A Mechanism of Anti-Oxidation Coating Design Based on Inhibition Effect of Interface Layer on Ions Diffusion within Oxide Scale

: In this paper, a mechanism of anti-oxidation coating design based on the inhibition effect of the interface layer on the diffusion of ions within oxide scale was introduced. The Fe 2+ ions diffusion behavior in Fe 3 O 4 , Cr 2 FeO 4 , and FeAl 2 O 4 were studied by molecular dynamics method of Nudged elastic bond. As the result shown, Fe 2+ ions tended to diffuse through the vacancy at tetrahedral site in Cr 2 FeO 4 and FeAl 2 O 4 , but diffuse through the octahedral vacancy in Fe 3 O 4 . When temperature ranged from 1073 to 1325 K, the energy barrier of Fe 2+ ions diffusion in Cr 2 FeO 4 was higher than that of FeAl 2 O 4 , and both of that were still obvious higher than that in Fe 3 O 4 . A new anti-oxidation coating was prepared based on the inhibition of interface layer consisted of FeAl 2 O 4 to protect the carbon steel S235JR at 1200 ◦ C for 2 h. The FeAl 2 O 4 region was formed and observed at the interface between coating and Fe element diffusion area, and the mullite phase was distributed outside of the FeAl 2 O 4 region. Comparing to the bare sample, the prepared coating exhibited an excellent anti-oxidation effect.


Introduction
In order to reduce the damage caused by the serious oxidation during the reheating process before hot rolling, temporary protective coating is usually utilized due to its low price and easy operation [1][2][3]. Recently, most of the research are depended on the preparation and the anti-oxidation of the coating [4,5], but there are few reports about the ideas of the anti-oxidation coating design. Referring to the theory of metal oxidation at high temperature, a mechanism of anti-oxidation coating design based on the inhibition effect of the interface layer on the diffusion of ions within oxide scale was introduced in this paper. According to the mechanism, a new ceramic coating was prepared to protect the carbons steel S235JR at 1200 • C for 2 h. The mechanism was verified with the anti-oxidation effect of the coating and structure of the interface layer.
The oxidation law of metal at high temperature was the basis of the anti-oxidation design. As we all known, there were two main stage during the oxidation of the metal at high temperature. At the initial stage, the oxidation rate was controlled by the reaction resulted from the direct contact between the oxygen and substrate and the kinetics could be expressed by linear law [6]. As the reaction went on, the oxide scale gradually turned thicker, and the kinetics followed the parabolic law, which meant that the ions diffusion played a significant role at this stage [6]. However, the current anti-oxidation coatings Cr 3+ ions occupied the octahedral site, while Fe 2+ ions filled the tetrahedral space. In the crystal lattice of Fe 3 O 4 , half of the Fe 3+ ions and all the Fe 2+ ions occupied the octahedral site, while the other Fe 3+ ions filled the tetrahedral space. According to the report of Frolich and Stiller [15], Fe-O bond in octahedral site in the crystal lattice of Fe 3 O 4 were prone to break and generated cation vacancy. In addition, the Fe 2+ ions were prone to diffuse through the cation vacancy at octahedral site based on the research of Dickman [14]. Therefore, it was possibly to infer that a crystal lattice with less Fe 2+ ions at octahedral site contributed to inhibition effect on Fe 2+ ions diffusion, such as FeAl 2 O 4 which could be expressed as (Fe 2+ 0.77 Al 3+ 0.23 ) tet (Fe 3+ 0.07 Fe 2+ 0.05 Al 3+ 0.88 ) 2oct O 4 according to the research operated by Jastrzebska [17]. Odashima et al. prepared a kind of anti-oxidation coating for 3% Si-steel [18]. In his work, FeAl 2 O 4 was firstly introduced as functional components to improve the anti-oxidation effect, but the mechanism of inhibition effect of FeAl 2 O 4 was not further studied.
With the development of computation science, the study of ions diffusion behavior could be researched by molecular dynamics. In this paper, the Fe 2+ ions diffusion behavior in Fe 3 O 4 , Cr 2 FeO 4 , and FeAl 2 O 4 were studied by molecular dynamics method of Nudged elastic bond. The diffusion path of Fe 2+ ions were analyzed by comparing the cationic defect formation energy at tetrahedral and octahedral sites in the crystal lattice above. The Fe 2+ ions diffusion energy barrier under the corresponding path conditions were calculated to verify the inhibition effect of Cr 2 FeO 4 and FeAl 2 O 4 on Fe 2+ ions diffusion at high temperature. A new anti-oxidation coating was prepared based on the inhibition of interface layer consisted of FeAl 2 O 4 to protected the carbon steel S235JR at 1200 • C for 2 h. The protective effect of the coating was investigated, and the mechanism based on the inhibition effect of interface layer was verified by the distribution of elements in the coating cross-section and the structure of interface layer.
S235JR was a kind of most common carbon steel, the reheating temperature before hot rolling usually ranged from 1100 to 1250 • C based on the size of the billet, which was closed to that of most other kinds of carbon steel. There was only trace element of Si and Mn, which had no obvious influence on the structure of the scale. S235JR was selected as the protected object in this paper, which could ensure the universality of the obtained mechanism suitable for most kind of carbon steel and low alloy steels with the scale consisted of FeO, Fe 3 O 4 , and Fe 2 O 3 . If some other kinds of steel, of which the kinetics followed by parabolic law, was selected as protective object, anti-oxidation coating could be designed and prepared by the method obtained in this paper. Therefore, this paper mainly provided method of anti-oxidation design based on the inhibition effect of interface layer on ions diffusion at high temperature, which had significance of guidance and reference.

Methodology of the Molecular Dynamics
In order to calculate the diffusion paths and energy barriers of an Fe 2+ [17]. A substitutional vacancy is introduced to the crystal by randomly deleting one of the Fe 2+ ions at the octahedral site or tetrahedral site. The crystal structure before and after the vacancies formation was shown as Figure 1.  [21,22]. In this potential, the system energy consists of two parts of contributions, i.e., the electrostatic part and the non-electrostatic part. A charge equilibration (Qeq) procedure is applied during the simulation to accurately capture the ionic interactions. A 12Å cutoff radius is adopted, and the Qeq minimization is performed at each time step. Throughout this study, a Nosé-Hoover thermostat is used and a 1 fs simulation time step is chosen. All simulations are performed using the open source software LAMMPS (V.2014) [22] and structures are visualized using Ovito (V.2.9.0) software [23]. Figure 1. Schematic of crystal structure (a-1) Fe3O4 without any vacancy (a-2) Fe3O4 with octahedral vacancy (b-1) FeAl2O4 without any vacancy (b-2) FeAl2O4 with tetrahedral or octahedral vacancy (c-1) Cr2FeO4 without any vacancy (c-2) Cr2FeO4 with tetrahedral vacancy. The path and energy transition of an Fe 2+ ion diffusing towards the vacancy at 0 K are determined by the nudged elastic band (NEB) method [19]. Five atomic locations are identified, including the starting/ending octahedral sites and 3 transitional sites along the diffusion path for Fe 3 O 4 and FeAl 2 O 4 , the starting/ending tetrahedral sites and 3 transitional sites along the diffusion path for Cr 2 FeO 4 and FeAl 2 O 4 . After determination of the diffusion path, the energy barriers of the diffusing Fe 2+ ion under finite temperatures are calculated. Five simulations are conducted at each temperature (i.e., 1073 K, 1173 K, 1273 K, 1373 K, 1473 K, and 1523 K), corresponding to the Fe 2+ ion initially located at the 5 sites along its diffusion path. The systems are allowed to equilibrate at the given temperature. In this case, the Fe 2+ ion will gradually diffuse to its stable locations under the thermodynamic driving force. The evolution of system energy is monitored and the corresponding energy barrier under the specific temperature can thus be calculated.
In these study, the charge transfer ionic potential (CTIP) originally proposed by Zhou et al. is adopted as the interatomic force filed [20]. Such a force filed has received wide applications and proved to be accurate in handling both ionic and covalent materials [21,22]. In this potential, the system energy consists of two parts of contributions, i.e., the electrostatic part and the non-electrostatic part. A charge equilibration (Qeq) procedure is applied during the simulation to accurately capture the ionic interactions. A 12Å cutoff radius is adopted, and the Qeq minimization is performed at each time step. Throughout this study, a Nosé-Hoover thermostat is used and a 1 fs simulation time step is chosen. All simulations are performed using the open source software LAMMPS (V.2014) [22] and structures are visualized using Ovito (V.2.9.0) software [23].

Preparation of the Sample
Carbon steel, S235JR, with a specimen size of 10 × 10 × 10 mm 3 was used for evaluating the oxidation resistance performance of anti-oxidation coating. The composition of S235JR was listed in Table 1. The samples were polished by abrading with SiC papers from 200# grit to 1200# grit, and then cleaned through an ultrasonic treatment.  (2)). However, this reaction is difficult to occur at low temperature and usually needs to be heated to more than 1400 • C or directly depends on electric fusion.
According to the above reactions, the FeAl 2 O 4 can also be synthesized through the reaction between Fe 3 O 4 and raw mineral materials containing Al 2 O 3 . In the process of using aluminum-based refractories, FeAl 2 O 4 usually exists as transition phase at the interface between the refractory brick and the metal oxide layer or molten metal iron. Therefore, mullite containing Al 2 O 3 are selected as principle raw materials of coating slurry in this paper. Sodium silicate was selected as binder in this paper. On one hand, dehydration and condensation of silanols could form inorganic polymer network, which could increase the curing property of coatings at room temperature. On the other hand, the amorphous SiO 2 exhibited excellent reactivity, which could improve the sintering of the ceramic particles [27]. Sodium polyacrylate was used as dispersant in this paper. In the dispersed system of ceramic clay and water, there was a large number of diffuse double electric layers on the surface of the ceramic clay. There were a lot of carboxyl groups on the main chain of sodium polyacrylate. When sodium polyacrylate solution severed as dispersant, the ceramic particles would be suspended and dispersed due to the charge repulsion [28]. The ceramic coating was prepared to prevent the carbon steel S235JR from oxidation at 1200 • C for 2 h. The composition of ceramic coating slurry is shown in Table 2. The above raw materials were added to a beaker in the proportion as shown in Table 1 and mixed under magnetic stirring at 500 r·min −1 for 30 min. The prepared coating slurry was sprayed onto the surface of S235JR sample. The sample size was 10 mm × 10 mm × 10 mm, and the thickness of coating was about 0.4 mm.

Evaluation of the Anti-Oxidation Coating
The bare and coated samples of S235JR were placed into a continuous thermos-balance (RZ, Luoyang Precondar, Luoyang, China), respectively. The samples were heated from room temperature to 1200 • C at a rate of 10 • C·min −1 and maintained for 2 h. The counting interval was set for 1 min, and the oxidation weight gain of the samples during heating process was recorded continuously.
The oxidation kinetics of the substrate usually followed the linear law at the initial stage of oxidation, namely, the oxidation rate was controlled by the oxidation reaction, which was relative to the partial pressure of oxygen. In this case, the oxidation kinetic equation should follow the linear rule, and its expression was shown in Equation (3). Here, the ∆ω was the weight gain of sample per unit area (mg·cm −2 ), H was a constant, k t was the oxidation reaction rate constant (mg·cm −2 ·s −2 ), ti was the reaction time (min). A linear fitting curve of ∆ω versus t i could be plotted, and the slope of the curve is the oxidation reaction rate constant of k s .
When the oxide layer reached to a certain thickness, the reaction rate was controlled by the diffusion of Fe 2+ ions. In this case, the oxidation kinetic equation should follow the parabolic rule, and its expression was shown in Equation (4). Here, the ∆ω was the weight gain of sample per unit area (mg·cm −2 ), H was a constant, k p was the oxidation reaction rate constant at stage for parabolic law (mg 2 ·cm −4 ·s −2 ), t i was the reaction time (min). A linear fitting curve of (∆ω) 2 versus t i could be plotted, and the slope of the curve is the oxidation reaction rate constant of k p .
The weight gain data during the temperature-holding stage at 1200 • C could be fitted by the method as follow. Frist of all, we set a time node per 5 min from 5 to 115 min, because at least 5 points were needed to ensure the accuracy of the curve fitting. The weight gain data from 0 min to the time node was fitted by the linear law, while that from time node to 120 min was fitted by the parabolic law. Both of the correlation coefficients were recorded when the time node changed from 5 to 115 min. By comparing the correlation coefficient, the time node was determined, and the oxidation weight gain data was fitted by different stages with linear law and parabolic law.
The anti-oxidation effect of the coating could be intuitively observed through the oxidation weight gain curve of the bare and coated sample. The inhibition effect of the prepared coating on the diffusion of Fe 2+ ions at high temperature could be evaluated by comparing the oxidation reaction rate constant of the bare and coated sample in the temperature-holding stage.
X-ray diffractometer was engaged to determine the phase formed on the inner-face of the coating, proving the formation of the FeAl 2 O 4 interface layer. The element distribution at cross section of the bare and coated sample was characterized by Scanning electron microscopy equipped with an Energy Dispersive X-ray Spectroscopy to analyze the composition of the interface layer between the coating and carbon steel substrate and verify whether the designed reaction path of FeAl 2 O 4 was rational or not. According to the difference of Fe distribution, the inhibition effect of interfacial layer structure on the diffusion of Fe 2+ ions at high temperature could be further investigated.
The experimental instruments used in this study were listed in Table 3.

Vacancy Formation Energy and the Diffusion Path of Fe 2+ Ions
As shown in Table 4, the vacancy formation energy of Fe 2+ ions at octahedral site was 3.859 eV/atom, which was lower than that of Fe 3+ ions at tetrahedral site in Fe 3 O 4 crystal lattice. However, the vacancy formation energy of Fe 2+ ions at octahedral site was 6.518 eV/atom, which was higher than that of Fe 2+ ions at tetrahedral site in FeAl 2 O 4 . In addition the he vacancy formation energy of Fe 2+ ions at tetrahedral site was 3.542 eV/atom and it was obviously lower than that of Cr 3+ ions at octahedral site. According to the data in Table 4, Fe 2+ ions tended to diffuse through the vacancy at tetrahedral site in Cr 2 FeO 4 and FeAl 2 O 4 , but diffuse through the octahedral vacancy in Fe 3 O 4 . The calculated result was in agreement with the research of Freer [29].

Energy Barrier of the Diffusion of Fe 2+ Ions
According to the diffusion path discussion in Section 3.1, the energy barrier of Fe 2+ ions diffusion in Fe 3 O 4 , FeAl 2 O 4 , and Cr 2 FeO 4 were calculated by molecular dynamics method. As shown in Figure 2, the energy barrier of the Fe 2+ ions diffusion in Cr 2 FeO 4 was higher than that in FeAl 2 O 4 , and obviously higher than that in Fe 3 O 4 at 0 K. The result in Figure 2 indicated that the Fe 2+ ions were prone to diffuse in Fe 3 O 4 , which also meant that the FeAl 2 O 4 and Cr 2 FeO 4 could effectively inhibited the diffusion of Fe 2+ ions.

Vacancy Formation Energy and the Diffusion Path of Fe 2+ Ions
As shown in Table 4, the vacancy formation energy of Fe 2+ ions at octahedral site was 3.859 eV/atom, which was lower than that of Fe 3+ ions at tetrahedral site in Fe3O4 crystal lattice. However, the vacancy formation energy of Fe 2+ ions at octahedral site was 6.518 eV/atom, which was higher than that of Fe 2+ ions at tetrahedral site in FeAl2O4. In addition the he vacancy formation energy of Fe 2+ ions at tetrahedral site was 3.542 eV/atom and it was obviously lower than that of Cr 3+ ions at octahedral site. According to the data in Table 4, Fe 2+ ions tended to diffuse through the vacancy at tetrahedral site in Cr2FeO4 and FeAl2O4, but diffuse through the octahedral vacancy in Fe3O4. The calculated result was in agreement with the research of Freer [29].

Energy Barrier of the Diffusion of Fe 2+ Ions
According to the diffusion path discussion in Section 3.1, the energy barrier of Fe 2+ ions diffusion in Fe3O4, FeAl2O4, and Cr2FeO4 were calculated by molecular dynamics method. As shown in Figure 2, the energy barrier of the Fe 2+ ions diffusion in Cr2FeO4 was higher than that in FeAl2O4, and obviously higher than that in Fe3O4 at 0 K. The result in Figure 2 indicated that the Fe 2+ ions were prone to diffuse in Fe3O4, which also meant that the FeAl2O4 and Cr2FeO4 could effectively inhibited the diffusion of Fe 2+ ions.  According to the result in Figure 3, when temperature ranged from 1073 to 1523 K, the energy barrier of Fe 2+ ions diffusion in Cr 2 FeO 4 was higher than that of FeAl 2 O 4 , and both of them were still obvious higher than that in Fe 3 O 4 . The variation rule of the diffusion energy barrier with temperature was shown in Figure 4, which was obtained by a summarization of data in Figure 3. As shown in Figure 4, the energy barrier of Fe 2+ ions diffusion decreased with the increasing of temperature, but the energy barrier of Fe 2+ ions diffusion in Cr 2 FeO 4 and FeAl 2 O 4 were still obviously higher than that in Fe 3 O 4 , which indicated an excellent inhibition effect of Cr 2 FeO 4 and FeAl 2 O 4 on diffusion of Fe 2+ ions diffusion at the temperature ranging from 1073 to 1325 K. Compared with Cr 2 FeO 4 , FeAl 2 O 4 could be prepared from a wide range of raw materials. Therefore, FeAl 2 O 4 was selected as the interface layer to prepare a new anti-oxidation coating to protect the carbon steel S235JR at 1200 • C for 2 h. According to the result in Figure 3, when temperature ranged from 1073 to 1523 K, the energy barrier of Fe 2+ ions diffusion in Cr2FeO4 was higher than that of FeAl2O4, and both of them were still obvious higher than that in Fe3O4. The variation rule of the diffusion energy barrier with temperature was shown in Figure 4, which was obtained by a summarization of data in Figure 3. As shown in Figure 4, the energy barrier of Fe 2+ ions diffusion decreased with the increasing of temperature, but the energy barrier of Fe 2+ ions diffusion in Cr2FeO4 and FeAl2O4 were still obviously higher than that in Fe3O4, which indicated an excellent inhibition effect of Cr2FeO4 and FeAl2O4 on diffusion of Fe 2+ ions diffusion at the temperature ranging from 1073 to 1325 K. Compared with Cr2FeO4, FeAl2O4 could be prepared from a wide range of raw materials. Therefore, FeAl2O4 was selected as the interface layer to prepare a new anti-oxidation coating to protect the carbon steel S235JR at 1200 °C for 2 h.

Anti-Oxidation Effect of the Coating
As shown in Figure 5a, the oxidation weight gain per unit area of coated sample during the temperature-rising process as well as the temperature-holding stage were obviously lower than those of bare sample, indicating that the prepared coating exhibited excellent anti-oxidation effect for S235JR. According to the correlation coefficients shown in the Figure 6a, the oxidation kinetics of the bare sample agreed better with the linear law from 0 to 65 min, namely, the oxidation rate at this stage was controlled by the oxidation reaction, which mainly effected by the partial pressure of oxygen. While oxidation kinetics of the bare sample was described well with the parabolic law from 65 to 120 min, which meant that the oxidation rate at this stage controlled by ions diffusion. The weight gain of the coated sample was refitted with the same method, and the result was shown in Figure 6b. The oxidation kinetics of the coated sample was fitted well with the linear law from 0 to 10 min, while that of coated sample was well described by the parabolic law from 10 to 120 min.

Anti-Oxidation Effect of the Coating
As shown in Figure 5a, the oxidation weight gain per unit area of coated sample during the temperature-rising process as well as the temperature-holding stage were obviously lower than those of bare sample, indicating that the prepared coating exhibited excellent anti-oxidation effect for S235JR.

Anti-Oxidation Effect of the Coating
As shown in Figure 5a, the oxidation weight gain per unit area of coated sample during the temperature-rising process as well as the temperature-holding stage were obviously lower than those of bare sample, indicating that the prepared coating exhibited excellent anti-oxidation effect for S235JR. According to the correlation coefficients shown in the Figure 6a, the oxidation kinetics of the bare sample agreed better with the linear law from 0 to 65 min, namely, the oxidation rate at this stage was controlled by the oxidation reaction, which mainly effected by the partial pressure of oxygen. While oxidation kinetics of the bare sample was described well with the parabolic law from 65 to 120 min, which meant that the oxidation rate at this stage controlled by ions diffusion. The weight gain of the coated sample was refitted with the same method, and the result was shown in Figure 6b. The oxidation kinetics of the coated sample was fitted well with the linear law from 0 to 10 min, while that of coated sample was well described by the parabolic law from 10 to 120 min. According to the correlation coefficients shown in the Figure 6a, the oxidation kinetics of the bare sample agreed better with the linear law from 0 to 65 min, namely, the oxidation rate at this stage was controlled by the oxidation reaction, which mainly effected by the partial pressure of oxygen. While oxidation kinetics of the bare sample was described well with the parabolic law from 65 to 120 min, which meant that the oxidation rate at this stage controlled by ions diffusion. The weight gain of the coated sample was refitted with the same method, and the result was shown in Figure 6b. The oxidation kinetics of the coated sample was fitted well with the linear law from 0 to 10 min, while that of coated sample was well described by the parabolic law from 10 to 120 min. Both the reaction rate constant at different stage of the coated sample and bare sample were calculated with the slope in Figure 7. The result in Figure 7 indicated that the coating exhibited excellent protective effect not only at the oxidation reaction-controlled stage, but also at the ions diffusion-controlled stage. According to the oxidation characterization at different stage, it was deduced that the prepared coating could effectively isolate the substrate from oxygen due to a lower oxidation rate constant at the stage following linear law, and that the coating could effectively inhibit the ions diffusion at high temperature due to a lower oxidation rate constant at the stage following parabolic law. As shown in Figure 8, when heated at 1200 °C for 2 h, the diffusion distance of Fe element in the oxide layer of the coated sample continued to increase with the extension of holding time. However, it was always lower than that of the bare sample, further indicating that the prepared ceramic coating effectively inhibited the diffusion of Fe 2+ ions. Both the reaction rate constant at different stage of the coated sample and bare sample were calculated with the slope in Figure 7. The result in Figure 7 indicated that the coating exhibited excellent protective effect not only at the oxidation reaction-controlled stage, but also at the ions diffusion-controlled stage. According to the oxidation characterization at different stage, it was deduced that the prepared coating could effectively isolate the substrate from oxygen due to a lower oxidation rate constant at the stage following linear law, and that the coating could effectively inhibit the ions diffusion at high temperature due to a lower oxidation rate constant at the stage following parabolic law. Both the reaction rate constant at different stage of the coated sample and bare sample were calculated with the slope in Figure 7. The result in Figure 7 indicated that the coating exhibited excellent protective effect not only at the oxidation reaction-controlled stage, but also at the ions diffusion-controlled stage. According to the oxidation characterization at different stage, it was deduced that the prepared coating could effectively isolate the substrate from oxygen due to a lower oxidation rate constant at the stage following linear law, and that the coating could effectively inhibit the ions diffusion at high temperature due to a lower oxidation rate constant at the stage following parabolic law. As shown in Figure 8, when heated at 1200 °C for 2 h, the diffusion distance of Fe element in the oxide layer of the coated sample continued to increase with the extension of holding time. However, it was always lower than that of the bare sample, further indicating that the prepared ceramic coating effectively inhibited the diffusion of Fe 2+ ions. As shown in Figure 8, when heated at 1200 • C for 2 h, the diffusion distance of Fe element in the oxide layer of the coated sample continued to increase with the extension of holding time. However, it was always lower than that of the bare sample, further indicating that the prepared ceramic coating effectively inhibited the diffusion of Fe 2+ ions. s 2021, 11, x FOR PEER REVIEW 11 of 15 According to the X-ray energy spectrum of oxide layer (Figure 9), the prepared coating consisted of two layers. The outer layer was made of element Si and Al oxide, which could be deduced as sintering layer of mullite due to the atom ratio of energy dispersive spectrometer (EDS) result. Comparing with the kinetics result at the stage following linear law, the sintering layer contribute to form a compact structure, which could isolate the substrate from oxygen. The inner layer consisted of Fe and Al oxide, of which the atom ratio was similar to FeAl2O4. As shown in Figure 10, there was obviously phase peak of FeAl2O4 rather than the Fe oxide. In addition, the phase peak of the solid solution of Fe2O3-Al2O3 was similar to that of FeAl2O4, but the phase peak of the solid solution of Fe2O3-Al2O3 was offset to the small angle position due to the lattice distortion. According to the difference between the phase peak of FeAl2O4 and the solid solution of Fe2O3-Al2O3, the formation of interface of FeAl2O4 could be distinguished from the Fe oxide and the solid solution of Fe2O3-Al2O3 based on the X-ray diffraction (XRD) result in Figure 10. In addition, the peak of the amorphous phase at the small angle from 10 to 20 °could be explained by the liquid phase containing Si oxide. Combined with the XRD result in Figure 10 and EDS result in Figure 9, the formation of FeAl2O4 interface layer could be proved. Therefore, the forming structure comply with the design principle of coating, and the anti-oxidation coating with FeAl2O4 served as interface layer could effectively prevent the oxidation loss of carbon steel at high temperature. According to the X-ray energy spectrum of oxide layer (Figure 9), the prepared coating consisted of two layers. The outer layer was made of element Si and Al oxide, which could be deduced as sintering layer of mullite due to the atom ratio of energy dispersive spectrometer (EDS) result. Comparing with the kinetics result at the stage following linear law, the sintering layer contribute to form a compact structure, which could isolate the substrate from oxygen. The inner layer consisted of Fe and Al oxide, of which the atom ratio was similar to FeAl 2 O 4 . As shown in Figure 10, there was obviously phase peak of FeAl 2 O 4 rather than the Fe oxide. In addition, the phase peak of the solid solution of  Figure 10. In addition, the peak of the amorphous phase at the small angle from 10 to 20 • could be explained by the liquid phase containing Si oxide. Combined with the XRD result in Figure 10 and EDS result in Figure 9, the formation of FeAl 2 O 4 interface layer could be proved. Therefore, the forming structure comply with the design principle of coating, and the anti-oxidation coating with FeAl 2 O 4 served as interface layer could effectively prevent the oxidation loss of carbon steel at high temperature.  As shown in Figure 11, residual oxide scale at the surface of the substrate was mainly consisted of element Fe and O, while Si and Al hardly occurred in the residual oxide scale, namely, the prepared coating were not harmful to the surface quality of the substrate. In addition, the gap between the coating and the substrate indicated that the coating could descaled from the substrate due to the difference of the thermal expansion coefficient during the cooling process.   Figure 11, residual oxide scale at the surface of the substrate wa mainly consisted of element Fe and O, while Si and Al hardly occurred in the res oxide scale, namely, the prepared coating were not harmful to the surface quality substrate. In addition, the gap between the coating and the substrate indicated th coating could descaled from the substrate due to the difference of the thermal exp coefficient during the cooling process.  Figure 11, residual oxide scale at the surface of the substrate was mainly consisted of element Fe and O, while Si and Al hardly occurred in the residual oxide scale, namely, the prepared coating were not harmful to the surface quality of the substrate. In addition, the gap between the coating and the substrate indicated that the coating could descaled from the substrate due to the difference of the thermal expansion coefficient during the cooling process.

Conclusions
Referring to the theory of metal oxidation at high temperature, a mechanism of antioxidation coating design based on the inhibition effect of the interface layer on the diffusion of ions within oxide scale was introduced in this paper. According to the mechanism, a new ceramic coating was prepared to protect the carbons steel S235JR at 1200 °C for 2h. The mechanism was verified with the anti-oxidation effect of the coating and structure of the interface layer.
Some results were obtained as follows: (1) The vacancy formation energy of Fe 2+ in Fe3O4, FeAl2O4, and Cr2FeO4 was calculated by molecular dynamics method of Nudged elastic bond. The diffusion path of Fe 2+ ions were analyzed by comparing the cationic defect formation energy at tetrahedral and octahedral sites in the crystal lattice above. The result indicated that Fe 2+ ions tended to diffuse through the vacancy at tetrahedral site in Cr2FeO4 and FeAl2O4, but diffuse through the octahedral vacancy in Fe3O4. (2) The Fe 2+ ions diffusion energy barrier under the corresponding path conditions were calculated to verify the inhibition effect of Cr2FeO4 and FeAl2O4 on Fe 2+ ions diffusion at high temperature. It could be indicated that when temperature ranged from 1073 to 1325 K, the energy barrier of Fe 2+ ions diffusion in Cr2FeO4 was higher than that of FeAl2O4, and both of that were still obvious higher than that in Fe3O4. (3) A new anti-oxidation coating was prepared based on the inhibition of interface layer consisted of FeAl2O4 to protect the carbon steel S235JR at 1200 °C for 2 h. According to the curve of weight gain per unit area during the temperature-rising process and temperature-holding stage, the oxidation loss of the substrate obviously decreased with the help of the coating. In addition, the oxidation rate constant of coated sample at the stage when the oxidation rate controlled by oxidation reaction was 0.005 mg·cm -2 ·s -1 , which was much lower than that of bare sample (0.01 mg·cm -2 ·s -1 ). It suggested that the prepared coating could effectively isolate the substrate from oxygen. The oxidation rate constant of coated sample at the stage when the oxidation rate controlled by ions diffusion was 0.36 mg 2 ·cm -4 ·s -1 , which was much lower than that of bare sample (1.71 mg 2 ·cm -4 ·s -1 ), indicating that the coating could effectively inhibit the ions diffusion at high temperature. (4) The design principle of the coating based on the inhibition effect of interface layer on the diffusion of Fe 2+ ions was verified by the X-ray energy spectrum of cross-section

Conclusions
Referring to the theory of metal oxidation at high temperature, a mechanism of antioxidation coating design based on the inhibition effect of the interface layer on the diffusion of ions within oxide scale was introduced in this paper. According to the mechanism, a new ceramic coating was prepared to protect the carbons steel S235JR at 1200 • C for 2h. The mechanism was verified with the anti-oxidation effect of the coating and structure of the interface layer.
Some results were obtained as follows: ( According to the curve of weight gain per unit area during the temperature-rising process and temperature-holding stage, the oxidation loss of the substrate obviously decreased with the help of the coating. In addition, the oxidation rate constant of coated sample at the stage when the oxidation rate controlled by oxidation reaction was 0.005 mg·cm −2 ·s −1 , which was much lower than that of bare sample (0.01 mg·cm −2 ·s −1 ). It suggested that the prepared coating could effectively isolate the substrate from oxygen. The oxidation rate constant of coated sample at the stage when the oxidation rate controlled by ions diffusion was 0.36 mg 2 ·cm −4 ·s −1 , which was much lower than that of bare sample (1.71 mg 2 ·cm −4 ·s −1 ), indicating that the coating could effectively inhibit the ions diffusion at high temperature. (4) The design principle of the coating based on the inhibition effect of interface layer on the diffusion of Fe 2+ ions was verified by the X-ray energy spectrum of cross-section of the coating and the XRD result of coating inner face. The FeAl 2 O 4 region was formed and observed at the interface between coating and Fe element diffusion area, and the mullite phase was distributed outside of the FeAl 2 O 4 region.