High-Temperature Oxidation Resistance of Alumina-Forming Austenitic Stainless Steels Optimized by Refractory Metal Alloying

Alumina-forming austenitic stainless steels are known for their superior high-temperature oxidation resistance. Following our previous work that solved the matching of major alloying elements in their specific 16-atom cluster formula, we here focus on the 800 °C air-oxidation resistance of 0.08 wt. % C alloy series satisfying cluster formula [(Al0.89Si0.05NbxTa0.06−x)-(Fe11.7−yNiyMn0.3)]Cr3.0−z(Mo,W)z, x = 0.03 or 0.06, y = 3.0 or 3.2, z = 0.07 or 0.2, to explore the effect of minor alloying elements Mo, Nb, Ta and W. This cluster formula is established particularly based on alloys which were originally developed by Oak Ridge National Laboratory. All samples are graded as complete oxidation resistance level according to Chinese standard HB 5258-2000, as their oxidation rate and oxidation-peeling mass are generally below 0.1 g/m2 × h and 1.0 g/m2, respectively. In alloys without Ta and W, a Cr2O3-type oxide layer is formed on the surface and Al2O3 particles of sizes up to 4 μm are distributed beneath it. In contrast, in Ta/W-containing alloys, a continuous protective Al2O3 layer is formed beneath the outer Cr2O3 layer, which prevents internal oxidation and provides the lowest weight gain. Instead of internal Al2O3 particles, AlN is formed in Ta/W-containing alloys. The W-containing alloy possesses the thinnest internal nitride zone, indicating the good inhibition effect of W on nitrogen diffusion.


Introduction
Alumina-forming austenitic (AFA) stainless steel is a type of heat-resistant stainless steel which can form a dense and stable aluminum oxide layer to protect it from hightemperature environments. Compared to Cr 2 O 3 film, which is formed in traditional austenitic stainless steels, Al 2 O 3 film has a lower growth rate (1-2 orders of magnitude slower), better thermal stability, and is more stable in water vapor, even in combustion and chemical reactions with carbon and sulfur [1][2][3]. Since the 1970s, Al with weight percentages of 4-5 has been added to austenitic stainless steel in order to improve its high-temperature oxidation resistance [4][5][6][7][8][9]. However, they can only be used as a protective coating or in low load environments because of their low creep resistance, which is caused by their ferrite-austenite dual phase structure. Until the beginning of this century, Oak Ridge National Laboratory (ORNL) in the United States found that 2.4 wt. % Al was sufficient to form a continuous, stable and dense Al 2 O 3 film in water vapor under 650~800 • C. A series of AFA stainless steels with excellent creep resistance and oxidation resistance at high temperature [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] were thereafter developed.
The priority when designing the composition of AFA stainless steels is to guarantee the formation of stable and highly uniform austenitic state, avoiding a ferrite-austenite

Principles of Alloy Design
This article analyzes the composition of AFA stainless steels by our cluster-plus-glueatom model. The number of atoms in a chemical structural unit of pure FCC structure has been calculated previously by atomic radius [32]. The closest integer is 16, which means the most stable FCC structure should be a CN12 cubic octahedral cluster plus three glue atoms. For solid solution alloys, the occupation of atoms is decided by the interaction between solute atoms and solvent atoms, which can be evaluated by the mixing enthalpy ∆H in binary systems. The general procedure to determine the ideal structural unit of a solid solution alloy is as follows: (1). Classify the solute atoms according to their mixing enthalpy ∆H with solvent atoms, so that their occupations (as center, shell or glue atoms) are preliminarily determined. (2). Set up a criterion: set either the number of shell atoms or total atoms in the cluster, then calculate the number of atoms in the cluster of each element. (3). Summarize the number of atoms in each occupation (center, shell and glue atoms) of typical compositions, and get the ideal structural unit of this kind of solid solution alloy, namely the general cluster formula, and afterwards design compositions according to this ideal cluster formula and verify its practicable by experiments.
To determine the cluster formula of multi-component AFA stainless steels, the occupation of atoms in the cluster should be decided according to the mixing enthalpy ∆H between solute atoms and solvent atoms, as listed in Table 1. On that basis, the alloying elements are classified into three groups: 1, Al, Si, Ti, V, Nb and Ta have negative and large value ∆H with Fe (−7-−35 kJ/mol), which means strong interaction. These Al-like atoms are therefore classified as center atoms; 2, Cr, Mo and W, which have weak interaction with Fe (−2-0 kJ/mol), are treated as glue atoms; 3, Ni and Mn also have weak interaction with Fe (∆H Fe-Ni = −2 kJ/mol, ∆H Fe-Mn = 0 kJ/mol). Their interaction with the center Al-like atoms is much stronger (i.e., ∆H Ni-Al = −22 kJ/mol, ∆H Mn-Al = −19 kJ/mol), so that they are treated as Fe-like atoms and classified as shell atoms together with Fe. Table 1. Mixing enthalpy ∆H between center atoms, glue atoms and shell atoms.

Mixing Enthalpy ∆H
Shell Atoms

Fe Mn Ni
Center atoms On the basis of occupation of each element, as many as 190 published compositions of AFA stainless steels [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][39][40][41][42][43][44] were analyzed under three criterions: (1) Set the number of shell atoms as 12; (2) Set the total number of atoms as 16; (3) Set the total number of atoms as 19. By comparison, the interaction between the atoms can be explained best when the number of shell atoms is set as 12, so that the first criterion is applied for AFA stainless steels. The number of atoms of each element are calculated based on (Fe + Ni + Mn) = 12 in 16 atom cluster, and the cluster formula of each reported composition can therefore be obtained. For example, a typical composition of ORNL: AFA2-1 (Fe-14.30Cr-20.00Ni-2.50Al-0.90Nb-2.50Mo-0.15Si-2.00Mn-0.08C) can be written as [Al 0.79 Si 0.04 Nb 0.08 -Fe 8.78 Ni 2.90 Mn 0.31 ]-Cr 2.34 Mo 0.22 , where the center, shell and glue atom can all be regarded as the average atom composed of various elements. For instance, the center atom can be regarded as the average atom composed of (Al,Si,Nb), and the glue atoms are average atoms made up by (Cr,Mo). The cluster formula of as many as 190 AFA stainless steels are calculated and summarized under the criterion that the number of shell atoms is 12, and it is found that mostly their cluster formulas are close to 1:3 model. This result is consistent with the previously calculated optimal chemical structural unit of an FCC solid solution, which is a CN12 cubic octahedron cluster plus three glue atoms [32].
Based on that, series-1 AFA stainless steels are designed to investigate the compromise of Ni and Al, in order to guarantee their single austenitic structure. After microstructural characterization, a general cluster formula for AFA stainless steels is determined as [(Al,Si,Nb) 1 -(Fe,Ni,Mn) 12 ](Cr,Mo,W) 3 [29]. On the fundamentals of this cluster formula, in this paper series-2 alloys are designed to further verify the guiding function of the cluster formula to design AFA stainless steels with single austenitic structure, and in addition to study the effect of minor elements such as Mo, Nb, Ta, W on its mechanical properties and oxidation resistance. The composition of both two series of designed AFA stainless steels are listed in Table 2 and the composition design flowchart of these two series is drawn as Figure 1.  Based on the general cluster formula of AFA stainless steels, our series-2 alloys decrease the content of Nb from Nb 0.15 to Nb 0.06 (in 16 atom cluster), to achieve Nb:C = 1:1 (in at. %), expecting that Nb can be fully precipitated as NbC. The content of Si is kept as Si 0.05 . Combined with the ideal number of center atom Al + Nb + Si = 1, the center of the cluster formula is decided as Al 0.89 Nb 0.06 Si 0.05, so that the basic composition of series-2 is designed as Al 0.89 Si 0.05 Nb 0.06 -Fe 8.7 Ni 3.0 Mn 0.3 -Cr 2.8 Mo 0.2 (2-1). Afterwards, series-2 alloys are designed by adjusting their alloying elements through the method of equal-proportion replacement. This method here refers to the design principle of high-entropy alloys and has been an effective alloy design method at present and appears in many systems. As shown in Figure 1 Table 2, wherein a 16-atom cluster x = 0.03 or 0.06, y = 3.0 or 3.2, z = 0.07 or 0.2, and all alloys are marked with Nb x Ta 0.06−x Ni y (Mo,W) z hereafter.

Materials and Methods
These eight series-2 alloy ingots with a weight of about 13 g were prepared by nonconsumable vacuum arc-melting furnace (WK model manufactured by Beijing Physcience Opto-electronics Co. Ltd., Beijing, China). The purities of the raw metals are 99.99 wt. % for Fe, Ni, C and Si, 99.5 wt. % for Cr, Mo, Nb, Ta and W, and 99.999% for Al, respectively. Before melting, the vacuum of the furnace was controlled below 6 × 10 −3 Pa, and the melting process were protected by the argon atmosphere with a purity of 99.999%. These alloy ingots were melted repeatedly at least five times for composition homogeneity, in which the mass loss was controlled below 0.1 wt. %. The alloy ingots were then prepared into alloy bars with a diameter of 6 mm by using vacuum copper mold suction followed by fast cooling. These alloy bars were solutionized at 1250 • C for 1.5 h plus water quenching, and then aged at 800 • C for 24 h plus furnace cooling. The high-temperature oxidation experiment was conducted in a muffle furnace (KSL-1400X-A2, Hefei Kejing Material Technology Co. Ltd., Hefei, China) at 800 • C in air. The sample size for oxidation is Φ6 × 12 mm. The samples were weighted after 0, 25, 50, 75, 100, 150 and 200 h, respectively.
Structural identification of alloy samples with different heat treatments was carried out by means of a BRUKER X-ray diffractometer (XRD) (Billerica, MA, USA) with a Cu K α radiation (λ = 0.15406 nm). The microstructure was observed using OLYMPUS light microscopy (LM) (Olympus Tokyo, Japan) and Zeiss Supra55 scanning electron microscopy (SEM) (Carl Zeiss AG, Oberkochen, Germany) with an etching solution of 20% HF + 10% HNO 3 + 70% H 2 O (volume fraction). The microhardness was tested with a HVS-1000 Vickers hardness tester with a load of 500 g and loading time of 20 s. The average value was calculated after each sample was measured 10 times.

Microstructural Characterization
XRD results of solutionized and aged alloys are shown in Figure 2a,b, respectively. The series-2 alloys, Nb x Ta 0.06−x Ni y (Mo,W) z , exhibit a single face-centered cubic γ austenitic structure after being solutionized at 1250 • C for 1.5 h and aged at 800 • C for 24 h. No diffraction peak of ferritic structure is observed in either of the states, though tiny amounts of NiAl-B2 phase should form in aged alloys. These results indicate that the general cluster formula of AFA stainless steels [(Al,Si,Nb) 1 -(Fe,Ni,Mn) 12 ](Cr,Mo,W) 3 guarantees a stable austenitic state. The optical microstructures of solutionized and aged series-2 alloys are shown in Figure 3. The suction-cast ingots show typical casting microstructure, with uniform equiaxial grains in the central region and columnar grains at the outer region. These graphs of the eight Nb x Ta 0.06−x Ni y (Mo,W) z series-2 alloys do not show any ferritic structure, which is consistent with the XRD results. Again, the austenite stability is reached within the framework of the general cluster formula for AFA stainless steels.
The  (2)(3)(4)(5)(6)(7)(8), are shown in Figure 4. The secondary electron morphologies after aging at 800 • C/24 h and the backscattered images after aging at 800 • C/200 h are placed on the left and right, respectively. No ferritic structure is observed that confirms the XRD and OM results. In addition, bulky NbC is not observed from the secondary electron morphologies, due to the decrease in Nb content, from Nb 0.15 (in series-1) to Nb 0.06 (in series-2). As shown in the backscattered images of 800 • C/200 h aged alloys, the NiAl-B2 (brighter) and Fe 2 Nb/Fe 2 Mo-Laves (darker) phases are uniformly distributed. After the 200 h aging, a bulky σ phase is formed as identified according to reference [11], showing a brightness between B2 phase and Laves phase and lengths up to 4 µm at the grain boundaries. By examining Figure 4 Figure 6 gives the composition distribution in terms of Cr eq and Ni eq on a Schaeffler constitution diagram of the two alloy series, designed according to the cluster formula as well as typical Al-modified austenitic stainless steels for high-temperature oxidation purpose reported in the literature [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][39][40][41][42][43][44]]. Uggowitzer's equivalent equations are used to calculate their Cr equivalent and Ni equivalent. It can be seen that this kind of Al-contained stainless steel mostly falls in the pure austenite region and the austenite plus 5 vol.% ferrite dual-phase region. The most concentrated region is the area between 20-30 Cr eq and 22-32 Ni eq , shown as the dashed rectangle. Within this concentrated region, relatively stable austenite can be achieved. The designed alloy series also fall within this region.  [28]: Ni eq = % Ni + % Co + 0.1% Mn − 0.01 Mn 2 + 18% N + 30% C; Cr eq = % Cr + 1.5% Mo + 1.5% W + 0.48% Si + 2.3% V + 1.75 Nb + 2.5% Al.
The austenite stability of our designed alloys is consistent with the prediction by the Schaeffler constitution diagram combined with Uggowitzer's equivalent equations, as shown in Figure 6. The reference composition Al 0.8 Ni 3.0 (1-1) from ONRL, which is located on the boundary of austenite and ferrite regions, maintains a single austenitic structure. With the increase in Al, Al 1.0 Ni 3.0 (1-2) and Al 1.1 Ni 3.0 (1-3), which have similar Ni eq to Al 0.8 Ni 3.0 (1-1) but gradually higher Cr eq , fall in the dual-phase region containing 5 vol.% ferrite. By increasing the amount of Ni, Al 1.0 Ni 3.2-4.0 (1-4-1-7) return to the pure austenite region. The microstructural characterization indicated that ferrite was only observed in Al 1.0 Ni 3.0 (1-2) and Al 1.1 Ni 3.0 (1-3), which agreed with their locations on the Schaeffler constitution diagram. A slight increase in Ni as Al 1.0 Ni 3.2 (1-4) is enough for austenite stability, which also means that alloys such as Al 1.0 Ni 3.4-4.0 (1-6-1-7) contain excessive Ni contents. This is why Nb x Ta 0.06−x Ni 3.0 (Mo,W) z (2-1-2-3) with similar Nieq but lower Cr eq than Al 0.8 Ni 3.0 (1-1) and Nb x Ta 0.06−x Ni 3.2 (Mo,W) z (2-5-2-8) with similar Ni eq but lower Cr eq than Al 1.0 Ni 3.2 (1-4) all fall into the pure austenite region. These results confirm the sufficient austenite stability of the series-2 alloys satisfying the cluster formula.

Hardness
The hardness of designed alloys versus Ni eq /Cr eq and (Ni eq 2 + Cr eq 2 ) 1/2 are plotted in Figure 7a,b, respectively. The equivalent ratio Ni eq /Cr eq reflects the stability of austenite relative to ferrite. The larger the ratio, the higher the relative austenite stability of an alloy is. It is noticed from Figure 7a that alloys with Ni eq /Cr eq ≥ 0.8 all have single austenitic structure, while Al 1.0 Ni 3.0 (1-2) and Al 1.1 Ni 3.0 (1-3) with Ni eq /Cr eq < 0.8 possess austenite-ferrite dual phase structure. (Ni eq 2 + Cr eq 2 ) 1/2 is the distance from point zero to the composition point on Schaeffler constitution diagram, which reflects the amount of alloying elements in the corresponding compositions.  [13,18,23] according to the conversion equations between the hardness and tensile strength of austenitic stainless steels [45].
All alloys in series-2 have similar hardness, approximately 200 HV after being aged at 800 • C/24 h and 150 HV after being solutionized at 1250 • C/1.5 h. This is because their composition difference is quite small. It is noticed that the series-2 alloys, which possess smaller (Ni eq 2 + Cr eq 2 ) 1/2 and henceforth less alloying elements than series-1, generally have lower hardness than those in series-1. This is because the decreases of C (from 0.1 wt. % to 0.08 wt. %), Nb (from 1.6 wt. % to 0.64/0.32 wt. %) and even Al (from as high as 3.4 wt. % to 2.75 wt. %) in series-2 lead to the decrease in the amounts of strengthening phases such as NbC, NiAl, and Fe 2 Nb. In addition, the strengthening effect of NiAl-B2, Fe 2 Nb/Fe 2 Mo-Laves and also MC (mainly NbC) is reflected by the increase of 30-70 HV of hardness after aging in comparison with samples in the solutionizing state.
According to the tensile test results of ORNL at room temperature, the yield and ultimate strength of the solutionized AFA4-1 (4Al/0.6Nb/0.1Ti) are, respectively, 270 MPa and 600 MPa [13]; those of solutionized B-1.0 (Fe-2.87Al-0.14Si-1.01Nb-20.11Ni-1.93Mn-14.24Cr-2.00Mo-0.99W-0.47Cu-0.10C) are, respectively, 261 MPa and 613 MPa [18]; those of 20Ni-(3-4)Al-(0.6-1)Nb based AFA stainless steels are 237-282 MPa (yield strength/solutionizing state), 568-660 MPa (ultimate strength/solutionizing state), 422-434 MPa (yield strength/ aging state) and 744-811 MPa (ultimate strength/aging state) [23]. For easy comparison, the tensile results of ORNL are converted to hardness, referring to the study on the conversion relationship between the hardness and tensile strength of austenitic stainless steels by Chen et al. [45], yield strength R P0.2 = 3.4 × HV − 212.90 and ultimate strength R m = 2.1 × HV + 252.46. The estimated hardness of ORNL's AFA stainless steels are therefore calculated as 132. .07 HV under solutionizing state and 186.74-265.97 HV under aging state (shown as the shaded regions in Figure 7). It should be noted that both the ONRL's and our designed series-1 alloys have a higher content of C (0.1 wt. % C) than the 0.08 wt. % C in series-2. Comparing the hardness of both solutionizing and aging state, the hardness of our series-1 alloys is generally higher than that of the ORNL, while the series-2 alloys with lower C/Nb/Al and thus fewer strengthening precipitates (such as MC, NiAl-B2 phase and Fe 2 Nb/Fe 2 Mo-Laves phase) still have hardness within the estimated range of the ORNL.

High-Temperature Oxidation Resistance
High-temperature oxidation resistance tests were performed on all bar samples of series-2 Nb x Ta 0.06-x Ni y (Mo,W) z (x = 0.03 or 0.06, y = 3.0 or 3.2, z = 0.07 or 0.2 in 16 atoms cluster) alloys in air at 800 • C. Their mass changes per unit area after 0, 25, 50, 75, 100, 150 and 200 h are plotted in Figure 8. From a general view, except Nb 0.06 Ni 3.0 Mo 0.07 (2-2), the oxidation weight gains are relatively smooth and are less than 0.5 mg/cm 2 within 200 h. However, Nb 0.06 Ni 3.0 Mo 0.07 (2-2), which has the most obvious oxidation weight gain in the first 50 h, experiences continuous and severe weight losses after that. Considering the exfoliation of the oxide layer observed during the weighting procedure of Nb 0.06 Ni 3.0 Mo 0.07  bar, it can be inferred that the abnormal weight loss is highly likely to be caused by the splashing of oxide exfoliation out of the crucible. The vertical range between 0 and 1.0 mg/cm 2 is magnified for a close-up view of the alloys' mass change. It can be observed that the smallest weight gain is possessed by Nb 0.03 Ta 0.03 Ni 3.2 Mo 0.2 (2)(3)(4)(5) and Nb 0.03 Ta 0.03 Ni 3.2 Mo 0.07 (2)(3)(4)(5)(6)(7)(8) alloys, which are the alloys with high Ni content and containing Ta, followed by Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 (2)(3)(4)(5)(6)(7), which also has high Ni and contains W. This indicates that the addition of Ta and W has a positive effect on improving the high-temperature oxidation resistance of AFA stainless steels. The effect of Ta on the oxidation resistance of AFA stainless steels at 800 • C is consistent with our team's previous study [46].
According to the Chinese aircraft industry's standard testing method of oxidation resistance for steels and superalloys (HB 5258-2000) [47], the level of oxidation resistance is determined by calculating the average oxidation rate per surface area of a sample, together with its average oxidation-peeling mass per surface area. The average oxidation rate and average oxidation-peeling mass of series-2 alloys, during 200 h oxidation, are calculated as listed in Table 3. The standard classifies our designed AFA stainless steels, with average oxidation rate <0.1 g/m 2 × h and average oxidation-peeling mass <1.0 g/m 2 , to a complete oxidation resistance level, except Nb 0.06 Ni 3.0 Mo 0.07  which has an abnormal weight loss.   (2)(3)(4)(5)(6)(7) has the most even and uniform oxide layer among these alloys, without any nodules. In addition, a large number of black particles appeared below the oxide layer, along with the needle-like NiAl-B2 phase. Among them, Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 (2-7) has the least number of black particles with a thickness of approximately 70 µm, while the others possess thickness more than 250 µm. It indicates that Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 (2-7) has the most uniform oxide layer and the least internal particles. Figure 10 is the SEM-EDS cross-section elemental mapping of Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 (2-7), Nb 0.03 Ta 0.03 Ni 3.2 Mo 0.07 (2)(3)(4)(5)(6)(7)(8) and Nb 0.06 Ni 3.0 Mo 0.2 (2-1), which, respectively, represent W-containing, Ta-containing, and (Ta, W)-free designed alloys. Composition mapping analysis of other alloys with relevant elements shows quite similar tendencies. It is observed that the distribution of elements is quite different between the Ta/W-containing and (Ta, W)-free alloys. In both of the Ta/W-containing alloys, the internal particles observed in SEM images are enriched with the elements Al and N, presumably AlN. More importantly, a continuous Al 2 O 3 layer is formed under the outer (Cr, Fe)-rich oxide layer. No oxygen concentration is observed in the matrix below the oxide layer of Ta/W-containing alloys, as shown in Figure 10a  By combining the SEM cross-section images and the corresponding elemental mapping results, we can see that Cr 2 O 3 -type layers with internal Al 2 O 3 particles are formed in (Ta, W)-free alloys, as shown in Figure 9a,b. Different from the above, the Ta/W-containing alloys have continuous protective Al 2 O 3 layers that inhibit oxygen from further diffusion inwards, so that internal AlN particles are formed instead of Al 2 O 3 . The internal nitride zone of Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 (2-7) is much thinner than those of Nb 0.03 Ta 0.03 Ni 3.2 Mo 0.2 (2)(3)(4)(5) and Nb 0.03 Ta 0.03 Ni 3.2 Mo 0.07 (2)(3)(4)(5)(6)(7)(8), as shown in Figure 9c-e. It seems to indicate that W has a much stronger inhibiting effect on nitrogen diffusion, compared to Ta. Considering the relatively high average oxidation-peeling mass of Nb 0.06 Ni 3.2 Mo 0.04 W 0.03 , W additionally seems to promote the peeling of the outer Cr 2 O 3 -type layer. In conclusion, the addition of Ta/W is beneficial for improving the high-temperature oxidation resistance of AFA stainless steels. The addition of both Ta and W will be considered to investigate their co-effect on the oxidation behavior of AFA stainless steels in the further work.

Conclusions
Based on a 16-atom cluster formula, which was obtained by studying as many as 190 alumina-forming austenitic (AFA) stainless steels, a series of AFA stainless steels alloys, with 0.08 wt. % C, [(Al 0.89 Si 0.05 Nb x Ta 0.06−x )-(Fe 11.7−y Ni y Mn 0.3 )]Cr 3.0−z (Mo,W) z , x = 0.03 or 0.06, y = 3.0 or 3.2, z = 0.07 or 0.2, were designed to verify the guiding function of the cluster formula to achieve austenitic structure and further to investigate the effect of minor alloying elements Nb, Ta, Mo, W on the high-temperature oxidation resistance. It is found that:
The hardness, under a load of 500 g, is approximately 150 HV at solutionizing state and 200 HV at aging state, which falls in the estimated range of Oak Ridge National Laboratory.

3.
After being air oxidized at 800 • C for up to 200 h, most samples can be classified to complete oxidation resistance level for their low oxidation rate, below 0.1 g/m 2 × h, together with low oxidation-peeling mass, below 1.0 g/m 2 . Among them, Nb 0.03 Ta