Electro-Discharge Machining of Zr67Cu11Ni10Ti9Be3: An Investigation on Hydroxyapatite Deposition and Surface Roughness

This study attempts to simultaneously machine and synthesize a biomimetic nanoporous hydroxyapatite coating on the Zr67Cu11Ni10Ti9Be3 bulk metallic glass (BMG) surface. The aim is to investigate and optimize the hydroxyapatite deposition rate and the surface roughness during the electro-discharge coating of Zr67Cu11Ni10Ti9Be3 BMG. Scanning Electron Microscopy (SEM), X-ray powder Diffraction (XRD) and Energy-dispersive X-ray Spectroscopy (EDS) were employed to characterize and analyze the results. Response Surface Methodology using D-optimum custom design approach was utilized to generate the models and optimize the input parameters. A globule nanostructured and nanoporous coating of about 25.2 µm thick, containing mainly Ca, O, and K were ascertained. Further XRD analysis confirmed the deposition of biocompatible oxides (HA, CaZrO3, and ZrO2) and hard ZrC coating on the Zr67Cu11Ni10Ti9Be3 BMG surface. A significant improvement in cell viability was observed in the HA electro-discharge coated BMG specimens. The numerical models for the Hydroxyapatite Deposition Rate (HDR) and Surface Roughness (SR) were developed and experimentally validated using the optimized parameters setting suggested by the software. The achieved average predicted error of 4.94 and 5.09% for the HDR and SR respectively confirmed the excellent reproducibility of the developed models.


Introduction
The liquid-like, non-crystalline (amorphous) alloy called Bulk Metallic Glass (BMG) is produced by rapid quenching of liquid melts. Unlike crystalline materials, BMG has unique properties like using D-optimum custom design approach was employed to formulate mathematical models for the two important responses-HDR and SR. The process parameters including Peak current (P c ), Discharge duration (D d ), HA concentration (C), and tool-electrode polarity (E p ) were optimized and experimentally validated.

Materials
This study adopted vit1b-X Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG produced by Materion (USA) as a workpiece (substrate) material. A 5 × 100 × 125 mm received Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG was sliced into 5 × 9 × 10 mm pieces using wire-EDM machine to produce the workpiece specimens. The nominal compositions of the as-received BMG are 67.51 wt. % Zr, 10.61 wt. % Cu, 9.8 wt. % Ni, 3.768 wt. % Be, <1 wt. % Be and <1 wt. % Sn. A commercial titanium plate (CpTi) with size 11 × 12 × 50 mm fabricated by wire-EDM was employed as a tool-electrode. To serve as a calcium and oxygen source, a bioceramic hydroxyapatite (Ca 5 (PO4) 3 (OH)) powder 12-64 µm size was used as a dielectric fluid additive. The SEM micrograph of the as-received Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG and the hydroxyapatite powder are shown in Figure 1. A non-distinct grain boundary in the BMG SEM micrograph shown in Figure 1a confirmed its amorphous nature and the HA particle size measurement is in Figure 1b. Processes 2020, 8, x FOR PEER REVIEW 3 of 16 using hydroxyapatite mixed EDM (HAm-EDM) process. This study synthesized a bioactive oxide coating on the Zr67Cu11Ni10Ti9Be3 BMG surface. Additionally, the Response Surface Methodology using D-optimum custom design approach was employed to formulate mathematical models for the two important responses-HDR and SR. The process parameters including Peak current (Pc), Discharge duration (Dd), HA concentration (C), and tool-electrode polarity (Ep) were optimized and experimentally validated.

Materials
This study adopted vit1b-X Zr67Cu11Ni10Ti9Be3 BMG produced by Materion (USA) as a workpiece (substrate) material. A 5 × 100 × 125 mm received Zr67Cu11Ni10Ti9Be3 BMG was sliced into 5 × 9 × 10 mm pieces using wire-EDM machine to produce the workpiece specimens. The nominal compositions of the as-received BMG are 67.51 wt. % Zr, 10.61 wt. % Cu, 9.8 wt. % Ni, 3.768 wt. % Be, <1 wt. % Be and <1 wt. % Sn. A commercial titanium plate (CpTi) with size 11 × 12 × 50 mm fabricated by wire-EDM was employed as a tool-electrode. To serve as a calcium and oxygen source, a bioceramic hydroxyapatite (Ca5(PO4)3(OH)) powder 12-64 µm size was used as a dielectric fluid additive. The SEM micrograph of the as-received Zr67Cu11Ni10Ti9Be3 BMG and the hydroxyapatite powder are shown in Figure 1. A non-distinct grain boundary in the BMG SEM micrograph shown in Figure 1a confirmed its amorphous nature and the HA particle size measurement is in Figure 1b.

BMG Shaping and Coating Preparation
Die-sinker EDM machine (Mitsubishi EA 60, Mitsubishi, Tokyo, Japan) was employed for simultaneous machining and coating of the Zr67Cu11Ni10Ti9Be3 BMG workpiece material. Prior to EDM operation, the HA powder was mixed in the fabricated 200 L capacity HAm-EDM reservoir. To allow homogeneous and contentious mixing of the HA powder, 6 and 3 stirrers were employed in both HAm-EDM reservoir and the fabricated machining tank respectively. The complete experimental set-up is depicted in Figure 2. To observe the HA coating morphology and its thickness the cross-section of the HAm-EDMed Zr67Cu11Ni10Ti9Be3 BMG specimens was grounded, polished and etched for 20 s using prepared etchant solution containing 2 mL HNO3, 2 mL HF and 96 mL distilled water. An optical microscope (LEICA, NICON, Tokyo, Japan) was employed to observe and validate the deposition of the HA on the BMG surface, synthesized by HAm-EDM process. The specimens were further characterized using Scanning electron microscopy (SEM) (Evo LS15), X-ray powder diffraction (XRD) (X'Pert3 powder and Empyrean, PANalytical) and energy-dispersive X-

BMG Shaping and Coating Preparation
Die-sinker EDM machine (Mitsubishi EA 60, Mitsubishi, Tokyo, Japan) was employed for simultaneous machining and coating of the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG workpiece material. Prior to EDM operation, the HA powder was mixed in the fabricated 200 L capacity HAm-EDM reservoir. To allow homogeneous and contentious mixing of the HA powder, 6 and 3 stirrers were employed in both HAm-EDM reservoir and the fabricated machining tank respectively. The complete experimental set-up is depicted in Figure 2. To observe the HA coating morphology and its thickness the cross-section of the HAm-EDMed Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG specimens was grounded, polished and etched for 20 s using prepared etchant solution containing 2 mL HNO 3 , 2 mL HF and 96 mL distilled water. An optical microscope (LEICA, NICON, Tokyo, Japan) was employed to observe and validate the deposition of the HA on the BMG surface, synthesized by HAm-EDM process. The specimens were further characterized using Scanning electron microscopy (SEM) (Evo LS15), X-ray powder diffraction (XRD) (X'Pert3 powder and Empyrean, PANalytical) and energy-dispersive X-ray spectroscopy (EDS) to observe the surface morphology, phases and elemental composition present in the coated specimens ray spectroscopy (EDS) to observe the surface morphology, phases and elemental composition present in the coated specimens respectively. The angle of 2θ (20°-90°) scanning range and 0.01 degree/step size were used during the XRD investigation.

Screening and Optimization Experiment
Screening or fractional factorial experiment was carried out to select the best suited and most significant parameters that affect the HDR and SR. The difference of the workpiece weight after and before processing was divided by the machining time to calculate the HDR (g/min) [15]. Screening experiment was planned and analyzed using ©Minitab 18 design software. For the screening experiment, six factors which include Pc, Dd, C, Ep, Gap voltage (Gv), and Off-time (Toff) were selected, which are reported to have an influence on the target output (HDR and SR) [16,17]. Two level fractional factorial design (resolution IV) was conducted. Therefore, a combination of 16 experiments will be carried out. Table 1 presents the screening input parameters and experimental levels. To generate the model equations for predicting the HDR and SR. Response Surface Methodology through D-optimum custom design was employed in this study due to its flexibility and ability to accommodate custom models and categorical factors [18,19]. The optimized equations are written based on Equation (1). Where Y is the response variable while X1 and X2 are the independent variables. In the current study, the four factors (Pc, Dd, C, and Ep) selected from the screening experiment were used to generate empirical models and optimize the responses (HDR and SR). The selected parameters Pc, Dd, C and Ep varies at 3, 3, 4, and 2 levels respectively, with values Pc (5, 8, and 12 A), Dd (4, 8, and 16 µs), C (5, 10, 20 g/L), and Ep (Negative and Positive). The developed models will be experimentally validated, and predicated error will be calculated using Equation (2).

Screening and Optimization Experiment
Screening or fractional factorial experiment was carried out to select the best suited and most significant parameters that affect the HDR and SR. The difference of the workpiece weight after and before processing was divided by the machining time to calculate the HDR (g/min) [15]. Screening experiment was planned and analyzed using ©Minitab 18 design software. For the screening experiment, six factors which include P c , D d , C, E p , Gap voltage (G v ), and Off-time (T off ) were selected, which are reported to have an influence on the target output (HDR and SR) [16,17]. Two level fractional factorial design (resolution IV) was conducted. Therefore, a combination of 16 experiments will be carried out. Table 1 presents the screening input parameters and experimental levels. To generate the model equations for predicting the HDR and SR. Response Surface Methodology through D-optimum custom design was employed in this study due to its flexibility and ability to accommodate custom models and categorical factors [18,19]. The optimized equations are written based on Equation (1). Where Y is the response variable while X1 and X2 are the independent variables. In the current study, the four factors (P c , D d , C, and E p ) selected from the screening experiment were used to generate empirical models and optimize the responses (HDR and SR). The selected parameters P c , D d , C and E p varies at 3, 3, 4, and 2 levels respectively, with values P c (5, 8, and 12 A), D d (4, 8, and 16 µs), C (5, 10, 20 g/L), and E p (Negative and Positive). The developed models will be experimentally validated, and predicated error will be calculated using Equation (2).  Figure 3 displays the SEM image of the simultaneously shaped and coated Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG. The HA coating of about 25.2-µm thick was deposited on the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG surface as observed in the cross-sectional SEM micrograph shown in Figure 3a. The electrodes and the added HA powder are melted at the point of spark during the HAm-EDM process. Thus, some of the melted HA additives and the CpTi electrode material are migrated in elemental or compound form to the BMG surface and solidified by the surrounding dielectric fluid. This produces oxides and carbide coating on the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG surface. Oxides are believed biocompatible and apatite inducers which promote biocompatibility of the synthetic tissues [20]. A thin recast layer of about 5.6-µm thick was also observed. At higher magnification, the HA coating microstructure shows globules nanostructured and nanoporous surface ( Figure 3b). This surface is suitable for tissues in-growth into the nano-size rough and porous structure, thereby enhancing the osteointegration of Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG as an implant. A very long peak of Ca observed in the EDS spectrum presented in Figure 4 confirmed the HA deposition on the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG workpiece surface. Other peaks representing K and O were also noticed. These elements are the major compositions of HA (Ca 5 (PO4) 3 OH) powder.  Figure 3 displays the SEM image of the simultaneously shaped and coated Zr67Cu11Ni10Ti9Be3 BMG. The HA coating of about 25.2-µm thick was deposited on the Zr67Cu11Ni10Ti9Be3 BMG surface as observed in the cross-sectional SEM micrograph shown in Figure 3a. The electrodes and the added HA powder are melted at the point of spark during the HAm-EDM process. Thus, some of the melted HA additives and the CpTi electrode material are migrated in elemental or compound form to the BMG surface and solidified by the surrounding dielectric fluid. This produces oxides and carbide coating on the Zr67Cu11Ni10Ti9Be3 BMG surface. Oxides are believed biocompatible and apatite inducers which promote biocompatibility of the synthetic tissues [20]. A thin recast layer of about 5.6-µm thick was also observed. At higher magnification, the HA coating microstructure shows globules nanostructured and nanoporous surface ( Figure 3b). This surface is suitable for tissues ingrowth into the nano-size rough and porous structure, thereby enhancing the osteointegration of Zr67Cu11Ni10Ti9Be3 BMG as an implant. A very long peak of Ca observed in the EDS spectrum presented in Figure 4 confirmed the HA deposition on the Zr67Cu11Ni10Ti9Be3 BMG workpiece surface. Other peaks representing K and O were also noticed. These elements are the major compositions of HA (Ca5(PO4)3OH) powder.  The elements distribution is depicted in the elemental mapping shown in Figure 5. The elemental analysis validated the presence of the BMG (Zr and Ti) and the HA (Ca, K, and O). The mapping  Figure 3 displays the SEM image of the simultaneously shaped and coated Zr67Cu11Ni10Ti9Be3 BMG. The HA coating of about 25.2-µm thick was deposited on the Zr67Cu11Ni10Ti9Be3 BMG surface as observed in the cross-sectional SEM micrograph shown in Figure 3a. The electrodes and the added HA powder are melted at the point of spark during the HAm-EDM process. Thus, some of the melted HA additives and the CpTi electrode material are migrated in elemental or compound form to the BMG surface and solidified by the surrounding dielectric fluid. This produces oxides and carbide coating on the Zr67Cu11Ni10Ti9Be3 BMG surface. Oxides are believed biocompatible and apatite inducers which promote biocompatibility of the synthetic tissues [20]. A thin recast layer of about 5.6-µm thick was also observed. At higher magnification, the HA coating microstructure shows globules nanostructured and nanoporous surface (Figure 3b). This surface is suitable for tissues ingrowth into the nano-size rough and porous structure, thereby enhancing the osteointegration of Zr67Cu11Ni10Ti9Be3 BMG as an implant. A very long peak of Ca observed in the EDS spectrum presented in Figure 4 confirmed the HA deposition on the Zr67Cu11Ni10Ti9Be3 BMG workpiece surface. Other peaks representing K and O were also noticed. These elements are the major compositions of HA (Ca5(PO4)3OH) powder.   The elements distribution is depicted in the elemental mapping shown in Figure 5. The elemental analysis validated the presence of the BMG (Zr and Ti) and the HA (Ca, K, and O). The mapping shows a homogeneous distribution of these elements on the coated BMG surface, except for Ca whereby some agglomeration was observed (encircled in red). The agglomeration might result due to non-uniform flushing whereby some HA are higher in some regions. shows a homogeneous distribution of these elements on the coated BMG surface, except for Ca whereby some agglomeration was observed (encircled in red). The agglomeration might result due to non-uniform flushing whereby some HA are higher in some regions.  Figure 6 displays the XRD pattern of the HA coated Zr67Cu11Ni10Ti9Be3 BMG processed at high discharge energy (Pc = 12 A, Dd = 16 µs) and C = (5, 10, and 20 g/L). The analysis using High score software revealed various crystalline phases, including biomimetic and bioceramic biocompatible oxides (HA, CaZrO3, and ZrO2) and hard zirconium carbide. While the oxide induces the apatite formation, the carbides enhance the hardness of the HA coated BMG surface [21]. Thus, promote the biocompatibility and the strength of the BMG respectively. The oxides are formed due to the reaction of the Ca and O (in the hydroxyapatite) to the Zr (in the Zr67Cu11Ni10Ti9Be3 BMG) workpiece material. It is obvious that some detected HA do not decompose, which might be due to poor flushing. The carbon supplied by the hydrocarbon-based dielectric fluid reacted with the Zr in BMG to produce ZrC. In a similar study, Sales et al. [22] investigated the role of calcium based oxide on the titanium alloy surface. The titanium perovskite (CaTiO3) formed on the EDMed surface greatly promote the tissues growth and cells adhesion after implantation. Some unknown phases were also detected by the XRD analysis. The XRD peaks of the specimen treated through 5 g/L are sharper and longer than those coated using 10 and 20 g/L HA concentrations. Increasing the HA from 5 to 20 g/L expand the electrodes gap, thereby improving the flushing capacity, stabilizes the HAm-EDM process and hence less machining time for the crystalline peaks formation.  Figure 6 displays the XRD pattern of the HA coated Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG processed at high discharge energy (P c = 12 A, D d = 16 µs) and C = (5, 10, and 20 g/L). The analysis using High score software revealed various crystalline phases, including biomimetic and bioceramic biocompatible oxides (HA, CaZrO 3 , and ZrO 2 ) and hard zirconium carbide. While the oxide induces the apatite formation, the carbides enhance the hardness of the HA coated BMG surface [21]. Thus, promote the biocompatibility and the strength of the BMG respectively. The oxides are formed due to the reaction of the Ca and O (in the hydroxyapatite) to the Zr (in the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG) workpiece material. It is obvious that some detected HA do not decompose, which might be due to poor flushing. The carbon supplied by the hydrocarbon-based dielectric fluid reacted with the Zr in BMG to produce ZrC. In a similar study, Sales et al. [22] investigated the role of calcium based oxide on the titanium alloy surface. The titanium perovskite (CaTiO 3 ) formed on the EDMed surface greatly promote the tissues growth and cells adhesion after implantation. Some unknown phases were also detected by the XRD analysis. The XRD peaks of the specimen treated through 5 g/L are sharper and longer than those coated using 10 and 20 g/L HA concentrations. Increasing the HA from 5 to 20 g/L expand the electrodes gap, thereby improving the flushing capacity, stabilizes the HAm-EDM process and hence less machining time for the crystalline peaks formation.

Effect of HA on the Surface Morphology
The SEM micrographs showing the influence of the HA concentration on the processed Zr67Cu11Ni10Ti9Be3 BMG surface is depicted in Figure 7. Numerous craters, microcracks, and porosities (encircled in red) could be observed in a specimen processed by EDM as seen in Figure 7a. The addition of 5 g/L HA produces a smoother surface with less cracks and shallower craters ( Figure  7b). Some droplets which might occur due to less gap flushing were also noticed in the craters. The

Effect of HA on the Surface Morphology
The SEM micrographs showing the influence of the HA concentration on the processed Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG surface is depicted in Figure 7. Numerous craters, microcracks, and porosities (encircled in red) could be observed in a specimen processed by EDM as seen in Figure 7a. The addition of 5 g/L HA produces a smoother surface with less cracks and shallower craters (Figure 7b). Some droplets which might occur due to less gap flushing were also noticed in the craters. The surface tends to be smoother when the HA concentration further increased to 15 g/L (Figure 7c). In addition, no cracks and less craters were noticed. The surface changes to a dendritic nanostructured and nanoporous coating when 20 g/L of HA powder was used (Figure 7d). Hydroxyapatite powder reduces the surface roughness by enlarging the machining gap, increases flushing capacity and stabilizes the HAm-EDM process. A similar result was achieved when HA powder was added to the dielectric fluid during EDM of β-titanium implant [23].

Screening Results Analysis
EDM machine has a wide range of parameters which might be influential to the responses HDR and SR. Based on the machine capability and literature survey six parameters including Pc, Dd, C, Ep, Gv, and Toff were selected for the screening experiment. A two-level fractional factorial (resolution IV) which gives a total of 16 experiments was used. The values of the HDR and SR were calculated and analysed to determine the most significant factors and the interactions. The normal plot and Pareto chart for the HDR presented in Figure 8a,b depicted that Pc, Dd, C, and Ep are the most significant factors on the HDR. Moreover, the interactions EpC and PcC were also found significant as observed in the Pareto chart for the HDR. Similarly, the factors Pc, Dd, C, Ep, and interaction DdC were found to have an influence on the SR as observed in the normal plot and Pareto chart of the SR shown in Figure  8c,d, respectively. Additionally, the factor Dd was found to have a major influence on the SR as confirmed by the Pareto chart. Generally, the factors Gv, Toff and/or their interactions were insignificant on both the HDR and SR. Therefore, these two non-significant factors were dropped, and hence further design of experiment (DOE) will only consider four significant factors including Pc, Dd, C, and Ep. The parameters obtained in this study were in agreement with those achieved when shaping siliconized silicon carbide in an aluminium powder mixed dielectric fluid [24].

Screening Results Analysis
EDM machine has a wide range of parameters which might be influential to the responses HDR and SR. Based on the machine capability and literature survey six parameters including P c , D d , C, E p , G v , and T off were selected for the screening experiment. A two-level fractional factorial (resolution IV) which gives a total of 16 experiments was used. The values of the HDR and SR were calculated and analysed to determine the most significant factors and the interactions. The normal plot and Pareto chart for the HDR presented in Figure 8a,b depicted that P c , D d , C, and E p are the most significant factors on the HDR. Moreover, the interactions E p C and P c C were also found significant as observed in the Pareto chart for the HDR. Similarly, the factors P c , D d , C, E p, and interaction D d C were found to have an influence on the SR as observed in the normal plot and Pareto chart of the SR shown in Figure 8c,d, respectively. Additionally, the factor D d was found to have a major influence on the SR as confirmed by the Pareto chart. Generally, the factors G v , T off and/or their interactions were insignificant on both the HDR and SR. Therefore, these two non-significant factors were dropped, and hence further design of experiment (DOE) will only consider four significant factors including P c , D d , C, and E p . The parameters obtained in this study were in agreement with those achieved when shaping siliconized silicon carbide in an aluminium powder mixed dielectric fluid [24].

Modelling and Optimization of HDR and SR
D-optimal design is a response surface methodology which generates a design that best estimate the influence of the process parameters particularly suited for screening studies [18]. Four factors, including Pc, Dd, C, and Ep and mixed level was used to achieve a total of 24 experiments. Table 2 displays the DOE matrix and the data for the selected responses, HDR and SR.

Modelling and Optimization of HDR and SR
D-optimal design is a response surface methodology which generates a design that best estimate the influence of the process parameters particularly suited for screening studies [18]. Four factors, including P c , D d , C, and E p and mixed level was used to achieve a total of 24 experiments. Table 2 displays the DOE matrix and the data for the selected responses, HDR and SR.  The contribution of each parameter on the HDR is indicated in the ANOVA shown in Table 3. The model value of 0.0001 ("Prob > F") justifies its significance. The table also shows that the factors P c , D d , C, E p , and interactions AB, AD, BC, CD, and B 2 with "Prob > F" values less than 0.05 are significant terms. The lack of fit "Prob > F" of 0.2170 indicates its insignificance. The model is required to fit the response (HDR), therefore it is good for the lack of fit to be non-significance. The analysis of variance (ANOVA) for the SR is depicted in Table 4. The regression model, significant factors, interactions and lack of fit tests are summarized by the ANOVA table. Model and the model terms with less than 0.05 "prob > F" are regarded as significant terms 18. Therefore, from the ANOVA table the model and the factors P c , D d , C, and E p are considered the significant terms of the SR. The model is expected to fit, because the lack of fit "prob > F" value of 0.2213 indicates its non-significance. The normal probability of the residuals and the residuals versus run plots for the HDR and SR are depicted in Figure 9. The normal plots for both HDR and SR shows that the data lies within the straight line as seen in Figure 9a,b respectively. This confirmed that the selected terms are only the significant factors and the errors are normally distributed. In the residuals versus run plots for HDR and SR presented in Figure 9c,d respectively, all the studentized residuals of regression lie within the required limit (±3 sigma), and not any outliers observed. This confirmed the capability of the model to predict the responses.

Std Order Run Order P c (A) D d (µs) C (g/L) E p HDR (g/min) SR (µm)
The normal probability of the residuals and the residuals versus run plots for the HDR and SR are depicted in Figure 9. The normal plots for both HDR and SR shows that the data lies within the straight line as seen in Figure 9a,b respectively. This confirmed that the selected terms are only the significant factors and the errors are normally distributed. In the residuals versus run plots for HDR and SR presented in Figure 9c,d respectively, all the studentized residuals of regression lie within the required limit (±3 sigma), and not any outliers observed. This confirmed the capability of the model to predict the responses. A curved plot 3D surface plots for the HDR and SR are presented in Figure 10. The curves surface observed in the HDR plots (Figure 10a-c) indicated the significance of the curvature and a quadratic model. The highest HDR is observed at 10 A and 8 µs parameters setting in the current versus discharge time 3D surface plot shown in Figure 10a. Moreover, the C versus Pc plot shows highest HDR of 0.002 g/min at C = 20 g/L and Pc = 5 A as observed Figure 10b. A similar HDR is achieved when C = 20 g/L and Dd = 8 µs parameters setting was employed as shown in Figure 10c. The influence of Pc and Dd on the SR is presented in the 3D surface plot shown in Figure 10d. A flat surface which indicated insignificant curvature is observed. From this plot, it can be noticed that the SR increases with increases in both Pc and Dd. Therefore, higher SR can be observed at Pc = 12 A and Dd = 16 µs while the lowest SR can be achieved at Pc = 5 A and Dd = 4µs parameters setting. A curved plot 3D surface plots for the HDR and SR are presented in Figure 10. The curves surface observed in the HDR plots (Figure 10a-c) indicated the significance of the curvature and a quadratic model. The highest HDR is observed at 10 A and 8 µs parameters setting in the current versus discharge time 3D surface plot shown in Figure 10a. Moreover, the C versus P c plot shows highest HDR of 0.002 g/min at C = 20 g/L and P c = 5 A as observed Figure 10b. A similar HDR is achieved when C = 20 g/L and D d = 8 µs parameters setting was employed as shown in Figure 10c. The influence of P c and D d on the SR is presented in the 3D surface plot shown in Figure 10d. A flat surface which indicated insignificant curvature is observed. From this plot, it can be noticed that the SR increases with increases in both P c and D d . Therefore, higher SR can be observed at P c = 12 A and D d = 16 µs while the lowest SR can be achieved at P c = 5 A and D d = 4µs parameters setting.
The ANOVA table presented produces the equation which relates the responses HDR and SR to the input parameters. The final predicted model equations in terms of the actual factors for HDR and SR are presented in Equations (3)- (6).
When E p = Negative: When E p = positive:  Table 5 shows the model summary statistic for HDR. The software recommended a quadratic model for the HDR, due to its least standard deviation (0.23), largest statistic R-square (0.7710), and lowest Predicated Error Sum of Squares (PRESS) (4.20) compared to the linear model.   Table 5 shows the model summary statistic for HDR. The software recommended a quadratic model for the HDR, due to its least standard deviation (0.23), largest statistic R-square (0.7710), and lowest Predicated Error Sum of Squares (PRESS) (4.20) compared to the linear model. The model summary statistic for the SR is shown in Table 6. It could be observed that the linear model for SR is suggested by the design expert software for the SR. This is due to its least standard deviation of 0.41, largest statistic (predicted) R-square of 0.7000 and lower Predicated Error Sum of Squares (PRESS) of 5.36 as required. The response optimization can be directly obtained from the design expert software by considering the response value and desirability. The software suggests the optimum parameters combination for maximizing HDR and minimizing SR. The solutions suggested by the software for maximizing HDR and minimizing SR are presented in Tables 7 and 8. Following a successful selection of the input parameters' optimum level, a confirmatory test was conducted to validate the numerical model developed for the responses HDR and SR. In this study, the optimum parameters recommended by the design software was used to conduct the confirmation test. Thus, it will be possible to establish the adequacy of the achieved numerical models. Optimum parameters setting plays a significant role not only in improving the quality but also in the industries by reducing parts production time and cost. This study planned to achieve a maximum rate of hydroxyapatite deposition and minimum surface roughness (nanostructured surface). Using the optimum parameters conditions generated by the software, five sets of confirmatory tests were carried out. The results of both responses are presented in Table 9. Table 9. Confirmation test results at optimized input parameters. The five sets of results for the HDR and SR provided by the software (predicated) and those conducted at optimum parameters setting (actual experiment) were compared in Table 10. To enable accurate estimation of the predicted models, prediction error (PE) of each response was determined. The average error of the five results was also calculated to achieve the average PE (APE). The PE is calculated through Equation (1). The APE for HDR and SR was found to be 4.94% and 5.09%, respectively. A study conducted by Mir et al. [25] and Aliyu et al. [26] reported that an APE of less than 10% confirmed the excellent reproducibility of the experimental conclusions. Therefore, the APE of 4.95% (HDR) and 5.09% (SR) in this study can be considered to be within the acceptable limit.

Conclusions
The main conclusions of this study are as follows: • HAm-EDM process can be used to synthesize a novel biomimetic biocompatible oxide and carbide coatings on the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG surface.

•
The experimental result revealed a HA coating containing mainly biocompatible oxides and hard carbide of 25.2-µm thickness, synthesized on the Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG material by HAm-EDM process. The main hydroxyapatite elements (Ca, O, and K) were found deposited on the HAm-EDMed Zr 67 Cu 11 Ni 10 Ti 9 Be 3 BMG surface.

•
The model equations for both HDR and SR were successfully developed. Furthermore, the optimum parameters setting for minimizing SR and maximizing HDR are achieved. The predicted error of both SR and HDR was found to be 5.09% and 4.94% respectively. Therefore, the errors were considered within the acceptable limit.