Application of chemical interaction between (Fe, Cr) oxides and Mo oxide at high temperature for self-healing intelligence on nuclear fuel cladding in LWRs

ABSTRACT

A novel scheme for a bilayer coating with self-healing ability is proposed in this study. The candidate materials for the coatings and the potential self-healing reaction are assessed in high-temperature aqueous environments and high-temperature air. The pure Cr₂O₃ layer and the composite of Cr₂O₃ and MoO₃ are the candidate materials for the outer layer and inner layer, respectively, due to their compatibility under normal condition and fabricability. Fe₂O₃–MoO₃ reactions exhibit a potential ability to heal the cracks because of a high reaction rate under normal condition. The self-healing process proceeds via the following mechanism under normal condition: Fe₂O₃ (a corrosion product in the coolant) diffuses into the cracks on the coating and reacts with MoO₃ (inner layer) to produce the insoluble Fe₂(MoO₄)₃, which deposits and repairs the cracks. In the loss-of-coolant accident (LOCA) situation, Cr₂O₃–MoO₃ reaction is expected to strengthen the adhesion of the coating.

KEYWORDS:

• Self-healing
• coating
• fuel cladding
• molybdate
• high temperature
• light water reactors (LWRs)

1. Introduction

Zirconium-based (Zr-based) alloys have been widely used as the materials for fuel cladding [1]. Their mechanical properties and corrosion resistance have been improved significantly by optimization of the chemical composition and/or heat treatment, generating advanced Zr-based alloys such as M5®, ZIRLO™, J-alloys™, and so on [2]. However, the inherent defects with Zr-based alloys, especially the Zr-steam reaction in the LOCA condition, are the largest threat to nuclear safety. After the Fukushima-Daiichi accident, more research has been devoted to search for substitute materials, like FeCrAl alloy [3] and silicon carbide composite [4], which are expected to tolerate a loss of active cooling for a longer time while maintaining or improving fuel performance. Also, some researchers are attempting to enhance the corrosion resistance of the current Zr-based cladding with coating technology, such as Cr [5] and MAX-phase coatings [6]. Compared with alternative materials, coating technology is much more economic and time-saving due to minor or no modifications of the base materials.

As a branch of coating technology, the self-healing coating is expected to provide much higher reliability and a wider safety margin for nuclear reactors. In our previous study [7], cracks are the critical defects for the ceramic coating. As-received cracks (formed during the fabrication process) were also found in the MAX-phase coatings [8] and even in the Cr coating [9] although they were prepared by the different methods. In addition, microcracks may form during the transportation and installation due to the poor toughness of the ceramic coatings.

It was reported that α-Fe₂O₃ and Fe₃O₄ are the principal components of the CRUD (corrosion products of the core structural materials) in light water reactors (LWRs), and other minor compounds, like NiO, Cr₂O₃, and ZrO₂, were also observed [10].

The compounds, continuously fed through the LWR coolant water, may trigger additional reactions at the tip of cracks. These reactions can be called as self-healing. One of the candidates is the reaction of iron oxide with MoO₃ to produce the insoluble molybdate compounds. The basis of this idea is to create a bilayer coating on the surface of cladding tubes. The outer layer must protect the inner layer from undesirable reactions with substances in the LWR water. Once a crack is introduced, the inner layer is exposed to the water and the self-healing reaction takes place. Based on this motivation, the purpose of this work is to survey the possible candidate substances for the outer and inner layers and to find the possible self-healing reaction under normal operating condition of LWR, as well as the accident condition at LOCA. In this work, they are set as 360 °C in pressurized pure water and as high temperature below 1000 °C in air, respectively. The required performance for the outer layer is to maintain the phase stability under normal and accident conditions. The requirement for the inner layer is to have reasonable reactions to produce insoluble substance under normal condition. Therefore, the coating is expected to increase the corrosion resistance and widen the safety margin of the fuel cladding.

2. Experimental

2.1. Specimens

As introduced above, CRUD mainly consists of metal oxides. In the high-temperature aqueous environment, the hydroxides may be the precursors of these oxides. Thus, investigations on the hydration-to-oxide transformation as well as the possibility of hydroxide–MoO₃ reactions are necessary. Oxides and hydroxides were taken into consideration in this study. Pure powders, such as MoO₃ (99.9%), Cr₂O₃ (99%), Cr(OH)₃ (99%), Zr(OH)₄ (98%), FeOOH (99%), Fe₂O₃ (99.9%), and ZrO₂ (99%), were used as specimens in the following six forms: (1) As-received powders; (2) Compound powders, the powders were mixed with MoO₃ powder at a mass ratio of 1:1; (3) Specimens (1) and (2) were dispersed in pure water; and (4) Specimens (1) and (2) were compressed by 30 MPa and shaped into pellet at the dimension of φ18× h2 mm.

The anticipated reaction between Fe₂O₃ and MoO₃ is

(1) $\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+3\mathrm{M}\mathrm{o}{\mathrm{O}}_3\to \mathrm{F}{\mathrm{e}}_2{\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$(1)

Therefore, specimen (5) was prepared by stirring the Fe₂O₃–MoO₃ compound powder with the molar ratio of 2:3 in pure water. This results in unity in the molar ratio of Fe₂(MoO₄)₃/Fe₂O₃ at the completion of the reaction (Equation (1)(1) $\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+3\mathrm{M}\mathrm{o}{\mathrm{O}}_3\to \mathrm{F}{\mathrm{e}}_2{\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$(1) ). For X-ray diffraction (XRD) quantitative analysis, the Fe₂O₃–αAl₂O₃ powder and MoO₃–αAl₂O₃ powder in the mass ratio of 1:1 were prepared as specimen (6).

2.2. Experiments

For the coating, the candidate materials should keep chemically and physically stable under normal and abnormal conditions as the phase transformation of the materials for the coating could threat the stability of the coating. For the self-healing, the candidate materials should react with MoO₃ under normal condition. In preliminary experiments, the stability and compatibility of the candidate materials were evaluated by autoclave and furnace experiments. A batch autoclave system was utilized to simulate the normal condition (360 °C, saturated pressure of 18.5 MPa, and aqueous environment), and specimen (3) was added to the autoclave under normal condition for 28 h, taken out, and dried below 50 °C in air. A furnace was employed to simulate an air environment for the abnormal conditions. Specimen (4) was put into the furnace for 24 h at 150 °C, 400 °C, 650 °C, 780 °C, 900 °C, and 1000 °C in an air environment.

The results of the preliminary experiments show that Fe₂O₃ reacted with MoO₃ under normal condition. Therefore, further experiments were conducted to investigate the effects of immersion temperature and time on the Fe₂O₃–MoO₃ reactions. Specimen (5) was immersed at different temperatures for 3 h under normal condition for various time intervals. After immersion, specimen (5) was taken out and dried below 50 °C in air.

2.3. Measurements

The XRD patterns of specimens (3), (4), and (5) after experiments, as well as that of specimen (6), were measured. In this study, the XRD measurements were performed using an Ultima IV instrument (Rigaku) with a Cu Kα source. Scanning rate was 1°/min and the 2θ angle scan range was set from 10° to 80°.

2.4. XRD quantitative analysis

The quantitative analysis was performed with the relative intensity ratio (RIR) method, which is known as a semiquantitative analysis to calculate the mass (or molar) ratio of components. The RIR values are available in the database of International Centre for Diffraction Data (ICDD). Since the strongest peaks of Fe₂O₃ (ICDD #72-0469) and MoO₃ (#76-1003) are so close to the peaks of MoO₃ and Fe₂(MoO₄)₃ (#83-1701), respectively, and would cause errors for the estimations, new RIR values for Fe₂O₃ and MoO₃ were measured taking (012) peak of Fe₂O₃ and (020) peak of MoO₃ to the strongest peaks of α-Al₂O₃ (#89-7715), respectively, and would be derived by the XRD patterns of specimen (6).

3. Results and discussion

3.1. Stability and compatibility of the candidate materials under normal and abnormal conditions

Figure 1 shows the XRD patterns showing phase change in FeOOH and Cr(OH)₃ after the autoclave experiments (360 °C for 28 h). The other specimens such as Fe₂O₃, Cr₂O₃, ZrO₂, and Zr(OH)₄ were found to be stable (not shown). The as-received FeOOH was goethite (#81-0464) and totally dehydrated into hematite upon exposure to the autoclave. The as-received Cr₂O₃ powder was eskolaite (#84-1616) and was stable. The as-received chromium hydroxide powder was amorphous and transformed into CrO(OH) (#89-2696) upon exposure to the autoclave. The as-received ZrO₂ was mainly m-ZrO₂ (#86-1451) and minor t-ZrO₂ (#79-1769). In the autoclaved ZrO₂, the intensity of the tetragonal phase relative to that of monoclinic phase became weaker, indicating phase transformation into the monoclinic phase upon autoclaving. The as-received zirconium hydroxide powder was amorphous and transformed into m-ZrO₂ (plus minor t-ZrO₂).

Figure 1. XRD patterns for (a) FeOOH and (b) Cr(OH)₃ before and after autoclave experiments.

Figure 2 shows the XRD patterns showing phase changes in the compounds under autoclave conditions. It was found that Fe₂O₃, FeOOH, Cr(OH)₃, and Zr(OH)₄ reacted with MoO₃, producing m-Fe₂(MoO₄)₃, m-Cr₂(MoO₄)₃ (#78-1654), and m-Zr(MoO₄)₂ (#86-1451), respectively. No obvious reaction products were detected in the other compounds, suggesting that Cr₂O₃ and ZrO₂ would not react with MoO₃ in the high-temperature aqueous environment.

Figure 2. XRD patterns for powder mixtures before and after autoclave experiments. (a) Fe₂O₃ and MoO₃; (b) FeOOH and MoO₃; (c) Cr₂O₃ and MoO₃; and (d) Cr(OH)₃ and MoO_3.

Figure 3 shows the examples of XRD measurement data showing phase changes in FeOOH and Cr(OH)₃ upon furnace experiments, namely exposure to air at temperatures ranging from 150 °C to 1000 °C for 24 h. No phase transformations were detected in Fe₂O₃ and Cr₂O₃. FeOOH and amorphous Cr(OH)₃ transformed into Fe₂O₃ and α-Cr₂O₃ (eskolaite) at 400 °C, respectively, and then remained unchanged until 1000 °C. The peaks of t-ZrO₂ disappeared above 900 °C. Amorphous Zr(OH)₄ was dehydrated and transformed into m- and t-ZrO₂ above 650 °C, while the intensity of the peaks of t-ZrO₂ became weaker at higher temperature but did not disappear. The XRD data showing phase changes in compounds exposed to air in the furnace experiment are collected in Figure 4. Fe₂O₃, Cr₂O₃, and ZrO₂ reacted with MoO₃ above 650 °C, producing m-Fe₂(MoO₄)₃, m-Cr₂(MoO₄)₃, and h-Zr(MoO₄)₂ (#77-1784), respectively. FeOOH, Cr(OH)₃, and Zr(OH)₄ were firstly dehydrated into the corresponding oxides at 400 °C, 400 °C, and 650 °C, respectively, and then reacted with MoO₃ to form the corresponding molybdate compounds at 650 °C.

Figure 3. XRD patterns for (a) FeOOH and (b) Cr(OH)₃ exposed to air at different temperatures for 24 h.

Figure 4. XRD patterns for powder mixtures exposed to air at different temperatures for 24 h. (a) Fe₂O₃ and MoO₃; (b) FeOOH and MoO₃; (c) Cr₂O₃ and MoO₃; and (d) Cr(OH)₃ and MoO_3.

FeOOH, Cr(OH)₃, and Zr(OH)₄ were unstable and transformed into Fe₂O₃, Cr₂O₃, and ZrO₂ in the 360 °C aqueous environment while the starting temperatures for dehydration reactions in air were higher than 360 °C. It was reported that high-temperature water can influence reactions through phase behaviors, solute–solvent collisions, diffusion limitations, and cage effects, while may also participate in a reaction as reactants or as catalysts, thereby lowering the activation energy and promoting the chemical reaction [11]. The lower dehydration temperature in the aqueous environment should be ascribed to the influence of the high-temperature water. FeOOH transformed into Fe₂O₃ at 150–400 °C in the furnace, which agrees with the report [12] that the decomposition of α-FeOOH to α-Fe₂O₃ occurs at 270–325 °C. For Cr(OH)₃ in the aqueous environment, the first dehydration to form CrO(OH) occurs at 55 °C or higher, and grimaldiite (CrO(OH)) is dehydrated to Cr₂O₃ at about 300–325 °C [13]. Thus, Cr(OH)₃ was hydrothermally decomposed into CrO(OH) in the 360 °C aqueous environment. In air, the literature [14] reported that chromium hydroxide firstly loses water to form amorphous CrO(OH) at temperatures ranging from room temperature to 215 °C, followed by complete transformation into Cr₂O₃ at 409 °C, which agrees with the phenomena that the amorphous form was detected until that Cr(OH)₃ transformed into Cr₂O₃ at 400 °C as shown in Figure 3(b). Picquart et al. [15] reported that the amorphous zirconium hydroxide begins to be gradually dehydrated into tetragonal zirconia at 400 °C, the bulk crystallization occurred at 447 °C, and the mixture of monoclinic and tetragonal phases formed at 600 °C while the monoclinic phase became the dominant form from 900 °C. This report agrees with the observation in this work that the amorphous Zr(OH)₄ transformed into ZrO₂ and crystalized at 400–600 °C. In addition, the monoclinic phase was dominant from 900 °C according to the increase in the relative intensity of the monoclinic phase.

For ZrO₂, three polymorphs can exist at different temperature ranges: monoclinic phase at <1170 °C, tetragonal phase at 1170–2370 °C, and cubic phase above 2370 °C; however, the cubic and tetragonal phases can be partially or fully stabilized at room temperature by several cations such as Y³⁺, Ca²⁺, and Mg²⁺ [16]. It has been reported that m-to-t and t-to-m phase transformations occur at 1127–1207 °C and 977–1052 °C, respectively [17]. But in an aqueous environment, the tetragonal phase could transform into monoclinic phase at 400 °C or even at room temperature due to the changes in the surface energy upon adsorption of water [18]. In this research, it was found that tetragonal phase partially transformed into the monoclinic phase at 360 °C and started to transform at 900 °C in the furnace. Therefore, these results coincide with the literatures [17,18].

In the furnace, solid-state reactions of Fe₂O₃, Cr₂O₃, and ZrO₂ with MoO₃ did not occur at 400 °C but at 650 °C. Therefore, it is reasonable to deduce that the starting temperature for these reactions is 400–650 °C. The starting temperature of Fe₂O₃–MoO₃ reaction reported in the literature is incongruent due to the different starting reactants. Brookes et al. [19] found that the Fe₂O₃–MoO₃ reaction occurred at 500 °C with Fe₂O₃ and MoO₃ as the reactants, while El-Geassy et al. [20] reported that ferric molybdate formed when the compound of ferrous oxalate and ammonium molybdate was heated up to 428 °C. Hence, the solid-state reaction between Fe₂O₃ and MoO₃ could occur at around 500 °C. Cr₂(MoO₄)₃ was synthetized by Oudghiri-Hassani via heating an oxalate precursor in static air at 600 °C [21]. Therefore, this report is consistent with our result that Cr₂O₃–MoO₃ reaction occurred at 400–650 °C. Xie et al. [22] have reported that the ZrO₂–MoO₃ reaction rate is very slow at 500–600 °C and became faster above 700 °C. The remaining ZrO₂ and MoO₃ were still detected after 24 h at 650 °C, which should be ascribed to the slow reaction rate below 700 °C. Therefore, it could be concluded according to the literature that the starting temperatures for Fe₂O₃–MoO₃, Cr₂O₃–MoO₃, and ZrO₂–MoO₃ reactions are 427–500 °C, 600 °C, and 500–600 °C, indicating that activation energy of Fe₂O₃–MoO₃ is lower than that for others.

m-Fe₂(MoO₄)₃, m-Cr₂(MoO₄)₃, and trigonal-Zr(MoO₄)₂ were detected in the furnace experiments. Many of molybdates are known to be polymorphic [23]. m-Fe₂(MoO₄)₃ reversibly transforms into orthorhombic at 518 °C [24]. Cr₂(MoO₄)₃ exhibits a monoclinic phase as well as a orthorhombic phase, and the transition temperature is 385 °C [25]. Zr(MoO₄)₂ was reported to undergo a reversible phase transformation at 679 °C from the low-temperature phase (monoclinic structure) to the high-temperature phase (trigonal structure) [26]. Therefore, Fe₂(MoO₄)₃ and Cr₂(MoO₄)₃ are in a monoclinic structure presumably transforming from an orthorhombic structure when cooled down. On the contrary, Zr(MoO₄)₂ is in a trigonal phase in the air environment. The lower phase transformation rate for Zr(MoO₄)₂ than that for Fe₂(MoO₄)₃ and Cr₂(MoO₄)₃ may contribute to the existence of trigonal Zr(MoO₄)₂ at room temperature. Garrido Pedrosa et al. [27] also obtained trigonal Zr(MoO₄)₂ from the solid-state reaction between ZrO₂ and MoO₃. Consequently, Fe₂(MoO₄)₃, Cr₂(MoO₄)₃, and Zr(MoO₄)₂ reversibly transform to the high-temperature forms from low-temperature forms around 500 °C, 400 °C, and 679 °C, respectively.

In light of decomposition, Fe₂(MoO₄)₃, Cr₂(MoO₄)₃, and Zr(MoO₄)₂ existed below 780 °C, suggesting that they are stable or that the decomposition rate is very low even at 780 °C. Information on the decomposition is limited, and the decomposition temperature of Fe₂(MoO₄)₃ seems inconsistent. Kersen et al. [28] have reported that Fe₂(MoO₄)₃ is highly stable below 850 °C and decomposed completely at 1200 °C. Said [29] found that Fe₂(MoO₄)₃ began to decompose at 800 °C. The accurate decomposition temperature of Cr₂(MoO₄)₃ is unavailable, and it could decompose above 810 °C, accompanied by sublimation of MoO₃ [25]. Zr(MoO₄)₂ decomposes above 800 °C accompanied by the sublimation of MoO₃ [30]. Accordingly, under the LWR normal and accident conditions, molybdates that can be formed are Fe₂(MoO₄)₃, Cr₂(MoO₄)₃, and Zr(MoO₄)₂, all stable below 800 °C.

In the high-temperature aqueous environment, Cr₂O₃ and ZrO₂ did not react with MoO₃, but all hydroxides and Fe₂O₃ reacted with MoO₃ and produced monoclinic molybdate compounds. In the high-temperature solution, MoO₃ reacts with water according to the following scheme [31]:

(2) $\mathrm{M}\mathrm{o}{\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}_2\mathrm{M}\mathrm{o}{\mathrm{O}}_4$(2)

Reaction (2) changed the solid–solid reaction to solid–liquid reaction (oxides and hydroxide with H₂MoO₄), thereby possibly decreasing the activation energy to form the molybdate compounds. Also, the activation energy of Fe₂O₃–MoO₃ is possibly lower than Cr₂O₃–MoO₃ and ZrO₂–MoO₃ because the starting temperature for the Fe₂O₃–MoO₃ reaction is lower than that for the latter two reactions. Therefore, Fe₂O₃ reacted with MoO₃ in 360 °C water, but others did not. In addition, reactions (2) produced molybdate acid, which prefers to react with hydroxides rather than the oxides. Accordingly, all hydroxides reacted with MoO₃ at 360 °C in the aqueous environment, much lower than that in the furnace. It is worth noting that all the resulting molybdate compounds in 360 °C water are in low-temperature forms (monoclinic structure). Up to date, Fe₂O₃–MoO₃, Cr₂O₃–MoO₃, and ZrO₂–MoO₃ reactions in the aqueous environments have not been reported in the published literature.

3.2. Scheme for a bilayer coating

The results of the preliminary experiments showed that MoO₃ reacted with Fe₂O₃, Cr(OH)₃, and Zr(OH)₄ under normal condition and can react with Fe₂O₃, Cr₂O₃, and ZrO₂ in abnormal conditions. Based on the results, a scheme for a bilayer coating with the inner and outer layer could be proposed. As the passive layer, the outer layer is expected to prevent the inner layer and the matrix under normal condition from contacting with the coolant or other oxidative compounds. As the active layer, the inner layer, mainly consisting of MoO₃, is expected to react with corrosion products in the coolant, thus healing the coating due to reaction product deposition when a crack occurs.

Under normal condition, the outer layer is not allowed to react with the inner layer (MoO₃). Hence, Fe₂O₃ is not suitable for the outer layer because of the Fe₂O₃–MoO₃ reaction in the aqueous environment. In the air environment, physical stability of the candidate materials is required to avoid the volume change which is the factor leading to the separation of the coating under LOCA condition. From this point of view, Cr₂O₃ and m-ZrO₂ are suitable as the candidate materials for the outer layer since they are physically stable up to 1000 °C. As found in the experiments, Cr₂O₃ and ZrO₂ reacted with MoO₃ to produce the corresponding molybdate compounds in the air environment above 650 °C. Accordingly, Cr₂O₃–MoO₃ and ZrO₂–MoO₃ reactions at high temperature may strengthen the adhesion of the coating in LOCA condition, and the two reactions could be considered as a non-autonomic process because the temperature change is the trigger for the reactions. These molybdate compounds, formed above 650 °C, will start to decompose when the temperature is higher than 800 °C. The decomposition of molybdate compounds and the sublimation of MoO₃ are endothermic processes, which would help to slow down the temperature increase under LOCA condition. Therefore, the inner layer of the coating could be made from the compound of MoO₃, Cr₂O₃, and ZrO₂.

Considering that the inner layer is made of MoO₃, Cr₂O₃, and ZrO₂, the fabrication temperature should be lower than 500 °C to avoid the Cr₂O₃–MoO₃ and ZrO₂–MoO₃ reactions. A MoO₃–Cr₂O₃ film with a thickness of 300 nm was obtained by atmospheric pressure chemical vapor deposition in oxygen under ambient conditions [32]. In the fabrication process, the precursors were Mo(CO)₆ and Cr(CO)₆, and the temperatures of the deposition substrate, sublimator, and annealing were 200 °C, 70 °C, and 300–500 °C, respectively. The resulting coating was reasonably smooth, and no Cr₂(MoO₄)₃ was detected in the coating. Plasma spraying was successful for the fabrication of MoO₃–Cr₂O₃ compound coating, and no combination reactions were found [33]. The sol–gel method is also an accessible method for low-temperature fabrication. (NH₄)₆Mo₇O₂₄·H₂O, MoO₂(OH)(OOH), and Mo(OC₃H₇)₅ can form the MoO₃ coating after heating to 160 °C, 275 °C, and 110 °C, respectively [34,35]. The mixture of CrCl₃·6H₂O and nitric acid [36] or the mixture of Cr(NO₃)₃·6H₂O and (NH₂)₂·H₂O [37] was used as the precursor of Cr₂O₃ below 500 °C. It is worth noting that Cr(OH)₃ would form firstly and be dehydrated to Cr₂O₃ at 400 °C as discussed above. Zirconium propoxide and zirconium oxychloride were used as the precursor of ZrO₂ [38]. Similarly, Zr(OH)₄ would be obtained before ZrO₂. However, as described above, Zr(OH)₄ would be dehydrated to form t- and m-ZrO₂ at 400–600 °C. Pure monoclinic phase could not be obtained until 900 °C. Therefore, two phases coexist if the precursor of ZrO₂ is heat treated below 500 °C to avoid the ZrO₂–MoO₃ reactions. It has been described in the previous part that t-ZrO₂ could transform into m-ZrO₂ in an aqueous environment. Thus, the coexistence of t- and m-ZrO₂ in the coating would deteriorate the stability of the coating. Consequently, it is a problem to add ZrO₂ into the inner layer of the coating. As a summary, pure Cr₂O₃ and Cr₂O₃–MoO₃ compounds are feasible as the outer and inner layers of the coating, respectively. The corrosion products of the fuel cladding, Zr(OH)₄ and ZrO₂, could react with MoO₃ in aqueous and air conditions at certain temperatures and could contribute to the self-healing, possibly resulting in adhesion of the coating.

3.3. Feasibility of Fe₂O₃–MoO₃ reaction as a self-healing reaction

As described in the previous part, Fe₂O₃ is the main component of the corrosion products and reacted with MoO₃ under normal condition. Therefore, the Fe₂O₃–MoO₃ reaction was chosen as the candidate self-healing process, and further investigation was required. The XRD patterns for Fe₂O₃–MoO₃ compound powder immersed at 100 °C, 200 °C, 300 °C, and 360 °C for 3 h and at 360 °C for 0.5, 3, 6, 9, and 12 h are shown in Figure 5. As shown in Figure 5(a), the peaks ascribed to Fe₂(MoO₄)₃ were detected on the Fe₂O₃–MoO₃ powders after immersion at 300 °C, so the critical starting temperature of the Fe₂O₃–MoO₃ reaction is between 200 °C and 300 °C. The relative peak intensity of MoO₃ became weaker when the immersion temperature was increased to 360 °C, suggesting that the rate of Fe₂O₃–MoO₃ reactions increased with increasing temperature.

Figure 5. XRD patterns for Fe₂O₃–MoO₃ composite powder immersed at (a) different temperatures for 3 h and (b) at 360 °C for different immersion time.

Figure 5(b) shows the XRD patterns for the compound of Fe₂O₃ and MoO₃ derived by autoclave experiments (360 °C in pure water). Fe₂(MoO₄)₃ was produced in the 0.5 h test, and the relative intensity of the spectra for Fe₂(MoO₄)₃ almost did not change when the immersion time was lengthened.

The defined RIR values derived from the XRD patterns (not shown here) of the Fe₂O₃–αAl₂O₃ powder and MoO₃–αAl₂O₃ powder were 4.88 and 1.9 for MoO₃ and Fe₂O₃, respectively. The RIR value for Fe₂(MoO₄)₃ in ICDD #83-1701 is 1.21. Using these values, the molar ratio of Fe₂(MoO₄)₃/Fe₂O₃ as a function of immersion temperature and time was estimated and is shown in Figure 6. The ratio of Fe₂(MoO₄)₃/Fe₂O₃ started increasing above 200 °C and approached unity at 360 °C. To derive the reaction rate of the Fe₂O₃–MoO₃ reaction, a model was employed to translate the reaction into a rate equation. For solid-state reactions, models have been proposed based on certain assumptions: (1) nucleation models, which consider the formation and growth of nuclei as the rate-limiting step; (2) geometrical contraction models, which consider the progress of the product layer from the surface to the inner crystal as the rate-limiting step; (3) diffusion models, where diffusion of reactant or product is considered to be rate limiting; and (4) reaction-order models, which consider the reaction as a homogeneous kinetic process [39]. In this research, prior to pouring into the autoclave, Fe₂O₃ powders were thoroughly stirred with MoO₃ powders in water. Additionally, the molar ratio of Fe₂(MoO₄)₃/Fe₂O₃ in Fe₂O₃–MoO₃ powders approached unity. First-order function based on the reaction-order model and Avrami–Erofeyev functions based on the nucleation models show a similar tendency [39]:

(3) $C=1-{\mathrm{e}}^{-{\left(k\cdot t\right)}^n}$(3)

Figure 6. The molar ratio of Fe₂(MoO₄)₃/Fe₂O₃ as a function of the immersion (a) temperature and (b) time.

where C is the concentration fraction, k is the rate constant, and t is the time; n = 1 in first-order function, while n = 2, 3, 4 for Avrami–Erofeyev functions. Thus, the rate of them can be written as a unified form:

(4) $R=\frac{\mathrm{d}C}{\mathrm{d}t}=\frac{n\cdot k^n{t}^{n-1}}{{\mathrm{e}}^{{\left(k\cdot t\right)}^n}}$(4)

where R is the rate of the reaction. Hence, the reaction rates of Avrami–Erofeyev functions increase at first and then decrease, while the rate of first-order function decreases with the reaction progress.

As shown in Figure 6(b), the molar ratio of Fe₂(MoO₄)₃/Fe₂O₃ increased quickly in the first 2 h and approached completion after 6 h, indicating that the reaction rate was fast initially but decreased subsequently. The curve in Figure 6(b) might follow the first-order function. The fitting equation is

(5) $C_1=1-{\mathrm{e}}^{-\left(2.3\pm 0.5\right)\times t}$(5)

The rate constant was (2.3 ± 0.5) h^–1, and the coefficient of determination (R²) was 0.96. However, the fitting curve deviates from the experimental data above 0.5 h and approached to unity much earlier than the experimental result. The reaction process was possibly hindered by the formation of products surrounding the reactants, and so the reaction rate decreased subsequently.

Accordingly, the n in Equation (4)(4) $R=\frac{\mathrm{d}C}{\mathrm{d}t}=\frac{n\cdot k^n{t}^{n-1}}{{\mathrm{e}}^{{\left(k\cdot t\right)}^n}}$(4) should be modified and is lower than 1 for Fe₂O₃–MoO₃ reaction and could be derived by refitting the experimental data with Equation (3)(3) $C=1-{\mathrm{e}}^{-{\left(k\cdot t\right)}^n}$(3) , thereby deducing Equation (6)(6) $C_2=1-{\mathrm{e}}^{-{\left(\left(3.0\pm 1.5\right)\times t\right)}^{\left(0.4\pm 0.1\right)}}$(6) as following:

(6) $C_2=1-{\mathrm{e}}^{-{\left(\left(3.0\pm 1.5\right)\times t\right)}^{\left(0.4\pm 0.1\right)}}$(6)

As shown in Figure 6(b), the fitting curve of Equation (6)(6) $C_2=1-{\mathrm{e}}^{-{\left(\left(3.0\pm 1.5\right)\times t\right)}^{\left(0.4\pm 0.1\right)}}$(6) matches well with the experimental data, and R² is 0.98. The rate constant is (3.0 ± 1.5) h^–1, and m = (0.4 ± 0.1), and the rate of the Fe₂O₃–MoO₃ reaction could be deduced by replacing k and n in Equation (4)(4) $R=\frac{\mathrm{d}C}{\mathrm{d}t}=\frac{n\cdot k^n{t}^{n-1}}{{\mathrm{e}}^{{\left(k\cdot t\right)}^n}}$(4) with the fitted results. The value of R that corresponds to the slope of the curve in Figure 6(b) approaches infinity when t is close to zero, but R drops close to zero in 2 h, indicating that the reaction rate is so fast that the products, which hinder the reaction process, could be formed in a short time.

The temperature of the bulk coolant ranges from 278 °C to 287 °C and from 275 °C to 315 °C in the boiling water reactor (BWR) and the pressurized water reactor (PWR), respectively. The surface temperature of the fuel cladding is about 360 °C. Since the Fe₂O₃–MoO₃ reaction in water takes place above 200 °C, and the reactions exhibited a fast rate at 360 °C, the reaction has the potential ability to produce the molybdate compounds in a short time. As previously described, Fe₂O₃ (a corrosion product in the coolant) is expected to diffuse into the cracks on the coating and react with MoO₃ (inner layer) to produce the insoluble Fe₂(MoO₄)₃. This insoluble compound deposits and repairs the cracks under normal condition, and this healing reaction is an autonomic process because the crack itself is the instigation for the healing reaction. In LOCA condition, the Fe₂(MoO₄)₃ would not decompose until 850 °C. The decomposition reactions produce Fe₂O₃, which could still fill the cracks and one more product, MoO₃, takes heat away by sublimation, helping to cool down the fuel to a certain extent.

With regard to the source of Fe₂O₃, Fe₂O₃ is the main corrosion product in the coolant, and it was reported that the crud in LWRs can grow to 10–100 μm thick [40]. Therefore, the corrosion products in the coolant would supply Fe₂O₃ for the Fe₂O₃–MoO₃ reaction. In addition, external injection of minor Fe₂O₃ to the coolant is also an alternative method to increase the concentration of Fe₂O₃ in the coolant. Consequently, this reaction is possible for use as the self-healing process.

4. Summary

In this study, a novel scheme for a self-healing coating was proposed, and the candidate materials for the coating and the potential self-healing reaction were assessed by means of autoclave and furnace experiments. The pure Cr₂O₃ layer and the compound of Cr₂O₃ and MoO₃ could be used as the outer layer and inner layer, respectively, due to their compatibility under normal condition and fabricability. Fe₂O₃–MoO₃ reactions exhibited a potential ability to self-heal the cracks because of a high reaction rate under normal condition. The self-healing mechanism involves Fe₂O₃ (a corrosion product in the coolant) diffusion into a crack on the coating and subsequent reaction with MoO₃ (inner layer) produces insoluble Fe₂(MoO₄)₃ which deposits and repairs the cracks under normal condition. Further work will involve determining the chemical concentration and the thickness of the coating.

Acknowledgments

This study is supported by the project of ‘The development of self-healing intelligence on nuclear fuel cladding’ carried out under the Center of World Intelligence Project for Nuclear S&T and Human Resource Development by the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Disclosure statement

No potential conflict of interest was reported by the authors.