Figure 2 shows the microstructure of the cross-section of the specimen surface oxidized at 1,150° C. The oxide scales on the specimen surfaces all had a duplex structure, including the EOL and IOL. Figure 2A describes the constructure and morphologies of the EOL and IOL. The IOL can be divided into two parts: the Ni-rich layer and the oxide dot layer. The upper interface of the EOL/Ni-rich layer and the lower interface of the Ni-rich layer/oxide dot layer were marked by red and yellow dash–dot lines, respectively. In the Ni-rich layer, there were white Ni–Fe particles with dense distribution (analyzed by EDS later). The typical shapes of dot-like, strip-like, net-like, and layered Ni–Fe particles in specimens oxidized at 1,150°C for 90 min are shown in Figure 2B.

The thickness of the Ni—rich layer and oxide dot layer with varying isothermal oxidation time at 1,150°C is shown in Figure 3. The thickness curve of the EOL was not drawn, due to the spallation of the EOL during cooling, when the isothermal time exceeded 10 min at 1,150°C. In all the tested samples, the thickness of the Ni-rich layer accounted for more than 70%, and the thickness of the oxide dot layer was lower than 30% in the IOL.

As shown in Figure 3A, the thickness of the Ni-rich layer kept increasing in the isothermal time range of 0–65 min, followed by an apparent reduction in 90 min. For isothermal time longer than 90 min, the thickness of the Ni-rich layer continued to increase rapidly. Therefore, it was recommended that the isothermal oxidation time at 1,150°C should be less than 90 min to avoid excessive growth of the IOL. The thickness growth rate changed from slow → fast → slow in 0–65 min, while the thickness growth rate remained nearly constant in 90–150 min. In addition, an evident increase in the thickness growth rate appeared after 150 min (1.789 μm/min) for the Ni-rich layer, which was higher than that in 0–65 min (0.621 μm/min) and 90–150 min (0.704 μm/min). There may be a dynamic oxidation mechanism in the Ni-rich layer, in which the change in composition and structure in the Ni-rich layer has an effect on the element transportation rate (Fukagawa and Fujikawa, 1999).

From Figure 3B, the thickness growth of the oxide dot layer followed a well-defined parabolic law with isothermal oxidation time, which meant the rate controlling factor in the oxide dot layer was the element diffusion distance (thickness of oxide dot layer), and the thickness growth rate decreased gradually with the increase in the oxide dot layer thickness (Liu et al., 2020).

The XRD diffraction patterns of the oxidation scale of 9% Ni steel oxidized at 1,150°C for 120 min are shown in Figure 4. From Figure 4, the outer surface of the EOL at location “a” of experimental steel consisted of Fe₂O₃, Fe₃O₄, and NiFe₂O₄ spinel phases. The oxides of the Ni-rich layer in the IOL at location “b” were identified as FeO, Fe₃O₄, and Fe₂SiO₄.

The oxides of the EOL were consistent with the typical external oxide scale of steel containing Fe₂O₃ and Fe₃O₄ (Guo et al., 2002), with additional inclusion of the NiFe₂O₄ spinel phase, which made the oxide scale of the EOL non-adherent and fragile (Douglass and Rizzo-Assuncao, 1988), resulting in the spallation of the EOL during the cooling process. In the EOL, in the case of sufficient O, Fe was oxidized completely forming Fe₂O₃ without remaining, and Ni began to oxidize into NiO. The following solid-state reaction formed NiFe₂O₄, which was expressed in Eq. 1, making it impossible for the stable existence of NiO in the EOL. Thus, NiO existed only as an intermediate product in the EOL during the oxidation process. F e 2 O 3 + N i O = N i F e 2 O 4 . (1)

FeO, Fe₃O₄, and olivine Fe₂SiO₄ existed at location “b” in the Ni-rich layer in the IOL, according to XRD analysis, attributed to the preferential oxidation and the low standard Gibbs free energy of SiO₂ and FeO, as shown in Table 1. Despite the high Ni content of experimental steel, there was no NiO found in the IOL, according to Figure 4B. Figure 5 presents the Fe–Ni–O ternary system at 1,200°C. As shown in Figure 5, with the increase in the oxygen partial pressure (P _O2) and Ni content in the oxide layer, the oxidation products transformed from alloy to (Fe, Ni)O/spinel/Fe₂O₃. There were two explanations on the absence of NiO in the IOL. First, when the P _O2 and Ni concentrations were relatively low, according to Figure 5, Ni would not be oxidized to NiO in the oxide layer. Second, if the P _O2 and Ni concentrations were relatively high, which would be those observed in the present study, according to the standard Gibbs free energy shown in Table 1, Ni would be oxidized to NiO after the formation of Fe₂O₃, Fe₃O₄, and FeO. However, there were reduction reactions between NiO and Fe, which were expressed in Eqs. 2 and 3 (Matsuyama et al., 1991): 3 N i O + 2 F e = F e 2 O 3 + 3 N i , (2) N i O + F e + F e 2 O 3 = F e 3 O 4 + N i . (3) It indicated that when Fe existed, NiO and Fe₂O₃ would not be produced in the IOL, only FeO, Fe₃O₄, and olivine Fe₂SiO₄ existed at location “b” in the IOL.

Figure 6 shows the distribution of Ni, Fe, O, and Si in the Ni-rich layer by the EDS elemental map. Elemental mappings showed the same segregated site of Fe/Ni and inconsistent segregated site of Ni/O in the IOL, which proved the ability of antioxidation of white Ni–Fe particles. In the isothermal oxidation stage, oxidation reactions mainly occur in Fe and O because of the inertness of Ni with the high standard Gibbs free energy. Naturally, Fe and Ni in the matrix diffused outward to the interface of the EOL/IOL, and O diffused inward to the steel matrix. Considering the low-diffusion rate of O in FeO, lack of O occurred and lots of Fe accumulated in the Ni-rich layer. As discussed in Section 3.2, Ni would remain only in the metallic state. Therefore, the consistent distribution site of Fe/Ni appeared and then formed Ni–Fe particles.

Combining with the EDS analysis of region 1 (Fe: 66.33%; Ni: 33.67%), region 6 (Fe: 76.33%; Ni: 23.67%), and region 7 (Fe: 86.38%; Ni: 11.96%) in Ni–Fe particles in Table 2, it was found that the Ni concentration increased from the lower interface to the upper interface of the Ni-rich layer. As the oxidation reaction proceeded, the Ni-rich layer grew inward to the matrix, resulting in the accumulation of Ni occurred (Shen et al., 2020). In the Ni-rich layer, by comparing region 3 (Fe:45.27%, O: 54.20%) near the EOL with region 5 (Fe: 50.37%, O: 48.78%) near the steel matrix in Table 2, it was found that iron oxide changed from the mixture of FeO/Fe₃O₄ to FeO. Combined with the results of XRD, it was proved that, from the upper interface near the EOL to the lower interface near the oxide dot layer in the Ni-rich layer, the oxidation degree of Fe decreased, verifying the surplus of Fe and lack of O in the Ni-rich layer, especially in the lower half of the Ni-rich layer.

By SEM observation and EDS analysis in Figure 6 and Table 2, combined with XRD analysis in Figure 4, which was verified by each other, there were the following three types of phases in the Ni-rich layer. (I) The white Ni–Fe particles in region 1 near the EOL had the Ni content of 33.67%, while in region 7 near the oxide dot layer, Ni content decreased to 11.96%; (II) the gray iron oxide phase in region 3 near the EOL contained FeO/Fe₃O_4, and region 5 near the oxide dot layer was FeO; (III) the black Fe₂SiO₄ olivine phase (region 4) had been observed by SEM. In general, EDS elemental mapping confirmed that the Ni-rich layer consisted of Ni–Fe particles in an iron oxide matrix. It was noticed that there were the blank regions without elements in Figure 6, which were the pores and cavities around the bulk Ni–Fe particles.

The cross-sections of the Ni-rich layer in 9% Ni steel oxidized at 1,100°C and 1,150°C in the air atmosphere are presented in Figure 7. The 1,100°C sample was presented as a comparison with the subsequent oxidation at 1,150°C. As shown in Figure 7A, at 1,100°C, discrete dot-like Ni–Fe particles are uniformly distributed in the gray iron oxide matrix without aggregation tendency (Liu et al., 2014). However, Ni–Fe particles in the Ni-rich layer showed an evident aggregation tendency at 1,150°C, according to Figures 7B–I.

Observing at 1,150°C for 0–240 min (Figures 7B–I), Ni–Fe particles increased evidently and tended to aggregate with isothermal oxidation time, which varied from dot-like, strip-like to net-like shape in the upper and in the lower halves of the Ni-rich layer. For isothermal time longer than 35 min, layered Ni–Fe particles were formed, which were thin and discontinuous, and after 90 min, they became continuous layered Ni–Fe particles with irregular thickness (Figure 7F). These kinds of layered Ni–Fe were located at approximately 1/3 of the thickness of the Ni-rich layer, close to the EOL/IOL interface. Between 90 and 120 min, the layered Ni–Fe particles continued to thicken (Figures 7F, G), and, at the same time, numerous voids formed, which would make gaseous oxygen rapidly diffuse into the IOL, accelerating the oxidation and making the Ni-rich layer thickness continue to increase, as shown in Figure 3A. By prolonging the isothermal time, the number and size of voids and cavities increased furtherly, aligning parallel to the surface (Figure 7H). This induced the fragmentation and spallation of layered Ni–Fe particles, resulting in the decrease of thickness of the Ni-rich layer for isothermal time of 240 min, compared with that of 180 min. New layered Ni–Fe particles began to form below the previously cracked particles, as shown in the yellow circle in Figure 7I. It was also noted that when the layered Ni–Fe particles began to form, the amount of Ni–Fe particles in the lower half became much more than that in the upper half. Thus, from the cross-sectional morphologies of the Ni-rich layer, it can be concluded that the growth process of Ni–Fe particles in the Ni-rich layer was as follows: 1) in the upper and lower halves: dot-like → strip-like → net-like; 2) layer-like Ni–Fe particles occurred at approximately 1/3 from the top of the Ni-rich layer when isothermal time was higher than 35 min.

In order to clarify the oxidation mechanism of the Ni-rich layer, the area fraction of Ni–Fe particles for varying isothermal time was counted by software Image-Pro Plus, which referred to the percentage of the Ni–Fe particle area in the Ni-rich layer area. Figure 8A shows that the area fraction of Ni–Fe particles increases gradually with the increase in isothermal time in the range of 0–150 min at 1,150°C, which meant that the Ni enrichment in the Ni-rich layer became more serious with the oxidation process. However, the area fraction of Ni–Fe particles in the upper half of the Ni-rich layer varied gradually from higher to lower than that in the lower half. Figure 8B gives the area fraction of Ni–Fe particles with different morphologies, and Figure 8C shows the specific details of Ni–Fe particles. Dot-like, strip-like, and net-like Ni–Fe particles were divided by the area (0–5, 5–350, and more than 350 μm², respectively) and covered with red, blue, and yellow colors, respectively. It was evident that Ni–Fe particles exhibited a growth pattern and transformed from dot-like to strip-like to net-like shapes with isothermal time.

The thickness of the Ni-rich layer exhibited an apparent reduction when isothermal time is in the range of 65–90 min (Figure 3A), due to the sharp increase in the area fraction of Ni–Fe particles from 65 to 90 min. This can be explained by the reasons as follows: volume expansion was inevitable during the oxidation process. Fe₃O₄ and FeO were mainly oxides in the Ni-rich layer, as stated in Section 3.2, which had large oxidation volume expansion with 110% expansion from Fe to Fe₃O₄ and 74% expansion from Fe to FeO, leading to the significant compressive stress during the oxidation process (Wilke and Dunand, 2020). However, the area fraction of Ni–Fe particles increased sharply from 65 to 90 min (Figure 8A), taking the place of the iron oxide matrix and decreasing the amount of iron oxide. In general, the decrease in the transformation amount of Fe to iron oxide contributed to a reduction in oxidation volume expansion, causing a thickness decrease in the Ni-rich layer at 90 min, as shown in Figure 3A.

In order to make the variation in the oxidation rate more intuitionistic, the oxidation rate was replaced by the mean diffusion coefficient reported by Abe et al. (1987), which can be described in Eq. 4: D m = △ X 2 t , (4) where D _m is the mean diffusion coefficient of reaction elements (Fe and O), cm²/s; t is the diffusion time, s; △X is the difference in the diffusion distance in different heating times, cm. Here, △X is considered the thickness difference of Ni-rich layers between the latter sample and the first sample (1,150°C for 0 min), cm, except the △X of the sample at 1,150°C for 0 min which is based on the Ni-rich layer thickness at 1,100°C for 0 min.

Figure 9 gives the D _m values of elements in the Ni-rich layer. Due to the fracture and spallation of layered Ni–Fe particles (as shown in Figures 7H, I), D _m was not calculated after 150 min. According to Figure 9, D _m decreased sharply from 300.07 × 10⁻¹⁰ cm²/s at 1,150°C for 0 min to 0.81 × 10⁻¹⁰ cm²/s at 1,150°C for 10 min and then increased from 0.81 × 10⁻¹⁰ to 44.17 × 10⁻¹⁰ cm²/s in 10–35 min; finally, D _m remained in a certain range from 44.17 × 10⁻¹⁰ to 55.56 × 10⁻¹⁰ cm²/s in 35–150 min, except for the value of 14.69 × 10⁻¹⁰ cm²/s in 90 min.

Hayden et al. (1972) pointed out that, at temperatures higher than 65% of the absolute melting point, the volume diffusion should be the dominant diffusion path. Therefore, the dominant diffusion path is volume diffusion at 1,100°C and 1,150°C. Figure 10 gives the volume diffusion coefficient of Fe and O in different materials. For the steel without Ni, the Ni-rich layer could be simplified to a single structure of the FeO layer, and the diffusion coefficient of Fe and O in the FeO layer was 2.86 × 10⁻⁷ cm²/s and 5.79 × 10⁻¹¹ cm²/s, respectively, according to Figure 10. Evidently, the diffusion coefficient of Fe was large enough to dominate the oxidation rate. However, the value of D _m (0.81 × 10⁻¹⁰–55.56 × 10⁻¹⁰ cm²/s) was apparently lower than the diffusion coefficient of Fe in the FeO layer (2.86 × 10⁻⁷ cm²/s). This can be explained by taking into account the diffusivity of Fe and O in Ni–Fe particles.

As shown in Figure 10, the diffusion coefficient of Fe in Ni–Fe particles (2.3–3.5 × 10⁻¹⁰ cm²/s, similar to Fe-(10–40) Ni alloy at 1,200°C) decreased largely, compared with that of the Fe in FeO (2.86 × 10⁻⁷ cm²/s), which resulted in the decrease of D _m in the Ni-rich layer. Due to the decrease in the diffusion coefficient of Fe, Ni-contained steel has a better oxidation resistance than steel without Ni. From Figure 10, the diffusion coefficient of O in Ni was 1.98 × 10⁻⁹ cm²/s, which was at least 34 times larger than the diffusion coefficient of O in FeO (5.79 × 10⁻¹¹ cm²/s) at 1,150°C. It can be inferred that the diffusion coefficient of O in Ni–Fe particles might be close to but bigger than the diffusion coefficient of O in Ni (about in the order of magnitude of 10⁻⁹ cm²/s). Ni–Fe particles provided a faster diffusion path for O than FeO, which increased the oxidation rate. Subsequently, the diffusion coefficient of O in the Ni-rich layer gradually increased from the order of magnitude of 10⁻¹¹ cm²/s in FeO to 10⁻⁹ cm²/s in Ni–Fe particles, which was consistent with the D _m from 8.06 × 10⁻¹¹ to 5.56 × 10⁻⁹ cm²/s (Figure 9).

From the aforementioned analysis, it was inferred that D _m of Ni-contained steel might vary with amount and morphology of Ni–Fe particles. According to Figure 9, the sharp decrease in D _m from 300.07 × 10⁻¹⁰ cm²/s at 1,150°C for 0 min to 0.81 × 10⁻¹⁰ cm²/s at 1,150°C for 10 min was caused by the rapid accumulation of Ni–Fe particles, where the diffusion coefficient of Fe was low. With the increase in area fraction of Ni–Fe particles, diffusion path of O kept enlarging. As for the quick increase in D _m from 10 min to 35 min during the isothermal stage, it could be attributed to the growth of Ni–Fe particles from dot-like to strip-like or net-like. When isothermal time was higher than 35 min, more than 90% area fraction of strip-like and net-like Ni–Fe particles was achieved, which would connect with each other to form a complete path for O diffusion in the Ni-rich layer, accelerating the oxidation.

Therefore, with the further increase in the area fraction of strip/net-like Ni–Fe particles during isothermal time for 35–150 min, D _m had only a slight fluctuation (Figure 8). In a word, the net-like and layered Ni–Fe particles provided a fast diffusion path for O in the Ni–rich layer, compared with the dot-like Ni–Fe particles.

As shown in Figures 6 and 7, pores/cavities always existed during the isothermal oxidation process. Kirkendall pores form when one metal diffuses more rapidly into another metal, and vice versa (Springer et al., 2011). The pores/cavities are formed due to the Kirkendall effect, leaving a fragile and porous Ni-rich layer. Therefore, the generation of pores/cavities in the IOL reduced the mechanical properties of the Ni-rich layer.

Beygelzimer and Beygelzimer (2022) reported the coefficient of linear thermal expansion (CTE) of FeO and Fe₃O₄, and Hausch (2007) reported the CTE of Fe–Ni alloys at different temperatures. Figure 11 gives the CTE of different materials with temperature. The difference in CTE between Ni–Fe particles (similar to Fe-(14–22) Ni-X alloy) and iron oxides increased quickly with the decrease in temperature and reached the maximum differences (approximately 13 × 10⁻⁶°C⁻¹) at approximately 200°C (Figure 11). The residual internal stress was caused by the difference between CTE of iron oxides and Ni–Fe particles during the cooling process, resulting in the formation of cracks at the boundary of the Ni–Fe particles and iron oxides, as displayed in Figures 6C, D.

When isothermal oxidation time is in the range of 0–65 min, numerous pores/cavities occurred around dot-like/strip-like/net-like Ni–Fe particles and discontinuous layered Ni–Fe particles (Figures 7A–E). However, the IOL still kept stability, attributed to the high proportion of iron oxide with a small shrinkage amount (Figures 8, 11). When isothermal time was higher than 90 min, continuous layered Ni–Fe particles had been formed (Figures 7F, G). In addition, the Ni–Fe particles with a high shrinkage amount increased evidently, accompanied by the significant increase in pores/cavities around the layered Ni–Fe particles, resulting in the weakening of the connectivity. Once the internal stress exceeded the interfacial binding force, the spalling behavior of layered Ni–Fe particles occurred, as presented in Figures 7H, I, making the thickness of the oxide layer at 1,150°C for 240 min less than that for 180 min.