1. Introduction

2. Cellular Automata as Tools in Corrosion Management.

2.1. Fundamentals of Cellular Automata for Corrosion.

The AC model was initially proposed by John Von Neumann and corresponds to an idealization of a physical system where time and space are discrete and physical quantities take on a finite set of values [5]. Space is represented on a grid of cells, and each cell has a specific state. In a simplistic way, the state of a cell can be assigned as either alive or dead (0 and 1), indicating its characteristic.

To clarify, for an entity to be classified as a CA (Counter Argument), it must adhere to the following structure. A regular grid of cells that covers a part of a d-dimensional space.

A set $\mathsf{\Phi }\left(\overrightarrow{\mathit{r},}\mathit{t}\right)=\left\{{\mathsf{\Phi }}_1\left(\overrightarrow{\mathit{r},}\mathit{t}\right),{\mathsf{\Phi }}_2\left(\overrightarrow{\mathit{r},}\mathit{t}\right),{\dots ,\mathsf{\Phi }}_{\mathbf{m}}\left(\overrightarrow{\mathit{r},}\mathit{t}\right)\}\right.$ of Boolean variables attached to each site r of the grid that gives the local state of each cell at time t = 0,1,2, …, n.

A rule R = {R₁, R₂, …, R_m} that specifies the time evolution of the states $\mathsf{\Phi }\left(\overrightarrow{\mathit{r},}\mathit{t}\right)$in the following form:

$${\mathsf{\Phi }}_{\mathrm{j}}\left(\overrightarrow{r,}t+1\right)=R_j\left(\mathsf{\Phi }\left(\overrightarrow{r,}t\right),\mathsf{\Phi }\left(\overrightarrow{r}+{\overrightarrow{\delta }}_1,t\right),\mathsf{\Phi }\left(\overrightarrow{r}+{\overrightarrow{\delta }}_2,t\right),\dots ,\mathsf{\Phi }\left(\overrightarrow{r}+{\overrightarrow{\delta }}_q,t\right)\right)$$

(1)

where $\overrightarrow{\mathbf{r}}+{\overrightarrow{\mathsf{\delta }}}_{\mathbf{k}}$ denotes cells belonging to a specific neighborhood.

In the above definition, the rule R is applied to all sites simultaneously, leading to synchronous dynamics [34].

In the context of corrosion, the cell state can represent the presence of an element, a compound, or a corrosion product. The state of a cell changes over time depending on its own state and that of its nearest neighbors. Figure 1 shows a grid of cells where the cell undergoing a state change is represented in black, while the cells enclosed in a black frame (neighborhood) are the ones that influence this change, considering the state of their neighbors. This figure represents the three most used types of neighborhoods: Von Neumann, Moore, and Margolus. In the Von Neumann neighborhood (a), four neighbors are considered, located to the east, north, west, and south of the changing cell. On the other hand, in the Moore neighborhood (b), there are six neighbors surrounding the central cell. Finally, in the Margolus neighborhood, the change process is more complex as it depends on both space and time. Firstly, the space is divided into a 2x2 square. The first state change of cell lr occurs during an odd time, considering the neighbors in the upper square (ul, ur, ll, lr). In the next iteration, during even time, the state of cell lr is updated considering the neighbors in the square represented by dashed lines.

The neighborhood used traverses the entire grid, and through a set of transformation rules, the new state of each cell will be determined until the total update of the grid is completed, which represents the first generation (iteration) of the model. The rules and configuration of the AC model in corrosion simulations are specific for each phenomenon to be studied.

Table 1 presents a comprehensive summary of the results published in popular science journals, which have been utilized to support our bibliographic review.

2.1.1. Uniform Corrosion Model.

Fairén et al. [28] analyzed the evolution of surface roughness in the studied corroded metal. They examined the agreement between a classical macroscopic description and a mesoscopic approach that accounts for the development of such roughness. They studied how morphology could influence the modeling, finding that the model could simulate the mesoscopic heterogeneity of the electrode surface and its impact on the uniform corrosion process. Part of their study determined that further research was still needed to fully understand the relationship between the electrochemical mechanism involved, the steps determining corrosion rate, and the morphology of the electrode surface.

Badiali et al. [35,36,37] studied the formation of films on a surface in the presence of corrosion, diffusion, and precipitation at the growth front. Obtaining results that show that the growth of the layer follows a parabolic law and that the model can be useful for predicting and controlling corrosion growth in metallic structures, pipes, and equipment, as well as for developing new corrosion-resistant materials. Chen et al. [38,39] studied the corrosion and oxidation mechanism of stainless steel in lead-bismuth eutectic (LBE) environments, a liquid metal used as a coolant in some advanced nuclear reactors and accelerator-driven systems, and in [40] the medium was supercritical water. The model considered diffusion, reaction, and precipitation processes occurring on the steel surface, and a mesoscopic description was used to explore the general characteristics of the evolution of the involved processes. Additionally, they aimed to predict how oxide scale removal occurs and how it affects metal corrosion, concluding that the CA model is useful for understanding these mechanisms. Chen et al. [41] focused on simulating the growth of the oxide layer in chromium-containing stainless steels. Their objective was to verify whether the stochastic nature of the CA model for uniform corrosion would generate unstable or unreasonable results deviating from the deterministic model for uniform corrosion of steel in flowing LBE. Their results showed that the CA model is stable and reliable for simulating the thickness of the oxide layer. Chen et al [33] proposed a numerical simulation method to predict the evolution of uniform corrosion damage of the outer steel tube in concrete-filled tubular columns subjected to corrosive environments. They discussed the influence of solution concentration and the probability of dissolution of corrosive agents. The obtained results were compared with theoretical solutions and experimental findings. They concluded that different concentrations of corrosive agents have different impacts on the degree of corrosion damage. Ren et al. [42] simulated the uniform corrosion of aluminum in various environmental conditions. They defined corrosion rules based on the actual electrochemical reactions and examined the corrosion process at a mesoscopic scale. By studying the corrosion formation and modifying the rules for different concentrations of corrosive solutions and ambient temperatures, they gained insights into corrosion mechanisms. The simulation results contribute to a better understanding of corrosion and can aid in its prevention and mitigation, especially in aeronautical structures where corrosion can lead to fatigue-induced damage, compromising structural integrity. Li et al [43] sought to gain a better understanding of the corrosion evolution of marine structural steel in the tidal zone and how corrosion can be prevented or mitigated in this environment. Their objective was to comprehend the corrosion mechanisms in the tidal zone, identify the factors influencing the corrosion rate, and propose possible strategies to prevent or mitigate corrosion in structures and equipment used in marine environments, ultimately offering solutions to extend their lifespan. Wang et al [29,44] investigated the corrosion of a metal in molten chloride salt and explored methods to enhance its corrosion resistance. A simplified model was established based on the reactive diffusion of corrosive gas and the metallic substrate. Both experiments and simulations were conducted using the cellular automaton (CA) method.

The physical model from the experimental work determined that the main reactions involved are:

$$Cr+2Mg{Cl}_2+O_2\to Cr{Cl}_4+2MgO$$

(2)

$$Ni+1/2O_2\to NiO$$

(3)

$$Cr{Cl}_4+2MgO+O_2\to Mg{Cr}_2{O}_4+{Cl}_2+Mg{Cl}_2$$

(4)

$$2{Cl}_2+Cr\to Cr{Cl}_4$$

(5)

They assumed the presence of corrosive substances in the molten salt from the beginning, where O₂ and H₂O diffuse into the molten salt from the air, leading to the formation of HCl and Cl₂ through a set of reactions. The dissolved O₂ in the salt rapidly reacts with Cr (2). When the Cr content is insufficient, O₂ reacts with Ni (3). The chloride containing Cr (mainly CrCl₄) forms a protective spinel layer composed of MgCr₂O₄ through (4). On the other hand, Cl₂ can react with Cr, resulting in a chromium-depleted layer (5).

To establish the CA model, the chemical reactions involved in the corrosion process were simplified by assigning letters to the compounds or elements present. A = Cr; B = Ni; O = O₂; C = Cl₂; D = CrCl₄; Mg = MgO; P = MgCr₂O₄; BO = NiO.

The lattice sites were classified into fixed compounds (A, B, MgO, P, and BO) and mobile compounds (O, C, D). The interaction of mobile compounds within the lattice occurs through a probabilistic random walk process. As an example, Figure 2 shows four grid schematics of the CA model. In (a), a grid is depicted with the fixed compounds located. In (b), the location of mobile compounds that diffuse toward the metal is shown. In (c), the elements that can diffuse in the outer corrosion layer are present, and in (d), a lattice is shown where all compounds present in the process are located.

In reactions (6) to (9), the modified reaction and transformation rules for the CA model are shown.

$$\mathrm{O}+\mathrm{A}\to \mathrm{D}+\mathrm{M}\mathrm{g}\mathrm{O}$$

(6)

$$\mathrm{O}+\mathrm{B}\to \mathrm{B}\mathrm{O}$$

(7)

$$\mathrm{D}+\mathrm{M}\mathrm{g}\mathrm{O}+\mathrm{O}\to \mathrm{P}+\mathrm{C}$$

(8)

$$\mathrm{C}+\mathrm{A}\to \mathrm{D}$$

(9)

The Margolus neighborhood was used to induce state changes in the different cells across generations. Figure 3 displays the results obtained by the model, where the left side (black color) represents the molten salt, while the right side (purple color) represents the metal under study. As the iterations progress, the growth of the oxide layer is observed. The number of iterations can be interpreted as representing an experimental time scale.

A comparison is shown in Figure 4 between the simulation results and a scanning electron microscopy (SEM) image. It was determined that 64,000 iterations correlate with the experimental results from 21 days of exposure, demonstrating that the AC simulation yields satisfactory results in the study of high-temperature corrosion of Fe-Cr alloys in the presence of molten salts.

2.1.2. Localized and pitting Corrosion model.

Localized corrosion encompasses corrosion processes that occur in specific areas of a material, leading to localized damage. Cellular automata simulate the initiation and propagation of localized corrosion, providing insights into factors influencing its occurrence, growth patterns, and evolution over time.

Di Caprio et al. [20,45] presented an electrochemical model for the corrosion of metals in contact with liquids, based on the description of chemical and electrochemical reactions occurring at the metal-liquid interface, which was simulated using CA. They investigated the corrosion process of each metallic site at the interface and compared the simulation results with experimental data. The proposed model reproduced experimental facts and trends without an explicit separation between anodic and cathodic sites. Overall, the study demonstrated that cellular automata-based models are a useful tool for simulating complex systems such as metal corrosion and can be adapted to include different rules and conditions according to the specific needs of the system under study. Cheng et al. [46] simulated the growth of metastable corrosion pits. The objective was to gain a better understanding of the mechanism behind the growth of these pits and compare the simulated results with experimental data. The researchers established a relationship between the current and current density of the pit over time to illustrate the mechanism of metastable pit growth. Additionally, they developed an optimal range of parameters for the simulation that allowed for visualizing the complete process of pit growth, including its geometry. The study built on previous work on the mechanism and electrochemical and mass transfer steps associated with the pitting corrosion process. Wang et al. [47] reproduced the interactions between metastable pits in stainless steel and analyzed how different factors affect their growth and stability. The model included corrosion, passivation, salt film hydrolysis, and hydrogen ion diffusion. Based on the model, they concluded that it is capable of accurately simulating the interactions between metastable corrosion pits in stainless steel. Wang et al. [48] investigated the interaction of metastable corrosion pits in stainless steel under mechano-electrochemical effects using an updated cellular automaton/finite element model, elucidating the mechanisms for pit interactions. In the study, they considered an electrochemical system where stainless steel is exposed to an aggressive chloride solution. The stainless-steel samples had passive layers of surface oxide, which can be damaged in the presence of chloride anions. Two breakdown locations in the passive film were included to study only the pit propagation and not its nucleation. They concluded that the cellular automaton/finite element model used was effective in predicting the interaction of corrosion pits on a mesoscopic scale. Torska et al. [49] discussed the fracture dynamics in the investigated areas and performed a comparative analysis of pitting corrosion rates under real and simulated conditions. They demonstrated that the simulation procedure using cellular automata accurately reproduced the physics of corrosion. The study proposed a new modeling algorithm and local transition rules for the automaton cells used in simulating pitting corrosion images. Hu et al. [50] simulated pitting corrosion in nickel alloys. The authors employed four fundamental elements of the model to simulate electrochemical reactions, chemical reactions, and diffusion processes. The obtained results were qualitatively and quantitatively compared with experimental data and analogous findings cited in the literature. The study suggested that this type of model could be useful in gaining a better understanding of corrosion processes and developing corrosion-resistant materials for various industrial applications. Fatoba et al. [51] employed a combination of cellular automata and finite element analysis to simulate the growth of localized corrosion under the influence of applied stress. The results demonstrated that mechanical effects, such as plastic deformation, accelerated the rate of localized corrosion development. The study focused on low-alloy steel, but the findings may be applicable to other materials as well. Rujin et al. [52] established a mathematical model based on a statistical approach to describe the evolution process of pitting corrosion. Additionally, they proposed a 3D stochastic CA model to replicate the simultaneous initiation and growth process of pits. The findings of the study can contribute to a better understanding of the laws governing pitting corrosion evolution and provide valuable insights into its prevention and control. To simulate localized corrosion, Pérez-Brokate et al. [31,53] aimed to gain a better understanding of hidden corrosion processes and pitting corrosion within corrosion cells by using a stochastic cellular automaton (CA) model. They studied the morphology, propagation, and influence of coupled diffusion within the corrosion cavity.

In the physical-chemical model, simplifications were made by assuming simplified electrochemical and chemical reactions (excluding contaminants and considering only H⁺ and OH^-). Localized corrosion, being a multi-scale phenomenon, depends not only on atomic-scale surface phenomena but also on macroscopic environmental conditions.

The electrochemical reactions used:

Anodic reactions.

$$M+H_{2}O\to MO{H}_{aq}+H^{+}+e^{-}$$

(10)

$$M+O{H}^{-}\to MO{H}_{solid}+e^{-}$$

(11)

Cathodic reactions.

$$H^{+}+e^{-}\to \frac{1}{2}{H}_2$$

(12)

$$H_{2}O+e^{-}\to \frac{1}{2}{H}_2+O{H}^{-}$$

(13)

Authors called SJ reactions when the anodic and cathodic half reactions occur at the same location:

$$M+H_{2}O\to MO{H}_{aq}+\frac{1}{2}{H}_2$$

(14)

$$M+H_{2}O\to MO{H}_{solid}+\frac{1}{2}{H}_2$$

(15)

$$MO{H}_{solid}\to MO{H}_{aq}$$

(16)

The anodic and cathodic sites are electrically connected through the metal and the solution. When they are separated, they are referred to as Spatially Separated Electrochemical (SSE) reactions. The diffusion of SSE reactions results in the generation of H⁺ and OH^- ions, mimicking a random walk. When these ions interact, neutralization takes place, as depicted in the study through the following reaction:

$$H^{+}+O{H}^{-}\to H_{2}O$$

(17)

The 3D lattice representation is depicted in Figure 5, illustrating a passivated metal in contact with a neutral electrolyte and the cathodic reaction takes place at a random point Figure 5a. The H⁺ and OH^- ions generated in the first reaction diffuse in the electrolyte. Each lattice site was determined by the dominant species. In Figure 5b the solid sites represent the metal (M), the metal in contact with the electrolyte (R), and the oxide layer providing passivity to the metal (P). Additionally, the electrolyte sites were differentiated into three different states based on pH. An acidic site (A), a basic site (B), and a neutral site (E) were considered. The Moore neighborhood was employed for the simulation.

In Figure 6, they showed the evolution of the pit. They indicated the presence of an anodic half-reaction at the initial defect of the passive layer. The ions are dispersed randomly in the electrolyte, resulting in the growth of the pit when an H+ ion encounters the metal, leading to an electrochemical reaction. As the pit reaches a certain size, the concentration of acidic ions increases, causing instability and further enlargement of the pit.

The model was considered a valuable tool for gaining a better understanding of localized and pitting corrosion processes and developing more effective strategies for corrosion prevention and treatment.

2.1.3. Stress Corrosion Cracking (SCC) model

Stress corrosion cracking is a phenomenon where the combination of tensile stress and a corrosive environment leads to crack initiation and propagation in a material. Cellular automata modeling the complex interactions between mechanical stress, electrochemical processes, and material degradation, helping to understand the conditions under which SCC occurs and its progression.

Zhu et al. [54] focused on predicting the service life of concrete bridges and preventing chloride-induced corrosion. They utilized 3D-CA, which accurately simulates chloride diffusion in concrete. Multiple factors were considered, such as ambient relative humidity, temperature variations, stress, water-cement ratio (w/c), concrete degradation, corrosion propagation, cracks, and time. The study provides a useful tool for predicting the service life of the bridge and designing preventive measures against chloride-induced corrosion in concrete bridges. Liu et al. [55] modeled the SCC process in steel pipes. They employed a combination of finite element analysis and cellular automata techniques to simulate the initiation and propagation of cracks.

The electrochemical model used considered only the species H₂O, Fe, Fe²⁺, H⁺ and FeOH⁺. The rules for corrosion evolution and cell diffusion were expressed in the following equations:

$$Fe\to {Fe}^{2+}+2e^{-}$$

(18)

$${Fe}^{2+}+2H_{2}O\to FeO{H}^{+}+2H^{+}$$

(19)

Based on the equations above, the authors formulated the rules of the AC model, where the diagram in Figure 7 represents the spatial layout of the model. The sites W represented a non-corrosive neutral solution (H₂O), H represented a corrosive acidic solution (H⁺), the site M represented the metal, which dissolves to form site R after being in contact with the corrosive solution. The site R represents the active metal (Fe²⁺), and site P represents the corrosion product (FeOH⁺).

The evolution rules for corrosion in the CA model were formulated based on the previous equations. Figure 8 shows the rules for the oxidation of Fe and the hydrolysis of Fe²⁺ to FeOH⁺. When a site M is in contact with at least one site H, reaction 1 will occur with a corrosion probability P_corr, transitioning from site M to site R. Additionally, when a site R is in contact with at least two sites W, Fe²⁺ hydrolyzes to FeOH⁺ with a probability P_Hyd, and both site R and the two W sites are replaced by the corrosion site P and two H sites, respectively.

The results demonstrated that prior to crack initiation, pitting corrosion was controlled by anodic reactions and mechanical factors, with electrochemical corrosion playing a significant role. During the crack propagation process, the mechano-chemical effects induced by plastic deformation promoted anodic dissolution at the crack tip, driving its propagation. This study may have significant implications for the pipe industry and help develop more effective strategies for corrosion prevention.

Figure 9. Evolution process of cross-sectional stress corrosion profiles: (a) 30 h, (b) 60 h, (c) 90 h, and (d) 120 h [55].

Figure 9. Evolution process of cross-sectional stress corrosion profiles: (a) 30 h, (b) 60 h, (c) 90 h, and (d) 120 h [55].

2.1.4. Intergranular Corrosion Model.

Intergranular corrosion occurs along the grain boundaries of a material, typically due to variations in composition or microstructure. Cellular automata can simulate the interactions between different grain boundaries, their susceptibility to corrosion, and the role of environmental factors in intergranular corrosion.

Chen et al. [56] developed a cellular automaton model to predict the susceptibility to intergranular corrosion in austenitic stainless steel and provide useful information on how to prevent or mitigate this problem. The results demonstrated how material properties change under different heat treatment and sensitization conditions. Additionally, they investigated factors affecting intergranular corrosion, such as the evolution of chromium-rich carbide precipitation and chromium concentration distribution [57]. They concluded that the CA model can be valuable for improving the design and performance of materials used in industrial applications.

Lishchuk et al. [58] utilized cellular automata to describe the propagation of intergranular corrosion and made simplifying assumptions that enabled them to predict the corrosion rate. The results of the model demonstrated good qualitative and quantitative agreement with experimental data regarding the advancement of the corrosion front.

Jahns et al. [59,60] develop a simulation to predict internal corrosion during high-temperature applications in metal alloys. They utilized the model to describe diffusion-controlled precipitation processes and enhance the understanding of high-temperature corrosion in metal alloys. The researchers' goal was to develop more effective strategies to prevent or mitigate corrosion.

Di Caprio et al. [61,62,63,64] conducted various studies on intergranular corrosion using 2D and 3D CA models. Their aim was to predict the rate and pattern of corrosion in stainless steel exposed to corrosive solutions. They quantitatively analyzed the surface morphology of the steel and grain boundary structures. They presented CA methodologies to understand and prevent corrosion, and experimental validation yielded positive results.

Wang et al. [65] focused on investigating the corrosion behavior of a nickel-based alloy in a molten chloride salt mixture. The CA model enabled them to reproduce the distribution of corrosion products and components, as well as changes in the morphology and thickness of the corrosion layer over time. The results of the study can help predict the corrosion behavior of different metals in similar molten salt environments.

The mechanism of high-temperature corrosion is relatively complex. In the study conducted by Wang et al. [44], due to the alloy being primarily composed of Cr, Fe, and Ni elements, which play a significant role in corrosion resistance and alloy microstructure, only Cr, Fe, and Ni were considered in the model, excluding other elements present in lower concentrations.

The mechanism considered by the authors primarily involved the migration of metallic elements, substance consumption, and generation of corrosion products through the following equations:

$$Cr+O_2\to {Cr}_2{O}_3$$

(20)

$$Fe+O_2\to {Fe}_2{O}_3$$

(21)

$$Ni+O_2\to NiO$$

(22)

$$Cr+{Cl}_2\to Cr{Cl}_4$$

(23)

$$Fe+{Cl}_2\to Fe{Cl}_3$$

(24)

$$Cr{Cl}_4+O_2\to {Cr}_2{O}_3+{Cl}_2$$

(25)

$$Fe{Cl}_3+O_2\to {Fe}_2{O}_3+{Cl}_2$$

(26)

Like the presented studies in the uniform corrosion section, the physical model was simplified to facilitate the programming language.

$$\mathrm{E}\mathrm{E}+\mathrm{O}\to \mathrm{Y}\mathrm{Y}$$

(27)

$$\mathrm{D}\mathrm{D}+\mathrm{O}\to \mathrm{Y}$$

(28)

$$\mathrm{A}\mathrm{A}+\mathrm{O}\to \mathrm{A}\mathrm{O}$$

(29)

$$\mathrm{E}\mathrm{E}+\mathrm{c}\to \mathrm{D}$$

(30)

$$\mathrm{D}\mathrm{D}+\mathrm{c}\to \mathrm{F}\mathrm{F}$$

(31)

$$\mathrm{D}+\mathrm{O}\to \mathrm{Y}\mathrm{Y}+\mathrm{c}$$

(32)

$$\mathrm{F}\mathrm{F}+\mathrm{O}\to \mathrm{Y}+\mathrm{c}$$

(33)

where: AA = Ni, DD = Fe, EE = Cr, O = O₂, c = Cl₂, Y = Fe₂O₃, YY = Cr₂O₃, AO = NiO, D = CrCl₄, and FF = FeCl₃. All elements except for O, c, and D were considered fixed in the lattice. The positions of O and c were randomly predetermined with an assigned probability, and the sites AA, DD, and EE represent the alloy elements.

To consider the simulation of intergranular corrosion, the authors evaluated the effect of grain size. To obtain the initial structure, they simulated the grain growth process at different time steps Figure 10.

Therefore, their simulation of intergranular corrosion consisted of obtaining the initial microstructure model, which was combined with the AC model. The result of the model is shown in Figure 11, which displays different structures of the model at various iterations. The development of intergranular corrosion in the studied steel by the researchers can be observed.

3. Modeling approach and methodology for simulating corrosion phenomena

The methodology for simulating corrosion phenomena involves several key steps and considerations.

Figure 12. Methodology for implementing a cellular cutomata model.

Figure 12. Methodology for implementing a cellular cutomata model.

Table 1. Summary of the results published.

Table 1. Summary of the results published.

CA type	Neighborhood	Model type	Boundary	Lattice size	Rules	Cycles	Corrosion type	Environment	Material	Temperature (°C)	Exposure time (h)	Validation type	Ref.
LGAa	n-vector	Probabilistic	Periodic	-	-	-	-	-	-	-	-	Boltzmann hypothesis	[66]
2D	n-vector	Probabilistic	Periodic	200x160	3	48.000	Kinetic of internal oxide precipitation	Oxygen	Metal	-	-	Theory of phase equilibrium	[67]
Theoretical	Moore	Probabilistic	Periodic	> 1000x1000	8	-	Uniform	Electrolyte	Metal	-	-	Previous work data	[28]
2D	Von Neumann	Probabilistic	Periodic	2000x1000	2	10.000 to 90.000	Uniform	Electrolyte	Metal	-	-	-	[35]
2D	Von Neumann	Probabilistic	Periodic	1000x1000	3	200.000	Uniform	Solvent	Metal	-	-	Parabolic law	[36]
2D	Von Neumann	Deterministic	Periodic	600x20000	2	150	Uniform	Electrolyte	Metal	-	-	Mott and Cabrera Parabolic’s law	[37]
2D	Von Neumann	Probabilistic	Periodic	1000x1000	2	25.000	Uniform	Liquid lead alloy	Metal	550	3.000	Wagner theory	[38]
3D	-	-	-	100x100	-	-	Intergranular	Sulfuric acid	Metal	1100	0-400	Electrochemical potentiodynamic reactivation	[56]
2D	Moore	Probabilistic	-	500x500	2	200.000	Uniform	LBE	Metal	535	3000	Wargner theory	[39]
LGA-2D	Von Neumann	Probabilistic	-	2000xLy	3	-	Pasivation	Solution	Metal	-	-	Passivation theory	[68]
2D	Moore	Deterministic	-	200x200	2	3	Intergranular	Solution	Metal	1100	2	-	[57]
2D	Von Neumann	Probabilistic	Periodic	-	2	7.200.000	Localised	Solution	Metal	360	-	Experimental	[45]
2D	Von Neumann	Probabilistic	-	1000x1000		399.577	Localised	Solution	Metal	-	-	Pistorius experimental results	[46]
2D-3D	Moore	Probabilistic	Periodic	640x320 – 240x280x240	3	-	Intergranular	Solution	Metal	-	144	Eperimental	[58]
LGA-2D	Von Neumann	Probabilistic	-	2000xLy	2	-	Pasivation	Solution	Metal	-	-	Passivation theory	[69]
2D	Moore	Probabilistic	-	500x500	2	5.000	Uniform	Water	Metal	600	1000	Experimental	[40]
2D	Von Neumann	Probabilistic	Periodic	900x300	2	70.000	Uniform, localised	Solution	Metal	300-360	-	Experimental	[20]
2D	Von Neumann and Moore	Probabilistic	Periodic	1000x1000	14	7.679	Localised, passivation	Solution	Metal	-	-	Theoretical corrosion and passivity phenomena	[70]
2D	Von Neumann and Moore	Probabilistic	Periodic	1000x1000	11	4.000	Crevice, passivation	Solution	Metal	-	-	Experimental	[71]
2D	Moore	Probabilistic	-	500x500	2	200.000	Uniform	LBE	Metal	-	-	Chi-square of goodness-of-fit	[41]
2D	Von Neumann and Moore	Probabilistic	-	512x512	3	2.000	Oxidation and nit	-	Metal	1100	100	Experimental data	[72]
3D	Moore	Probabilistic	Periodic	151x200x200	3	200	Pitting	Solution	Metal	-	0.5	Experimental data	[73]
2D	Von Neumann and Moore	Probabilistic	-	512x512	3	20.000	Oxidation and nitridation	Solution	Metal	1100	100	Experimental data	[74]
3D	Moore	Probabilistic	Periodic	-	4	124	Pitting	Solution	Metal	-	480	Experimantal data	[75]
2D	Moore and Von Neumann 2nd order	Probabilistic	-	1000x1000	4	1.000	Pitting	Solution	Metal	-	-	Experimental data	[76]
2D	Von Neumann	Probabilistic	-	1024x1024	2	-	Pitting	Solution	Metal	-	-	Experimental data	[47]
2D	Moore	Deterministic	Reflect	-	2	-	Pitting	Solution	Metal	-	-	Experimental data	[77]
2D	Von Neumann	Probabilistic	Periodic	1024x1024	5	-	Pitting	Solution	Metal	-	-	Experimental data	[48]
2D	Von Neumann 2nd order	Probabilistic	-	-	3	-	Pitting	Solution	Metal	Room	-	Experimental data	[49]
2D	Von Neumann	Probabilistic	Periodic	2000x2000	3	6.000	Pitting	Water	Metal	-	1.600	Experimental data	[50]
2D	Von Neumann and Moore	Probabilistic	-	500x500	3	3.000	Intergranular	Air	Metal	1100	100	Experimental data	[59]
3D	Moore	Probabilistic	-	512x512x512	4	> 5.000	Occluded, localized	Solution	Metal	-	-	Experimental data	[53]
3D	-	Probabilistic	Periodic	512x512x4096	-	4.000	Intragranular	Solution	Metal	-	7.000	Experimental data	[61]
2D	Von Neumann	Probabilistic	-	-	3	25.000	Electrochemical oxidation	Solution	Metal	600	30	Experimental data	[78]
2D	Von Neumann and Moore	Probabilistic	-	512x512	3	-	Intergranular oxidation	Air	Metal	1100	100	Experimental data	[60]
2D	Moore and Von Neumann extend	Probabilistico	Periodic	1000x1000	-	2.000	Uniform	Solution	Metal	-	-	Theoretical and experimental	[33]
3D	Moore	Probabilistic	-	256x256x256	7	45.000	Pitting	Solution	Metal	-	-	Experimental data	[31]
3D	Moore	Probabilistic	Periodic	512x512x512	7	7.000	Generalized	Solution	Metal	-	-	Experimental data	[79]
CA-FE-2D	Moore	Probabilistic	-	2000x1000	4	-	Localized	Solution	Metal	-	-	Experimental data	[80]
3D	Von Neumann	Probabilistic	Constant and periodic	100x100x100	4	400	Atmospheric corrosion	Atmosphere	Metal	-	-	Theoretical and experimental data	[81]
3D	Von Neumann	Deterministic	Periodic	100x100x100	5	1.000	Uniform	Solution	Metal	20	-	-	[42]
3D	Von Neumann	Probabilistic	-	7500x7500x1500	-	-	Pitting	Salt-Spray	Metal	35	1.440	Experimental data	[52]
2D	Margolus	Probabilistic	Rigid	400x400	4	25.000	Uniform	Solution	Metal	600	504	Experimental data	[29]
LGA-3D	Von Neumann	Probabilistic	Periodic	-	-	-	Passivation	Solution	Metal	-	-	Passivation theory	[82]
3D	12-neighbors	Probabilistic	Periodic	1280x1280x1280	-	-	Intergranular	Solution	Metal	-	2.000	Experimental data	[62]
2D-bi plane	Von Neumann	Probabilistic	-	500x500	5	100	Pitting	Solution	Metal	-	-	Experimental data	[83]
3D	-	-	-	2048x2048x256	3	350	Intergranular	Solution	Metal	-	-	Experimental data	[63]
2D	Margolus	Probabilistic	Periodic	400x400	7	70.000	Uniform, intergranular	Solution	Metal	600	504	Experimental data	[44]
3D	Margolus	Probabilistic	Periodic	1280x1280x1280	-	21.555	Intergranular	Solution	Metal	111	17.783	Experimental data	[64]
2D-3D	Margolus	Probabilistic	Periodic	40x400 - 100x100x100	10	50.000	Intergranular, pitting	Solution	Metal	700	168	Experimental data	[65]
3D	Von Neumann	Probabilistic	Periodic	1000x1000x1000	5	-	Uniform, pitting	Solution	Metal		168	Experimental data	[43]
2D	Moore	Probabilistic	-	1024x1024x128	4	2.000.000	Aqueous	Solution	Metal	50	853	Experimental data	[84]
2D	Von Neumann	Probabilistic	-	250x250	2	2.000	Cracking	Solution	Metal	27	-	Experimental data	[55]
3D	Von Neumann	Probabilistic	-	2000x2000x1000	2	-	Cracking	Concrete	Metal	23	672	Experimental data	[54]
3D	Moore	Probabilistic	Periodic	104x104x104	5	-	Atmospheric corrosion	Atmosphere	Metal	-	-	Experimental data	[30]

4. Future Perspectives and Emerging Trends.

5. Conclusions

• Most studies focus on uniform corrosion, localized corrosion, and intergranular corrosion. These three mechanisms account for almost 80% of all studies to date, leaving other types of corrosion, such as stress cracking corrosion, with only around 4% of the found studies. This indicates that there is a gap to be explored using cellular automaton for other existing corrosion mechanisms.
• On the other hand, it is observed that the CA model in all reviewed studies has a similar structure. It starts with a known phenomenon, either theoretical or experimental, which is sought to be simulated using CA. Then, the physicochemical or electrochemical model that governs the process is defined, and it is translated into a simplified language that facilitates programming. Each study generates its own reaction and transformation rules, dependent on the initially proposed physicochemical or electrochemical model so that these rules can simulate the desired process.
• There is variability in the mesh size used, the boundary conditions, the type of neighborhood utilized, or the number of transformation rules. Each study considers these aspects in a personalized manner, seeking the suitability of the result depending on the complexity of the corrosion process being studied. Therefore, there is still no single rule that encompasses all processes in a single comprehensive CA model.
• Most studies conclude that the CA model has tremendous potential for simulating the corrosion process of different alloys under different conditions. By using simple rules, it can generate complex patterns, and the obtained results closely match the experimental behavior. Furthermore, the model's ability to represent multiple types of physical phenomena makes it a powerful tool that can help researchers see the studied phenomena from a different perspective.

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