Optimization of Process Parameters for electrodeposited Watts Nickel Coating Using a Genetic Algorithm Approach

Electrodeposition of the coating

The electrolyte is prepared by dissolving 300 g·L^–1 of nickel sulfate heptahydrate (NiSO₄·7H₂O), 35 g·L^–1 of nickel chloride hexahydrate (NiCl₂·6H₂O), and 10–25 g·L^–1 of boric acid (H₃BO₃) in deionized water. The coatings were electrodeposited onto low carbon steel plates with the size of 50 × 15 ×1 mm. Prior to electroplating, the surface of the substrate was polished using metallographic paper. The polished substrates and the anode nickel plates are then immersed in a 40% hydrochloric acid solution and cleansed for 15 minutes using an ultrasonic cleaner (KH-250DE) to remove surface impurities. After ultrasonic cleaning, the substrates are rinsed with deionized water. To prevent deposition in non-target areas, all excess parts of the plates, except for the areas to be coated and those connected to the electrodes, are covered with insulating tape.

For the electroplating process, a nickel anode with dimensions of 50 × 20 × 2 mm and a cathode measuring 50 × 15 × 1 mm are used. The distance of two electrodes are approximately 30 mm in the beaker, positioned directly opposite each other. The solution chemistry and deposition parameters are listed in Table 1. To evaluate the microhardness of the cross-section of the coatings, the deposition time is typically set to 90 minutes. The electrolyte pH is adjusted with either 25% ammonia or 0.5 M sulfuric acid, with pH levels monitored using a pH meter (pH-220). A hot plate stirrer (DF-101S) controls the bath temperature and is equipped with a magnetic stir bar to maintain a constant stirring speed of 500 RPM. The bath temperature is accurately measured using an electronic thermometer with an accuracy of ±1°C. The current density is regulated by a DC power supply device (ITECH, type IT6133B). The weight of the reagent is measured using an electronic balance (model: LICHEN) with an accuracy of 0.1 mg.

Table 1.

Plating solution composition

In this work, an orthogonal matrix design was employed to account for four influencing variables, resulting in 16 experimental groups. Each group varied in the input variables: current density ranged from 1 to 6 A·dm^–2, pH values ranged from 3.5 to 5, boric acid concentrations ranged from 10 to 25 g·L^–1, and bath temperature ranged from 40 to 70°C. The optimal process conditions were determined through a comparative analysis of the test data, aiming to minimize the number of experiments. The detailed experimental group is present in Table 2.

Table 2.

Experimental design using orthogonal array

Characterization

The samples were embedded in epoxy resin in small molds and then cured to create solid blocks. The cross-section of the coating was sequential polished using metallurgical sandpaper (5–20 μm grit), followed by 1 μm diamond suspension, and finally 0.5 μm alumina solution. The surface morphology of the coatings was analyzed using a scanning electron microscopy (SEM; TESCAN VEGA LMS). The thickness of the crosssectional coating was measured with a digital optical microscope (OM; VHX-900), while the phase composition and grain orientation of the deposits were identified using X-ray diffraction (XRD; D/max2500 PC, Rigaku Corp, Japan). The testing parameters for XRD were set to: Cu target with Kα radiation, X-ray wavelength of 0.15406 nm, scan range of 30–90°, scan speed of 5° min^–1, and a step interval of 0.05°.

Microhardness of the coating

The microhardness of the coating was measured using the SHIMADZU HMV-2000 Vickers Microhardness Tester. Each measurement was conducted for 15 seconds under a load of 0.1 kg. The hardness value for each sample was obtained by averaging the results from three indentations. Additionally, the morphology of the indentation was examined using an optical microscope.

Crystallographic texture

The relationship between the electroplating process parameters and the crystallographic texture of the nickel coating is illustrated in Fig. 2. The standard JCPDS cards for Ni (PDF#04-0850) and Fe (PDF#06-0696) were analyzed. Two distinct peaks at 65.0° and 82.3° correspond to the Fe (200) and Fe (221) planes, respectively, indicates that the substrate used for depositing the Watts Ni coating is low-carbon steel.. Additionally, as the thickness of the deposit increases, the intensity of the substrate’s diffraction peaks decreases. The nickel crystals were found to exhibit a face-centered cubic (FCC) polycrystalline structure. There are three prominent diffraction peaks corresponding to the (111), (200), and (220) planes of nickel. The 2θ diffraction angles for these peaks were observed at 44.4°, 51.8°, and 76.4°, respectively. The relative texture coefficient (RTC) for each crystal plane of the nickel deposition can be calculated using the following formula (1):

Fig. 2.

XRD patterns of the coatings.

where, I_(hkl) and I_0(hkl) are the intensity of diffraction peak from the coating and the standard sample from JCPDS data, respectively. According to Eq. (1) and Fig. 2, the calculated RTC data are present in Table 3.

Table 3.

Relative texture coefficients of 16 groups of samples under different plating conditions

Samples #4, #7, #10, and #14 exhibit the highest concentration of boric acid. Notably, samples #4 and #14 show a pronounced Ni (220) orientation, while samples #7 and #10 predominantly exhibit the (200) orientation. This difference may be attributed to the increased molecular mobility in solution due to high bath temperature, which enhances the effect of boric acid and favors the (220) crystal orientation. Wu et al. [5] observed that, under constant plating times, increasing boric acid concentration shifts the preferred orientation of the coatings from (200) plane to (220) plane. Specifically, when the plating time is fixed at one hour, Ni (220) orientation becomes more dominant when the H₃BO₃ concentration exceeds 15 g·L^–1. As the concentration of H₃BO₃ continues to increase, the samples show a more pronounced Ni (220) orientation, consistent with the findings of this study.

Interestingly, sample #11, despite having a low boric acid concentration, predominantly exhibits a Ni (220) orientation. This observation deviates from the typical trend, where higher boric acid concentrations are usually associated with a stronger Ni (220) orientation. However, it is observed that the plating temperature is relatively high for this sample, and its Ni (220) orientation is weaker than that of samples #4 and #14. This suggests that the high Ni (220) orientation is influenced by both temperature and boric acid concentration. Similarly to sample #11, samples #2, #3, and #9 also exhibit this trend. Sample #3, which has both lower temperature and boric acid concentration than sample #11, also shows a predominance of Ni (220) orientation, though to a lesser extent than sample #11. Samples #2 and #9 follow the same pattern, although the decrease in orientation strength for sample #9 is less pronounced compared to sample #2, resulting in a slightly higher Ni (220) orientation in sample #9 than that in sample #2.

Samples #1 and #6 demonstrate the strongest orientation of Ni (111) plane. Both samples have a low concentration of boric acid, about 10 g·L^–1. Boric acid with low concentration not forms stable complexes with nickel ions, leading to a reduced growth rate of nickel crystals [28,29]. This facilitates easier nucleation and growth of crystals on the (111) plane, resulting in a high Ni (111) orientation.

Samples #7, #8, #10, #12, #13, #15, and #16 exhibit a prominent Ni (200) plane orientation, along with relatively smooth surface morphologies. The Ni (200) plane has a lower surface energy, which facilitates the formation of smaller grains during crystal growth, contributing to a smoother surface. These samples also tend to have higher pH values. Hu et al. [30] found that high pH values promote Ni (200) orientation due to the formation of nickel hydroxide precipitates by OH⁻ ions, which influences the deposition process and enhances the growth of the Ni (200) plane.

Moreover, current density is a crucial parameter that significantly influences the crystallographic orientation of nickel coatings. At low current densities, the nucleation rate is slow, allowing for more uniform growth that typically favors the (220) orientation, as observed in samples #2, #3, #4, and #5. In contrast, at high current densities, the rapid deposition can promote the formation of the (200) orientation. This is attributed to the increased availability of nickel ions and the kinetic factors that affect crystal growth, as demonstrated in samples #10, #12, #13, #15, and #16, which exhibit a pronounced Ni (200) plane orientation. This observation aligns with the refs. [31,32], indicating that at lower current densities, the crystallographic orientation of nickel coatings tends to favor (220), while an increase in current density leads to a transition towards (220) and (111) orientations.

In summary, the crystallographic texture of nickel coatings is significantly influenced by the interplay of boric acid concentration, temperature, pH, and current density. The optimization of these parameters can lead to desired orientations that enhance the mechanical properties of the coatings.

In this study, the Scherrer formula (Eq. 2) was employed to estimate the grain size of the coating. The grain size for the coatings is present in Table 4.

Table 4.

Grain size of nickel coatings

where D is the grain size, typically measured in nanometers (nm). K is the shape factor, which is typically set to 0.89 for spherical particles.  is the wavelength of the incident X-ray, usually measured in angstroms (Å).  is the full width at half maximum (FWHM) of the diffraction peak, measured in radians. θ is the diffraction angle, which is the angle between the X-ray and the crystal plane, measured in degrees (°). Table 4 presents the grain size distribution of the as-deposited coatings. The grain sizes are found to be relatively uniform within a single order of magnitude, ranging from approximately 13.21 nm to 24.51 nm. This indicates a consistent grain structure across the samples, which is crucial for the uniformity of material properties such as mechanical strength and corrosion resistance.

At a current density of 1 A·dm^–2, the grain size tends to be small. As the current density increases, the grain size increases. This is due to the slow nucleation rate at 1 A·dm², which provides more time for grain growth. At a high current density of 6 A·dm^–2, excessive grain growth occurs, resulting in larger grain sizes. For example, samples #1, #2, and #3, electroplated at 1 A·dm^–2, have fine grain sizes, while samples #13, #14, #15, and #16, electroplated at 6 A·dm^–2, show relatively large grains. This phenomenon can be attributed to the slow nucleation rate at low current densities, allowing more time for grain growth. In contrast, high current densities lead to excessive grain growth and large grain sizes. Wang et al. [33] observed that when the current density is below 7 A·dm^–2, the (111) and (200) planes of the coating exhibit strong diffraction intensities, which correlates with the findings of this study where some samples show enhanced orientation of the (111) and (200) planes.

At a pH of around 3.5, the grain size tends to be small, while at a pH of 6.0, the grain size increases. This trend is due to the low concentration of OH^– ions at pH 3.5, which hinders the formation of nickel hydroxide precipitates and limits grain growth. In contrast, high pH value increases the concentration of OH^– ions, promoting the formation of nickel hydroxide precipitates and facilitating grain growth [16]. For example, samples #1, #5, and #9, with a pH of 3.5, exhibit fine grains, while samples #4, #8, #12, and #16, with a pH of 5.0, display large grain.

Regarding bath temperature, the grain size of the nickel coating tends to be small at 40°C and generally increases with rising temperature. Higher temperatures accelerate the migration rate of nickel ions and the rate of reduction reactions, both of which promote grain growth. For instance, samples electroplated at 40°C, such as sample #1, exhibit fine grains, while those electroplated at 70°C, such as samples #4 and #14, display larger grains. XRD analysis further reveals that process parameters—including current density, pH, bath temperature, and solution chemistry, particularly boric acid concentration—significantly affect the crystal texture of the nickel coating. By optimizing these parameters, it is possible to control the orientation and grain size of the nickel coating, thereby influencing microhardness of the coating.

Regarding boric acid concentration, when the concentration is low, the grain size tends to be small, and as the boric acid concentration increases, the grain size tends to grow large. For example, samples #1, #6, and #11, with a boric acid concentration of 10 g·L^–1, show a trend of fine grain sizes, while samples #4, #7, #10, and #14, with a concentration of 25 g·L^–1, exhibit large grain sizes. This can be explained by the fact that at high boric acid concentrations, the boric acid adsorbs onto the cathode and inhibits nickel nucleation. However, after long deposition times (over 15 minutes), differences in the growth rates of crystal planes (220 > 200 > 111) lead to the formation of larger grain-sized deposits [5].

Morphology

Fig. 3 illustrates the relationship between various process parameters and the resulting surface morphology and microstructure of the nickel coatings. The samples exhibit distinct deposition characteristics, reflecting the diversity of electroplating parameters and relative texture coefficients. Samples #1, #7, #10, and #13 exhibit relatively smooth surfaces, with sample #10 (Fig. 3j) standing out due to its exceptional smoothness. This superior surface quality can be attributed to the optimization of the electroplating process parameters. The moderate current density facilitates a uniform deposition rate, promoting even crystal growth and reducing the formation of defects that can lead to increased surface roughness. Additionally, the pH level of 4.0 can maintain the stability of the electrolyte, minimizing the likelihood of flocculent deposits during the deposition process. The bath temperature of 40°C further enhances ion mobility and diffusion rates, contributing to a more homogeneous coating. The optimized process parameters enable a more uniform deposition of nickel ions on the electrode surface, resulting in smaller particles and a dense coating. Oliveira et al. [34] indicate that coatings deposited under favorable temperature and pH conditions typically achieve good smoothness, which aligns with our findings. The exceptional smoothness of sample #10 is indeed a result of its optimized combination of process parameters, ultimately leading to a high quality of nickel coating. The smooth surface of sample #1 (Fig. 3a) is associated with a lower deposition current density. Lins et al. [35] found that lower deposition current densities favor lower porosity and more compact nickel coatings, resulting in smoother surfaces. In contrast, the smoothness of samples #7 (Fig. 3g) and #13 (Fig. 3m) is slightly reduced, likely due to increased temperature, which raises deposition rates and consequently increases surface roughness. The higher temperatures improve the current efficiency by enhancing ion migration and deposition, but this simultaneously raises surface roughness [34].

Fig. 3.

SEM images of top-surface of the coatings for 16 sets of samples, (a) #1, (b) #2, (c) #3, (d) #4, (e) #5, (f) #6, (g) #7, (h) #8, (i) #9, (j) #10, (k) #11, (l) #12, (m) #13, (n) #14, (o) #15 and (p) #16.

Next, samples #2, #8, #9, and #11 displayed distinct flocculent deposition characteristics, which can be attributed to the interplay between their crystallographic texture and growth dynamics. Specifically, samples #2 (Fig. 3b) and #9 (Fig. 3i) are particularly noteworthy due to their predominant (220) plane orientation, which influences the growth behavior of the nickel crystals. The presence of a strong (220) orientation can lead to uneven growth rates across different crystal planes, resulting in the observed flocculent morphology. This phenomenon is further supported by the texture coefficient ratios, where the (220) plane is favored, while the (111) plane remains secondary. The minor differences in their texture coefficients suggest that even slight variations in the growth dynamics can significantly impact the surface morphology. This observation aligns with the findings of Nasirpouri et al. [36], which indicates that if nickel crystals exhibit a pronounced preferential growth on certain mirror planes, the growth rates on other crystal planes will be suppressed, leading to uneven growth rates and flocculent deposition. The effects on samples #8 (Fig. 3h) and #11 (Fig. 3k) are less pronounced, likely due to their higher pH levels. On the other hand, sample #15 (Fig. 3o) exhibits a distinct morphology that is similar to sample #11 (Fig. 3k), characterized by a more uniform and compact structure, with no signs of flocculent deposition. This can be attributed to the high pH environment and low bath temperature, which promote a more stable deposition process, thereby reducing the likelihood of flocculent characteristics. Oliveira et al. [34] also observed that nickel deposition is more favorable in high pH environments. They highlighted that, under such conditions, the surface morphology of the nickel crystals is improved.

Samples #3, #4, #5, #6, and #14 have a distinct and uniform particle distribution, reflecting effective deposition control and ensuring the stability of the overall deposition outcome. This uniform distribution may be attributed to higher temperatures, with samples #5 (Fig. 3e) and #14 (Fig. 3n) also exhibiting good uniformity, indicating stable process parameter control during deposition. The surface of samples #12 and #16 was composed of a distinct micro-conical particle structure, potentially linked to low boric acid concentrations. At low H₃BO₃ concentrations, prolonged electroplating time promotes the development of a preferred (200) crystal plane orientation, resulting in an uneven micro-conical grain structure on the surface. Wu et al. [5] support this observation, noting that low H₃BO₃ concentrations have minimal effect on the deposition process, which leads to relatively higher deposition rates. Consequently, the surface morphology typically features a pyramidal crystal structure with a dominant (200) orientation, and in some areas, the aggregate size can reach several micrometers.

The thickness of the coating is primarily determined by the current density and the duration of the electroplating process. Variations in current efficiency between different electroplating systems can also lead to differences in coating thickness. In practical applications, the uniformity of coating thickness is influenced by several factors, including electrolyte distribution, the geometry of the parts, the electroplating technique used, and the concentration polarization level. In this study, the plating duration was set to 90 minutes. It was observed that the coating thickness varies with process parameters such as current density, boric acid concentration, bath temperature, and pH.

Fig. 4 presents the optical images of the cross section of the coatings, and Table 5 summarizes the thickness data for these samples. Sample #10 exhibited the thickest value, which can be attributed to its higher (200) orientation. The coating with a (200) orientation often shows lower residual stress and microhardness, which may facilitate the formation of thicker coatings due to the reduced resistance to grain growth. This can be further influenced by the process parameters, particularly the current density and boric acid concentration. For sample #10, with the highest boric acid concentration and a current density of 4 A·dm^–2, the growth of the (200) plane was promoted. Higher current densities typically favor the formation of (200) oriented crystals, while the higher boric acid concentration helped stabilize the plating process, leading to more uniform growth and thicker coatings. However, it is important to note that while boric acid contributes to the stability of the electrodeposition process, concentrations exceeding 15 g·L^–1 can inhibit crystal growth in specific orientations, leading to a less uniform grain structure. This effect is particularly pronounced at high concentrations, where the adsorption of boric acid on the cathode surface can impede the nucleation and growth of nickel crystals, ultimately affecting the overall microstructure and mechanical properties of the coating.

Fig. 4.

OM images of the cross-section of the coating. Samples (a) #1, (b) #2, (c) #3, (d) #4, (e) #5, (f) #6, (g) #7, (h) #8, (i) #9, (j) #10, (k) #11, (l) #12, (m) #13, (n) #14, (o) #15 and (p) #16.

Table 5.

Thickness (μm) of the nickel coatings

Conversely, the thickness of sample #2 had the thinnest value, which may be related to its higher (111) orientation. Hashemzadeh et al. [37] observed that nickel coatings with a (111) orientation generally exhibit larger grain sizes and lower deposition efficiency, potentially leading to thinner coatings. Additionally, the lower current density and boric acid concentration for this sample restricted grain growth and deposition efficiency, resulting in the formation of thin coating. Zhang et al. [38] reported that low current density during nickel-plating results in slow deposition rates, necessitating long deposition times to achieve the desired thickness.

The thicknesses of the coatings for the other samples were in the range from 20.4 μm to 79.6 μm. This variation indicates that current density and boric acid concentration have a substantial impact on coating thickness. While the changes in pH value and bath temperature also affect coating thickness, their influence is comparatively less significant than that of current density and boric acid concentration.

The coating thickness of the other samples ranged from 20.4 μm to 79.6 μm. This variation indicates that changes in pH value and bath temperature also have an impact on the coating thickness. The pH value influences the deposition rate by affecting the concentration of complexes in the electrolyte. A high pH can lead to an increased concentration of these complexes, which may hinder the availability of nickel ions for deposition, potentially resulting in reduced coating thickness. On the other hand, the bath temperature affects the kinetic energy of the ions in solution, thereby influencing their diffusion rates and the overall deposition process. Generally, higher temperatures enhance ion mobility, which can lead to thicker coatings. However, excessively high temperatures may promote rapid deposition, resulting in uneven thickness, and can also lead to the evaporation of the solution. This evaporation can increase the concentration of ions in the remaining solution, potentially causing further inconsistencies in the deposition process and affecting the overall quality of the coatings [39]. These variations in coating thickness are closely linked to the structural integrity of the coatings. For example, the interface in Fig. 4b, m, n shows delamination, which may be attributed to insufficient surface preparation or high internal stress within the coating. However, in Fig. 4i, despite the sample being bent, the coating remains intact without delamination, indicating strong adhesion. In contrast, Fig. 4a displays through-thickness micro-cracks that penetrate the coating, which could compromise the coating’s structural integrity. Additionally, Fig. 4j, l, o, p show some interface defects, which may negatively impact the coating’s adhesion strength. These observations suggest that while thicker coatings are generally obtained under higher current densities and boric acid concentrations, attention must also be paid to the internal stresses and interface quality to ensure optimal performance of the coatings.

Microhardness

Table 6 illustrates the microhardness of nickel coatings. The microhardness values range widely, from a minimum of 170 ± 3.5 HV_0.1 to a maximum of 259 ± 38.2 HV_0.1, highlighting significant influences of process parameters on hardness. Notably, coatings with smaller grain sizes in the (220) orientation exhibit higher hardness values compared to those with larger grains. As the process parameters are adjusted, an increase in grain size of the (220)-oriented coating generally leads to a decrease in microhardness. This relationship aligns with the Hall-Petch effect, which states that smaller grains enhance microhardness due to the increased number of grain boundaries that impede dislocation movement, thereby strengthening the material. Similarly, the (111)-oriented coating also demonstrates a positive correlation between smaller grain sizes and higher hardness, although its impact is less pronounced than that of the (220)-oriented coating. In contrast, the (200)-oriented coating, which typically has larger grain sizes, results in lower hardness values. This indicates that while smaller grains in the (220)- and (111)-oriented coatings contribute to increased hardness, the larger grains associated with the (200) orientation diminish the overall hardness of the coating. Therefore, the effects of grain size variations on hardness differ across the orientations, with the (220) orientation having the most substantial influence. This finding is consistent with the research conducted by Wu et al. [5]. This indicates that grain size is a critical factor influencing the hardness of nickel coatings. These findings align with the Hall-Petch relationship, indicating that reducing grain size enhances the strength of polycrystalline metals, whether at submicron or micron scales. The relationship between microhardness (H_V) and grain size (D) is expressed by Eq. (3) [40].

Table 6.

Microhardness (HV_0.1) of the group coatings

where H₀ and k_H are constants. However, when the grain size falls into the nanometer range, the inverse Hall-Petch relationship may occur [41,42].

The coatings oriented along the (200) plane typically exhibit low residual stress and microhardness due to their relatively loose crystal arrangement and larger grain size, as noted by Wu et al. [5]. In contrast, coatings with a (220) orientation tend to show higher residual stress and microhardness, attributed to their denser structure and more compact crystal lattice, which aligns with findings by Aatif et al. [44]. This difference in properties can be linked to the Hall-Petch relationship, where smaller grain sizes hinder dislocation motion, thereby increasing hardness [40]. Experimental results from this study support these findings, with sample #14 exhibiting a dominant (220) orientation and a relatively high hardness value, influenced by higher boric acid concentration and deposition parameters. Additionally, the microhardness of the coatings is significantly affected by grain size. According to the Hall-Petch relationship, the strength of polycrystalline metals increases as grain size decreases, as observed in this study. Most experimental data align with this phenomenon, showing that samples with smaller grain sizes tend to exhibit higher microhardness. This highlights the critical role of grain size refinement in enhancing the mechanical properties of electrodeposited coatings.

The (220) crystal plane has the most substantial impact on coating hardness. For example, sample #14, which has the highest RTC value for the (220) plane, exhibits a hardness of 239 HV_0.1. This suggests that the coating with (220) orientation contributes to increasing the hardness of the coating due to its dense plane structure and compact crystal arrangement. Although sample #5 shows notable microhardness, it does not have a particularly prominent (220) orientation but rather tends towards a combination of (220) and (111) planes. This behavior may be attributed to the interplay of electroplating parameters, particularly boric acid concentration and current density, which influence the growth rates of different crystal planes. Higher boric acid concentrations tend to enhance the formation of (220) orientation [5]. However, moderate levels, like those for sample #5, allow competitive growth between the (220) and (111) planes. Additionally, the (111) plane, known for its relatively low surface energy, facilitates easier nucleation and growth under specific conditions, such as low current density and boric acid concentration, as observed in ref. [43]. Consequently, the coexistence of these orientations leads to a combination of characteristics that contribute to the enhanced hardness of sample #5.

The (111) crystal plane also significantly influences coating hardness. Samples #1 and #6, with the highest RTC for the (111) plane, show hardness values of 241 HV_0.1 and 199 HV_0.1, respectively. This indicates that the (111)-oriented coating contributes to coating hardness, albeit to a lesser extent than the (220)-oriented coating. Agnieszk et al. [43] reported that in a citrate bath, nickel coatings with a prominent (111) orientation exhibited high hardness, which aligns with the findings of this study. However, it is important to note that the hardness values of these samples are also influenced by grain size, as the (111)-oriented coating generally tends to have smaller grains compared to the (200)-oriented coating. Smaller grains, in accordance with the Hall-Petch relationship, typically enhance hardness by impeding dislocation movement. Thus, although the (111) plane contributes to hardness, its effect is also moderated by the grain size in the sample.

Fig. 5.

OM images of the typical pyramid indention on the top surface of nickel coatings. Samples (a) #1, (b) #2, (c) #3, (d) #4, (e) #5, (f) #6, (g) #7, (h) #8, (i) #9, (j) #10, (k) #11, (l) #12, (m) #13, (n) #14, (o) #15 and (p) #16.

Conversely, the (200) crystal plane has the least impact on coating hardness. Sample #13, with the highest RTC value of (200) plane, displays the lowest hardness of 187 HV_0.1. This lower hardness may be attributed to the relatively loose structure and large grain size of the (200) plane crystals. The larger grains associated with the (200) orientation reduce the number of grain boundaries, which are crucial for strengthening the material. In this case, despite the prominent (200) plane, the large grain size limit the ability of the coating to resist dislocation movement, leading to reduced hardness. This more comprehensive analysis suggests that both crystal orientation and grain size play key roles in determining the hardness of the coating.

Algorithm modeling and optimization

The experimental results reveal that the microhardness of the nickel-plated layer varies in response to adjustable parameters such as current density, pH value, boric acid concentration, and plating bath temperature. The input variables include current density X (1), pH X (2), boric acid concentration X (3), and bath temperature X (4), with microhardness as the output variable to be optimized.

By incorporating quadratic polynomial features into the linear model using MATLAB, simultaneously incorporating multiple datasets regarding the hardness of nickel coating, the coefficient of determination (R²) of the model increased significantly to 0.973. This indicates that the model can now account for approximately 97.3% of the variance in the microhardness. The high R² value suggests the presence of nonlinear relationships and interactions among the independent variables, which are effectively captured by the polynomial features. The mathematical model can be expressed by the following function [46]:

where f stands for microhardness. β₀ is a constant term. β₁, β₂, β₃, β₄ are factors, β₅, β₆, β₇, and β₈ are the quadratic coefficients of β₉, β₁₀, β₁₁, β₁₂, β₁₃, and β₁₄ are the β coefficients, and the cross terms of the ε is error term. The constraints are:

In the experimental setup, a BP neural network combined with a real-number-encoded GA was utilized. Fig. 6 illustrates the relationship between the BP neural network and the GA. A systematic approach was employed for fitness evaluation and genetic operations, encompassing key steps such as selection, crossover, and mutation. The GA-driven optimization process led to the development of an optimized algorithm. To validate the effectiveness and superiority of the proposed method, the electroplating process parameters obtained were compared with optimized results from published literatures. In the GA framework, a chromosome is represented as a one-dimensional string data structure, with each position corresponding to a gene value. The core components of the GA include chromosome encoding, initial population creation, fitness function design, and genetic operations [37,38]. Fig. 7 provides a flowchart illustrating the GA process.

Fig. 6.

BP neural network and genetic algorithm flow chart.

Fig. 7.

Flowchart of the genetic algorithm.

GA provide a robust method for tackling nonlinear programming challenges. This approach involves encoding problem parameters into chromosomes, initializing a population, and utilizing an iterative process that incorporates selection, crossover, and mutation to facilitate the exchange of genetic information among population members. Through this iterative process, chromosomes are evolved to meet the specified optimization criteria. In the GA framework, chromosomes are analogous to data arrays and are typically represented as one-dimensional string data structures. Each position within this string corresponds to a specific gene value. Fig. 8 illustrates the iterative process of the GA algorithm, demonstrating how the optimal orientation evolves and gradually converges to a stable value.

Fig. 8.

Iteration diagram of the genetic algorithm.

Based on experimental results, the optimal parameters for the electrodeposition of nickel coatings were determined as a current density of 1.3 A·dm^–2, pH of 3.6, boric acid concentration of 20.5 g·L^–1, and plating temperature of 42.3°C. This optimization successfully met the target outcomes. As shown in Fig. 9, validation experiments confirmed that the optimized sample #17 with an average thickness of 34.3 μm achieved a hardness of 267 HV_0.1. The parameters of the optimized sample #17 closely with the predicted values from the algorithm, remaining within an acceptable range. Analysis of the optimized sample #17 revealed a smooth and flat surface, bright silver coloration, and high density. The surface morphology of the optimized coating is notably improved compared to the unoptimized samples. As shown in previous figures, such as Fig. 3, unoptimized coatings often exhibit surface roughness and flocculent deposition characteristics, which may lead to higher porosity and lower density. In contrast, the optimized sample #17 (Fig. 9) presents a smoother, more uniform surface with reduced surface defects and voids. These results indicate that the GA-based parameter optimization not only enhanced the coating’s hardness but also significantly improved its surface morphology, reducing porosity and enhancing uniformity and overall coating quality.

Fig. 9.

(a) SEM image of the surface of the optimized sample #17, (b) OM image of the cross-section of the optimized sample #17, and (c) OM image of the pyramid indentation on the top surface of the optimized sample #17.

The crystallographic texture of the optimized Ni coating is depicted in Fig. 10, The relative texture coefficients and grain sizes calculated from Eq. (5) and (6) are presented in Table 7, respectively. The optimized sample #17 displayed a high RTC value for the (220) crystal plane, indicating that this plane is the most prevalent and well-ordered within the coating. The (111) and (200) crystal plane orientations were moderate and balanced, avoiding issues related to the overdevelopment of a single crystal plane.

Fig. 10.

XRD patterns of the optimized nickel coatings for sample #17.

Table 7.

The relative texture coefficients and grain size of the optimized sample #17

Furthermore, the average grain size of the optimized sample #17 is relatively small within the sample group, indicating that the grains in the coating are finer and more densely packed. This refinement in grain size aligns with the Hall-Petch relationship, which states that materials with smaller grain sizes exhibit higher hardness. Consequently, the optimized samples demonstrated superior hardness, consistent with the expected outcomes of the optimization algorithm.

Weighted analysis was used to evaluate the overall impact of electroplating parameters on hardness and grain size, converting multiple indicators into a single composite indicator. This approach facilitated the identification of optimal process parameters for preparing Watts nickel coatings. The magnitude of the range value Y_i is positively correlated with the degree of influence of each factor on the experimental outcomes. That is, a large Y_i value indicates a great impact of the process parameter on the experimental indicators. A comprehensive evaluation was performed using a weighted scoring method, as outlined in Eq. (6) [47]. The experimental groupings and their corresponding comprehensive scores are detailed in Table 8.

Table 8.

Analysis table of orthogonal experimental results

In the formula, m_ij represents the weighted coefficient, indicating the proportion of each indicator in the weighted score, while n_ij denotes the corresponding factor score value. The score value for each indicator is calculated as follows:

The subscripts i and j refer to the indicator value for the i_th experimental group and the j_th indicator, respectively. The ranges of change for the two experimental indicators, hardness and grain size, are as follows: For hardness, K₁=267.0-170=97, where the hardness of sample # 12 and sample #17 were 170 HV_0.1 and 267.0 HV_0.1, respectively. For grain size, K₂=24.53−13.21=11.32, where 24.53 nm and 13.21 nm represents the grain size of samples #12 and #1 respectively. Assuming that the maximum comprehensive score is 100 points, the full score of coating hardness is 70, and the full score of grain size is 30, the index coefficient is set to m_i1=70 and m_i2=30.

The calculation formula for the comprehensive performance score Y_i is provided in Eq. (9).

Table 8 shows that the optimized sample #17 attained the highest score among the 16 experimental samples, representing the best balance of hardness and grain size. Conversely, sample #12 received the lowest score, highlighting the least effective combination of these properties, with other groups scoring within this range. Additional analysis shows that the optimized sample #17 has the highest score of 91.04, surpassing all other experimental groups. This outcome verifies the effectiveness of the optimization algorithm in refining electroplating parameters, achieving superior coating hardness and finer grain size. These improvements in uniformity and quality underscore the potential of this optimization approach for advancing coating performance.