately steady. This occurs when the gas supply is higher than the critical gas velocity. As a consequence of the lower diffusion at 900 °C, k_l, k_p, and t_t are shifted to lower values compared to 1200 °C. However, the trends of the determined data remain the same; see Figure 9.

In a study by Abuluwefa et al. [24], at a temperature of 1150 °C, a critical gas velocity of 4.3 cm·s⁻¹ was determined for an overall constant mass gain in the parabolic range. Below this value, the gas velocity influenced the oxidation rate significantly. Compared to the value obtained by Abuluwefa et al. [24], the values in this study are significantly smaller. In studies from the early 1930s, values for the critical velocity at 927 and 1230 °C were determined with 2.7 and 2.0 cm·s⁻¹, respectively [5,54,55]. The obtained value of 1.87 cm·s⁻¹ at 1200 °C is similar to this value, but at 900 °C, it (0.37 cm·s⁻¹) differs significantly. According to the results, the range of the gas velocity influencing parabolic oxidation drops with decreasing oxidation temperature because of the lower diffusivity of the iron ions.

For oxidation experiments in laboratories (e.g., thermogravimetric analysis), the critical gas velocity is an essential parameter for the investigation of oxidation experiments as the gas supply can significantly influence the results, especially for short oxidation times. For industrial processes, the gas velocity is difficult to describe respectively since, in many cases, neither the atmosphere, nor the speed of oxidation medium supply, can be controlled entirely. Furthermore, turbulent atmospheric conditions (e.g., secondary cooling zone in continuous casting) will probably lead to location-dependent high gas velocities. Thus, the data generated in laboratory experiments improve the overall understanding of the process and may serve as input data for industrial process simulations.

Figure 10a shows the resulting mass gain for water vapor variation experiments at 1200 °C. The purging rate of synthetic air is 200 mL·min⁻¹ for all experiments. A higher volume fraction of water vapor means a higher total gas quantity. The experiment with 50.1 vol.-%water vapor corresponds to a theoretical gas quantity of 548 mL·min⁻¹ at 100 °C and was performed twice. The rate constant for linear oxidation is almost independent of the water vapor content. Only in atmospheres that contain higher water vapor contents (above 30.7 vol.%), a slight increase of k_l noticeable. It can be concluded that adsorption/dissociation of O₂ on the scale surface is the time-controlling step for k_l and the dissociation of H₂O is considerably slower due to more complex reactions at the interface. However, the transition from linear to parabolic oxidation is smoother in its presence. The linear/parabolic transition time, t_t, is in the range of 120 to 173 s. Compared with the previously explained experimental series, there is no clear pattern for the transition time, t_t. For up to 40.3 vol.-%water vapor in the oxidation medium, t_t is almost unaffected and basically corresponds to that of pure synthetic air. The slight variations are due to measurement errors. The presence of water vapor favors parabolic scaling and consequently improves the diffusion of the iron ions through the scale. However, in the range of linear scaling, this is not yet decisive since the provision of oxygen is the rate-determining step. As a result, there is no noticeable change in the transition time. For the highest water vapor content in the oxidation medium, there is a slight decrease in the transition time, which cannot be explained with the hypothesis, just discussed. The meager increase in k_l should not be responsible for the decrease of t_t. Consequently, it can be concluded that a further mechanism is affecting the transition time, which has to be studied in more detail. For a water vapor content of 9.4 vol.%, the mass gain increases to approximately 145 mg·cm⁻², which corresponds to an increase of approximately 30% compared to synthetic air. A further rise in the water vapor content to 20.6 vol.-%results in a mass gain of 161 mg·cm⁻². At a water vapor content of 30.7, 40.3, and 50.1 vol.%, the mass gain increases to 170, 175, and 180 mg·cm⁻², respectively. The increased scaling in water vapor atmospheres is attributable to the mechanisms described in the literature section. With increasing water vapor content in a mixture with synthetic air, the influence of water on the mass gain decreases. Scale detachments are compensated in the presence of water vapor resulting in a larger area for diffusion of iron ions to the outside and, therefore, in a massive increase in scaling. The differences for lower water vapor contents in the oxidation medium are particularly distinct since the compensation is just starting. With further increasing water vapor content in the oxidation medium, the scale mostly remains in complete contact with the specimen surface during oxidation. As a result, the outward diffusion of iron ions remains almost constant and the influence of water vapor on scaling decreases at higher contents.

Table 6. Values for k_l, k_p, and t_t at 1200 °C in a mixture of 200 mL·min⁻¹ synthetic air with different water vapor contents.

Temperature [°C]	Gas Medium	kl [mg·cm−2·s−1]	tt [s]	kp [mg2·cm−4·s−1]
1200	synthetic air with 0.0 vol.-%H2O	0.17	169	2.56
	with 9.4 vol.-%H2O	0.17	157	3.68
	with 20.6 vol.-%H2O	0.17	173	6.80
	with 30.6 vol.-%H2O	0.18	158	8.08
	with 40.3 vol.-%H2O	0.18	172	8.64
	with 50.1 vol.-%H2O	0.19	120	10.44

and Figure 10b summarize the values attained for k_l, k_p, and t_t.

Figure 11a,b shows a comparison of the steel/scale interface for the oxidation temperatures of 900 and 1200 °C and 200 mL·min⁻¹ synthetic air after 3600 s of oxidation. The scale layer at 900 °C is still in contact with the steel surface, while at 1200 °C, a lift-off from the steel surface is notable. Due to the presence of oxygen and the ongoing reactions at the outer surface of the scale, wustite is transformed to magnetite and finally to hematite. The transformation is visible as a bright gray layer on the scale outside; see Figure 11b. The optical interpretation of the wustite transformation is based on an evaluation performed by Chen et al. [46]. The scale layer itself hardly shows any pores at 900 °C, while the complete scale layer at 1200 °C is covered with pores. For the 1200 °C sample, an incorrect metallographic preparation can largely be excluded since the other examined samples do not show any accumulation of pores. In addition, a localized occurrence of the pores in the scale is recognizable, which also contradicts the metallographic preparation as the source. A higher tendency to pore formation in the detached scale was found among others by Engell et al. [50]. The change in the scale morphology could be explained by the progressing transformation of wustite and the necessary diffusion processes of the iron ions to reach the reaction interfaces. Furthermore, density changes and changes in the crystal structure of the scale layer occur. However, it should be noted that Chen et al. [46] found no increased tendency to the formation of porosities in a detached scale during the wustite transformation. Compared to the experimental parameters in this publication, the experiments performed by Chen et al. [46] were at lower temperatures, which could be a reason for the differences. The exact processes leading to this occurrence of the scale cannot be clearly determined based on this series of experiments alone and further investigations are still required. The scales at 1000 and 1100 °C are similar to the 900 °C sample.

The samples oxidized in a mixture of air and water vapor, shown in Figure 12a,b, show a significantly denser scale with a lower quantity of pores than those that oxidized in synthetic air. The appearing pores are located at the steel/scale interface. It can be concluded that the void formation theory described by Rahmel and Tobolski [45] is not primarily responsible for the increased oxidation in the presence of water vapor for the present experiments. As mentioned by Tuck [47], the appearance of voids in the scale does not always occur. Nevertheless, oxidation is still increased in water vapor due to the increased flowability of the scale, which ensures a permanent contact of the steel and scale, resulting in a higher outward diffusion of iron ions.

4. Conclusions

In the framework, pure iron was isothermally oxidized in a temperature range from 900 to 1200 °C in various atmospheres containing synthetic air and water vapor and with different linear flow rates. The following results can be highlighted:

• An iterative regression model was presented to attain values for k_l, k_p, and the transition time t_t where oxidation changes from linear to parabolic. The measured mass gain curve is approximated by a linear and parabolic function, considering that the slope of both functions is identical at the transition point linear/parabolic to ensure an overall continuous function.
• For oxidation with synthetic air, an increase in temperature only leads to a slight increase in the linear oxidation constant, k_l, whereas the transition time, t_t, increases significantly. Furthermore, the parabolic oxidation constant, k_p, becomes considerably larger with increasing temperature.
• A higher water vapor content in a constant flow rate of synthetic air significantly increases scaling respectively the parabolic oxidation constant, k_p. The linear oxidation constant, k_l, is almost independent of the water vapor content, indicating that the linear oxidation is mainly controlled by the oxygen from synthetic air.
• In some cases, the values determined for the critical gas velocity differ significantly from those from the literature. For synthetic air at 1200 °C, an increase in gas velocity above 1.87 cm·s⁻¹ does not result in a higher mass gain after 60 min. The parabolic rate constant, k_p, stays approximately the same. At 900 °C, a value of 0.37 cm·s⁻¹ is determined as the critical gas velocity. A higher gas velocity in the linear oxidation segment significantly influences scaling behavior, especially for lower gas velocities.