Oxidation Kinetics of FeCr and FeCrAl Alloys: Influence of Secondary Processes (Continuation)

Abstract

This paper discusses the influence of the secondary processes of reaction product evaporation and the reduction of the effective diffusion area into the scale on the kinetics (change in sample mass–time) of the high-temperature oxidation processes, in air, of alumina- and chromia-forming alloys.

1. Introduction

Alloys consisting of iron with a main addition of chromium or nickel (stainless steel) has a long history. As early as the first half of the 19th century, M. Faraday and P. Berthier established the ability of an iron–chromium alloy to resist acid corrosion. Stainless steel was patented in 1912 by the German company Krupp, and the name was given by the English engineer G. Brierley. From this time on, the interest of scientists and engineers in FeCr and FeCrAl alloys began to awaken. FeCr and FeCrAl alloys are widely used because they have many positive properties—The use temperature in the atmosphere can reach 1400 °C long service life, high surface load, good oxidation resistance, low specific gravity, high resistance, good resistance to sulfur, cheap price, etc.

Much information about the resistance of these alloys has been obtained by studying the kinetics of their high-temperature oxidation, which has been undertaken from the early years of this process to the present [1,2,3,4,5,6,7,8,9,10] (only a small portion of the huge number of works are cited here). When FeCr is oxidized, a protective layer of chromia (Cr₂O₃) is formed, and in the case of FeCrAl, Alumina (Al₂O₃) is formed. To improve the film adherence and a number of the properties (stability, slow growth, etc.) of the alloy, alloying with rare earth metals (lanthanum, yttrium, cerium, etc.) is widely used. A large number of works are also devoted to this [8,9,10,11,12,13,14,15].

The distinctive feature between the Cr₂O₃ and Al₂O₃ films is that the former evaporates while the latter does not. This leads to a significant difference in the kinetics of the oxidation process of FeCr and FeCrAl alloys. Therefore, after the experimental section, the simpler case with FeCr will be considered first, and in the conclusion of this section, we will point out the main feature distinguishing the oxidation processes of FeCr and FeCrAl and FeCrREM and FeCrAlREM alloys; i.e., that in the presence of rare earth (Re) metals, chromites (LaCrO₃, YCrO₃, CeCrO₃, etc.) are formed. With densely packed sublattices, these chromites create barriers for cation diffusion. This leads to a deviation in the oxidation process kinetics from the usual power (parabolic, cubic, and, in rarer cases, fourth-degree) law mⁿ = k_nt (m—mass gain per unit area at the time t; k_n—constant of the nth degree). In Refs. [16,17,18], the decrease in the effective area of the oxidation reaction was taken into account, and the corresponding kinetic equations were derived. These equations contain the following distinctive parameters: S = S₀e^−km and φ = S/S₀, where k is a constant of reduction of the reaction area, and S, S₀ are the current and initial sizes. The resulting equations are Equation (1) [16] and Equation (2) [17]:

$$\mathrm{m}={\displaystyle \frac{1}{\mathrm{k}}}\mathrm{l}\mathrm{n}\left(\mathrm{k}\sqrt{{\mathrm{k}}_{\mathrm{p}}\mathrm{t}}-1\right),$$

(1)

$$\mathrm{m}={\displaystyle \frac{1}{\mathrm{k}}}\mathrm{l}\mathrm{n}\left(\mathrm{k}\sqrt{{\mathrm{k}}_{\mathrm{p}}\mathrm{t}}-1\right)-{\mathrm{v}}_{\mathrm{m}},$$

(2)

as well as Equation (3) [18]:

$$\mathrm{t}={\displaystyle \frac{2}{{\mathrm{k}}^2{\mathrm{k}}_{\mathrm{p}}}}[{\mathrm{e}}^{\mathrm{k}\mathrm{m}}(\mathrm{k}\mathrm{m}-1)+1],$$

(3)

where ${\mathrm{k}}_{\mathrm{p}}$ is the parabolic rate constant (n = 2) and ${\mathrm{v}}_{\mathrm{m}}$ is the rate of evaporation of metallic component of Cr₂O₃. (The rate of evaporation of the main reaction product (v_p) can be represented as the sum of the rates of the metallic and gaseous (v_g) components: v_p = v_m + v_g. Since oxygen continuously diffuses into the scale to the alloy surface during the oxidation process, it is obvious that the decrease of the mass of the entire system will be determined by evapoation of the metallic component.)

In Equation (3), as in (1), scale evaporation is not taken into account. In Ref. [18], it is indicated that if we take into account the simultaneous processes of evaporation and the change in the reaction surface, then we should be able to solve the differential equation dm/dt = [k_p/(2m + k_p/k_r)]e^−km − v_m (k_r is the rectilinear constant, and v_g is the evaporation rate of reaction products by the gaseous component of the scale). However, the integral $\int {\displaystyle \frac{\mathrm{x}{\mathrm{e}}^{\mathrm{a}\mathrm{x}}}{\mathrm{b}+\mathrm{c}\mathrm{x}{\mathrm{e}}^{\mathrm{a}\mathrm{x}}}}$dx (a, b, and c are constants; in this case, x = m, a = k, b = k_p/2v_g, and c = −1) cannot be represented by means of elementary functions [18]. More discussion can be found in Appendix A.

From Equation (3), S = S₀e^−km and φ = S/S₀ it follows that

$$\mathrm{t}={\displaystyle \frac{2}{{\mathrm{k}}^2{\mathrm{k}}_{\mathrm{p}}}}[1-{\mathsf{\phi }}^{-1}\mathrm{l}\mathrm{n}(\mathrm{e}\mathsf{\phi })].$$

(4)

And in the case of k_r ≠ $\infty$, we will obtain

$$\mathrm{t}={\displaystyle \frac{2}{{\mathrm{k}}^2{\mathrm{k}}_{\mathrm{p}}}}[1-{\mathsf{\phi }}^{-1}\mathrm{l}\mathrm{n}(\mathrm{e}\mathsf{\phi })]+{(\mathrm{k}{\mathrm{k}}_{\mathrm{r}})}^{-1}({\mathsf{\phi }}^{-1}-1).$$

(5)

Below, we will consider the kinetics (mass change of sample–time) of the oxidation processes, in air, of alumina- and chromia-forming alloys using Equations (3)–(5). (Equations (1)–(3) are obtained on the basis of a “simple” parabolic dependence. But then in origin of coordinate system (t = 0, m = 0) it turns out that dm/dt =$\infty$. However, it is impossible for the reaction to proceed with an infinite initial velocity. To eliminate this infinity, instead of a “simple”, a “complex” (and sometimes complete) parabolic equation is considered: $\mathrm{t}={\displaystyle \frac{{\mathrm{m}}^2}{{\mathrm{k}}_{\mathrm{p}}}}+{\displaystyle \frac{\mathrm{m}}{{\mathrm{k}}_{\mathrm{r}}}}$ and solving the corresponding differential equation we will have:

t = 2(k²k_p)⁻¹[e^km(km − 1)+1] + (kk_r)⁻¹(e^km − 1).

(6)

We will use this implicit dependence further in those cases when k_r ≠ $\infty$. (Sometimes the tangent to the kinetic curves at the origin of coordinates practically coincides with the ordinate axis. In such cases, it can be assumed that k_r→$\infty$.).)

2. Experimental Section

The research alloys are well suited for preliminary thermochemical treatment [19,20]. As a result of this process, re-ions are localized via diffusion on the surface of the sample. This improves the heat resistance of the material by one order. Of the rare earth elements, lanthanum was used. The compositions of the alloys were Fe-44Cr-4Al-0.3La and Fe-44Cr-0.3La. The samples were in the form of low cylinders, with a diameter of bases of 30 mm and a height of 1 mm. Scanning electron microscopy (device SEC SNE-4500 Plus, Suwon, Republic of Korea), X-ray analysis (HZG-4A, Freiberger Präzisionsmechanik GmbH, Freiberg, Germany), and Auger spectroscopy (LAS-2000, ULT AG, Löbau, Germany) methods were used to analyze the samples. The research conducted by these methods shows that during the oxidation process, a grainy film of aluminum closely grown with the matrix is formed, the thickness of which is (100–500) nm. In addition, the composition of the scale is multiphase; together with Al₂O₃, complex oxides Fe(Cr₂O₃Al₂O₃), FeAl₂O₄, and FeCr₂O₄ are formed (Figure 1 and Figure 2).

The oxidation temperature was (1100–1300) °C. The temperature of the electric heater was regulated using a high-precision regulator VRT–3 with an accuracy of ±0.5 °C. The samples were heated at a rate of 25 °C/min.

Kinetic measurements were carried out by continuously weighing the samples during the oxidation process. For this purpose, a homemade microbalance built into a vacuum unit was used (Figure 3). Electromagnetic compensation for changes in the sample mass was carried out automatically (Figure 4).

The balance beam made of molybdenum glass, 180 mm long and 2.5 mm in diameter, was fixed on a tungsten filament with a diameter of 20 μm. The balance settling time was 10–15 s, and the maximum load was 5 g. The sensitivity of the balance was 10⁻⁶ g.

The electrical signal compensating for the balance beam deviation was recorded on a V-7-16-A digital voltmeter and recorded on a KSP-4 recorder. The signal was calibrated using special reference weights.

3. Results and Discussion

First, let us consider the question of which of the Equations (1)–(3) should be used further. It turned out that the calculated kinetic curves constructed according to Equation (2) differ significantly from the experimental ones. This is clearly revealed with an increase in the oxidation temperature (Figure 5). The curves constructed according to Equation (3) are also shown there. It is evident that this equation should be used further.

3.1. Oxidation Kinetic of Alumina-Forming Alloy in Air

A detailed study of the oxidation kinetics of the Fe-Cr-Al-La system alloys with variable content of chromium at an optimal ratio of aluminum and lanthanum showed that increasing the chromium concentration to 45 wt.% helps to achieve the maximum positive effect [21,22,23].

Figure 6 shows a typical experimental kinetic curve of the oxidation of the FeCrAl(La) alloy in air (curve 1). The nature of this curve indicates that with continuous oxidation for at least 10 h, the oxide film remains intact. This indicates its sufficient strength and plasticity. The same figure also shows a theoretical curve calculated using Equation (3). And in

Table 1. Kinetic parameters of high-temperature oxidation of alumina-forming alloy.

Parameters	Temperature, °C
	1200	1250	1300
k, cm2/mg	1.99	1.68	1.46
kr, mg/cm2·h	0.65	0.78	0.95
kp, mg2/cm4·h	0.12	0.27	0.59
mA, mg/cm2	0.4	0.5	0.7
tA, h	4	2.7	2.4
φA, relat. units	0.45	0.43	0.36

, the values of kinetic parameters are given. They are calculated/according to the methodology given in [24]. It can be seen that the experimental and theoretical curves are in satisfactory agreement.

Figure 7 shows the experimental and calculated kinetic curves denoting the decrease in the effective diffusion area during the oxidation of the FeCrAl(La) alloy at 1300 °C (curves 1 and 2, respectively). It also shows that the experimental and theoretical curves are in satisfactory agreement.

Let us introduce a new parameter: t_A = 2k⁻²k_p⁻¹. From Formulae (4) and (5), it is clear that this parameter characterizes a certain period of time during which the formation of diffusion barriers in the scale is practically completed. At the same time, from Equation (4), in the first approximation, it turns out that t ≈ (2m²/k_p) + (m/k_r). Then, by combining it with equations e^−km and φ = S/S₀ = e^−km and (5), one can easily verify that by the time the formation of diffusion barriers is complete, φ $\equiv$ φ_A ≈ ${\mathrm{e}}^{{\displaystyle \frac{\mathrm{k}{\mathrm{k}}_{\mathrm{p}}}{2{\mathrm{k}}_{\mathrm{r}}}}-1}$.

It is evident from Figure 5 that the experimental and theoretical curves intersect at the point with coordinates (t_A, φ_A). Based on all of the above, it can be concluded that after the t time interval, φ drops sharply to level φ_A and subsequently changes comparatively little during the alloy oxidation process. This is obviously due to the fact that the predominant amount of lanthane contained in the alloy has already passed into the scale, which limits the further formation of diffusion barriers near the matrix–scale interface.

3.2. Oxidation Kinetic of Chromia-Forming Alloy in Air

A large number of works, both previously and recently, have also been devoted to the study of high-temperature oxidation of chromia-forming alloys [25,26,27,28,29,30,31], etc. As already indicated above, the distinctive feature of this process from the high temperature oxidation of alumina-forming alloys is the evaporation of Cr₂O₃ [17,18,32,33,34], etc., which introduces a change of the nature of the process.

Figure 8 shows the results of a separate experiment on the evaporation of Cr₂O₃ in a vacuum.

The chromite LaCrO₃ formed during oxidation of the alloy also evaporates, but at a very low rate—i.e., an order of magnitude lower than the evaporation rate of Cr₂O₃ at the same temperatures. Therefore, it can be ignored in the overall change in the mass of the sample when weighing it.

Figure 9 shows a typical experimental and calculated kinetic curves denoting the oxidation of the FeCr(La) alloy in air; and the kinetic curves denoting the decrease in the effective diffusion area during the process are presented in Figure 10. The values of the kinetic parameters are given in

Table 2. Kinetic parameters of high-temperature oxidation of chromia-forming alloy.

Parameters	Temperature, °C
	1100	1200	1300
k, cm2/mg	2.32	1.55	0.69
kr, mg/cm2·h	18.9	0.28	1.07
kp, mg2/cm4·h	3.85	3.6	3.93
mA, mg/cm2	0.4	0.7	1.5
tA, h	4	4	4
φA, relat. units	0.39	0.37	0.36

.

It should be noted that the high value of the rectilinear constant (see Table 2) simplifies the expression φ_A ≈ ${\mathrm{e}}^{{\displaystyle \frac{\mathrm{k}{\mathrm{k}}_{\mathrm{p}}}{2{\mathrm{k}}_{\mathrm{r}}}}-1}$ to φ_A ≈ ${\mathrm{e}}^{-1}$(lnφ_A + lne = lnφ_A + 1 ≈ 0); i.e., φ_A ≈ 0.37. Thus, it can be concluded that during the high-temperature oxidation of chromium-forming alloys, the effective diffusion area initially decreases by 2.72 times, after which, the process practically enters a stationary mode.

Below are the empirical formulae compiled from the data of Table 1 and Table 2, according to which the kinetic curves were constructed in the corresponding figures:

• t ≈ 4.04 [e^1.99m (1.99m − 1) + 1] + 0.77 (e^1.99m − 1);
• t ≈ 4.04 [1 − φ⁻¹ln(eφ)] + 0.77 (φ⁻¹ − 1) for alumina-forming alloy at 1200 °C;
• t ≈ 4.04 [e^1.99m (1.99m − 1) + 1];
• t ≈ 4.04 [1 – φ⁻¹ln(eφ)] for chromia-forming alloy at 1200 °C (t is in hours, m is in mg/cm²).

In conclusion, we note the following: in Ref. [25], the dependence of the maximum achievable value of mass increase ($\overline{\mathrm{m}}$) of the sample on parameter k_p/v_gin logarithmic coordinates is given. This work provides data for the following compounds: B₂O₃, SiO₂, CrCl₂, PbCl₂, and Cr₂O₃. The dependence has a rectilinear character, on which our data for Ge₃N₄ [26] fit well (Figure 11). In our case, when, along with the evaporation of Cr₂O₃, a decrease in the effective diffusion area also occurs, this rectilinearity is already realized in coordinates $\overline{\mathrm{m}}$ − lg(k_p/v_g) (Figure 12). In most cases, three dots are not enough to build an experimental points dependence, but their almost-ideal arrangement in Figure 12 allows us to consider our case acceptable.

4. Conclusions

All kinetic models of oxidation processes are simplified schemes of conditions in which all real systems of alloys are located. The appearance of diffusion/low-permeability phases in the scale is equivalent to a decrease in the effective reaction area, since certain micro-areas of the scale become difficult to overcome for the interacting components. Here, we show the correspondence of some of these models to experimental data on the high-temperature oxidation of alloys FeCr and FeCrAl with the addition of La. It is shown that the selected kinetic equations describe these processes well.

5. Future Research Directions

Future research should aim to improve the thermoelectric characteristics of the SiGe alloy listed in the main text. This will serve to increase the figures of merit and efficiency of the alloy.