Study on characterization technology of porosity and fractal dimension of micro-arc oxidation coating

The porosity of the micro-arc oxidation coating of pure titanium was assessed through the utilization of Mercury intrusion porosimetry (MIP). The porosity values were subsequently adjusted by accounting for the proportion of coating volume, resulting in a more precise determination of the coating’s porosity. Additionally, the fractal dimension of the pore structure was determined through the application of a linear regression equation utilizing the Mercury intrusion data. The findings indicate that the observed numerical dispersion from image metohd is substantial, with a range of 34.9% between the minimum and maximum values. This suggests that the precision and validity of the porosity outcomes derived from this approach are inadequate; The MIP is capable of determining both the porosity, average pore size and pore size distribution of the sample, while also mitigating the impact of the matrix through test result correction, thereby yielding precise porosity values. Additionally, the results of the verification experiment demonstrate a positive correlation between the porosity alteration of the MIP and oxidation duration, thereby affirming the reliability of the test outcomes; Through the analysis of pressure, pore size, cumulative Mercury intrude volume, and incremental Mercury intrude volume data obtained from MIP, the fractal dimension of the coating’s pore structure then be determined. Research showed that as the oxidation time increases, the pore fractal dimension of the MAO coating gradually expands within a narrow range, from 2.57 and finally stabilized at 2.77, indicating a gradual increase in pore structure complexity.


Introduction
Micro-arc oxidation (MAO), or plasma electrolytic oxidation (PEO), is a novel surface treatment technique that utilizes arc discharge to generate in situ ceramic coatings on Ti alloy substrates, thereby enhancing surface hardness and wear resistance. Furthermore, this technology offers several benefits, including straightforward operation, facile regulation of the functional color of the film, uncomplicated process flow, and robust bonding strength of the substrate [1]. This novel and proficient technology has garnered significant interest from scholars both domestically and internationally, and exhibits vast potential for practical application. Nonetheless, the rapid oxidation process induces thermal stress, resulting in the formation of numerous micropores and microcracks within the MAO coating, ultimately compromising its mechanical properties [2,3]. Research has demonstrated that reduced porosity engenders a heightened barrier effect, thereby enhancing corrosion resistance [4]. Hence, the advancement of MAO coating porosity characterization technology is advantageous not only in terms of demonstrating the coating's corrosion and wear resistance, but also in facilitating the creation of MAO coatings with exceptional surface properties.
Numerous techniques exist for characterizing the pore structure of coatings, including image analysis (utilizing optical, scanning, and transmission electron microscopes), infiltration pressure methodology, gas adsorption and desorption, atomic force probe contact measurement, x-ray three-dimensional scanning Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
imaging (employing x-ray and neutron rays), and ultrasonic imaging analysis [5][6][7]. Only the image analysis method, infiltration pressure method, and small angle neutron scattering method are suitable for characterizing porosity parameters. Nevertheless, the complexity of coating structures and the diversity of coating types necessitate different applications for each method.
The utilization of Mercury intrusion porosimetry (MIP) has been extensively applied in the analysis of porous materials [8]. Its primary function is to identify the distribution of microscopic pores in various inorganic non-metallic materials, including rock strata [9], cement [10], coal seam [11], electrode materials [12], ceramics [13], concrete [14], adsorption materials [15], refractory materials [16] and some organic materials. Additionally, the Mercury porosimeter can be employed to investigate the impact of microscopic pore structure on material properties. Furthermore, the MIP method enables the determination of pore size distribution and pore fractal dimension in addition to porosity. In this study, the porosity of the titanium-based micro-arc oxidation coating was assessed using both image and Mercury intrusion methods. The results obtained from both methods were compared, and the fractal dimension of the coating pores was calculated based on the data acquired from the Mercury intrusion method.

Sample preparation
The micro-arc oxidation electrolyte is mainly sodium silicate with a mass concentration of 20 g l −1 , and the remaining components are 5 g l −1 potassium hydroxide, 2 g l −1 sodium hexametaphosphate, 2 g l −1 sodium citrate, and 2 g l −1 sodium fluoride. Through the self-made micro-arc oxidation electrolytic cell with ultrasonic, cooling and stirring devices, the electrolyte temperature is maintained at about 25°C and its pH value is about 13. The micro-arc oxidation power supply adopts WHD-60 D unipolar micro-arc oxidation pulse power supply manufactured by Harbin Institute of Technology. The output current of the power supply is 3 A, the working time is 5,10,15,20 min separately, the duty cycle is 30%, and the frequency is 500 Hz.

Image method
The image method involves utilizing the grid function of image processing software to examine and evaluate the scanning electron microscope topography of the sample surface. This process entails recording the quantity of cells that descend upon the pore and designating 1/4 as the minimum unit. Any value greater than 1/4 grid is classified as 1/2 grid, while any value greater than 1/2 grid is categorized as 3/4 grid. Similarly, any value greater than 3/4 grid is deemed as 1 grid. The porosity of the sample is then determined by calculating the ratio of the total pore area to the photomicrograph area [6].

Mercury intrusion method
The MIP experiments were conducted on the sample utilizing the micromeritics AutoPore IV9520 Mercury porosimeter. The experimental parameters were established, including a Mercury contact angle of 130°, a surface tension of 485 dyn cm −1 , and a Mercury density of 13.5335 g cm −3 .

Experimental verification
According to research findings, the porosity of micro-arc oxidation (MAO) coating on pure titanium surfaces decreases as the oxidation time increases, while all other micro-arc oxidation parameters remain constant [17]. The study utilized micro-arc oxidation ceramic coating on pure titanium as the subject of investigation, with sample preparation oxidation times of 5, 10, 15, and 20 min, while keeping other parameters constant. The porosity of the prepared samples was quantified through image analysis and Mercury intrusion porosimetry (MIP).

Fractal dimension
The notion of fractals was initially introduced by the French mathematician Mandelbrot and has gained recognition among scholars and experts across various disciplines. The development of the fractal model for pore structure is predicated on the measurement technique employed for pore structure analysis. Among the various testing methodologies, the MIP approach is commonly utilized due to its broader range of test apertures. Consequently, the thermodynamic relationship model, which is founded on the MIP method, is frequently employed to compute the fractal dimension of pores. The calculation formula is presented below: Where: i is the record point of MIP pressure and amount; Pi is the pressure of the i mercuric injection operation, Pa; ΔVi is the Mercury intake of the i mercuric injection operation, m 3 ; C is constant; rn is the pore radius corresponding to the NTH MIP, m; Vn is the total Mercury intake, m 3 ; D is the fractal dimension of pores. Let: Then: Acquire experimental data for MIP, perform calculations using equations (2) and (3), apply logarithmic functions as appropriate, utilize equation (4) for further computation, and determine the fractal dimension D through analysis of the slope of the linear regression equation [18,19].

Results and discussion
3.1. SEM results of MAO coating Figure 1 depicts the surface and cross-sectional morphology of the MAO coating. The cross-sectional SEM image in figure 1(a) reveals that the coating surface is ablative, with a thickness of approximately 21.4 μm. Additionally, figure 1(b) illustrates that the coating surface is uneven, characterized by a profusion of pores and fissures of varying depths. The phenomenon can be attributed to the discontinuous lattice shape of the melted surface of the metal matrix during the micro-arc oxidation experiment, which is caused by the high-density discharge sparks. This results in the simultaneous eruption of molten oxide and plasma bubbles, leading to the formation of a bulge with a pore structure, commonly referred to as 'volcanic ejection,' in the cooling electrolyte. Additionally, the rapid cooling of the molten oxide in the cooling liquid induces cracks in the coating.

Porosity test results by image method
The 'display grid' function within the image processing software serves as a replacement for transparent grid paper or transparent mm paper, as depicted in figure 2. In accordance with the operational procedure outlined in GBT 3365-2008, the porosity of the sample is determined by calculating the ratio of the pore area to the micrograph area. Figure 2 presents the scanning electron microscopy (SEM) outcomes of four distinct regions of a single sample and their corresponding porosity, respectively 12.9%, 8.4%, 9.5%, 11.2%. The results indicate significant variations in porosity across different microscopic regions. The observed numerical dispersion is substantial, with a range of 34.9% between the minimum and maximum values. This suggests that the precision and validity of the porosity outcomes derived from this approach are inadequate. Moreover, the findings suggest that to obtain a more precise characterization of the sample's porosity using image analysis, it is imperative to consider the statistical average of multiple regions on the sample surface. Upon further examination, it has been determined that the surface structure of the coating primarily consists of holes with varying diameters. The depth of these holes is inconsistent, and the presence of internal connecting holes remains unknown. Consequently, the porosity calculated through statistical analysis of the two-dimensional flat face area ratio underestimates the actual porosity and lacks significant guidance.

MIP test results
The cumulative intrusion curve in the MIP characterizes the volume of Mercury intrusion in the sample at the corresponding pressure during the pressure increase process. This curve represents the amount of Mercury intrusion and is depicted in figure 3(b). The entire process of Mercury injection can be divided into three stages based on the change in the rate of Mercury inlet: rapid low-pressure period, slow medium-pressure period, and stable high-pressure period. During the rapid low-pressure period, there was a notable increase in Mercury intake, with initial entry occurring through apertures greater than 10 μm. This phenomenon can be attributed to the 'pockmark effect', wherein the initial stage of Mercury intrusion experiment results in a false increase in Mercury intrusion volume due to the adhesion of non-wetting phase Mercury to pits on the sample's rough surface. As pressure gradually increases, Mercury fills the pits without actually entering the pore throat system. The accumulation of cavity volume in this area contributes to the overall Mercury intrusion of the pore throat system, resulting in a higher saturation value [20]. During the slow medium-pressure period, the associated pore size falls within the approximate range of (0.2-10) μm, and the cumulative intrusion curve exhibits a gradual upward trend. The pore size distribution chart indicates that the Mercury intrusion during this phase accurately represents the penetration of Mercury into the sample's pores. During the stable high-pressure period, the cumulative intrusion curve exhibits a horizontal trend, signifying that the cumulative Mercury uptake remains constant within this pressure range. This observation suggests the absence of pores that correspond to the pore size distribution curve below 0.2 μm.
In conjunction with the aforementioned analysis and taking into account the impact of the chosen pore size range on porosity [21], it is recommended that the calculation of porosity encompass the pore size range of (0.006-10) μm. Upon undergoing software processing, the obtained test results indicate an average pore size of 1.76 μm and a porosity of 0.15%. It is noteworthy that the porosity outcome is notably lower than that obtained through the image method test, which can be attributed to the influence of the matrix on the sample volume during testing. The porosity P 0 , ascertained through the MIP, represents the proportion of the pore volume of the ceramic coating to the entirety of the sample volume, as depicted in figure 4. The sample volume comprises of a porous coating and a non-porous substrate, and the porosity P of the coating ought to denote the percentage of the coating's pore volume to its volume. Prior to conducting the MIP, it is necessary to utilize the SEM findings to quantitatively differentiate the volume of the coating from that of the substrate, ascertain the coating volume percentage (j) relative to the sample volume, and subsequently calculate the coating porosity (P).
Where P is the corrected porosity of the coating; P 0 is the porosity measured by MIP; Φ The size of the coating as a percentage of the sample's volume; d S is the total thickness of the sample (including coating); d C is the coating thickness. The scanning electron microscope results of the coating section in figure 1(a) reveal that the coating thickness d C , which is double-sided, is 42.8 μm, calculated as 21.4 μm × 2. The thickness of the sample, encompassing both the coating and substrate, d S , was measured using a micrometer and found to be 4.880 mm. The porosity of the modified coating was determined to be 17.0% after computation. This value exceeds that obtained through image analysis, indicating the presence of a complex internal pore structure and the possibility of interconnected pores.
In summary, the utilization of MIP for the purpose of testing the porosity of the coating enables the acquisition of both the average pore size and pore size distribution, as well as the true porosity of the coating through correction. Additionally, this method eliminates the interference of the substrate, thereby optimizing the coating preparation process.   Figure 5 presented the SEM outcomes under diferent oxidation time and their corresponding porosity by image method, respectively 15.4%, 5.0%, 9.0%, 3.7%, was showed in table 1. The findings presented in table 1 indicate a positive correlation between the porosity change measured by MIP and the duration of oxidation. Specifically, as the oxidation time increases, the porosity of the MAO coating decreases, resulting in the disappearance of larger pores and the accumulation of small particles near the surface micropores. This trend continues to intensify with prolonged oxidation time. The observed phenomenon can be attributed to the thickening of the MAO coating, which leads to an increase in the thickness of the layer. This, in turn, results in an elevated coating resistance and a greater challenge in achieving breakdown discharge [22]. It is noteworthy that, unlike the scenario of constant current, the resistance increases and the current decreases with the thickening of the coating under constant voltage conditions. Consequently, the arc power and discharge decrease, leading to the disappearance of large aperture micropores. This finding is supported by the average pore size and pore size distribution obtained through MIP analysis.

Experimental verification
The pore size distribution map in figure 6 reveals that the MAO coating materials with a rough surface exhibit a discernible 'mask effect,' wherein the quantity of Mercury infiltrating the portion exceeding 10 μm in the figure is either augmented or diminished. This phenomenon is evidenced by the emergence of a minor peak Note: The Mercury intrusion experiment takes the results of the pore size range of (0.006-10) μm. 'a' near 10 μm, which is attributed to the high and low pressure alternation during the Mercury intrusion experiment. Following the low-pressure MIP, the sample necessitates depressurization and transfer to the highpressure chamber. Prior to commencing high-pressure analysis, the Mercury pressure within the dilatometer housing the sample shall be returned to atmospheric pressure, resulting in a partial withdrawal of Mercury from within the sample. Upon initiation of high-pressure analysis, the previously withdrawn Mercury shall be reintroduced into the sample pores under pressure. Consequently, a minor plateau denoted as 'A' shall manifest on the cumulative intrusion curve during the initial stages of high pressure, which shall be reflected in the pore size distribution map. Nevertheless, the sequence of occurrences resulting from the conversion of high and low pressure does not impact the overall Mercury intrusion. Following the high and low pressure conversion, the cumulative intrusion curve persisted in its upward trend, with the amount of Mercury intrusion continuing to escalate, and the corresponding main peak 'b' appearing in the pore size distribution. The figure demonstrates that the MAO coating pores exhibit a predominant concentration of pore sizes within the range of (1-5) μm, with a limited number of pores measuring less than 1 μm. The relative content of these smaller pores can be accurately quantified by analyzing the original data obtained from the Mercury intrusion experiment.

Fractal dimension
The pressure, pore size, cumulative Mercury intake, and incremental Mercury intake resulting from the Mercury injection experiment were utilized to derive  Figure 7 demonstrates a clear linear relationship between the fitting lines, with a correlation coefficient (R 2 ) exceeding 0.99, indicating a strong correlation. This suggests that the pore size distribution of the MAO coating exhibits discernible fractal characteristics and aligns with the thermodynamic classification model. Furthermore, as the oxidation time increases, the pore fractal dimension of the MAO coating, respectively 2.57, 2.75, 2.77, 2.77, gradually expands within a narrow range, indicating a gradual increase in pore structure complexity. The observed phenomenon can be attributed to the gradual buildup of minute particles on the surface of the coating, the augmentation of coating thickness, and the heterogeneous pore structure resulting from prolonged oxidation. Nonetheless, the limited range of variation in fractal dimension implies that the diversity of pore structure is confined within a specific range, indicating a high level of consistency in the pore structure of the MAO coating across different oxidation periods. This suggests that the formation of pores with dissimilar structures during the coating preparation process is unlikely.

Conclusion
The porosity of the MAO coating was evaluated using a Mercury intrusion porosimeter, and subsequently adjusted based on the coating volume ratio, resulting in a more precise determination of the coating's porosity. The experimental outcomes of the coating samples, which were subjected to varying oxidation times, demonstrate that the Mercury intrusion technique effectively characterizes the porosity of the coating.
(1) Image method of four distinct regions of a single sample and their corresponding porosity were respectively 12.9%, 8.4%, 9.5%, 11.2%. The substantial numerical dispersion suggests that the conventional image method's observed area is limited, resulting in inadequate representativeness, and solely capable of characterizing the pore distribution on the sample's surface. Conversely, the MIP test offers a broader detection area and superior representativeness, enabling the reflection of the pore volume proportion within the coating, as well as the acquisition of the average pore size and distribution of the coating pores.
(2) By utilizing the ratio of coating volume to sample volume to adjust the porosity test outcomes of MIP, it is possible to derive the porosity of the coating, exclusive of the substrate. As the results show, when the oxidation time of MAO coating increases by 5 min,10 min,15 min and 20 min respectively, the calculated porosity of the coating decreases by 25.2%,18.2%,15.3% and 9.4% respectively, which reflects the positive correlation between oxidation time and porosity. This outcome serves as a valuable guide in the coating preparation and application process.
(3) Through the analysis and computation of pressure, pore size, cumulative Mercury intrusion, and incremental Mercury intake data obtained from Mercury intrusion experiments, the fractal dimension of the coating's pore structure can be determined. Research showed that as the oxidation time increases, the pore fractal dimension of the MAO coating gradually expands within a narrow range, indicating a gradual increase in pore structure complexity. This information provides supplementary factors for understanding the correlation between coating performance and pore structure.