Oxidation Kinetics of FeCr and FeCrAl Alloys: Influence of Secondary Processes

1. Introduction

Scale growth on the surface of a metal or alloy is often accompanied by secondary processes that limit the kinetics of the process. Scale can partially sublimate, it is also possible to change the reaction surface for the growth of the main oxide. These processes - separately or together - lead to a significant change the form of equations used to describe the kinetics of the interaction of active gases with the surface of solids.

In the absence of secondary processes, the kinetics of scale growth on the surface of a metal or alloy is parabolic. In some cases, subparabolic, cubic and quaternary processes are also realized. In general: mⁿ=k_nt or (in differential form)

dm/dt = k_n/nm^n-1 ,

(1)

where m is a specific mass gain of oxidized object over time t (mass change due to reacted oxigen), kn is the reaction constant, n = 2, 3, 4 and can also take fractional values.

From Eq.(1) it follows an infinite initial value dm/dt=∞ (at the origin: t=0, m=0). To eliminate this infinity, instead of a simple parabolic equation, a “complex” equation (m/kr)+(m2/kp)=t qan be used, where kr is rectilinear constant (dm/dt at the origin). In this case we will have:

$$\mathrm{d}\mathrm{m}/\mathrm{d}\mathrm{t}=\frac{{\mathrm{k}}_{\mathrm{n}}/\mathrm{n}}{{\mathrm{m}}^{\mathrm{n}-1}+{\mathrm{k}}_{\mathrm{n}}/\mathrm{n}{\mathrm{k}}_{\mathrm{r}}}$$

(2)

In particular, for parabilic kinetic:

$$\mathrm{d}\mathrm{m}/\mathrm{d}\mathrm{t}=\frac{\mathrm{k}\mathrm{p}}{2\mathrm{m}+\mathrm{k}\mathrm{p}/\mathrm{k}\mathrm{r}}$$

(3)

Chromium-based alloys (alumina and chromium-forming alloys) are materials for coating hot parts of gas turbine and jet engines, solar power plants, etc. These alloys have been studied both earlier [1,2] and recently [3,4]. During the oxidation of these alloys, Al₂O₃ or Cr₂O₃ scale is formed on their surface. To improve the adhesion of the scale, doping of the alloy with rare earth metals (REM: La, Y, Ce etc.) is used [5,6,7,8], as for other alloys [9,10,11,12,13].

In this case, fine particles of perovskites are formed - compounds of the RMO₃ type, where R is a rare earth element, and M is one of the two (three) main components of the alloy. The boundaries of oxide grains (the main arteries of mass transfer) in it are blocked by diffusion barriers made of chromites (LaCrO₃, YCrO₃, CeCrO₃). Having close-packed sublattices, these particles are barriers to cation diffusion. This leads to a significant change in the oxidation kinetics (in contrast to the usual parabolic). U.R. Evans [14] defined reduction of surface (S) as:

dS/dm=-kS

(4)

or (in integral form):

S=S₀e^-km,

(5)

where k is a constant of reduction of the reaction area, and S₀ is the initial size. Taking into account that in the absence of a change in the effective area (k=0), the scale growth occurs according to the parabolic law

m²=k_pt

(6)

k_p - parabolic constant, t - time). From Eqs(3-6):

dm/dt=(k_p/2m)e^km.

(7)

The solution to Eq.(7) is the implicit expression (boundary conditions t=0, m=0):

t=2(k²k_p)^-1[e^km(km-1)+1].

(8)

By using of ‘’complex’’ parabola we will have:

dm/dt = k_pe^-km/(2m+k_p/k_r)

(9)

and

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

(10)

It can be seen that for kr→∞ Eq.(9) goes over to Eq.(8).

By combining of Eq.(5) with Eqs (8) and (10) we can write:

t=[2(kk_p)^-1][1-φ^-1ln(eφ)],

(11)

(12)

where $\mathsf{\phi }$ = S/S₀.

The above equations are used in subsequent sections to describe the kinetics of high-temperature oxidation in air of FeCr and FeCrAl alloys doped with La.

The results obtained in [15,16,17] are combined in this paper. The following experimental data for FeCrAl differ from [17], since the experiment was carried out at a different temperature.

2. Results and Discussion

2.1. Oxidation of alloy Fe44Cr4Al0.25La at 1300^oC

There are a large number of publications devoted to the study of high-temperature oxidation of FeCrAl alloys. In this case, a protective film of aluminum oxide is formed [15,16,17,18]. When using lanthanum, to improve of film adhesion and mechanical properties of the alloy, the formation of non-basic oxides and aluminates (in particular LaAlO₃) occurs [26,27]. As mentioned above, this phase belongs to perovskites [28,29] and is diffusely impermeable. During the oxidation of FeCr, FeCrAl, FeCrAl(REM) and other similar reactions, a parabolic, sub-parabilic or cubic law of kinetics is observed [30,31,32,33,34,35,36,37,38].

In this section, the process of oxidation of Fe44Cr4Al0.3La (wt.%) in air at 1300°C is considered. The resulting experimental curve is presented in Figure 1 (curve 1). In this case, the total mass change M = m. The tangent at the origin gives a high value of k_r. Therefore, equations (8) and (10) can be used (kr→∞). Using the OriginPro8 program to determine other constants, we obtain the following empirical equations:

t≅4.77[e^1.49m(1.49m-1)+1]

(13)

t≅4.77[1-φ^-1ln(eφ)].

(14)

The curves plotted using these expressions are presented in Figure 1.

Let's briefly mention the previously established advantages of FeCrAl(La) and other FeCrAl(REM) system alloys [39,40,41]: relatively less weight, heat capacity, greater stability in aggressive gases, as well as high resistance to mechanical wear as determined by us.

2.2. Oxidation of alloy Fe45Cr0.3La at 1300^oC

Lanthanum-doped FeCr alloys have high heat resistance up 1300 to 1400 ^oC. Similar to alumina-forming alloys, during the oxidation of FeCr(La), along with the main oxide Cr₂O₃, difficult-to-permeate chromite LaCrO₃ is formed. At the same time, a characteristic property of Cr₂O₃ is intense evaporation at 1100-1400^oC (evaporation of Al₂O₃ requires a higher temperature). In this case, the total mass change is M = m-v_mt, where v_m is the evaporation rate of reaction products by the metal component. In this case:

$$\mathrm{d}\mathrm{m}/\mathrm{d}\mathrm{t}=\frac{\mathrm{k}\mathrm{p}}{2\mathrm{m}+\mathrm{k}\mathrm{p}/\mathrm{k}\mathrm{r}}{\mathrm{e}}^{-\mathrm{k}\mathrm{m}}–{\mathrm{v}}_{\mathrm{g}}$$

(15)

and

$$\mathrm{d}\mathrm{m}/\mathrm{d}\mathrm{t}=\frac{\mathrm{k}\mathrm{p}}{2\mathrm{m}+\mathrm{k}\mathrm{p}/\mathrm{k}\mathrm{r}}{\mathrm{e}}^{-\mathrm{k}\mathrm{m}}–{\mathrm{v}}_{\mathrm{g}}-{\mathrm{v}}_{\mathrm{m}}=\frac{\mathrm{k}\mathrm{p}}{2\mathrm{m}+\mathrm{k}\mathrm{p}/\mathrm{k}\mathrm{r}}{\mathrm{e}}^{-\mathrm{k}\mathrm{m}}–{\mathrm{v}}_{\mathrm{p}},$$

(16)

where v_g is the evaporation rate of reaction products by the gaseous component, and v_p=v_g+v_m. Differential equations (15) and (16) lead to an integral of the form y=$\int \frac{\mathrm{x}{\mathrm{e}}^{\mathrm{a}\mathrm{x}}}{\mathrm{b}+\mathrm{c}\mathrm{x}{\mathrm{e}}^{\mathrm{a}\mathrm{x}}}\mathrm{d}\mathrm{x}$, which cannot be represented using elementary functions.

The total mass change can be represented only in the parametric form:

(17)

with the parameter m=M+v_mt. This means that when constructing the calculated dependences M - t, t is first found by m using Eq.(10), and then, given the same m, M is calculated using M = m-v_mt. Consequently, the m - t dependence can be constructed as m = M +v_mt (Figure 1) (in case of alumina-forming alloy m=M).

According to our data, at 1300°C the evaporation rate of C₂O₃ is $\cong$4•10^-3 mg/cm²h, and for LaCrO₃ is $\cong$8•10^-4 mg/cm²h. Taking this into account, Figure 2, along with experimental curve 1, shows the curve of alloy mass change due to reacted oxygen (curve 2). It can be seen from the figure that the slope of the tangent to the experimental curve at the origin of coordinates has a real value (in the case of an alumina-forming alloy, the tangent practically coincided with the ordinate axis). In this case, Eqs(10) and (12) must be used in full. Empirical expressions will be:

t≅6.04[e^0.59m(0.59m-1)+1]+0.59(e^0.59m-1)

(16)

and

(17)

where m is in mg/cm² and t is in hours. The curves plotted using these expressions are presented in Figure 2.

FeCr and FeCr(REM), as well as FeCrAl alloys, are widely used in technology both previously and today [42].

2.3. Consideration of initial non-isothermal heating during oxidation of alloys: Oxidation of alloy Fe45Cr0.32Y at 1400^oC

In a number of works, the oxidation of alloys was studied under non-isothermal conditions [39,40,41]. A similar situation occurs in isothermal processes, when the operating temperature is reached within a certain time. Figure 3 schematically shows the kinetic curve of such a process: the initial non-isothermal heating lasts for a time t₀, while the mass of the alloy increases by m₀. It is obvious that in the future it is necessary to use a new coordinate system (m = w-m₀ ; t = t_w-t₀) with the beginning at the inflection point (from Eqs(9) and (10) it follows that the graphs of mass increase should be convex in the positive direction). The branch of the curve lying in the first quadrant of the new coordinate system can already be described by Eq.(10). A formal mathematical study of this implicit function shows that its graph has a vertex in the third quadrant of the m - t coordinate system with the ordinate m_dt/dm=0$\equiv \overline{\mathrm{m}}$=-k_p/2k_r (the corresponding abscissa ($\overline{\mathrm{t}}$) can be found by substituting $\overline{\mathrm{m}}$ into equation (10)).

The curve in Figure 3 is constructed so that m₀=-$\overline{\mathrm{m}}$=k_p/2k_r. However, there is no mathematical justification for the statement that the initial mass gain (m₀) and the ordinate of the peak of the curve ($\overline{\mathrm{m}}$) must be equal in absolute value. However, the validity of this relationship was empirically established earlier during relatively slow heating of iron-chromium alloys doped with lanthanum or yttrium [43,44,45,46]. Here, heating to the operating temperature occurred at a rate of 24^oC/min (in the processes described in sections 2.1 and 2.2, the operating temperature was reached in 2-3 minutes and the effects considered in this section could be ignored).

Shifting the origin of the coordinates again to the point ($\overline{\mathbf{t}}$,$\overline{\mathbf{m}}$), we can consider the ideal kinetic curve in the coordinate system (m',t'), corresponding to the mass gain of the alloy with the instantaneous achievement of the operating temperature. In these coordinates we can already use Eq.(8).

During the oxidation of FeCr(Y), chromite is also formed - YCrO₃ [15,47,48,49,50,51], which creates diffusion barriers in the scale [15,47]. Figure 4 shows the kinetic curve of the increase in mass during the oxidation of Fe45Cr0.32Y at 1400°C (curve 1). Heating was carried out at a rate of 35^oC/min. The lower section of curve 1 corresponds to heating the sample from room- to operating temperature.

To describe the process under consideration, equation (9) must be solved with the boundary conditions t=0, m=m₀ (or, which is the same, t=t₀, m=0). This solution is:

(18)

Time shift between (9) and (18) is:

(19)

Empirical expression of Eq.(19): t=843.313[e^0.022m(0.022m-1)-0.999]+14.205(e^0.022m-1.018) (m - in mg/cm², t - in hours), m₀$\cong$0.83 mg/cm², and t₀$\cong$-0.43 h. For comparison, we point out that m₀=-$\overline{\mathrm{m}}$=k_p/2k_r$\cong$0.77 mg/cm².

2.4. Formal kinetics of growth of scale with the increase of the reaction area

Kinetic models of the oxidation processes of alloys could be considered as simplified diagrams of the ambient conditions in which they are located. In the case when are formed easily permeable phases that serve as arteries for diffusion mass transfer, the scale growth kinetic equation can be derived by analogy with the Eq.(5):

(20)

where S and So are the current and initial values of the effective reaction area, respectively, and K is the constant of the incyrase of the reaction surface. Wherein S>So.

By analogy of Eqs(9), (10) and (12) we will have:

(21)

(22)

(23)

where Φ=ϕ^-1= S_o/S. Graphs of Eqs(22) and (23) are shown in Figure 5.

Kinetic curves of a similar shape are presented in a number of works for chromium, nickel-based and other alloys or metals [52,53,54,55,56,57,58,59,60,61,62]. However, it should be noted that purely parabolic kinetics are considered here. Such curves were also obtained during nitriding of germanium powder, where the metal grains are crushed and, therefore, the reaction surface increases [63]. Prout-Tompkins kinetic model [64] is used here.