Electrochemical Performance of Aluminum Doped Ni 1 − x Al x Co 2 O 4 Hierarchical Nanostructure: Experimental and Theoretical Study

: For electrochemical supercapacitors, nickel cobaltite (NiCo 2 O 4 ) has emerged as a new energy storage material. The electrocapacitive performance of metal oxides is signiﬁcantly inﬂuenced by their morphology and electrical characteristics. The synthesis route can modulate the morphological structure, while their energy band gaps and defects can vary the electrical properties. In addition to modifying the energy band gap, doping can improve crystal stability and reﬁne grain size, providing much-needed surface area for high speciﬁc capacitance. This study evaluates the electrochemical performance of aluminum-doped Ni 1 − x Al x Co 2 O 4 (0 ≤ x ≤ 0.8) compounds. The Ni 1 − x Al x Co 2 O 4 samples were synthesized through a hydrothermal method by varying the Al to Ni molar ratio. The physical, morphological, and electrochemical properties of Ni 1 − x Al x Co 2 O 4 are observed to vary with Al 3+ content. A morphological change from urchin-like spheres to nanoplate-like structures with a concomitant increase in the surface area, reaching up to 189 m 2 /g for x = 0.8, was observed with increasing Al 3+ content in Ni 1 − x Al x Co 2 O 4 . The electrochemical performance of Ni 1 − x Al x Co 2 O 4 as an electrode was assessed in a 3M KOH solution. The high speciﬁc capacitance of 512 F/g at a 2 mV/s scan rate, 268 F/g at a current density of 0.5 A/g, and energy density of 12.4 Wh/kg was observed for the x = 0.0 sample, which was reduced upon further Al 3+ substitution. The as-synthesized Ni 1 − x Al x Co 2 O 4 electrode exhibited a maximum energy density of 12.4 W h kg − 1 with an outstanding high-power density of approximately 6316.6 W h kg − 1 for x = 0.0 and an energy density of 8.7 W h kg − 1 with an outstanding high-power density of approximately 6670.9 W h kg − 1 for x = 0.6. The capacitance retention of 97% and 108.52% and the Coulombic efﬁciency of 100% and 99.24% were observed for x = 0.0 and x = 0.8, respectively. First-principles density functional theory (DFT) calculations show that the band-gap energy of Ni 1 − x Al x Co 2 O 4 remained largely invariant with the Al 3+ substitution for low Al 3+ content. Although the capacitance performance is reduced upon Al 3+ doping, overall, the Al 3+ doped Ni 1 − x Al x Co 2 O 4 displayed good energy, powder density, and retention performance. Thus, Al 3+ could be a cost-effective alternative in replacing Ni with the performance trade off. saturated calomel electrode (SCE) as a reference electrode, and pasted samples on nickel foam as a working electrode were utilized in the electrochemical cell. The electrochemical performance of the electrode was assessed in 3 M KOH as an electrolyte. The electrochemical performance of the as-prepared electrode was evaluated using cyclic voltammetry (CV), galvanostatic charge-discharge techniques, and electrochemical impedance spectroscopy (EIS) by using a Versastat4-500 electrochemical workstation (Princeton Applied Research, Oak Ridge, TN, USA).


Introduction
Researchers are actively engineering an efficient, clean, and cost-effective electrode for better electrochemical performance [1]. Conventional capacitors and batteries are broadly exploited by energy storage devices [2]. Previously, secondary batteries were suitable electrical energy storage devices, but they were not very satisfactory because of their smaller power density, presence of toxic waste substances, and shorter lifetime [3]. On the

Synthesis
The required high purity nitrate salts, viz. Al(NO 3 ) 2 .6H 2 O, Co(NO 3 ) 2 .6H 2 O, and Ni(NO 3 ) 2 .6H 2 O, were purchased from Sigma Aldrich (St. Louis, MO, USA). Table 1 lists the required amount of precursor salts needed to prepare Ni 1−x Al x Co 2 O 4 . The nitrate salts were dissolved in 35 mL of water with a fixed amount of Urea (CO(NH 2 ) 2 ) and stirred for 30 min. The solution was then transferred to a 45 mL Teflon-lined autoclave and maintained at 190 • C for 12 h, followed by a natural cooling to room temperature. The precipitates were washed with distilled water and acetone several times by centrifugation and then dried for 12 h at 80 • C. After this, the as derived metal hydroxide composite particles were calcined at 350 • C in the air for 3.5 h.

Characterization
X-ray diffraction (XRD) was used to examine the crystalline structure of calcined powder using a Bruker D8 Advance X-ray diffractometer (Bruker, Billerica, MA, USA). The surface morphology of prepared samples was studied by a scanning electron microscope (SEM) (at 10 keV using Phenom, Oak Park, CA, USA). Autosorb (Quantachrome, Boynton Beach, FL 33426, USA, model No. AS1MP) was used to quantify specific surface area and pore volume at 77K using nitrogen as the adsorbing gas. The Brunauer-Emmett-Teller (BET) method was used to measure the specific surface area of as-prepared samples. Also, surface area, average pore volume, and pore radius were obtained from the Barret-Joyner-Halenda (BJH) model. Between 400 and 1000 cm −1 , FTIR spectra were acquired using an FTIR spectrometer (Nicolet iS10, Thermo Fisher Scientific, Waltham, MA, USA). The x-ray photoelectron spectrometer (Thermo Scientific K-alpha, XPS) equipped with a monochromatic X-ray source at 1486.6 eV, corresponding to the Al K α line, was employed to collect XPS data (for the brevity XPS spectra not shown). The atomic weight percent of elements was determined using XPS.
The working electrode was prepared using nickel foam. Nickel foam was first cleaned with acetone and 3 M HCl solution for 10 min, which helped remove the oxide layer from the nickel foam's surface. After washing and drying the nickel foam, the working electrode was made by combining 80 wt.% of the synthesized powder, 10 wt. % of acetylene black, and 10 wt. % of polyvinylidene difluoride (PVDF) with N-methyl pyrrolidinone (NMP). The slurry paste was obtained after thoroughly mixing the components and pasted onto the nickel foam. The prepared electrode on nickel foam was placed in a vacuum oven at a temperature of 60 • C for 10 h. The actual sample loading on nickel foam was determined by weighing the nickel foam before and after loading the nickel foam sample using an analytical balance (MS105DU, Mettler Toledo, max. 120 g, 0.01 mg of resolution). A platinum wire counter electrode, a saturated calomel electrode (SCE) as a reference electrode, and pasted samples on nickel foam as a working electrode were utilized in the electrochemical cell. The electrochemical performance of the electrode was assessed in 3 M KOH as an electrolyte. The electrochemical performance of the as-prepared electrode was evaluated using cyclic voltammetry (CV), galvanostatic charge-discharge techniques, and electrochemical impedance spectroscopy (EIS) by using a Versastat4-500 electrochemical workstation (Princeton Applied Research, Oak Ridge, TN, USA).

DFT Study
First-principles density functional theory (DFT) calculations were performed using the Perdew-Burke-Ernzerhof (PBE) [33] exchange-correlation functional for self-consistent calculations and geometry optimization along with the advanced hybrid functional HSE06 method to find the electronic density of states of the Al x Ni 1−x Co 2 O 4 structure. The variable x ranges from 0 to 1 with a step of 0.25. Calculations were performed using VASP [34] (Vienna ab initio simulation package) with the projected augmented wave (PAW) [35] type pseudo-potential and the plane-wave basis set. The exchange and correlation part for the HSE calculations was described by hybrid functional [36] containing 40% Hartree-Fock exchange. We used a 4 × 4 × 2 k-points mesh centered at the Gamma point with a plane wave cutoff of 400 eV, which is enough for the self-consistent calculation. The global break condition for the electronic and ionic self-consistent (SC) loop was set to be 10 −4 eV and 10 −3 eV, respectively.

Results and Discussion
The room temperature powder XRD patterns of Ni 1−x Al x Co 2 O 4 samples are shown in Figure 1 Table 2 and is within the accepted range of stoichiometry of the compound.     Figure 2 shows the SEM images of Ni 1−x Al x Co 2 O 4 as a function of Al 3+ content. Figure 2 shows the gradual evolution of Ni 1−x Al x Co 2 O 4 nanostructures from an urchinlike architecture for x = 0.0 to nanoplates for x = 0.8. It is evident that the initial urchin whiskers slowly merge and morph into a plate-like structure with increasing Al content. The morphology of Ni 1−x Al x Co 2 O 4 is dependent on the Al 3+ content in the sample. Usually, the morphology of hierarchal nanostructures depends on the synthesis techniques and urea concentration [4]. As a dispersing agent, urea helps avoid agglomeration by finely separating nanoparticles and plays a vital role in controlling the particles' morphology [39][40][41].  Furthermore, NH3 reacts with water to form NH4 + and OH − , and CO2 hydrolyzes to form Co3 2− ions [42]. Tiny crystalline nuclei are created during the oxide crystal development phase, and nanoparticles of this oxide are precipitated by a rise in pH caused by NH4 + ions generated from NH3 owing to urea breakdown at higher temperatures [43,44]. Urea's hydrolysis leads to a rise in the pH due to the increased release of NH4 + in the solution [45]. The urea hydrolysis progresses slowly at milder circumstances and at a certain urea level, and the basic solution undergoes supersaturation of the metal-hydroxide species [46]. Figure 3a shows N2 adsorption/desorption measurements were performed at 77 K between relative pressures of P/Po ~ 0.029 to 0.99. From these curves, BET-specific surface areas and corresponding pore sizes were calculated by the BJH method for all Ni1-xAlxCo2O4 (0 ≤ x ≤ 0.8). Figure 2c inset shows the pore distribution. These curves show the largest number of pores distribution at around 3 nm for all Ni1-xAlxCo2O4. This pore distribution lies between ~2.0 and 6.0 nm, a range best suited to electrode materials [46]. The larger pore volume helps boost the diffusion kinetics inside the electrode material Furthermore, NH 3 reacts with water to form NH 4 + and OH − , and CO 2 hydrolyzes to form Co 3 2− ions [42]. Tiny crystalline nuclei are created during the oxide crystal development phase, and nanoparticles of this oxide are precipitated by a rise in pH caused by NH 4 + ions generated from NH 3 owing to urea breakdown at higher temperatures [43,44]. Urea's hydrolysis leads to a rise in the pH due to the increased release of NH 4 + in the solution [45]. The urea hydrolysis progresses slowly at milder circumstances and at a certain urea level, and the basic solution undergoes supersaturation of the metal-hydroxide species [46]. Figure 3a shows N 2 adsorption/desorption measurements were performed at 77 K between relative pressures of P/P o~0 .029 to 0.99. From these curves, BET-specific surface areas and corresponding pore sizes were calculated by the BJH method for all Ni 1−x Al x Co 2 O 4 (0 ≤ x ≤ 0.8). Figure 2c inset shows the pore distribution. These curves show the largest number of pores distribution at around 3 nm for all Ni 1−x Al x Co 2 O 4 . This pore distribution lies between~2.0 and 6.0 nm, a range best suited to electrode materials [46]. The larger pore volume helps boost the diffusion kinetics inside the electrode material [40,46,47]. Table 2 lists the measured BJH pore radius, volume, and BET surface area of Ni 1−x Al x Co 2 O 4 samples. The high surface area of samples, in the range of 81.74-189 m 2 /g, indicates that the hydrated electrolyte ions could have an increased contact area at the electrolyte/electrode surface for the Faradaic redox reaction [48,49]. The FTIR spectrum Figure 3b shows two different bands arising from the stretching vibrations of the metal-oxygen bonds at 534.2 (ν1) and 628.7 (ν2) cm −1 [1]. For the crystal structure of NiCo2O4, the ν1 band is attributed to M-O (M = Ni) bond vibrations in octahedral coordination, whereas the ν2 band is attributed to M-O (M-Co) bond vibrations in tetrahedral coordination. The stretching vibration of Co 3+ -O 2− in the octahedral sites is shown by the FTIR spectrum at 534.2 cm −1 , and the vibration of Ni 2+ -O − at the tetrahedral sites is indicated by the FTIR spectrum at 628.7 cm −1 for NiCo2O4, respectively [50]. The presence of these vibration bands indicates that pure phase spinel NiCo2O4 nanostructures have formed. Table 3 lists the band positions for the tetrahedral and octahedral sites of the compound. Aluminum doping brings the shift of the stretching peak towards the right with an increase in Al 3+ content. As the vibrational frequency is inversely proportional to the mass, the increase in vibrational frequency with Al 3+ is expected due to the lower atomic weight of Al 3+ replacing the Ni ion. Cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD) measurements give the electrochemical performance of Ni1-xAlxCo2O4 nanostructures. Figure 4a-e shows the cyclic voltammograms obtained at different scan rates (2-300 mV/s) in a voltage window of 0-0.6 V (vs. SCE). The Faradaic reaction for NiCo2O4, x = 0 is given by the equation below [51,52]. The FTIR spectrum Figure 3b shows two different bands arising from the stretching vibrations of the metal-oxygen bonds at 534.2 (ν 1 ) and 628.7 (ν 2 ) cm −1 [1]. For the crystal structure of NiCo 2 O 4 , the ν 1 band is attributed to M-O (M = Ni) bond vibrations in octahedral coordination, whereas the ν 2 band is attributed to M-O (M-Co) bond vibrations in tetrahedral coordination. The stretching vibration of Co 3+ -O 2− in the octahedral sites is shown by the FTIR spectrum at 534.2 cm −1 , and the vibration of Ni 2+ -O − at the tetrahedral sites is indicated by the FTIR spectrum at 628.7 cm −1 for NiCo 2 O 4 , respectively [50]. The presence of these vibration bands indicates that pure phase spinel NiCo 2 O 4 nanostructures have formed. Table 3 lists the band positions for the tetrahedral and octahedral sites of the compound. Aluminum doping brings the shift of the stretching peak towards the right with an increase in Al 3+ content. As the vibrational frequency is inversely proportional to the mass, the increase in vibrational frequency with Al 3+ is expected due to the lower atomic weight of Al 3+ replacing the Ni ion. Cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD) measurements give the electrochemical performance of Ni 1−x Al x Co 2 O 4 nanostructures. Figure 4a-e shows the cyclic voltammograms obtained at different scan rates (2-300 mV/s) in a voltage window of 0-0.6 V (vs. SCE). The Faradaic reaction for NiCo 2 O 4, x = 0 is given by the equation below [51,52].
Processes 2021, 9, x FOR PEER REVIEW 8 of 18 In both the cathodic and anodic scans, there are noticeable oxidation and reduction peaks [53]. Obtained non-rectangular and unsymmetric CV curves indicate the pseudocapacitive nature of electrodes [54]. The CV curves of Ni1-xAlxCo2O4 show no extra redox peaks, implying that Ni1-xAlxCo2O4 redox processes are very similar to NiCo2O4 redox processes. The peaks are due to the redox reaction related to M-O/M-O-OH, where M stands for Ni or Co ions [55]. A positive shift in oxidation peak potential and a negative shift in reduction peak potential are found as scan rate increases [56]. This PC characteristic is derived from the Faradaic redox reaction related to the reversible reaction of Ni 2+ /Ni 3+ and Co 3+ /Co 4+ transitions.  In both the cathodic and anodic scans, there are noticeable oxidation and reduction peaks [53]. Obtained non-rectangular and unsymmetric CV curves indicate the pseudocapacitive nature of electrodes [54]. The CV curves of Ni  [55]. A positive shift in oxidation peak potential and a negative shift in reduction peak potential are found as scan rate increases [56]. This PC characteristic is derived from the Faradaic redox reaction related to the reversible reaction of Ni 2+ /Ni 3+ and Co 3+ /Co 4+ transitions.  The Randles-Sevcik plots of the Ni1-xAlxCo2O4 samples are shown in Figure 5f. When the scan rate is increased from 2 to 300 mV s −1 , the anodic peak current (Ipa) and the cathodic peak current (Ipc) both increase. More precisely, the Randles-Sevcik equation shows that both Ipa and Ipc change linearly with the square root of the scan rate (ν 1/2 ) [57,58]. These results suggest that the electrode-electrolyte interface's redox events are rapid, quasi-reversible, and only limited by electrolyte diffusion [59]. The positive shift of oxidation peak and negative shift of reduction peak potential indicate relatively low electrode materials resistance and good electrochemical reversibility [1].
The calculation of specific capacitance was done from CV curves using the equation below [60]: Where I (A) is current, m (g) is the mass of the active material, v (mV/s) is the scan rate, V1 and V2 (V) are the start and end voltage of the CV scan. Figure 4f shows the Csp of Ni1-xAlxCo2O4 samples as a function of scan rates. The obtained values of Csp for Ni1-xAlxCo2O4 nanostructures are 512, 368, 371, 380, and 356 F/g at a scan rate of 2 mV/s for Ni1-xAlxCo2O4 x = 0.0, 0.2, 0.4, 0.6, and 0.8, respectively. Compared to all Ni1-xAlxCo2O4 nanostructures, NiCo2O4 x = 0.0 exhibited the highest specific capacitance at all scan rates with a maximum value of 512 F/g at 2 mV/s. The higher electrochemical utilization and high electroactive surface area of the synthesized nanostructure occur for Ni1-xAlxCo2O4, x = 0. The observed decrease in Csp with Al 3+ substitution suggests that in the presence of Al 3+ , the Ni and Co in Ni1-xAlxCo2O4 may not behave synergistically as an effective Faradaic charging site as compared with the Ni and Co sites in NiCo2O4. Moreover, it can be deduced that, with the increase in Al 3+ content, overall effective redox sites have decreased, which leads to a decrease in the specific capacitance.
The total charge storage process is affected by factors such as the Faradaic contribution from the insertion process of electrolyte ions, the Faradaic contribution from the charge-transfer process, and due to the high surface area, the contribution from both The Randles-Sevcik plots of the Ni 1−x Al x Co 2 O 4 samples are shown in Figure 5f. When the scan rate is increased from 2 to 300 mV s −1 , the anodic peak current (I pa ) and the cathodic peak current (I pc ) both increase. More precisely, the Randles-Sevcik equation shows that both I pa and I pc change linearly with the square root of the scan rate (ν 1/2 ) [57,58]. These results suggest that the electrode-electrolyte interface's redox events are rapid, quasi-reversible, and only limited by electrolyte diffusion [59]. The positive shift of oxidation peak and negative shift of reduction peak potential indicate relatively low electrode materials resistance and good electrochemical reversibility [1].
The calculation of specific capacitance was done from CV curves using the equation below [60]: where I (A) is current, m (g) is the mass of the active material, v (mV/s) is the scan rate, V 1 and V 2 (V) are the start and end voltage of the CV scan. Figure 4f shows The total charge storage process is affected by factors such as the Faradaic contribution from the insertion process of electrolyte ions, the Faradaic contribution from the charge-transfer process, and due to the high surface area, the contribution from both pseudocapacitance and the non-Faradaic contribution from the double layer effects [61]. CV data are analyzed at different scan rates and can characterize capacitive effects by equation [62,63].
where the peak current is I (A), the scan rate is v (mV/s), and a and b are adjustable parameters. The value of b specifies the charge storage mechanism. If b = 1, it indicates a surface-controlled reaction that the capacitive surface mechanism is dominant, and if b = 0.5, it indicates a diffusion-controlled Faradaic reaction during the charge storage mechanism [64]. Figure 5f shows the peak current vs. square root of the scan rate curve. These curves are fitted with the Equation (2) [54]. Moreover, in Figure 5f, the lower value of the scan rate region has a linear dependence relation with the square root of the scan rate; this indicates a quasi-reversible electrochemical reaction [65]. Figure 5f also indicates that, at a higher scan rate > 100 mV/s, the ion diffusion is limited to the surface of the active material of the electrode, i.e., EDLC dominates the pseudocapacitor, and diffusion of OH − ions can adhere only to the outer layer of the nanostructure, which contributes less to the electrochemical capacitive behavior [66]. On the other hand, the Faradaic redox reaction dominates at scan rates < 100 mV/s due to more effective usage of the working electrode's active material [67]. Moreover, the diffusion of OHions can easily penetrate deep into the nanostructure's interlayer, which leads to adsorption of more ions and hence ends up with higher specific capacitance [68]. The capacitive and diffusion processes are the two mechanisms for current response at a fixed potential [69,70]. The equation below gives their contributions [71].
k 1 and k 2 are determined from the C sp vs.V −1/2 linear plot, where k 2 is the slope and k 1 is the intercept. k 1 indicates diffusion and k 2 capacitance contribution to the total specific capacitance for a given voltage. For the calculation, the specific capacitance is plotted against the slow scan rate up to a value of 20 mV/s and performed a regression fit using Equation (3). The obtained value for k 1 and k 2 was used to determine the fractional contribution in terms of diffusion and capacitance from total specific capacitance [72], as given in Figure 5g. Figure 5g shows that the contribution to the current response at a fixed potential is more diffusive than capacitive and decreases with the Al content.
To further estimate the potential application of as-prepared electrodes for supercapacitors, the galvanostatic charge-discharge (GCD) measurement was performed. GCD was measured within the voltage window of 0.0 to 0.6 at different current densities between 1 A/g to 30 A/g in 3 M KOH solution are given in Figure 6a-e. These figures indicate that prepared electrodes of Ni 1−x Al x Co 2 O 4 can charge and discharge rapidly with good electrochemical reversibility at different constant current densities. As in CV curves, the non-linear relationship between the potential and time in both the charge-discharge cycle indicates the capacitance of studied nanomaterials is not constant in between the potential range and reflects typical PCs behavior [73]. The non-linearity of the GCD curve is a consequence of the Co 3+ /Co 4+ , and Ni 2+ /Ni 3+ ions redox reactions with OH − . The discharge process occurs in three distinct steps. First, there is a rapid potential drop that occurs owing to the internal resistance. The second is a slow potential decay at an intermediate time, which is due to the Faradaic redox reaction. The third is a fast potential decay which is created by electric double layer capacitance [74]. The specific capacitance values for electrodes of Ni 1−x Al x Co 2 O 4 were calculated by using Equation (4) [75].
where C sp is the specific capacitance (F/g), I (A) is the charge-discharge current, ∆V (V) is the potential range, m (g) is the mass of the electroactive materials and t (s) is the discharging time. Where Csp is the specific capacitance (F/g), I (A) is the charge-discharge current, V (V) is the potential range, m (g) is the mass of the electroactive materials and t (s) is the discharging time. The pseudocapacitance behavior of electrodes with respect to their discharging time is confirmed by the presence of voltage plateau on GCD curves [76]. The specific capacitance values of Ni1-xAlxCo2O4 were calculated using Equation (4) at 0.5 A/g are 268, 194, 192, 176, and 167 F/g for x = 0.0, 0.2, 0.4, 0.6, and 0.8, respectively, and are listed in Table 4. Figure 6f shows the dependence of current density with specific capacitance. A decrease in the specific capacitance with the increase of the discharge current is caused by the insufficient time available for the diffusion of the electrolyte ions into the inner electrode surface and the increase of the potential drop towards higher discharge currents [77].  The pseudocapacitance behavior of electrodes with respect to their discharging time is confirmed by the presence of voltage plateau on GCD curves [76]. The specific capacitance values of Ni 1−x Al x Co 2 O 4 were calculated using Equation (4) at 0.5 A/g are 268,194,192,176, and 167 F/g for x = 0.0, 0.2, 0.4, 0.6, and 0.8, respectively, and are listed in Table 4. Figure 6f shows the dependence of current density with specific capacitance. A decrease in the specific capacitance with the increase of the discharge current is caused by the insufficient time available for the diffusion of the electrolyte ions into the inner electrode surface and the increase of the potential drop towards higher discharge currents [77]. The cyclic stability of Ni 1−x Al x Co 2 O 4 , x = 0.0, and x = 0.8, electrodes were evaluated by the repeated charge-discharge measurements up to 5000 cycles at a constant current density of 10 A/g and 5 A/g in the potential range between 0.0 and 0.6 V in 3 M KOH, shown in Figure 7a,b respectively. The percentage retention in specific capacitance was calculated using Equation (5) [78]. % retention in specific capacitance = (C # /C 1 ) × 100 (5) where C # and C 1 are specific capacitance at various cycles and the 1st cycle, respectively. Hence, the % retention in specific capacitance after 5000 cycles for Ni 1−x Al x Co 2 O 4 x = 0.0 and x = 0.8 is 97% and 108.5% respectively. This shows that even after 5000 cycles, the electrode shows outstanding cyclic stability, and hence there is not much high specific capacitance fade from its initial values in x = 0.0. Similarly, in the case of x = 0.8, the specific capacitance improves to 108.5% of its initial value, and this suggests an improvement in the surface moistened by electrolyte ions, access of electrolyte ions up to the pore of electrode materials, and activation of electrodes by electrolyte ions upon cycle repetition [79]. Furthermore, the Coulombic efficiency for x = 0.0 and x = 0.8 is 100% and 99.2%, as shown in Figure 7a,b, respectively. The cyclic stability of Ni1-xAlxCo2O4, x = 0.0, and x = 0.8, electrodes were evaluated by the repeated charge-discharge measurements up to 5000 cycles at a constant current density of 10 A/g and 5 A/g in the potential range between 0.0 and 0.6 V in 3 M KOH, shown in Figure 7a,b respectively. The percentage retention in specific capacitance was calculated using equation (5) [78]. % retention in specific capacitance = (C#/C1)  100 (5) Where C# and C1 are specific capacitance at various cycles and the 1st cycle, respectively. Hence, the % retention in specific capacitance after 5000 cycles for Ni1-xAlxCo2O4 x = 0.0 and x = 0.8 is 97% and 108.5% respectively. This shows that even after 5000 cycles, the electrode shows outstanding cyclic stability, and hence there is not much high specific capacitance fade from its initial values in x = 0.0. Similarly, in the case of x = 0.8, the specific capacitance improves to 108.5% of its initial value, and this suggests an improvement in the surface moistened by electrolyte ions, access of electrolyte ions up to the pore of electrode materials, and activation of electrodes by electrolyte ions upon cycle repetition [79]. Furthermore, the Coulombic efficiency for x = 0.0 and x = 0.8 is 100% and 99.2%, as shown in Figure 7a,b, respectively. Cyclic stability and Coulombic efficiency tested at 10 A/g and 5 A/g current density up to 5000 cycles in 3M KOH electrolytes for Ni1-xAlxCo2O4, x = 0, and x = 0.8.
Ragone plots of synthesized Ni1-xAlxCo2O4 are given in Figure 8a. The energy (E) and power (P) densities are determined using the equations below [32], Where C is the electrodes' specific capacitance, V is the operating voltage, and the letter t denotes the discharge time in seconds. An excellent-performance supercapacitor must exhibit a high value of both energy density and power density together. Figure 8a shows the superior performance of electrodes with an energy density of up to 12.4 Wh/kg for x = 0.0, with up to a peak power density of 6670.9 W/kg for x = 0.6. Furthermore, Table 5 compares the electrodes' specific capacitances derived from the doping of transition elements on NiCo2O4 using the hydrothermal method. Ragone plots of synthesized Ni 1−x Al x Co 2 O 4 are given in Figure 8a. The energy (E) and power (P) densities are determined using the equations below [32], where C is the electrodes' specific capacitance, V is the operating voltage, and the letter t denotes the discharge time in seconds. An excellent-performance supercapacitor must exhibit a high value of both energy density and power density together. Figure 8a shows the superior performance of electrodes with an energy density of up to 12.4 Wh/kg for x = 0.0, with up to a peak power density of 6670.9 W/kg for x = 0.6. Furthermore, Table 5 compares the electrodes' specific capacitances derived from the doping of transition elements on NiCo 2 O 4 using the hydrothermal method. Processes 2021, 9, x FOR PEER REVIEW 13 of 18   Ni1-xZnxCo2O4 (x = 0.5) -------2 1228 F/g [30] Ni1-xFexCo2O4 (x = 1) --------1 2237 F/g at 1 h, 2208 F/g at 3 h, 1976 F/g at 5 h. [31] Ni1-xCaxCo2O4 (x = 0.0, 0.2, 0.4, 0.6, 0.8) 2 506 F/g,508 F/g, 355 F/g, 934 F/g, 571 F/g 0.5 284 F/g, 365 F/g, 317 F/g, 558 F/g, 253 F/g [32] Ni1-xAlxCo2O4 (x = 0.0, 0. The superior electrochemical performance of as-synthesized Ni1-xAlxCo2O4 nanostructure electrode materials was further confirmed by the electrochemical impedance spectroscopy (EIS) measurement held at 10 mV AC perturbation in the frequency range from 10 kHz to 0.05 Hz. Figure 8b shows the tendency of the real part of the impedance (Z′) to decrease with increasing frequency for all samples. When x = 0.0, it has the lowest real part of the impedance. The magnitude of the real part of the impedance (Z') increases as Al 3+ content increases, which affects the rise of grains, grain boundaries, and electrode interface resistance. Figure 8c shows the Nyquist plots for all of the Ni1-xAlxCo2O4 nanostructures. In this plot, the NiCo2O4 nanostructure electrode exhibits a small semicircle that suggests low internal resistance and charge transfer resistance, and hence this resistance is smaller than Al 3+ doped NiCo2O4. Towards higher frequencies, the real part (Zreal) of the impedance represents a combined resistance of contact resistance at active material/current collector interface, ionic resistance of the electrolyte, and intrinsic resistance of the nanomaterials used in the electrode [80]. The semicircle at the high-frequency range is due to the Faradaic charge transfer resistance (Rct) of the redox reaction between the electrode and electrolyte. The decrease in the diameter of the semicircle indi-  The superior electrochemical performance of as-synthesized Ni 1−x Al x Co 2 O 4 nanostructure electrode materials was further confirmed by the electrochemical impedance spectroscopy (EIS) measurement held at 10 mV AC perturbation in the frequency range from 10 kHz to 0.05 Hz. Figure 8b shows the tendency of the real part of the impedance (Z ) to decrease with increasing frequency for all samples. When x = 0.0, it has the lowest real part of the impedance. The magnitude of the real part of the impedance (Z') increases as Al 3+ content increases, which affects the rise of grains, grain boundaries, and electrode interface resistance. Figure 8c shows the Nyquist plots for all of the Ni 1−x Al x Co 2 O 4 nanostructures. In this plot, the NiCo 2 O 4 nanostructure electrode exhibits a small semicircle that suggests low internal resistance and charge transfer resistance, and hence this resistance is smaller than Al 3+ doped NiCo 2 O 4 . Towards higher frequencies, the real part (Z real ) of the impedance represents a combined resistance of contact resistance at active material/current collector interface, ionic resistance of the electrolyte, and intrinsic resistance of the nanomaterials used in the electrode [80]. The semicircle at the high-frequency range is due to the Faradaic charge transfer resistance (R ct ) of the redox reaction between the electrode and electrolyte. The decrease in the diameter of the semicircle indicates lower charge transfer resistance [81]. These variations of the EIS curve from semicircle towards higher frequencies and linearity towards lower frequencies relate to reversible Faradaic redox reaction and access of OH − ions into the pore of the electrode material. This behavior of the EIS curve describes the PCs properties of the prepared Ni 1−x Al x Co 2 O 4 nanostructure electrode [82]. The slope of the 45 • portion of the curve is called Warburg resistance (Z w ) and results from the frequency dependence of ion diffusion/transport in the electrolyte to the electrode surface [83,84]. The Nyquist plot is a vertical line for an ideal electrode material, and more is the vertical line represents better electrolyte diffusion and capacitive behavior [85]. Figure 8c shows that R ct is smaller for NiCo 2 O 4 and has a more vertical line, which offers better rate capability.
First-principles density functional theory (DFT) calculations were performed using VASP 2 [34] (Vienna ab initio simulation package) with the projected augmented wave (PAW) [35] type pseudo-potential and the plane-wave basis set. The exchange and correlation part for the HSE calculations was described by hybrid functional [36] containing a 40% Hartree-Fock exchange. Here, we used a 4 × 4 × 2 k-points mesh centered at the Gamma point with a plane wave cutoff of 400 eV, which is enough for the self-consistent calculation. The global break condition for the electronic and ionic self-consistent (SC) loop was set to be 10 −4 eV and 10 −3 eV, respectively. In our calculation, we dealt with a cell containing 28 atoms as a total. The value of gaussian smearing was adjusted to be 0.20. Even though the ratio of x is 20% in the experiment, we chose 25% in the calculations because changing it to 20% would require a much larger supercell, which eventually increases the computing time and memory excessively. Figure 9a shows the side view along the x-axis of the crystal structure of Ni 1−x Al x Co 2 O 4 , while Figure 9b shows the band-gap variation from 2.42 eV to 4.82 eV for the different values of x. For the system without Al atom, which is Ni 1 Co 2 O 4, the band gap was found at 2.42 eV, which agrees with the previously reported experimental values of 2.06 eV [86] and 2.64 eV [87]. This value is the minimum among all the cases of adding Al to the system. Adding an Al atom above 0.8, the band-gap reached its maximum value of 4.82 eV for the case where Al completely replaces Ni, as shown in Figure 9a. These results suggest that the energy band-gap of Ni 1−x Al x Co 2 O 4 remains largely unaltered (x < 0.8) with the Al 3+ substitution, which translates to the fact that the electrical conductivity of Ni 1−x Al x Co 2 O 4 could remain unaltered with the Al 3+ substitution below x = 0.8. In the absence of the contribution of electrical conductivity to the electrochemical performance of Ni 1−x Al x Co 2 O 4, at least for x < 0.8, it can be concluded that the electrochemical performance of Ni 1−x Al x Co 2 O 4 could be dictated by other factors, such as morphology, the oxidation potential of participating ions, active metal sites, and the internal resistance of the compound.
cates lower charge transfer resistance [81]. These variations of the EIS curve from semicircle towards higher frequencies and linearity towards lower frequencies relate to reversible Faradaic redox reaction and access of OH − ions into the pore of the electrode material. This behavior of the EIS curve describes the PCs properties of the prepared Ni1-xAlxCo2O4 nanostructure electrode [82]. The slope of the 45° portion of the curve is called Warburg resistance (Zw) and results from the frequency dependence of ion diffusion/transport in the electrolyte to the electrode surface [83,84]. The Nyquist plot is a vertical line for an ideal electrode material, and more is the vertical line represents better electrolyte diffusion and capacitive behavior [85]. Figure 8c shows that Rct is smaller for NiCo2O4 and has a more vertical line, which offers better rate capability.
First-principles density functional theory (DFT) calculations were performed using VASP 2 [34] (Vienna ab initio simulation package) with the projected augmented wave (PAW) [35] type pseudo-potential and the plane-wave basis set. The exchange and correlation part for the HSE calculations was described by hybrid functional [36] containing a 40% Hartree-Fock exchange. Here, we used a 4 × 4 × 2 k-points mesh centered at the Gamma point with a plane wave cutoff of 400 eV, which is enough for the self-consistent calculation. The global break condition for the electronic and ionic self-consistent (SC) loop was set to be 10 −4 eV and 10 −3 eV, respectively. In our calculation, we dealt with a cell containing 28 atoms as a total. The value of gaussian smearing was adjusted to be 0.20. Even though the ratio of x is 20% in the experiment, we chose 25% in the calculations because changing it to 20% would require a much larger supercell, which eventually increases the computing time and memory excessively. Figure 9a shows the side view along the x-axis of the crystal structure of Ni1-xAlxCo2O4, while Figure 9b shows the band-gap variation from 2.42 eV to 4.82 eV for the different values of x. For the system without Al atom, which is Ni1Co2O4, the band gap was found at 2.42 eV, which agrees with the previously reported experimental values of 2.06 eV [86] and 2.64 eV [87]. This value is the minimum among all the cases of adding Al to the system. Adding an Al atom above 0.8, the band-gap reached its maximum value of 4.82 eV for the case where Al completely replaces Ni, as shown in Figure 9a. These results suggest that the energy band-gap of Ni1-xAlxCo2O4 remains largely unaltered (x < 0.8) with the Al 3+ substitution, which translates to the fact that the electrical conductivity of Ni1-xAlxCo2O4 could remain unaltered with the Al 3+ substitution below x = 0.8. In the absence of the contribution of electrical conductivity to the electrochemical performance of Ni1-xAlxCo2O4, at least for x < 0.8, it can be concluded that the electrochemical performance of Ni1-xAlxCo2O4 could be dictated by other factors, such as morphology, the oxidation potential of participating ions, active metal sites, and the internal resistance of the compound.

Conclusions
Finally, a simple and cost-effective technique was developed to report the effect of Al 3+ doping on the structural and electrochemical performance of the NiCo 2 O 4 nanostructure. The experimental results revealed the dependence of surface area, specific capacitance, and electrochemical performance of NiCo 2 O 4 on Al 3+ content. The doped compound's overall electrochemical performance, viz. energy and power density, was observed to be significantly superior to other doped NiCo 2 O 4 compounds. The DFT calculation suggests that the energy band-gap of Ni 1−x Al x Co 2 O 4 (<0.8) remains largely invariant, and hence the electrical conductivity. Thus, the observed reduction in the specific capacitance of doped Ni 1−x Al x Co 2 O 4 could be attributed to the decrease in active redox sites with Al 3+ substitution. The study indicates that Al 3+ can be an excellent cost-effective substitution for expensive cobalt in NiCo 2 O 4 to provide the desired electrochemical performance. Hence, this work highlights the development of cheaper and more promising electrode doped materials without sacrificing the performance of NiCo 2 O 4 .