*2.4. Pulse Reversal Current Electrodeposition*

There are nine waveform parameters that can be used to represent the waveform characteristics according to the definition of bidirectional pulse parameters: (i) forward conduction time *tc*, (ii) reverse conduction time *td*, (iii) forward peak current density *Ip*+, (iv) reverse peak current density *Ip*−, (v) average current density *Iav*, (vi) pulse period *T*, (vii) reverse current coefficient *x*, (viii) duty cycle λ, and (ix) frequency *f* [42]. The nine parameters are interrelated and they do not change independently. Where average current density *Iav*, duty cycle λ, reverse pulse coefficient *x*, and frequency *f* are considered as the independent variables, the parameters can be related mathematically, as shown in Equations (4)–(12) [43]:

$$I\_{p+} = \frac{I\_{av}}{\mathbf{x}\lambda + \lambda - \mathbf{x}}\tag{4}$$

$$I\_{\mathbb{P}^-} = \mathbb{x}I\_{\mathbb{P}^+} \tag{5}$$

$$t\_{\mathcal{E}} = \lambda T = \frac{\lambda}{f} \tag{6}$$

$$t\_d = T - t\_c = \frac{1 - \lambda}{f} \tag{7}$$

$$T = t\_c + t\_d \tag{8}$$

$$I\_{av} = \frac{\mathbf{t}\_{\mathcal{E}} \ I\_{p+} - \mathbf{t}\_{\mathcal{E}} \ I\_{p-}}{T} \tag{9}$$

$$
\lambda = \frac{t\_c}{t\_d} \tag{10}
$$

$$\mathbf{x} = \frac{I\_{\text{p-}}}{I\_{\text{p+}}} \tag{11}$$

$$f = \frac{1}{T} \tag{12}$$

Figure <sup>2</sup> shows the schematic diagram of a typical pulse-current wave form when *Iav* <sup>=</sup> 15 A·dm2, λ = 0.5, *x* = 0.5, and *f* = 10 Hz.

**Figure 2.** Schematic diagram of pulse waveform when *Iav* <sup>=</sup> 15 A·dm2, <sup>λ</sup> <sup>=</sup> 0.5, *<sup>x</sup>* <sup>=</sup> 0.5, and *<sup>f</sup>* <sup>=</sup> 10 Hz.

Pulse reversal current (PRC) electrodeposition has been used over the years owing to its unique ability to enhance nanoparticle incorporation in electrodeposited composite coatings, with the highest reported content being 23 wt% [44–46]. Ni–Co coatings produced using the PRC synthesis technique have been reported to exhibit higher hardness, better anti-wear properties, more compact surfaces, lower residual macro stress and better compact surfaces than those produced using DC and PC electrodeposition techniques [6,40]. In particular, the hardness improvement has been attributed to increased distribution of nanoparticles in the deposited Ni–Co matrix. As for lower residual macro stress, PRC deposits are characterized by uniform coatings since the technique hinders thickening of the corners and edges, as is common with DC electrodeposition. It can also be postulated that adsorption of H atoms by the deposited coatings is suppressed by pulse intervals and reversal current in PRC technique [40]. PRC deposited Ni–Co nanocomposite coatings possess smoother surfaces, finer Ni matrix crystals, and smaller grain sizes compared to DC technique deposited coatings [40].

The smooth surfaces coupled with high hardness increase the load-carrying capacity of Ni–Co nanocomposite coatings and thereby improves their wear resistance properties. The lower macro-residual stress also plays a great part in wear resistance, where it causes lower brittleness and higher toughness in the coatings, and this decreases the rate of nanoparticle flaking and metal matrix peeling during wear testing [40]. PRC technique can be used in ultrasonic power conditions and this presents desirable effects on deposited Ni–Co coatings [47,48]. Overall, it presents several advantageous effects on the electrochemical process:


It has been reported that Ni–Co nanocomposite coatings electrodeposited using the PRC technique subject to ultrasonic conditions present finer grained, compact, and uniform coatings [6].

#### **3. Electrodeposition Parameters for Ni–Co Alloys**
