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Cellular automata simulation on the corrosion behavior of Ni-base alloy in chloride molten salt
Solar Energy Materials and Solar Cells 203 (2019) 110170
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Solar Energy Materials and Solar Cells journal homepage: www.elsevier.com/locate/solmat
Cellular automata simulation on the corrosion behavior of Ni-base alloy in chloride molten salt
T
Weilong Wanga,∗, Bang Guana, Xiaolan Weib, Jianfeng Lua, Jing Dinga a b
School of Materials Science and Engineering, School of Intelligent Systems Engineering,Sun Yat-Sen University, Guangzhou, 510006, China School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, 510640, PR China
ARTICLE INFO
ABSTRACT
Keywords: Cellular automaton Molten chloride melt Ni-base alloy Corrosion
Chloride molten salt is required to study its corrosion behavior since it is recommended to be used as heat transfer and heat storage material in high-temperature thermal power generation system. In this paper, a simplify model was established by the reaction of diffusive corrosive gas and metal substrate in a chloride molten salt. A cellular automaton model based on the stochastic approach is adopted to simulate the uniform corrosion and the migration of metallic element. The corrosion behavior is also simulated considering the practical working condition, such as oxygen, moisture and so on. By comparing the simulation results with experimental data, it proves that the cellular automata simulation is an effective alternative method to describe the hightemperature corrosion process of molten salts. Simulation results of 25,000 time steps is taken as a comparison of the 21-day corrosion which reflects the Cr distribution, and the growth of corrosion layer with the migration of Cr element was reproduced. The change of corrosion layer thickness is similar to the mass loss. The simulation method provides insight on the distribution of corrosion products, corrosion kinetics and morphologies for the long-term application.
1. Introduction
thermodynamic potential-pO2- diagram for Cr, Ni at 700 °C [2]. Ding studied three commercial alloys (including stainless steel SS 310, Incoloy 800 H, Hastelloy C-276) in molten MgCl2/NaCl/KCl (60/20/ 20 mol%) under inert atmosphere, and proposed an impurity-driven corrosion mechanism to describe the hot corrosion behavior [3]. Crdeficient region was found in Ni-based alloy under uniform corrosion [1,4,5]. However, it is lack of learning the inner structure or component change of matrix alloy during the corrosion by using the experimental method. Moreover, it is also hard to obtain the long-term corrosion data due to the strict experimental condition. To our best knowledge, no simulation work has been done to study the corrosion characters of Nibase alloy in chloride molten salt. Thus, it is required to find an effective way to study the long-term high-temperature corrosion behavior of molten salts. Cellular automata model is developed as a powerful tool for modeling physical, chemical systems, especially for the high-temperature corrosion [6,7]. It can be simplified into a two-dimensional schematic to study both localized corrosion and uniform corrosion based on a stochastic approach [6,8–11]. Beside, cellular automata models can also simulate the chemical - electrochemical reaction based on diffusion of corrosive species and the reaction - passivation - dissolution process of metal, which can simulate the formation of oxide
Molten salt is used as heat transfer and heat storage material in thermal power generation system, with the feature of high working temperature, small vapor pressure/viscosity and low cost. The challenge we have to face is the high temperature corrosion occurring when metals are in long contact with chloride salts. Recently, two commercial concentrating solar power stations took place serious leakage of the molten salt tank, and it costs millions of dollars for this suffering. It is reported that the accident is caused by high temperature corrosion stress of the matrix alloy. Thus, it is urgent for us to find the matchable alloy and the solution to prevent high-temperature corrosion for various molten salts in practical devices. Chloride salts have drawn more attention due to its higher working temperature range, and it is also abundant in the nature salt lake. Some experimental work has been done to study the corrosion behavior of chloride salts. Hua Sun investigated the corrosion of Fe-based 316SS and seven Ni-based alloys in molten NaCl–KCl–MgCl2 under N 2 at 700 °C. They found all alloys suffered the selective dissolution of Cr, resulting in the formation of subsurface voids [1]. They investigate the effects of alloying elements on corrosion of Ni-based alloys in NaCl–KCl–MgCl2 under Ar at different temperature, and drew a ∗
Corresponding author. E-mail address: [email protected] (W. Wang).
https://doi.org/10.1016/j.solmat.2019.110170 Received 7 July 2019; Received in revised form 5 September 2019; Accepted 7 September 2019 Available online 27 September 2019 0927-0248/ © 2019 Elsevier B.V. All rights reserved.
Solar Energy Materials and Solar Cells 203 (2019) 110170
W. Wang, et al.
Fig. 1. Schematic diagram showing transition of corrosion scales on substrate during high-temperature corrosion in molten salts [4].
Fig. 3. Schematic plot of Margolus neighbors.
Fig. 2. Schematic plot of the CA model: (a) grid spaces one (b) grid spaces two (c) grid spaces three (d) three overlapped grid space.
films, and reproduce the growth of corrosion layers [12–14]. In this paper, the cellular automata model is used to study the corrosion process of Incon625 alloy in chloride molten salt. A two-dimensional cellular automata simulation corrosion modeling is established aim to simulate the growth of corrosion layers. The migration of Cr element in In625 has been studied in the entire corrosion process.
Fig. 4. Snapshots of simulation process, o% = 0.25, Nt = 0.
2. Methodology A simplify corrosion model is established based on the mechanism obtained in our previous experimental analysis, and the program of the CA model is programmed with software (matlab).
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The main chemical composition and reaction path determines the structure of the alloy. For In625 alloy, it is noticed that elements (Fe, Mo) have similar properties to Cr elements that are prioritized in reaction. We assume that the alloy consists of only Ni and Cr elements. Thus, in this model we take the amount of Ni and Cr into account.
Table 1 Main parameters in the model. No.
C (c%)
O (o%)
P3
Cr (cr%)
Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
0 0.05 0.1 0 0 0 0 0 0 0
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.1 0.5
0.01 0.01 0.01 0.02 0.05 0.01 0.01 0.01 0.01 0.01
0.5 0.5 0.5 0.5 0.5 0.3 0.4 0.6 0.5 0.5
2.2. CA model Cellular automata model was established based on the above discussion. A series of evolutionary rules are defined to form the discrete dynamical systems. We use a rectangular box of 400×400 vertical and horizontal sites with rigid boundary and Margolus neighbors. 2.2.1. Definition of sites There are eight types of lattice sites, displayed in various color and filling pattern. Each site does not have to represent a specific chemical component but a group of substance at the mesoscopic scale. A site is mainly occupied by Cr, B site is mainly occupied by Ni, O site is occupied by O2, C site is mainly occupied by Cl2, D site is mainly occupied by CrCl4, Mg site is mainly occupied by MgO, P site is mainly occupied by MgCr2O4, BO site is occupied by NiO. All these sites scatters across three parallel grid spaces in Fig. 2, where A, B, MgO, P, BO site are considered fixed and grid space one is used. O2 can diffuse into the outer corrosion layer, O use the grid space two. Cl2 can diffuse into inner corrosion, C and D use grid space three. Initially, O and C site exist randomly in the left half space of grid with a certain probability to represents the initial concentration. A and B site exist in all the right half space with a certain proportion representing the metal.
2.1. Corrosion mechanism and physical model The defined corrosion mechanism is necessary for modeling corrosion processes. In our previous experiment [4], we studied the corrosion behavior of Ni-based alloys in molten NaCl–CaCl2–MgCl2 eutectic salt and the corrosion mechanism was discussed according to the Gibbs function from thermodynamic calculation. The detailed formation process of the Cr-deficient region in corrosion layer of In625 alloy is proposed in Fig. 1. However, the mass transportation is complex in the corrosion process, since various element transports in the corrosion layer and molten salt, and some even penetrates into the metal substrate. Simultaneously, all the substances took place complex chemical reactions. Therefore, some assumptions are necessary to establish a simplified mode for simulating the complicated corrosion process. In the corrosion process of In625 alloy, the diffusion of O2 and substances containing Cl− takes place chemical reactions in a short time at high temperature. The diffusion rate and concentration of corrosive substance are supposed to control the corrosion process. In particular, the selective reaction of Cr elements correspond to the simulation of inner oxidation in the alloy [15,16]. The simplified mode is described as fellows. The area of reaction is divided into four zones in Fig. 1, including high temperature molten salt layer, outer corrosion layer, inner corrosion layer and matrix. In high temperature molten salt layer, O2 and H2O diffuses into high temperature molten salt from air. Subsequently, HCl and Cl2 are formed through a series of reaction. Therefore, we assume that corrosive substances already exist with a certain concentration in the molten salt in the beginning, and then these substances are continuously diffused from the upper layer of the molten salt into the corrosion layer. In outer corrosion layer, O2 dissolves in the molten salt and reacts preferentially with Cr in a short time. Also, it is consumed by other reactions. Therefore, the main reaction is assumed to be expressed as follows, Cr + 2MgCl2 + O2→CrCl4 + 2MgO
2.2.2. Diffusion process Margolus neighbors is used to describe diffusion and represented in Fig. 3. The upper left four grids are selected as neighbors at odd number of steps. Otherwise, lower right are chose, which has faster computation speed, all four site are computed together. We use a random walk process simulates the diffusion process of O, C and D with Margolus neighbors [17]. At each discrete interval, the wanderer occupies a neighbor randomly and this process occurs with a certain probability, which corresponds to the diffusion coefficient. The decrease of probability indicates the decrease of diffusion coefficient. For example, P site occupied by protective substance, we define the CA rules of diffusion as following: If walkers (O, D) are not in contact with any P, the random walk process takes place with a probability of 1. If all the four neighbors are P, the random walk process takes place with a probability of Pd4. According to the number of P in the neighborhood, other cases are Pd1, Pd2, Pd3, respectively, and the numerical value can be expressed as: 1 > Pd1 > Pd2 > Pd3 > Pd4. To simplify the calculation, Pd1 = 0.8, Pd2 = 0.6, Pd3 = 0.4, Pd4 = 0.2. If all the four neighbors are A or B, the state of site returns to the previous step. C can random walk in the whole space.
(1)
When Cr element content is insufficient, O2 reacts with Ni as the following reaction: Ni+1/2O2→NiO
(2)
The chloride containing Cr (CrCl4 mainly) in the inner corrosion layer diffuses into the outer corrosion layer, and participates in the reaction forming MgCr2O4 protective layer as follows, CrCl4+2MgO + O2→MgCr2O4+Cl2+MgCl2
2.2.3. Reaction and transformation rules We define some transformation rules of site to correspond to the simplified model above as follows:
(3)
In inner corrosion layer, Cl2 and other corrosive substances can react with Cr leading to a Cr-deficient corrosion layer. The mainly reaction is expressed as follows, 2Cl2+Cr→CrCl4
(4)
3
O + A→D + MgO
(5)
O + B→BO
(6)
D + MgO + O→P + C
(7)
C + A→D
(8)
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If A or B and O exit in the same position of their grid space, formula (5) or (6) occur with a probability of P1, P2, respectively. Similarly, formula (7) or (8) occur with probability of P3 and P4. The left side of formula means that the site is no longer occupied and the right side of
formula mean the site is occupied in respective grid space. The dissolution of O2 in MgCl2 participates in the reaction (1) and (3), and thus the consumption and formation of MgCl2 are neglected. Because the volume of each substance is not considered, every MgO site in formula
Fig. 5. Snapshots of corrosion layer growth process (left) and cumulative number of Cr. 4
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Fig. 5. (continued)
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Fig. 6. Comparison of simulation morphology and experiment SEM photograph, (a) cross-sectional SEM photograph of In625 after 21 days immersion at 600 °C [4], (b) Snapshots of simulation results of corrosion morphology, for time steps Nt = 25000.
Fig. 7. Comparison of Cr distribution of In625 alloy and collection of all site containing Cr.
color as the metal. The number of diffusion step Nt represents the evolution time step of system. According to Ref. [17], the probability for clockwise and counterclockwise deflection is assumed equal. Therefore, diffusion coefficients are determined by Nt and lattice width together. Some parameters for the corrosion process simulation are important, For example, o% represents the number of O, c% represents the number of C, cr% represents the number of Cr. P1,P2 and P4 is set as 0.1, 0.01,1, respectively. P3 is set as several different values representing the rate of major reactions in the system to some extent. P1 is set much larger than P2.When there is Cr near B, the reaction between O and Cr dominates. When there is no Cr, O reacts with Ni with a low probability. We set a particle source of O and C with constant concentration of o% and c% at the left boundary, which simulates the diffusion of substance from the air into molten salt. In particular, o% can represents the concentration of oxygen, and c% can represents the concentration of water vapor by some mathematical association. In the
(5) or (6) can represent 2MgO in reaction (1) and (3). The rate of chemical reaction can be calculated from the reaction probability and the change of the concentration of each substance refer to the fifth chapter of literature [17].But the specific relational expressions is difficult for us to deduce, and therefore, we use cellular automata model to study some property which have the similar behavior to corrosion test, instead of solving them by numerical methods. 3. Results and discussion The corrosion experiment results are greatly affected by the corrosion environment, the simulation is conducted to describe the impact of corrosion environment. In our model, O random exists on the left side of the space with o % percent and metal exists on all the right side of the space initially as shown in Fig. 4. A and B are represented in the same
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Fig. 8. Comparison of the change tendency of the Cr content with the thickness of metal. Fig. 9. (a) Simulated thickness of whole corrosion layer, (b) Simulated thickness of outer and inner corrosion layer.
simulation process, when the content of Cr element is too low, it is found that the protective layer cannot be formed effectively. Besides, considering Cr element consumes more O2 than Ni, the percentage of Ni and Cr is set as a series of values. In the first case, cr% is set as 0.5 for the related corrosion system. Each fixed parameter has no particular significance for the model, but the impact of the changeable parameter is important to understand the relationship between the model and the corrosion process of experimental. The influence of these parameters is investigated and the correlation of characteristic between simulation and experiment result is analyzed. The study on the effect of main parameters are listed in Table 1, the repeated simulation results of the same case show little difference. 3.1. Simulation verification Case 1 is simulated for comparison, and the related experimental data is obtained from Ref. [4]. Fig. 5 shows the snapshots of corrosion layer growth process, on the left side of each subgraph is the morphology of the corrosion layer. The right is the cumulative number of Cr corresponding to the depth of corrosion layer. In the initial stage, the cumulative number of Cr decreases gradually and there is no obvious boundary between internal and external
Fig. 10. Similar tendency of corrosion layer growth and mass loss.
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reaction of O2 takes place, and the thickness of whole corrosion layer is calculated same as outer corrosion layer, but the reaction of any substance. The change of corrosion layer thickness reflect the diffusion reaction process. Initially, higher oxygen concentration promotes reaction, and then the formation of protective layer prevents the diffusion of corrosive substance after a period. At the same time, the concentration of oxygen gradually decreases resulting in a slow increase in the thickness of the corrosive layer. In Fig. 9 (b), at the initial stage of simulation, the thickness of inner corrosion layer increases rapidly, and the thickness of inner and outer corrosive layer reaches the same thickness at about 6000 time steps. Thereafter, the inner corrosion layer is continuously forming and transforming into outer corrosion layer, and the thickness keeps unchanged. In Fig. 10, mass loss value and simulated thickness of entire corrosion layer is plotted in the same figure. Corrosion experiment time is transformed into corresponding simulation time steps. The mass loss of 25000 simulated time step falls on the growth curve of corrosion layer thickness, and the change of corrosion layer thickness and mass loss is the same.
Table 2 Simulated thickness of corrosion layer after 25,000 time steps. No.
C (c%)
O (o%)
P3
(cr%)
hin
h
Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
0 0.05 0.1 0 0 0 0 0 0 0
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.1 0.5
0.01 0.01 0.01 0.02 0.05 0.01 0.01 0.01 0.01 0.01
0.5 0.5 0.5 0.5 0.5 0.3 0.4 0.6 0.5 0.5
69.7 78.2 86.2 63.0 59.4 100.3 81.6 59.6 39.6 101.3
49.5 56.2 62.0 50.1 52.1 19.2 60.8 40.4 19.0 81.1
corrosion layers, which corresponds to the snapshot of 1000 time step. Then, protective layer containing high Cr is formed, and it can hinder the diffusion of CrCl4. Higher concentration of CrCl4 at the inside of protective layer lead to growth of the protective layer inward. As shown in the snapshots of 9000 time steps and 16000 time steps, the peak of Cr is evident, and the width of the peak increases. Finally, the width of the peak maintains a constant for the formation of protective layer is far from the peak. The thickness of the inner approaches to the maximum, growth rate of inner and outer corrosion layers tend to be stable. Fig. 6 shows the comparison of corrosion morphology between experiments and simulation. The simulation results of 25,000 time steps is taken as a comparison of the 21-day corrosion experimental and each simulation step represents 79.65 s. When the corrosion continues for 21 days, corrosion layer changes regularly, and the corresponding chemical reaction is simple. When the simulation step is about 25,000 steps, the change of corrosion layer and the transformation process is similar to experimental results. At the same time, the morphology of corrosion layer and distribution of Cr element have a good agreement with experimental results. Fig. 6 (a) shows the thickness of the inner corrosion layer is 2.5 μm and outer corrosion layer is 7.08 μm. The thickness of simulation result is 49.5 lattice widths of outer corrosion layer and 20.2 lattice widths of inner corrosion layer. As we know, the experimental measurement of the inner corrosion layer is inaccurate, we assume that simulation thickness of outer corrosion layer is consistent with that of the experimental and each lattice width represents 0.143 μm. The simulation thickness of the inner corrosion layer is calculated as 3.1746 μm. Considering the dissolution of the outer corrosion layer in corrosion experiment, the simulation results of 25,000 steps are well matched with the corrosion experimental results of 21 days. Hence, this model to simulate the corrosion process is meaningful for us to understand corrosion mechanism. Fig. 7 and Fig. 8 both show the distribution of Cr element with different forms. Fig. 7 (a) shows cross-sectional SEM image and the Cr elemental distribution of In625 alloy, Fig. 7 (b) shows the simulation result, especially the right image is a collection of all site containing Cr, and MgCr2O4 is counted as double. Simulation result reflects the Cr distribution overall and Cr-deficient region is obvious. Fig. 8 (a) shows the EDX - ray line scan results of Cr elemental distribution, and Fig. 8 (b) is plotted with the cumulative numbers of site containing Cr as the Y-axis and the thickness of alloy as the X-axis. The Cr content in the two figures shows the similar change. The high Cr content position appears on outside of outer corrosion layer, while the region with low Cr content locates on interface of inner and outer corrosion layer. In case 1, the thickness of the outer and entire corrosion layer are simulated as shown in Fig. 9. The lattice number in ordinate represents the depth of the corrosion layer. The thickness of outer corrosion layer is calculated by the average of the depth at which the transverse
3.2. Model analysis and parameter study In this model, some parameters such as c%, o% are important which represent to the content of H2O, O2 dissolved in molten salt, but it is difficult for us to carry out experimental research. We study the influence of variable parameters on corrosion layer thickness. The corrosion layer thickness simulated by 25,000 steps is listed on Table 2, hin represents the thickness of inner corrosion layer, and h represents total corrosion layer thickness. The thickness of the corrosion layer is taken as a function of the simulated time step, Fig. 11 shows results of simulated thickness of entire corrosion layer (left) and outer corrosion layer (right). Fig. 11 (a) shows the influence of C concentration on the corrosion layer growth. The increase of C concentration has a significant effect on the initial growth rate of the whole corrosion layer. For the thickness of outer corrosion layer, it increases after a certain number of steps. The thickness of inner and outer corrosion layer reaches the same thickness at about 6000 steps in all three cases.Fig. 11 (b) shows the influence of the value of P3. The increase of P3 promotes the consumption of C in metal matrix, and C cannot penetrate into metal matrix. By comparison, it has small impact on outer corrosion layer. Fig. 11 (c) shows that when the content of Cr exceeds a certain value, an effective protective layer can be formed. When it is less than it, the thickness of corrosion will increase in a straight line. Fig. 11 (d) shows O is the main factors controlling corrosion process, when the concentration of O is low, the thickness of corrosion layer increases linearly with the concentration of O. 4. Conclusion According to the corrosion behavior of Ni-based alloy in chloride molten salt, a simple CA model is established. By selecting the appropriate simulation time step, we correlate the corrosion process with the experiment, and the growth of corrosion layers and the migration of Cr element are successfully simulated. The corrosion process involves complex system, and the corrosion condition has great influences. Simulation results reflect the Cr distribution overall and Cr-deficient region is obvious. The high Cr content position appears on outside of outer corrosion layer, while the region with low Cr content locates on interface of inner and outer corrosion layer. The relationship between the mass loss of alloy and corrosion layer thickness was observed, which show a similar change trend.
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Fig. 11. Simulated thickness of whole corrosion layer (left) and outer corrosion layer (right).
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Acknowledgements [3]
This work was supported by the funding of Nature Science Foundation of China (U1707603), Nature Science Foundation of China (51436009), Science and Technology Planning Project of Guangdong Province (2015A010106006), Nature Science Foundation of Guangdong (2016A030313362).
[4] [5]
Abbreviation A B O C D P Mg BO P di Pi Nt o% cr % c%
[6]
state variable of Cr state variable of Ni state variable of O2 state variable of Cl2 state variable of CrCl4 state variable of MgCr2O4 state variable of MgO state variable of NiO probability of the random walk process takes place（O, D） reaction of probability of the formula the simulation time step of system the percentage of O the percentage of Cr the percentage of C
[7] [8] [9] [10] [11] [12] [13]
Appendix A. Supplementary data
[14]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.solmat.2019.110170.
[15]
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Contents lists available at ScienceDirect
Solar Energy Materials and Solar Cells journal homepage: www.elsevier.com/locate/solmat
Cellular automata simulation on the corrosion behavior of Ni-base alloy in chloride molten salt
T
Weilong Wanga,∗, Bang Guana, Xiaolan Weib, Jianfeng Lua, Jing Dinga a b
School of Materials Science and Engineering, School of Intelligent Systems Engineering,Sun Yat-Sen University, Guangzhou, 510006, China School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, 510640, PR China
ARTICLE INFO
ABSTRACT
Keywords: Cellular automaton Molten chloride melt Ni-base alloy Corrosion
Chloride molten salt is required to study its corrosion behavior since it is recommended to be used as heat transfer and heat storage material in high-temperature thermal power generation system. In this paper, a simplify model was established by the reaction of diffusive corrosive gas and metal substrate in a chloride molten salt. A cellular automaton model based on the stochastic approach is adopted to simulate the uniform corrosion and the migration of metallic element. The corrosion behavior is also simulated considering the practical working condition, such as oxygen, moisture and so on. By comparing the simulation results with experimental data, it proves that the cellular automata simulation is an effective alternative method to describe the hightemperature corrosion process of molten salts. Simulation results of 25,000 time steps is taken as a comparison of the 21-day corrosion which reflects the Cr distribution, and the growth of corrosion layer with the migration of Cr element was reproduced. The change of corrosion layer thickness is similar to the mass loss. The simulation method provides insight on the distribution of corrosion products, corrosion kinetics and morphologies for the long-term application.
1. Introduction
thermodynamic potential-pO2- diagram for Cr, Ni at 700 °C [2]. Ding studied three commercial alloys (including stainless steel SS 310, Incoloy 800 H, Hastelloy C-276) in molten MgCl2/NaCl/KCl (60/20/ 20 mol%) under inert atmosphere, and proposed an impurity-driven corrosion mechanism to describe the hot corrosion behavior [3]. Crdeficient region was found in Ni-based alloy under uniform corrosion [1,4,5]. However, it is lack of learning the inner structure or component change of matrix alloy during the corrosion by using the experimental method. Moreover, it is also hard to obtain the long-term corrosion data due to the strict experimental condition. To our best knowledge, no simulation work has been done to study the corrosion characters of Nibase alloy in chloride molten salt. Thus, it is required to find an effective way to study the long-term high-temperature corrosion behavior of molten salts. Cellular automata model is developed as a powerful tool for modeling physical, chemical systems, especially for the high-temperature corrosion [6,7]. It can be simplified into a two-dimensional schematic to study both localized corrosion and uniform corrosion based on a stochastic approach [6,8–11]. Beside, cellular automata models can also simulate the chemical - electrochemical reaction based on diffusion of corrosive species and the reaction - passivation - dissolution process of metal, which can simulate the formation of oxide
Molten salt is used as heat transfer and heat storage material in thermal power generation system, with the feature of high working temperature, small vapor pressure/viscosity and low cost. The challenge we have to face is the high temperature corrosion occurring when metals are in long contact with chloride salts. Recently, two commercial concentrating solar power stations took place serious leakage of the molten salt tank, and it costs millions of dollars for this suffering. It is reported that the accident is caused by high temperature corrosion stress of the matrix alloy. Thus, it is urgent for us to find the matchable alloy and the solution to prevent high-temperature corrosion for various molten salts in practical devices. Chloride salts have drawn more attention due to its higher working temperature range, and it is also abundant in the nature salt lake. Some experimental work has been done to study the corrosion behavior of chloride salts. Hua Sun investigated the corrosion of Fe-based 316SS and seven Ni-based alloys in molten NaCl–KCl–MgCl2 under N 2 at 700 °C. They found all alloys suffered the selective dissolution of Cr, resulting in the formation of subsurface voids [1]. They investigate the effects of alloying elements on corrosion of Ni-based alloys in NaCl–KCl–MgCl2 under Ar at different temperature, and drew a ∗
Corresponding author. E-mail address: [email protected] (W. Wang).
https://doi.org/10.1016/j.solmat.2019.110170 Received 7 July 2019; Received in revised form 5 September 2019; Accepted 7 September 2019 Available online 27 September 2019 0927-0248/ © 2019 Elsevier B.V. All rights reserved.
Solar Energy Materials and Solar Cells 203 (2019) 110170
W. Wang, et al.
Fig. 1. Schematic diagram showing transition of corrosion scales on substrate during high-temperature corrosion in molten salts [4].
Fig. 3. Schematic plot of Margolus neighbors.
Fig. 2. Schematic plot of the CA model: (a) grid spaces one (b) grid spaces two (c) grid spaces three (d) three overlapped grid space.
films, and reproduce the growth of corrosion layers [12–14]. In this paper, the cellular automata model is used to study the corrosion process of Incon625 alloy in chloride molten salt. A two-dimensional cellular automata simulation corrosion modeling is established aim to simulate the growth of corrosion layers. The migration of Cr element in In625 has been studied in the entire corrosion process.
Fig. 4. Snapshots of simulation process, o% = 0.25, Nt = 0.
2. Methodology A simplify corrosion model is established based on the mechanism obtained in our previous experimental analysis, and the program of the CA model is programmed with software (matlab).
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The main chemical composition and reaction path determines the structure of the alloy. For In625 alloy, it is noticed that elements (Fe, Mo) have similar properties to Cr elements that are prioritized in reaction. We assume that the alloy consists of only Ni and Cr elements. Thus, in this model we take the amount of Ni and Cr into account.
Table 1 Main parameters in the model. No.
C (c%)
O (o%)
P3
Cr (cr%)
Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
0 0.05 0.1 0 0 0 0 0 0 0
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.1 0.5
0.01 0.01 0.01 0.02 0.05 0.01 0.01 0.01 0.01 0.01
0.5 0.5 0.5 0.5 0.5 0.3 0.4 0.6 0.5 0.5
2.2. CA model Cellular automata model was established based on the above discussion. A series of evolutionary rules are defined to form the discrete dynamical systems. We use a rectangular box of 400×400 vertical and horizontal sites with rigid boundary and Margolus neighbors. 2.2.1. Definition of sites There are eight types of lattice sites, displayed in various color and filling pattern. Each site does not have to represent a specific chemical component but a group of substance at the mesoscopic scale. A site is mainly occupied by Cr, B site is mainly occupied by Ni, O site is occupied by O2, C site is mainly occupied by Cl2, D site is mainly occupied by CrCl4, Mg site is mainly occupied by MgO, P site is mainly occupied by MgCr2O4, BO site is occupied by NiO. All these sites scatters across three parallel grid spaces in Fig. 2, where A, B, MgO, P, BO site are considered fixed and grid space one is used. O2 can diffuse into the outer corrosion layer, O use the grid space two. Cl2 can diffuse into inner corrosion, C and D use grid space three. Initially, O and C site exist randomly in the left half space of grid with a certain probability to represents the initial concentration. A and B site exist in all the right half space with a certain proportion representing the metal.
2.1. Corrosion mechanism and physical model The defined corrosion mechanism is necessary for modeling corrosion processes. In our previous experiment [4], we studied the corrosion behavior of Ni-based alloys in molten NaCl–CaCl2–MgCl2 eutectic salt and the corrosion mechanism was discussed according to the Gibbs function from thermodynamic calculation. The detailed formation process of the Cr-deficient region in corrosion layer of In625 alloy is proposed in Fig. 1. However, the mass transportation is complex in the corrosion process, since various element transports in the corrosion layer and molten salt, and some even penetrates into the metal substrate. Simultaneously, all the substances took place complex chemical reactions. Therefore, some assumptions are necessary to establish a simplified mode for simulating the complicated corrosion process. In the corrosion process of In625 alloy, the diffusion of O2 and substances containing Cl− takes place chemical reactions in a short time at high temperature. The diffusion rate and concentration of corrosive substance are supposed to control the corrosion process. In particular, the selective reaction of Cr elements correspond to the simulation of inner oxidation in the alloy [15,16]. The simplified mode is described as fellows. The area of reaction is divided into four zones in Fig. 1, including high temperature molten salt layer, outer corrosion layer, inner corrosion layer and matrix. In high temperature molten salt layer, O2 and H2O diffuses into high temperature molten salt from air. Subsequently, HCl and Cl2 are formed through a series of reaction. Therefore, we assume that corrosive substances already exist with a certain concentration in the molten salt in the beginning, and then these substances are continuously diffused from the upper layer of the molten salt into the corrosion layer. In outer corrosion layer, O2 dissolves in the molten salt and reacts preferentially with Cr in a short time. Also, it is consumed by other reactions. Therefore, the main reaction is assumed to be expressed as follows, Cr + 2MgCl2 + O2→CrCl4 + 2MgO
2.2.2. Diffusion process Margolus neighbors is used to describe diffusion and represented in Fig. 3. The upper left four grids are selected as neighbors at odd number of steps. Otherwise, lower right are chose, which has faster computation speed, all four site are computed together. We use a random walk process simulates the diffusion process of O, C and D with Margolus neighbors [17]. At each discrete interval, the wanderer occupies a neighbor randomly and this process occurs with a certain probability, which corresponds to the diffusion coefficient. The decrease of probability indicates the decrease of diffusion coefficient. For example, P site occupied by protective substance, we define the CA rules of diffusion as following: If walkers (O, D) are not in contact with any P, the random walk process takes place with a probability of 1. If all the four neighbors are P, the random walk process takes place with a probability of Pd4. According to the number of P in the neighborhood, other cases are Pd1, Pd2, Pd3, respectively, and the numerical value can be expressed as: 1 > Pd1 > Pd2 > Pd3 > Pd4. To simplify the calculation, Pd1 = 0.8, Pd2 = 0.6, Pd3 = 0.4, Pd4 = 0.2. If all the four neighbors are A or B, the state of site returns to the previous step. C can random walk in the whole space.
(1)
When Cr element content is insufficient, O2 reacts with Ni as the following reaction: Ni+1/2O2→NiO
(2)
The chloride containing Cr (CrCl4 mainly) in the inner corrosion layer diffuses into the outer corrosion layer, and participates in the reaction forming MgCr2O4 protective layer as follows, CrCl4+2MgO + O2→MgCr2O4+Cl2+MgCl2
2.2.3. Reaction and transformation rules We define some transformation rules of site to correspond to the simplified model above as follows:
(3)
In inner corrosion layer, Cl2 and other corrosive substances can react with Cr leading to a Cr-deficient corrosion layer. The mainly reaction is expressed as follows, 2Cl2+Cr→CrCl4
(4)
3
O + A→D + MgO
(5)
O + B→BO
(6)
D + MgO + O→P + C
(7)
C + A→D
(8)
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If A or B and O exit in the same position of their grid space, formula (5) or (6) occur with a probability of P1, P2, respectively. Similarly, formula (7) or (8) occur with probability of P3 and P4. The left side of formula means that the site is no longer occupied and the right side of
formula mean the site is occupied in respective grid space. The dissolution of O2 in MgCl2 participates in the reaction (1) and (3), and thus the consumption and formation of MgCl2 are neglected. Because the volume of each substance is not considered, every MgO site in formula
Fig. 5. Snapshots of corrosion layer growth process (left) and cumulative number of Cr. 4
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Fig. 5. (continued)
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Fig. 6. Comparison of simulation morphology and experiment SEM photograph, (a) cross-sectional SEM photograph of In625 after 21 days immersion at 600 °C [4], (b) Snapshots of simulation results of corrosion morphology, for time steps Nt = 25000.
Fig. 7. Comparison of Cr distribution of In625 alloy and collection of all site containing Cr.
color as the metal. The number of diffusion step Nt represents the evolution time step of system. According to Ref. [17], the probability for clockwise and counterclockwise deflection is assumed equal. Therefore, diffusion coefficients are determined by Nt and lattice width together. Some parameters for the corrosion process simulation are important, For example, o% represents the number of O, c% represents the number of C, cr% represents the number of Cr. P1,P2 and P4 is set as 0.1, 0.01,1, respectively. P3 is set as several different values representing the rate of major reactions in the system to some extent. P1 is set much larger than P2.When there is Cr near B, the reaction between O and Cr dominates. When there is no Cr, O reacts with Ni with a low probability. We set a particle source of O and C with constant concentration of o% and c% at the left boundary, which simulates the diffusion of substance from the air into molten salt. In particular, o% can represents the concentration of oxygen, and c% can represents the concentration of water vapor by some mathematical association. In the
(5) or (6) can represent 2MgO in reaction (1) and (3). The rate of chemical reaction can be calculated from the reaction probability and the change of the concentration of each substance refer to the fifth chapter of literature [17].But the specific relational expressions is difficult for us to deduce, and therefore, we use cellular automata model to study some property which have the similar behavior to corrosion test, instead of solving them by numerical methods. 3. Results and discussion The corrosion experiment results are greatly affected by the corrosion environment, the simulation is conducted to describe the impact of corrosion environment. In our model, O random exists on the left side of the space with o % percent and metal exists on all the right side of the space initially as shown in Fig. 4. A and B are represented in the same
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Fig. 8. Comparison of the change tendency of the Cr content with the thickness of metal. Fig. 9. (a) Simulated thickness of whole corrosion layer, (b) Simulated thickness of outer and inner corrosion layer.
simulation process, when the content of Cr element is too low, it is found that the protective layer cannot be formed effectively. Besides, considering Cr element consumes more O2 than Ni, the percentage of Ni and Cr is set as a series of values. In the first case, cr% is set as 0.5 for the related corrosion system. Each fixed parameter has no particular significance for the model, but the impact of the changeable parameter is important to understand the relationship between the model and the corrosion process of experimental. The influence of these parameters is investigated and the correlation of characteristic between simulation and experiment result is analyzed. The study on the effect of main parameters are listed in Table 1, the repeated simulation results of the same case show little difference. 3.1. Simulation verification Case 1 is simulated for comparison, and the related experimental data is obtained from Ref. [4]. Fig. 5 shows the snapshots of corrosion layer growth process, on the left side of each subgraph is the morphology of the corrosion layer. The right is the cumulative number of Cr corresponding to the depth of corrosion layer. In the initial stage, the cumulative number of Cr decreases gradually and there is no obvious boundary between internal and external
Fig. 10. Similar tendency of corrosion layer growth and mass loss.
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reaction of O2 takes place, and the thickness of whole corrosion layer is calculated same as outer corrosion layer, but the reaction of any substance. The change of corrosion layer thickness reflect the diffusion reaction process. Initially, higher oxygen concentration promotes reaction, and then the formation of protective layer prevents the diffusion of corrosive substance after a period. At the same time, the concentration of oxygen gradually decreases resulting in a slow increase in the thickness of the corrosive layer. In Fig. 9 (b), at the initial stage of simulation, the thickness of inner corrosion layer increases rapidly, and the thickness of inner and outer corrosive layer reaches the same thickness at about 6000 time steps. Thereafter, the inner corrosion layer is continuously forming and transforming into outer corrosion layer, and the thickness keeps unchanged. In Fig. 10, mass loss value and simulated thickness of entire corrosion layer is plotted in the same figure. Corrosion experiment time is transformed into corresponding simulation time steps. The mass loss of 25000 simulated time step falls on the growth curve of corrosion layer thickness, and the change of corrosion layer thickness and mass loss is the same.
Table 2 Simulated thickness of corrosion layer after 25,000 time steps. No.
C (c%)
O (o%)
P3
(cr%)
hin
h
Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
0 0.05 0.1 0 0 0 0 0 0 0
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.1 0.5
0.01 0.01 0.01 0.02 0.05 0.01 0.01 0.01 0.01 0.01
0.5 0.5 0.5 0.5 0.5 0.3 0.4 0.6 0.5 0.5
69.7 78.2 86.2 63.0 59.4 100.3 81.6 59.6 39.6 101.3
49.5 56.2 62.0 50.1 52.1 19.2 60.8 40.4 19.0 81.1
corrosion layers, which corresponds to the snapshot of 1000 time step. Then, protective layer containing high Cr is formed, and it can hinder the diffusion of CrCl4. Higher concentration of CrCl4 at the inside of protective layer lead to growth of the protective layer inward. As shown in the snapshots of 9000 time steps and 16000 time steps, the peak of Cr is evident, and the width of the peak increases. Finally, the width of the peak maintains a constant for the formation of protective layer is far from the peak. The thickness of the inner approaches to the maximum, growth rate of inner and outer corrosion layers tend to be stable. Fig. 6 shows the comparison of corrosion morphology between experiments and simulation. The simulation results of 25,000 time steps is taken as a comparison of the 21-day corrosion experimental and each simulation step represents 79.65 s. When the corrosion continues for 21 days, corrosion layer changes regularly, and the corresponding chemical reaction is simple. When the simulation step is about 25,000 steps, the change of corrosion layer and the transformation process is similar to experimental results. At the same time, the morphology of corrosion layer and distribution of Cr element have a good agreement with experimental results. Fig. 6 (a) shows the thickness of the inner corrosion layer is 2.5 μm and outer corrosion layer is 7.08 μm. The thickness of simulation result is 49.5 lattice widths of outer corrosion layer and 20.2 lattice widths of inner corrosion layer. As we know, the experimental measurement of the inner corrosion layer is inaccurate, we assume that simulation thickness of outer corrosion layer is consistent with that of the experimental and each lattice width represents 0.143 μm. The simulation thickness of the inner corrosion layer is calculated as 3.1746 μm. Considering the dissolution of the outer corrosion layer in corrosion experiment, the simulation results of 25,000 steps are well matched with the corrosion experimental results of 21 days. Hence, this model to simulate the corrosion process is meaningful for us to understand corrosion mechanism. Fig. 7 and Fig. 8 both show the distribution of Cr element with different forms. Fig. 7 (a) shows cross-sectional SEM image and the Cr elemental distribution of In625 alloy, Fig. 7 (b) shows the simulation result, especially the right image is a collection of all site containing Cr, and MgCr2O4 is counted as double. Simulation result reflects the Cr distribution overall and Cr-deficient region is obvious. Fig. 8 (a) shows the EDX - ray line scan results of Cr elemental distribution, and Fig. 8 (b) is plotted with the cumulative numbers of site containing Cr as the Y-axis and the thickness of alloy as the X-axis. The Cr content in the two figures shows the similar change. The high Cr content position appears on outside of outer corrosion layer, while the region with low Cr content locates on interface of inner and outer corrosion layer. In case 1, the thickness of the outer and entire corrosion layer are simulated as shown in Fig. 9. The lattice number in ordinate represents the depth of the corrosion layer. The thickness of outer corrosion layer is calculated by the average of the depth at which the transverse
3.2. Model analysis and parameter study In this model, some parameters such as c%, o% are important which represent to the content of H2O, O2 dissolved in molten salt, but it is difficult for us to carry out experimental research. We study the influence of variable parameters on corrosion layer thickness. The corrosion layer thickness simulated by 25,000 steps is listed on Table 2, hin represents the thickness of inner corrosion layer, and h represents total corrosion layer thickness. The thickness of the corrosion layer is taken as a function of the simulated time step, Fig. 11 shows results of simulated thickness of entire corrosion layer (left) and outer corrosion layer (right). Fig. 11 (a) shows the influence of C concentration on the corrosion layer growth. The increase of C concentration has a significant effect on the initial growth rate of the whole corrosion layer. For the thickness of outer corrosion layer, it increases after a certain number of steps. The thickness of inner and outer corrosion layer reaches the same thickness at about 6000 steps in all three cases.Fig. 11 (b) shows the influence of the value of P3. The increase of P3 promotes the consumption of C in metal matrix, and C cannot penetrate into metal matrix. By comparison, it has small impact on outer corrosion layer. Fig. 11 (c) shows that when the content of Cr exceeds a certain value, an effective protective layer can be formed. When it is less than it, the thickness of corrosion will increase in a straight line. Fig. 11 (d) shows O is the main factors controlling corrosion process, when the concentration of O is low, the thickness of corrosion layer increases linearly with the concentration of O. 4. Conclusion According to the corrosion behavior of Ni-based alloy in chloride molten salt, a simple CA model is established. By selecting the appropriate simulation time step, we correlate the corrosion process with the experiment, and the growth of corrosion layers and the migration of Cr element are successfully simulated. The corrosion process involves complex system, and the corrosion condition has great influences. Simulation results reflect the Cr distribution overall and Cr-deficient region is obvious. The high Cr content position appears on outside of outer corrosion layer, while the region with low Cr content locates on interface of inner and outer corrosion layer. The relationship between the mass loss of alloy and corrosion layer thickness was observed, which show a similar change trend.
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Fig. 11. Simulated thickness of whole corrosion layer (left) and outer corrosion layer (right).
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Acknowledgements [3]
This work was supported by the funding of Nature Science Foundation of China (U1707603), Nature Science Foundation of China (51436009), Science and Technology Planning Project of Guangdong Province (2015A010106006), Nature Science Foundation of Guangdong (2016A030313362).
[4] [5]
Abbreviation A B O C D P Mg BO P di Pi Nt o% cr % c%
[6]
state variable of Cr state variable of Ni state variable of O2 state variable of Cl2 state variable of CrCl4 state variable of MgCr2O4 state variable of MgO state variable of NiO probability of the random walk process takes place（O, D） reaction of probability of the formula the simulation time step of system the percentage of O the percentage of Cr the percentage of C
[7] [8] [9] [10] [11] [12] [13]
Appendix A. Supplementary data
[14]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.solmat.2019.110170.
[15]
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