4.1 Influence of oxidation & composition on stress states at the interface and the effect of interfacial stress gradient on adsorption of water
Figure 2. Temporal variations of mean stress profiles from pre-oxidation (0 ~ 0.5 ns) to early stage oxide film formation (1.5 ~ 2.0 ns) for (a)bcc, (b)fcc alloys and (c)pure Fe. Each alloy near-surface region is set to 50% Fe, 25% Al and 25% Cr in the initial condition (Table I) and the orientation of all structures is the (100) surface. H2O and O2 adsorption and reaction on alloy surfaces are monitored pre-oxidation and then after the formation of the initial oxide film on alloy surfaces compared to pure iron. The evolution of the number of free H2O and O2 molecules in the simulation cells with time is shown for (d)Alloy B1(0 ~ 20 ps), (e) Alloy F1(0 ~ 20 ps), (f)pure Fe (0 ~ 20 ps), (g)Alloy B1(1.5 ~ 1.65 ns), (h)Alloy F1(1.5 ~ 1.65 ns) and (i)pure Fe (1.5 ~ 1.65 ns),respectively. The exhaust gases consist of O2 and H2O (O2: H2O = 1:3). The temperature is 800 K (527oC), i.e. the lower bound on exhaust gas temperatures.
$${\sigma }_{v}=\sqrt{\frac{1}{2}\left[{\left({\sigma }_{xx}-{\sigma }_{yy}\right)}^{2}+{\left({\sigma }_{yy}-{\sigma }_{zz}\right)}^{2}+{\left({\sigma }_{zz}-{\sigma }_{xx}\right)}^{2}+6\left({\sigma }_{xy}^{2}+{\sigma }_{yz}^{2}+{\sigma }_{zx}^{2}\right)\right]}$$
1
where the \({{\sigma }}_{xx}\), \({{\sigma }}_{yy}\), and \({{\sigma }}_{zz}\) are the normal stresses, and the \({{\sigma }}_{xy}\), \({{\sigma }}_{yz}\), and \({{\sigma }}_{zx}\) are the shear stresses in an x-y-z coordinate system. Each alloy near-surface region is set to 50% Fe, 25% Al and 25% Cr. These surfaces are exposed to exhaust gas like environments composed of O2 and H2O at 800 K (527oC). The ratio of O2 to H2O is 3:1. As is shown in Fig. 2, at the initial stage of time (pre-oxidation, 0-0.5ns), all the materials/environment interfaces (for bcc, fcc alloys and pure Fe) have a steep/vertical stress gradient (> 0.6 GPa/Å) at the edges. Following the formation of an initial oxide film (from 1.5–2ns), an oxide scale grows on all of the materials studied, but one distinguished behavior is observed: The Alloy B1 has a relatively gradual stress gradient across the early stage oxide scale, while the fcc alloy and Fe maintain their initial, steep stress gradients at the interface. This difference arises due to the segregation of Al and Cr in the outermost part of the oxide scale of the alloy B1 during the oxidation process (Fig. 3). Evaluations have been made of these three materials in terms of their peak stresses, stress gradient and summation of stresses in the oxide scales. (Table 2).
Table 2
Peak stresses and stress gradients at the surface of the oxide scales, and summation of stresses in the oxide scales for the three structures during 1.5 ~ 2ns (O2: H2O = 1:3, 800K)
Metal
|
Peak stresses
|
Stress gradient
|
Summation of stresses
|
Alloy B1
|
3.5 GPa
|
0.27 GPa/Å
|
80.6 GPa
|
Alloy F1
|
5.1 GPa
|
0.63 GPa/Å
|
95.6 GPa
|
Fe
|
5.7 GPa
|
1.10 GPa/Å
|
148.5 GPa
|
According to these three evaluation criteria, the bcc alloy has the lowest values and Fe has the highest ones. Thus, the bcc alloy is the most resistant to oxidation in a H2O rich environment at 800 K in the very early stage of oxidation up to 2 ns. Fe has the lowest ranking for all the criteria. Figure 2 (d ~ i) shows the variation in the number of H2O and O2 molecules with time for 0–20 ps (d ~ f) and 1.5–1.65 ns (g ~ i), respectively for bcc (Alloy B1), fcc alloy (Alloy F1) and pure Fe, respectively. The initial number of H2O is 150, and 50 is used for the initial O2 number. At the very initial stage of time (0–20 ps), the numbers of H2O and O2 molecules drop very sharply, which means both H2O and O2 adsorb and react on the bare metal surface very quickly. However, for the later time period (1.5–1.65 ns), quite different behaviors are observed. The rate of H2O reaction slows down. The reaction rate of H2O is lowest for the bcc alloy followed by fcc alloy and pure Fe, which is the same order of the stress gradients produced at the interface (Table I). The lower stress gradient at the metal surface effectively means that the surface atoms are less reactive (i.e. in a lower energy state) and so they are less likely to adsorb and react with H2O. On the other hand, a sharp stress gradient at the interface means that the surface atoms are in a higher energy state, and so can react with and adsorb H2O more easily. In other words, a sharp stress gradient surface is indicative of higher energy states and therefore implies a more activated surface. On the other hand, we do not find that the stress gradient has such a pronounced effect on O2 adsorption. We interpret this phenomenon to the significantly higher driving force for O2 dissociation compared to H2O, meaning that the dissociation of water will be more sensitive to mechanical vs chemical effects.
The relative extent of H2O reaction does not just depend on the stress gradient at the surface. For pure Fe, H2O preferentially reacts compared to O2. This results in Fe forming a more hydroxylated surface scale rather than a simple oxide28,29. Hydrogen atoms may diffuse through the scale to reside in interstitial sub-surface sites. Further effects of stress gradient under different conditions of pressure and temperature related to H2O adsorption and alloy composition are presented in Figure S1 and S2 of Supporting Information, respectively.
Figure 3(a) shows the elemental distributions of the bcc alloy during oxidation. Surface segregation of Al and Cr is detected. The outermost element is Al, followed by Cr and Fe. When Al, Cr and Fe are oxidized, AlxOy, CrxOy and FexOy are made. Among these various oxidized structures, the most common species expected to form from thermodynamic arguments are Al2O3, Cr2O3 and Fe2O3, respectively30. This observation is consistent with the heat of formation order (Al2O3, Cr2O3 and Fe2O3). Also, the Young’s modulus of Al2O3 is highest followed by Cr2O3 and Fe2O3. Therefore, the modulus gradient layering in the oxide scale appears to prompt the reduction in the stress concentration31,32. Figure 3(b) also shows that the outer stress profile is aligned with the oxygen distribution and that hydrogen sorption contributes to the inner portion of the stress profile (i.e. the metal-facing side of the nascent oxide scale). Figure 3(c) shows the Fe distribution during oxidation for the pure Fe case. A very sharp gradient of Fe is found at the interface, which is correlated with the sudden increase of the oxygen distribution profile and the sharp, steep stress gradient (Fig. 3(d)). The stress profile at the materials/environment interface is aligned again with the oxygen distribution, and the hydrogen sorption contributes to the increase of stress gradient at the the metal/oxide interface. Compared to the bcc alloy, more hydrogen is found to diffuse into the oxide scale for pure Fe, which suggest that H2O adsorption happens easily and can diffuse fast in the early-stage oxide scale of pure Fe. Figure 3(e) compares oxygen distribution in oxide scales between bcc alloy and pure Fe. The oxygen concentration for pure Fe is higher than for the bcc alloy. For the bcc alloy, both Al and Cr segregate to the surface region, forming a protective passive layer, through which significantly smaller amounts of oxygen can penetrate into the alloy compared to pure Fe.33 Phenomenologically, it is known that surface segregation is responsible for the formation of passive films in iron-based alloys. Even a relatively small concentration of solute atoms in the alloy can lead to significant coverage of these atoms on a free surface of the alloy due to enrichment in the near-surface region. In this context, passivity is achieved through favorable surface segregation of the more thermodynamically stable oxides as a compact film with fewer stresses at the material/environment interface.33
Oxygen in the scale that originates from H2O and oxygen that originates from molecular O2 reaction with the materials are distinguished and quantified as presented in Table 3.
Table 3
Oxygen ratio between O (H2O) and O(O2)
Oxygen ratio
|
Alloy B1
|
Fe
|
O(H2O)/ O(O2)
|
1.42
|
1.51
|
The number of oxygen atoms derived from H2O is less than the number of oxygen atoms originating from O2 for the bcc alloy compared to pure Fe. This suggests that less H2O is adsorbed for the bcc alloy material and this further supports the inference that the bcc alloy is more resistant to a H2O-rich environment. It can be interpreted that surface segregation of Al and Cr plays a role for producing a more gradual stress gradient at the interface, blocking oxygen diffusion, and slowing down H2O adsorption. However, surface segregation does not occur unless a minimum initial bulk concentration of Al or Cr is met during oxidation33.
Surface segregation of Al or Cr appears to be correlated with the development of a more gradual stress gradient at the metal/environment interface. The anti-corrosion properties of Fe-Cr-Al alloys strongly depend on the initial bulk concentration. Figure 4(a) shows that there is a significant amount of Al and a lesser amount of Cr segregation at the materials/environment interface when the bulk concentration is set to Fe 50% Al25% Cr25%.
For Fe 75% Al20% Cr5% bulk concentration, only Al segregation is observed (Fig. 4(b)). For Fe 75% Al5% Cr20%, neither Al nor Cr segregate to the interface (Fig. 4(c)). We explain this result by considering that the Al portion must be below the threshold and the 20% Cr is also insufficient to cause it to segregate to the surface within the scope and timescale of our simulation. It can be concluded that a minimum portion of Al is required to prompt surface segregation, which leads to gradual stress gradient at the interface of oxide scale. To have Cr segregation, the minimum portion of Cr should be larger than Al.
So far, we have discussed the corrosion behavior of hypothetical Fe-Cr-Al alloy systems in a water-rich environment (O2:H2O = 1:3). The same kinds of simulations were conducted in an oxygen-rich environment (O2:H2O = 3:1) and presented in Figure S5 of S.I. A comparison was made for bcc, fcc alloy and pure Fe based on the three evaluation criteria (peak stress, stress gradient and summation of stress in oxide scale) under water-rich, raised temperature and oxygen rich environment in Figure S6 and Table S1 of S. I.. We found that the lower stress gradient at the alloy surface does not appear to influence the O2 adsorption and reactivity. Thus the bcc alloy is not the most corrosion resistant under these conditions. Based on our three evaluation criteria, the fcc alloy has better resistance in the early stages of corrosion than the bcc alloy under the oxygen rich environment.
4.2 Relation of stress gradient to diffusivity of oxygen and hydrogen in the oxide scale
Figure 5 shows the relation between stress gradient at the interface and the diffusivity of hydrogen and oxygen. As shown in Fig. 5(a) and (b), the diffusivities of O and H decrease very rapidly when they pass into the oxide scale, which is expected because (a) there is a change of state across the interface from gas, to surface adsorbate, to interstitials or other defects in the oxide and metal, and (b) it is known that stress slows down diffusivities34–36. The alloy and pure Fe have quite different diffusion profiles of the environmental species. For the alloy material, the diffusivities of O and H drop sharply for that section of the profile that has increasing stresses at the surface (the green rectangular bounding box) (Fig. 5(a)). On the contrary, in pure Fe, the diffusivities of O and H do not decrease rapidly for the stress increasing section; O and H diffuse more rapidly inward, beyond the peak stress point. In addition, although diffusivity of H is higher than that of O for both alloy and pure Fe, the difference between H and O diffusivity narrows for the alloy materials, whereas in pure Fe they maintain this gap in diffusivities through the oxide layer. The inset figures in Fig. 5(a) and (b) support this result, showing a mixed-disordered distribution of O and H for the alloy but a layered ordered distribution of O and H for pure Fe. To highlight distributions of oxygen and hydrogen, metal atoms are not shown in the inset figures. Due to the different bond lengths for Al-O, Cr-O and Fe-O, this mixed-disordered distribution of oxygen is made and creates a ‘self-blocking effect’ of diffusion of oxygen and hydrogen as well hindering the growth of oxide scale for the alloy. On the contrary to the alloy case, for pure Fe layered O and H distributions are observed in the inset figure of Fig. 5(b) since only a single bond-type, the Fe-O bond, exists. Diffusivity of hydrogen is higher than that of oxygen, which explains the locations of oxygens and hydrogens in the oxide scale. Diffusion is dominated by interstitial diffusion.
Figures 5(c) and (d) show the diffusivity changes with time for the bcc alloy and for pure Fe, respectively. For the section of 0-0.5 ns (yellow box) in Fig. 5(c), the diffusivities do not change significantly, while a more significant decrease in diffusivities happens for the section of time from 1.5-2 ns (green box). The developing region of lower stress gradient across the emergent oxide causes the diffusivities to decrease significantly. The lower stress gradient of the alloy system contributes to lowering the diffusivities of O and H. For pure Fe, the diffusivities do not decrease much for both 0-0.5 ns and 1.5-2ns (Fig. 5(d)). The H diffusivity in pure Fe lies between 2×10− 7 and 5×10− 7 m2/s at the interface region, which agrees well with the experimental value37 of 2.24×10− 7 m2/s. Figure 5(e) and (f) show the diffusivity change with increasing exhaust gas pressure for the bcc alloy and for pure Fe, respectively. The lower stress gradient that occurs in the higher-pressure simulation (green box) makes the diffusivities decrease more than in the reference pressure case (yellow box) (Fig. 5(e)), while this same effect is not observed for pure Fe (Fig. 5(f)). In summary, the lower stress gradient of the alloy, resulting from the surface segregation or (alternatively) from a pressure increase, appears to play a role in decreasing the diffusivities of the oxidizing gases during corrosion processes.