**4. Discussion**

#### *4.1. Oxidation Behavior of Fe2Zr Phase*

The oxidation behaviors of the Fe-Cr-Zr alloy reveal the delayed oxidation of the Fe2Zr phase with respect to the α-Fe matrix. The incorporated Fe2Zr phase with low oxygen concentration could be observed in the oxide scale close to the matrix/scale interface (Figure 5). With increased oxidation time, the incorporated Fe2Zr phase with increased oxygen concentration in the scale indicates the gradual oxidation of Fe2Zr phase. It is shown that iron oxide in the form of Fe2O3 is determined by EDS and XRD during oxidation in air at 923 K, and Zr is reported to be oxidized to ZrO2 [25]. The oxidation reaction of the Fe2Zr phase could be written as follows:

$$\text{Fe2Zr (s)} + 5/2\text{O2 (g)} = \text{Fe2Cr (s)} + \text{ZrO2 (s)}\tag{1}$$

It is concluded that the oxygen concentration should be between 60 and 66 at.% at the fully oxidized Fe2Zr phase site. It is assumed that the lower measured oxygen concentration at the incorporated Fe2Zr phase site is caused by the partially oxidized Fe2Zr phase. An approximate fraction of oxidized Fe2Zr phase can be calculated according to the quantitative EDS results at the incorporated Fe2Zr phase sites considering that the ratio of Fe to Zr is close to 2 at these sites (Figure 6c). This calculation is made assuming that each analysis point inside the incorporated Fe2Zr phase consists of oxidized Fe2Zr and metallic Fe2Zr. According to the hypotheses, compositions of the incorporated Fe2Zr phase can be calculated by using the following relations:

$$\mathbf{x\_{Fe}} = \mathbf{2x\_{oxidized}} + \mathbf{2x\_{metallic}} \tag{2}$$

$$\mathbf{x}\_{\mathbf{Z}x} = \mathbf{x}\_{\text{oxidized}} + \mathbf{x}\_{\text{metallic}} \tag{5}$$

$$\mathbf{x}\_{\text{O}} = \mathbf{5} \mathbf{x}\_{\text{oxidized}} \tag{4}$$

The resolution of Equations (2)–(4) leads to:

$$0.\,\text{x}\_{\text{oxidized}}/(\text{x}\_{\text{oxidized}} + \text{x}\_{\text{metallic}}) = 0.2(\text{x}\_{\text{O}}/\text{x}\_{\text{Zr}}) = 0.4(\text{x}\_{\text{O}}/\text{x}\_{\text{Fc}}) \tag{5}$$

For each analysis point inside the incorporated Fe2Zr phase, the ratio of O to Fe or O to Zr could be obtained by EDS. As a consequence, the mole fraction of oxidized Fe2Zr at the incorporated Fe2Zr phase sites can be determined by the Equation (5). For the incorporated Fe2Zr phase (marked position #1 in Figure 5a) in the oxide scale close to the matrix/scale interface after oxidation of 10 min, the calculated mole fraction of oxidized Fe2Zr phase is ~4%. For the incorporated Fe2Zr phase (marked position #1 in Figure 6b) in the scale after oxidation of 2 h, the calculated mole fraction of oxidized Fe2Zr phase reaches ~34.5%.

Based on the oxidation reaction of Fe2Zr (1), standard Gibbs free energy change of the oxidation of metallic Fe2Zr phase to oxides could be calculated as

$$
\Delta G^{\circ} \text{ox(Fe}\_{2}\text{Zr)} = -744268 + 175.87 \,\text{J/mol} \tag{6}
$$

where the standard Gibbs free energy changes of the formation of Fe2O3 and ZrO2 are obtained from the Ellingham/Richardson diagram [26,27] and the standard Gibbs free energy changes of the Fe2Zr formation from the constituting elements (2Fe + Zr = Fe2Zr) is given as Δ *G*◦ = −30400 + 12.7 *T* J/mol [28]. At 923 K, Δ *G*◦ox(Fe2Zr) = −582004 J/mol, and the calculated equilibrium oxygen partial pressure value of *p*O2 is 1.2 × 10−<sup>33</sup> atm. For the alloy matrix with the chemical composition of 86Fe-12Cr-2Zr (at.%), the calculated equilibrium oxygen partial pressure value of *p*O2 for the oxidation of Cr solute and Zr solute is 5.2 × 10−<sup>34</sup> atm and 2.6 × 10−<sup>51</sup> atm, assuming that Cr and Zr solutes would oxidize to their respective oxides. The maximum value of *p*O2 available to a dilute Fe-Cr alloy could be set by Fe-Fe2O3 equilibrium because a scale forms on the alloy surface. Accordingly, the maximum value of *p*O2 available is 1.3 × 10−<sup>22</sup> atm at 923 K. It is demonstrated that oxidation of metallic Fe2Zr phase and alloy matrix at 923 K in stagnant air is

thermodynamically favorable as evidenced by the initial oxidation behavior (Figure 5). As the oxidation process continues, the oxide scale formed around the Fe2Zr phase would prevent the inward diffusion of O into the phase, leading to a lower oxygen partial pressure value inside the Fe2Zr phase. Once the value of *p*O2 is lower than 1.2 × 10−<sup>33</sup> atm inside the Fe2Zr phase, there would be delayed oxidation of the Fe2Zr phase with respect to the alloy matrix (Figure 6).

Oxidation results of Fe-Cr-Zr alloy in air and liquid Pb-Bi eutectic also show that the presence of incorporated Fe2Zr phase could significantly affect the oxidation behaviors of the alloy. In order to evaluate the oxidation resistance of the Fe-Cr-Zr alloy, the oxidation behaviors of Fe-Cr-Zr alloy in air and liquid Pb-Bi eutectic are compared with that of ferritic/martensitic steels and ODS steels with the similar Cr content of 9~12 wt.% [29–36]. As shown in Figure 10, the weight gain curves after oxidation at 923 K in air reveal that the weight gain of Fe-Cr-Zr alloy is significantly greater than that of ferritic/martensitic steels, and the obtained parabolic rate constant of Fe-Cr-Zr alloy (~3.8 × 10−<sup>2</sup> mg<sup>2</sup> cm<sup>−</sup><sup>4</sup> <sup>h</sup>−1) is much higher than that of ferritic/martensitic steels (4.4 × 10−3~9.4 × 10−<sup>6</sup> mg<sup>2</sup> cm<sup>−</sup><sup>4</sup> <sup>h</sup>−1) according to the parabolic kinetic law. However, the thickness of the oxide scale after oxidation in oxygen-saturated liquid Pb-Bi eutectic at 823 K shows that the growth rate of oxide scale thickness of Fe-Cr-Zr alloy is similar to that of ferritic/martensitic steels and ODS steels (Figure 11), demonstrating that the experimental parabolic rate constants of Fe-Cr-Zr alloy, ferritic/martensitic steels and ODS steels are in the range of 1.9 × 10−<sup>7</sup> μm<sup>2</sup> h−<sup>1</sup> to 4.4 × 10−<sup>7</sup> μm<sup>2</sup> h−<sup>1</sup> according to the parabolic kinetic law. Therefore, the oxidation mechanism of the Fe-Cr-Zr alloy in air and liquid Pb-Bi eutectic will be discussed separately.

**Figure 10.** The weight gain curves of Fe-Cr-Zr alloy oxidized in air at 923 K compared with the ferritic/martensitic steels (Data from [29–33]).

**Figure 11.** Thickness of oxide scale of Fe-Cr-Zr alloy obtained by oxidation in oxygen-saturated liquid Pb-Bi eutectic at 823 K compared with the ferritic/martensitic steels (Data from [19,34–36]).

#### *4.2. Oxidation Mechanism in Air*

During oxidation in air, oxidation process involves the diffusion of reactants through the oxide scale (i.e., solute is transported through the matrix to the scale/air interface and oxygen is transported to the scale/matrix interface). Generally, diffusion of solutes in the matrix is usually correlated with the bulk diffusion and grain boundary diffusion, and the grain boundary diffusion rate is widely considered to be much larger than the bulk diffusion rate [37–39]. For the Fe-Cr-Zr alloy, the presence of incoherent α-Fe/Fe2Zr interface could also affect the diffusion rate of solutes. Investigations on the interface diffusivities along the metal/ceramic interface, metal/SiC interface, and metal/SiN interface have revealed that interfaces were the high-diffusivity paths for metal atoms, which was much faster than the bulk diffusion [40,41]. Therefore, diffusion along the α-Fe/Fe2Zr interface might promote the outward diffusion of solutes.

In the early stage of oxidation, Cr is preferentially oxidized to form Cr2O3 due to its higher affinity to oxygen according to Ellingham/Richardson diagram. However, a continuous Cr2O3 oxide scale could not be formed due to that the low content of Cr (~9 wt.%) in the Fe-Cr-Zr alloy. Fe would also diffuse outward to form Fe2O3 oxide, and thus (Fe,Cr)2O3 oxide scale are generated in the scale. Compositional analysis in the vicinity of the matrix/scale interface reveals that the incorporated Fe2Zr phase in the oxide scale exhibits delayed oxidation with respect to the α-Fe (Figure 5a). With increased oxidation time, Fe/Cr and O continually penetrate through the less compact (Fe,Cr)2O3 scale. The inadequate supply of Cr in the matrix could not replenish the Cr consumed by the scale due to the lower concentration of Cr. As a result, Fe2O3 is formed in the outer oxide layer and (Fe,Cr,Zr)2O3 is present in the inner oxide layer (Figure 7c). The Fe2Zr phases showing delayed oxidation are incorporated in the scale (Figure 7b), and the presence of incorporated phase would obstruct the diffusion of solute/oxygen through the scale. It can be concluded that the oxidation process would be affected by the number density of the incorporated Fe2Zr phase. A higher density of the incorporated Fe2Zr phase could effectively retard the outward diffusion of Fe during oxidation process. Thus, a thinner Fe2O3 layer is formed in the area with higher density of Fe2Zr phase due to the lower external oxidation rate, which is consistent with the concave surface on the cross-sectional morphologies (Figure 7b) and pits on the surface morphologies (Figure 3d). The schematic illustration of oxidation behaviors in air is shown in Figure 12a.

**Figure 12.** The schematic illustration of oxidation mechanism of Fe-Cr-Zr alloy after oxidation (**a**) in air and (**b**) in oxygen-saturated liquid Pb-Bi eutectic.

It is shown that the growth rate of oxide scale in Fe-Cr-Zr alloy after oxidation in air is mainly controlled by diffusion of solutes/oxygen through the scale, which is similar to that of ferritic/martensitic steels [29,30]. A large disparity in the oxidation rates between the Fe-Cr-Zr alloy and ferritic/martensitic steels is correlated with their different microstructural features. Firstly, the grain size of Fe-Cr-Zr alloy (in the micrometer-sized range) is much larger than the sub-grain size (in the nanometer-sized range) of ferritic/martensitic steels [7], and as a consequence, higher diffusivity of Cr from matrix could promote the formation of continuous Cr-rich (Fe,Cr)2O3 inner oxide layer via short-circuit diffusion of sub-boundary in ferritic/martensitic steels. Secondly, a higher density of dislocations in the lath martensite of ferritic/martensitic steels could facilitate the bulk diffusion and then accelerate the

delivery of solutes into fringes around the grain boundaries, which also promotes the formation of continuous Cr-rich (Fe,Cr)2O3 inner oxide layer. Finally, α-Fe/Fe2Zr interfaces serve as the preferential oxidation sites could promote the internal oxidation, and the incorporated Fe2Zr phase might causes the thermal and growth stress in the oxide scale.

#### *4.3. Oxidation Mechanism in Pb-Bi Eutectic*

Oxidation results of Fe-Cr-Zr alloy in oxygen-saturated Pb-Bi eutectic also show that Fe2Zr phase shows delayed oxidation with respect to α-Fe. It is found that the magnetite/Fe-Cr spinel interface is the original alloy/Pb-Bi interface according to the spatial position of Fe2Zr phase in the oxide scale (Figure 8), demonstrating that outward diffusion of Fe until oxide/liquid Pb-Bi interface to form the outer magnetite layer while the inner Fe-Cr spinel layer grows at the scale/matrix interface. Unlike the air oxidation in Section 4.2, inward diffusion of O is not achieved by the diffusion inside the oxide lattice, but the presence of nano-channels caused by the Pb-Bi penetrations (Figure 9) are considered as a fast diffusion path for O in the Pb-Bi eutectic [22–24]. The constant ratio (~1.2) of outer magnetite layer thickness on the inner Fe-Cr spinel layer thickness is observed throughout the oxidation process (Figure 8), demonstrating that fast O diffusion paths inside nano-channels do not account for the growth of inner Fe-Cr spinel layer (since it is suggested that the growth rates of outer magnetite layer and inner Fe-Cr spinel layer are directly correlated). It is shown that growth rate of the outer magnetite layer is controlled by the outward diffusion of Fe across the scale by EPMA, and the outward diffusion of Fe would generate vacancies at the scale/matrix interface. The generated vacancies would be accumulated to form nano-cavities at the scale/matrix interface, which is verified by the porous morphology at this interface (Figure 8). The presence of Cr and W with a much slower diffusion rate than Fe could impede the vacancies annihilation through inhibiting Fe vacancies movement to the oxide/metal interface [23]. Meanwhile, O transported by diffusion in the nano-channel could react with the alloy inside the nano-cavities. An equivalent amount of Cr in the matrix and in the Fe-Cr spinel through EPMA analysis (Figure 9) also revealed that the diffusion of Cr in both matrix and Fe-Cr spinel is negligible. It could be deduced that thickness of the newly-formed Fe-Cr spinel is equivalent to the consumed matrix volume, implying that the growth rate of Fe-Cr spinel is also dependent on the outward diffusion of Fe across the scale.

The incorporated Fe2Zr phase in the inner Fe-Cr spinel scale would impede the diffusion of Fe across the Fe-Cr spinel scale. As a result, a reduction in the Fe supply to the magnetite/Fe-Cr spinel interface is present adjacent to the Fe2Zr phase, and looser magnetite would be formed around the Fe2Zr phase, resulting in the creation of cavities in the outer magnetite layer with prolonged oxidation time (arrows in Figure 8). Moreover, grain dissociation of scale above the nano-cavities is responsible for the nano-channels formation in the scale according to dissociative/perforative growth theory [22]. The presence of Fe-Cr spinel/Fe2Zr interface is the preferential sites for grain dissociation, and would promote the formation of nano-channels at these interfaces. The schematic illustration of oxidation behaviors in oxygen-saturated Pb-Bi eutectic is shown in Figure 12b.

Unlike the large disparity in the oxidation rates between the Fe-Cr-Zr alloy and other ferritic/martensitic steels after air oxidation, the growth rate of oxide scale thickness of Fe-Cr-Zr alloy in oxygen-saturated Pb-Bi eutectic is similar to that of ferritic/martensitic steels and ODS steels. On the one hand, the growth rates of outer magnetite layer and inner Fe-Cr spinel layer in oxygen-saturated Pb-Bi eutectic are both related with the Fe diffusion across the oxide scale, but differences in the microstructural features between Fe-Cr-Zr alloy, ferritic/martensitic steels and ODS steels have little effect on the out-ward diffusion behavior of Fe. On the other hand, diffusion of Cr in both matrix and Fe-Cr spinel is negligible due to the rapid diffusion of O inside the nano-channels, and similar Cr content of 9~12 wt.% in these materials could lead to the same growth rate of inner Fe-Cr spinel layer. Finally, the incorporated Fe2Zr phase could affect the compactness of the outer magnetite layer, but do not significantly affect the growth rate of scale.
