A cellular automaton model for simulation of growth and cracking of passive film on stainless steel

Abstract

This invention provides a cellular automaton model for simulating the growth and rupture of a passivation film in stainless steel. This model meticulously replicates the passivation film growth process of stainless steel from a reaction principle perspective, calculating and analyzing the effects of different applied potentials on the passivation film thickness, point defect concentration, and passivation film rupture time. Using stainless steel as a prototype, the model simulates the passivation film growth and rupture process, establishing a model of the internal ion diffusion and reaction processes during passivation film formation, and simulating the influence of applied potential on various properties of the passivation film.

Description

Technical Field

[0001] The present invention belongs to the field of computational material simulation, and specifically relates to a cellular automaton model for simulating the growth and rupture of a stainless steel passivation film. Background Art

[0002] Many researchers use cellular automata to simulate corrosion processes because their characteristics are very consistent with the corrosion process, and simulation is more economical and convenient than experimental research. However, the passive film grown during corrosion has the characteristics of extremely thin thickness (<10nm) and high concentration of point defects, which makes the existing formation theory very complicated, and the previous models are very simplified, which can only simulate the morphology of passive film formation, but cannot correctly simulate its electrochemical properties. Summary of the invention

[0003] In order to solve the defects of the prior art, the present invention provides a stainless steel passivation film growth and rupture model based on cellular automata.

[0004] The technical solution to achieve the purpose of the present invention is: a cellular automaton model for simulating the growth and rupture of a stainless steel passive film is established and verified by the following steps:

[0005] (1) Simulate the process of forming a passive film on stainless steel in an aqueous environment, and abstract the molecules, atoms or ions involved in the reaction into cells, where the cells include: M cells, which represent the metal matrix, which is corroded by the metal-solution interface potential; I cells, which represent the metal ions generated by the metal being corroded; P cells, which represent the passive film formed by corrosion; S cells, which represent the ambient aqueous solution; F cells, which represent the hydrolysis products generated by the hydrolysis of metal ions after entering the solution; and H cells, which represent the final corrosion products of the hydrolysis.

[0006] (2) According to the cell type set in step 1, the main reaction in the formation process of the passivation film is abstracted as the conversion rules between cells, and the diffusion process of ions is abstracted as the movement of cells, and the simulation parameters of the cell reaction and movement are determined;

[0007] The main reaction and simulation parameters include:

[0008] The process of M cells being corroded to generate I cells, and the corrosion probability p is obtained according to the point defect model pas ;

[0009] The process of H cell nucleation to generate P cell, the probability p of this reaction process is determined according to the nucleation theory in solution pre ;

[0010] The process of P cell dissolving to generate H cell, the dissolution probability p is obtained according to the point defect model dis ;

[0011] The diffusion process and simulation parameters include:

[0012] I cell, F cell and H cell have diffusion process, and their diffusion probabilities are denoted as D i , D f and D h ;

[0013] (3) Determine the cell size in the cellular automaton model and the unit time length of the cellular automaton model simulation;

[0014] (4) Determine the passivation film rupture rule and set the cellular automaton model simulation to stop when the rule is reached;

[0015] (5) Repeat the simulation multiple times to obtain the results of the influence of potential parameters on the properties of the passivation film after simulation.

[0016] Compared with the prior art, the beneficial effects of the present invention are: the model provided by the present invention takes stainless steel as the prototype, simulates the process of its passive film growth and rupture, realizes the establishment of a model of internal ion diffusion and reaction process during the formation of the passive film, and realizes the simulation of the influence of external potential on various properties of the passive film. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The cross sections at different time periods during the growth of the passivation film of this embodiment, wherein a) is a simulation diagram at the beginning, and b) and c) are cross sections when the passivation film gradually becomes thicker with increasing time.

[0018] Figure 2 This is a graph of the current variation with time obtained by simulation in this embodiment, wherein the illustration is a fitting result after taking the logarithm with base 10 for both the x-axis and the y-axis.

[0019] Figure 3 The fitting diagram of the average thickness of the passivation film under different potentials is simulated for this embodiment.

[0020] Figure 4 The fitting diagram of the point defect concentration in the passivation film at different potentials was simulated for this embodiment.

[0021] Figure 5 This is the cross section when the passivation film is broken in the simulation of this embodiment.

[0022] Figure 6 3 is a fitting curve of the average rupture time of the passivation film at different potentials obtained by simulation in this embodiment, wherein the inset is the distribution of the rupture time of the passivation film at different potentials obtained by fitting. DETAILED DESCRIPTION

[0023] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0024] The formation of the passive film is affected by its formation potential, and each reaction process in corrosion has a certain probability of randomness. Based on the cellular automaton method, this model establishes a simulation model that can describe the growth and rupture of the passive film, so that the simulation results can reflect the influence of potential on the formation thickness of the stainless steel passive film, the internal point defect concentration and the passive film rupture time.

[0025] The model provided by the present invention takes into account the phenomena of metal dissolution, ion diffusion, ion hydrolysis, nucleation film formation in solution and film dissolution in the process of passive film growth and rupture, reproduces the characteristics of passive film formation affected by potential, and obtains the influence of potential on passive film thickness, point defects in passive film and passive film rupture time through a large number of repeated calculations. Since the main component of the stainless steel matrix is ​​Fe, the corrosion process of other metals is similar to that of Fe. Therefore, the following process takes Fe as an example and includes the following steps:

[0026] Step 1: Abstract the molecules, atoms or ions involved in the passive film formation reaction into cells, including: M cells, which represent the metal Fe matrix, which is corroded by the metal-solution interface potential; I cells, which represent the Fe generated by the corrosion of Fe. 2+ ; P cell, represents the passive film formed by corrosion; S cell, represents the environmental solution; F cell, represents Fe 2+ After entering the solution, the hydrolysis produces Fe(OH) + ; H cells represent the final corrosion product Fe(OH)2 of hydrolysis. Among them, I cells can be co-lattice with P cells and can also move within P cells, which means that ions or vacancies can exist and diffuse in the passivation film, while F cells and H cells existing in the solution can move freely in the solution;

[0027] Step 2: According to the cell type set in step 1, the main reaction in the formation of the passivation film is abstracted as the conversion rules between cells, and the diffusion process of ions is abstracted as the movement of cells, and the simulation parameters of the cell reaction and movement are determined. In this model, only the main reaction, i.e., the anodic reaction, is considered. The dissolution of the metal matrix can be written as the following reaction:

[0028] Fe→Fe 2+ +2e -

[0029] Denoted as:

[0030]

[0031] p pas The values ​​are:

[0032] p pas =p pas0 *exp(b1(V SHE -ε*L))

[0033] p in the formula pas0 The metal substrate is at a potential V SHE and the thickness of the passive film L are both 0, b1 is the parameter affecting the corrosion probability of the potential, b1 = α1αχF / RT, where α1 is the transfer coefficient of metal dissolution, α is the potential influence coefficient defined by the point defect model, χ is the average number of electrons lost by a single atom when the metal dissolves, F is the Faraday constant, R is the gas constant, T is the absolute temperature, and ε is the electric field strength in the passive film. According to multiple experiments and reference to existing literature, the basic dissolution probability p pas0 The value is 0.0006, and the parameter b1 that affects the corrosion probability is 0.3, where ε can be replaced by the electric field strength in the passivation film formed by Fe, and the experimentally measured value is 0.62V / nm.

[0034] Fe 2+ The following hydrolysis reactions can occur:

[0035] Fe 2+ +H2O→Fe(OH) + +H +

[0036] Fe(OH) + +H2O→Fe(OH)2+H +

[0037] They are recorded as:

[0038]

[0039]

[0040] The hydrolysis probability P I The value is 0.9, P L The value is 0.1. Both probabilities are empirical values. Multiple experiments also show that the values ​​of these two probabilities have little effect on the simulation results.

[0041] The final product of hydrolysis, H cell, nucleates on the surface of cell M or cell P and transforms into passivation membrane cell P. The reaction process can be written as:

[0042]

[0043] p pre The values ​​are:

[0044]

[0045] Where m represents the supersaturation during nucleation, which is generally the number of cells M and P in the neighborhood of the corrosion product H cell. The parameter k is a comprehensive coefficient related to temperature. Through multiple experiments and reference to existing literature, the parameter k in the passive film formation process is 0.0013, p pre The calculation formula of is simplified from the nucleation rate formula in the literature. The nucleation rate v n for:

[0046]

[0047] Where n is a constant, A is the molecular diffusion coefficient, Ω is the volume of a single molecule, γ is the surface energy corresponding to the critical nucleation size, and k B is the Boltzmann constant, T is the absolute temperature, and σ is the relative supersaturation.

[0048] At the same time, the passive film P will also dissolve into hydrolysis product H cells. This process is recorded as:

[0049]

[0050] p dis The values ​​are:

[0051] p dis =p dis0 *exp(c1V sHE )*N s

[0052] p in the formula dis0 The metal substrate is at a potential V SHE = 0, c1 is the influence parameter of potential on the dissolution probability of the passive film, c1 = α2αγF / RT, where α2 is the transfer coefficient of the passive film dissolution, α is the potential influence coefficient defined by the point defect model, γ is the average number of electrons lost by a single atom when the passive film dissolves, F is the Faraday constant, R is the gas constant, T is the absolute temperature, N S is the number of S cells in contact with the aqueous solution during dissolution.

[0053] According to multiple tests and reference to existing literature, the dissolution probability of the passive film is p dis0 The value is 0.00189, and the parameter c1 that influences the probability of dissolution of the passivation film is 1.4.

[0054] For the diffusion of cells, this model assumes that diffusion is the exchange of positions between cells. The diffusion probabilities of I cells, F cells, and H cells are D i , D f and Dh Since this model does not consider the change of temperature, the diffusion probability of the cells is a constant. For the diffusion of I cells, refer to the existing literature, D i is the ion diffusion gradient in the passivation film, which is 0.0025, D f Then with D h Consistent, value 0.1.

[0055] Step 3: Determine the cell size in the cellular automaton model and the unit time of the cellular automaton model simulation; from the literature, it is known that the thickness of the passivation film is generally less than 10nm, and the model needs to simulate the internal structure of the passivation film, so the cell size is Δx = 1nm. Since it is a simulation of the reaction at the mesoscopic scale, the model also requires a smaller unit time, so the unit time of the model should also be as small as possible, taking dt = 0.01s, and the current density i(t) function is:

[0056]

[0057] The formula is derived as follows:

[0058] Since the passivation film is a thin film of uniform thickness obtained by uniform corrosion, it can be concluded that the volume of the corroded cell at time t is:

[0059] V m =Δx 3 N(t)L z

[0060] Where N(t) is the number of corroded metal cells at that moment. Since the simulation model is a two-dimensional model, to calculate the three-dimensional corroded volume, it needs to be expanded to three dimensions, so it needs to be multiplied by the length of the z axis L z The number of moles of corroded metal at time t is obtained from the corroded volume n(t):

[0061]

[0062] Where ρ is the density, M is the molar mass, and the current conservation equation during the reaction is as follows:

[0063] I(t)dt=zF*dn(t)

[0064] z is the average number of electrons lost by each metal atom during the corrosion reaction, and F is the Faraday constant. Combining the above two formulas, we can get the current I(t) at time t as:

[0065]

[0066] The current density i(t) is obtained from the current:

[0067]

[0068] Where L x represents the length along the x-axis, N f (t) is the number of metal cells corroded within the time dt at time t.

[0069] For commonly used stainless steel materials, the average number of electrons lost by a single atom during the corrosion process is z, which is 2.19, and the average density of stainless steel is ρ, which is 7.93 g / cm 3 , the average molar mass M of stainless steel is 55.4 g / mol.

[0070] Step 4: Determine the passivation film rupture rule, and set the cellular automaton model simulation to stop when the rule is reached; point defects such as ions and vacancies inside the passivation film will aggregate, hindering the growth of the film and making the film thinner. When the point defects aggregate to a certain concentration, the film will rupture. Therefore, the I cell aggregation rule is added to this model. It is known from the literature that the aggregation rate of point defects inside the passivation film is much smaller than the directional diffusion rate of point defects. Then according to the previous passivation film diffusion probability D i The set value of and experimental experience can set the point defect aggregation probability D l The rupture rule is: when the I / P ratio exceeds 80% within the width of 5 cells in the horizontal direction of the model, the passive film ruptures, and the simulation time is the rupture time.

[0071] Step 5: Repeat the simulation multiple times to obtain the effect of potential parameters on the properties of the passivation film after simulation. SHE After repeated simulation calculations, the change curves of the current density in the simulation process, the thickness of the passivation film, the point defect concentration and the rupture time of the passivation film under different potentials were obtained.

[0072] Example

[0073] This model sets the total number of cells to L x *L y =400*400, all cells in the 1st to 125th rows are set as the aqueous solution S, and the cells in the 126th to 400th rows are set as the metal matrix M.

[0074] In the simulated external potential V SHE = 0.3V, the passivation film interface diagram under different simulation time is as follows Figure 1 As shown, Figure 1 a) is the initial interface, where the metal and solution have not yet started to react; b) is the interface at 30 seconds, where the precipitate generated by the reaction has basically completely covered the metal surface, forming a passivation film, which slows down the corrosion of the metal; c) is the interface at 60 seconds, where the passivation film covering the metal substrate becomes thicker.

[0075] Similarly, when the external potential is 0.3V, the simulated current change curve is as follows Figure 2 As shown in the figure, the current density drops rapidly in a short time after the simulation starts, which shows that the formation of the passivation film has a significant inhibitory effect on metal corrosion. The subsequent current density decreases slowly and finally reaches a relatively stable state. The attached figure is the fitting result after taking the logarithm of the current density and time with the base 10. The fitting slope is -0.486, which is very close to the empirical value of -0.5 in the experiment, indicating the rationality of the model.

[0076] The potential distribution was set between -0.5V and 0.5V, and a group of potential values ​​was taken every 0.1V. At each potential, 100 simulation results were taken for analysis, and the average thickness L of the passivation film was obtained. SS With potential V SHE The relationship between Figure 3 As shown, it was finally found that there was a good linear relationship between the thickness of the passivation film and the potential, which is consistent with the experimental results.

[0077] Under the same potential value conditions as above, after 100 simulations, the ratio of I / P of the point defects inside the film is obtained. D With potential V SHE The relationship between Figure 4 As shown, the point defect concentration inside the passivation film and the potential show a modified e-exponential relationship, which is consistent with the experimental data.

[0078] The rules for the rupture of the passive film have been set in the previous section. The model simulation section at the time of rupture in the actual simulation is as follows: Figure 5 As shown in the figure, the set area width is shown in the figure, the width is L0, and the passivation film breaks when the proportion of point defects within the width exceeds the set value. After 20 simulations at potentials of 0.65V, 0.67V, 0.7V, 0.72V, 0.75V, 0.78V, 0.8V and 0.85V, the rupture time of the passivation film was recorded respectively. The results are shown in Figure 6 As shown in the illustration, this figure shows the distribution of rupture time after multiple tests. It can be found that although the rupture time of the passive film is t ind It is random, but generally decreases with the increase of potential. Take the average value of the rupture time at each potential and then compare it with the potential V SHE The fitting result is as follows Figure 6 As shown, the average rupture time t ind With potential V SHE There is a modified e-exponential relationship between them, which is consistent with the actual experimental results.

Claims

1. A method for establishing a cellular automaton model for simulating the growth and rupture of a stainless steel passive film, characterized in that: The following steps are involved: (1) Simulate the process of forming a passive film on stainless steel in an aqueous environment, and abstract the molecules, atoms or ions involved in the reaction into cells, where the cells include: M cells, which represent the metal matrix, which is corroded by the metal-solution interface potential; I cells, which represent the metal ions generated by the metal being corroded; P cells, which represent the passive film formed by corrosion; S cells, which represent the ambient aqueous solution; F cells, which represent the hydrolysis products generated by the hydrolysis of metal ions after entering the solution; and H cells, which represent the final corrosion products of the hydrolysis. (2) According to the cell type set in step 1, the main reaction in the formation process of the passivation film is abstracted as the conversion rules between cells, and the diffusion process of ions is abstracted as the movement of cells, and the simulation parameters of the cell reaction and movement are determined; The main reaction and simulation parameters include: The process of M cells being corroded to generate I cells, and the corrosion probability p is obtained according to the point defect model pas ; The process of H cell nucleation to generate P cell, the probability p of this reaction process is determined according to the nucleation theory in solution pre ; The process of P cell dissolving to generate H cell, the dissolution probability p is obtained according to the point defect model dis ; The diffusion process and simulation parameters include: I cell, F cell and H cell have diffusion process, and their diffusion probabilities are denoted as D i , D f and D h ; (3) Determine the cell size in the cellular automaton model and the unit time length of the cellular automaton model simulation; (4) Determine the passivation film rupture rule, and set the cellular automaton model simulation to stop when the rule is reached. Specifically: Determine the passivation film rupture rule: I cell aggregation probability D l =0.00005, at the same time, when the I / P ratio within the width of 5 cells in the lateral direction of the model exceeds 80%, the passive film breaks; (5) Repeat the simulation multiple times to obtain the effect of the potential parameters on the properties of the passivation film after simulation, including current density, passivation film thickness, point defect concentration, and passivation film rupture time; in, The corrosion probability p is obtained based on the point defect model pas , p pas =p pas0 *exp(b1(V SHE -ε*L)) p in the formula pas0 The metal substrate is at a potential V SHE and the dissolution probability when the thickness of the passive film L is 0, b1 is the influence parameter of the potential on the corrosion probability, b1 = α1αχF / RT, where α1 is the transfer coefficient of metal dissolution, α is the potential influence coefficient defined by the point defect model, χ is the average number of electrons lost by a single atom when the metal dissolves, F is the Faraday constant, R is the gas constant, T is the absolute temperature, and ε is the electric field strength in the passive film; According to the nucleation theory in solution, the probability p of the reaction process is determined pre : In the formula, m represents the supersaturation during nucleation, k is the comprehensive coefficient related to temperature, and p pre The calculation formula of is simplified from the nucleation rate formula, the nucleation rate formula v n for: Where n is a constant, A is the molecular diffusion coefficient, Ω is the volume of a single molecule, γ is the surface energy corresponding to the critical nucleation size, and k B is the Boltzmann constant, T is the absolute temperature, and σ is the relative supersaturation; the dissolution probability p is obtained according to the point defect model dis : p dis =p dis0 *exp(c1V SHE )*N S p in the formula dis0 The metal substrate is at a potential V SHE = 0, c1 is the influence parameter of potential on the dissolution probability of the passive film, c1 = α2αγF / RT, where α2 is the transfer coefficient of the passive film dissolution, α is the potential influence coefficient defined by the point defect model, γ is the average number of electrons lost by a single atom when the passive film dissolves, F is the Faraday constant, R is the gas constant, T is the absolute temperature, N S is the number of S cells in contact with the aqueous solution during dissolution.

2. The method for establishing a cellular automaton model according to claim 1, wherein: The current density i(t) is expressed as follows: Where z is the average number of electrons lost by a single atom of stainless steel during corrosion, F is the Faraday constant, ρ is the average density of stainless steel, N f (t) is the number of metal cells corroded within the time dt at time t, Δx is the cell size in the model, M is the average molar mass of stainless steel, Lx represents the length along the x-axis, and dt is the unit time of the simulation.

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