**3.2. Co-deposition of particles on metal surface**

crystalline structure, micro-hardness and frictional behavior. The result obtained indicated that co-deposited lubricant particles strongly influenced the composite Ni-W coating proper‐ ties. As the MoS2 concentration in the coating increases, both the tungsten content and the coating micro-hardness decrease while the average grain size increases. With low MoS2 content, result showed lesser friction coefficients and similar micro-hardness. Therefore, there is a solid lubricant concentration regime where co-deposition of MoS2 particles into Ni-W nanostructure alloys improves the frictional characteristics of the coating with a consistently

Sangeetha used direct current and pulse current methods to incorporate polytetrafluoroethy‐ lene (PTFE) polymer to an optimized Ni-W-BN nano -composite coating deposited on a mild steel substrate [14]. It was observed that the co-deposition of PTFE solid lubricant particles on the Ni-W-BN nano-composite coating resulted in a moderately smooth surface, greater microhardness, a lower friction coefficient, excellent water repellency and enhanced corrosion resistance. The pulse current technique showed enhanced performance over the direct current

Composite coatings have been successfully used to overcome high temperature corrosion, oxidation and wear in many ground breaking applications. Nickel coatings with 8-10 volume % of silicon carbide are used to increase the life of internal combustion engine cylinder bores and in portable chain saws. Composite coatings based on chromium carbide in a cobalt matrix are used as wear-resistant coatings in gas turbines, where they are required to perform for

are used in piston rings for diesel engines. Single crystal diamonds locked into a nickel matrix

Co-deposition is a process of incorporating fine particles of metallic, non-metallic compounds, or polymers from an electrolytic or an electroless bath in the electroplated layer to improve material properties such as: hardness, wear-resistance, corrosion-resistance, tribological

Co-deposition of particles into metal deposit is governed by physical dispersion of parti‐ cles in the electrolyte and electrophoretic migration of particles [33]. Among different models presented for co-deposition mechanism of solid particles into a metal matrix, Guglielmi's model is the most adopted one. It has also been examined with different co-deposition systems such as: Ni−SiC, Ni−TiO2, Ni- Al2O3, Cu- Al2O3, Cr-C, Zn-Ni particles, Co-SiC, and

form the cutting-edge in tools such as chainsaws, grinding disks or dental drills [31].

C. Chromium deposits with alumina inclusions

lower friction coefficient.

48 Electrodeposition of Composite Materials

coating due to uniform and smaller grain deposits.

**2.2. Applications of composite coatings**

extended periods at temperatures of up to 8000

**3. Mechanisms of co-deposition process**

control, lubrication, tensile, and fracture strength [32].

**3.1. Definition of Co-deposition process**

Ni-MoS2 [33, 34]

One of the common mechanisms of co-deposition process consists of five consecutive steps:


**Fig. 4: The processes involved in co‐electro‐deposition of insoluble particles into a growing metal matrix to form a composite metal coating Figure 4.** The processes involved in co-electro-deposition of insoluble particles into a growing metal matrix to form a composite metal coating

#### **3.3. Description of Guglielmi's model**

are as follows: 

surface. 

16

Guglielmi established in his findings that concentration of bath particles affects the rate at which an electro-deposit gets incorporated on metal. He therefore quantified the rate of particle incorporation as a function of current density. Guglielmi based his model on the similarity between the experimental co-deposition and Langmuir isotherm curves. Assumptions of Langmuir are as follows:


between the experimental co‐deposition and Langmuir isotherm curves. Assumptions of Langmuir 

 The surface of the adsorbant (cathode) is in contact with a solution (electrolytic bath) containing adsorbate (second phase nanoparticles) which is strongly attracted to the  Using co-deposition of Ni-Al system as a case study [27], the mathematical equations deduced by Guglielmi's model are governed by the following parameters and equations:

*α -* Volume fraction of particles in the deposit; *C* - concentration of particles in the plating bath;

*W*- Relative atomic mass of metal; *n*- Valence of deposited metal; *F*- Faraday's constant; *d* - Density of deposited metal; *v*0 - Constant for particle deposition; *A* and *B* are constant for metal deposition and particle deposition; *k*– Adsorption coefficient; *J <sup>o</sup>* - Exchange current density of deposited metal; *η* - over-potential; *θ*- Surface coverage of embedded particles.

$$\frac{\alpha}{1-\alpha} = \frac{nFdv\_0}{Wl\_0} \exp\left[\left(A-B\right)\eta\right] \cdot \frac{kC}{1+kC} \tag{1}$$

Divide through by C: *<sup>α</sup> <sup>C</sup>*(1 <sup>−</sup> *<sup>α</sup>*) <sup>=</sup> *nFd <sup>v</sup>*<sup>0</sup> *<sup>W</sup> <sup>J</sup>* <sup>0</sup> exp (*A*<sup>−</sup> *<sup>B</sup>*)*<sup>η</sup>* <sup>⋅</sup> *<sup>k</sup>* 1 + *kC*

Multiply through by (1−*α*) ( *B <sup>A</sup>* <sup>−</sup>1) :

$$\frac{a}{C\left(1-\alpha\right)^{\left(2-\frac{B}{A}\right)}} = \frac{nFdv\_0}{Wl\_0} \exp\left[\left(A-B\right)\eta\right] \cdot \frac{k}{1+kC} \left(1-\alpha\right)^{\left(\frac{B}{A}-1\right)}$$

Take the reciprocal of each term:

$$\frac{C(1-a)^{\left(2-\frac{B}{A}\right)}}{a} = \frac{Wl\_0}{nFd v\_0} \exp\left[\left(B-A\right)\eta\right] \cdot \left(\frac{1+kC}{k}\right) (1-a)^{\left(1-\frac{B}{A}\right)}$$

Rearrange the terms on the right:

$$\frac{\mathbb{C}\left(1-\alpha\right)^{\left(2-\frac{B}{A}\right)}}{\alpha} = \frac{\mathsf{W}\mathsf{I}\_{0}^{\frac{B}{A}}}{nFdv\_{0}} J\_{0}^{\left(1-\frac{B}{A}\right)} \cdot \left(\frac{1}{k} + \mathsf{C}\right) \cdot \left\{ \exp\left[ \left(B-A\right)\eta \right] \cdot \left(1-\alpha\right)^{\left(1-\frac{B}{A}\right)} \right\} \tag{2}$$

Assuming:

$$\exp\left[\left(B-A\right)\eta\right]\cdot\left(1-\alpha\right)^{\left(1-\frac{B}{A}\right)}=1 \quad or \quad \exp\left[\left(A-B\right)\eta\right]=\left(1-\alpha\right)^{\left(1-\frac{B}{A}\right)}.$$

Then

Parametric Variables in Electro-deposition of Composite Coatings http://dx.doi.org/10.5772/62010 51

$$\frac{\mathcal{K}\left(1-\alpha\right)^{\left(2-\frac{B}{A}\right)}}{\alpha} = \frac{\mathcal{W}I\_0^{-\frac{B}{A}}}{nFd\upsilon\_0} J\_0^{\left(1-\frac{B}{A}\right)} \cdot \left(\frac{1}{k} + \mathcal{C}\right) \tag{3}$$

Expand the bracket on the right to get

Using co-deposition of Ni-Al system as a case study [27], the mathematical equations deduced

*α -* Volume fraction of particles in the deposit; *C* - concentration of particles in the plating bath;

*W*- Relative atomic mass of metal; *n*- Valence of deposited metal; *F*- Faraday's constant; *d* - Density of deposited metal; *v*0 - Constant for particle deposition; *A* and *B* are constant for metal deposition and particle deposition; *k*– Adsorption coefficient; *J <sup>o</sup>* - Exchange current density of

by Guglielmi's model are governed by the following parameters and equations:

deposited metal; *η* - over-potential; *θ*- Surface coverage of embedded particles.

0 exp 1 1

<sup>2</sup> <sup>0</sup>

*B A*

ç ÷ - è ø

a

Divide through by C: *<sup>α</sup>*

50 Electrodeposition of Composite Materials

Multiply through by (1−*α*)

Take the reciprocal of each term:

Rearrange the terms on the right:

a

æ ö

a

Assuming:

Then

a

*<sup>C</sup>*(1 <sup>−</sup> *<sup>α</sup>*) <sup>=</sup> *nFd <sup>v</sup>*<sup>0</sup>

( *B <sup>A</sup>* <sup>−</sup>1) :

( )

a

a

2

1 1

*B A* h

a

a

*B*

0 0

*<sup>C</sup> WJ J C BA nFdv k*

 a

æ ö

( ) <sup>0</sup>

= -× é ù

*<sup>W</sup> <sup>J</sup>* <sup>0</sup> exp (*A*<sup>−</sup> *<sup>B</sup>*)*<sup>η</sup>* <sup>⋅</sup> *<sup>k</sup>*

<sup>1</sup> <sup>1</sup>

0 (1 ) 1

( ) ( ) ( ) <sup>2</sup> <sup>1</sup> <sup>1</sup> <sup>0</sup>

*WJ kC <sup>C</sup>*

ë û <sup>+</sup> -

*nFdv kC A B WJ kC*

h

1 + *kC*

( ) ( ) <sup>1</sup> <sup>0</sup>

( ) ( )

è ø

exp 1

h

h

*B B*

*A A or A B*

<sup>1</sup> <sup>0</sup>

exp 1

ë û ç ÷

h

*A B*

ç ÷ - è ø æ ö ç ÷ - è ø - + æ ö = -× - é ù

*<sup>A</sup> <sup>C</sup> WJ kC B A nFdv k*

*<sup>B</sup> <sup>B</sup> <sup>B</sup> <sup>A</sup> <sup>A</sup> <sup>B</sup> <sup>A</sup> <sup>A</sup>*

( ) ( ) ( ) ( ) 1 1

æ ö æ ö ç ÷ - - ç ÷ é ù - ×- = è ø é ù - =- è ø ë û ë û

exp 1 1 exp 1

ç ÷ - æ ö - æ ö è ø ç ÷ ç ÷ - è ø è ø - æ ö ì ü ï ï = × + × - ×- é ù ç ÷ í ý ë û è ø ï ï î þ

*B A*

æ ö

 a

> a

 a

> a

(2)

exp 1

ç ÷ - è ø æ ö

= -× - é ù

h

*nFdv <sup>k</sup> A B*

ë û - + (1)

$$\frac{C\left(1-\alpha\right)^{\left(2-\frac{B}{A}\right)}}{\alpha} = \frac{\mathsf{WJ}\_{0}^{\frac{B}{A}}}{nFd\upsilon\_{0}}J\_{0}^{\left(1-\frac{B}{A}\right)}\left(\frac{1}{k}\right) + \frac{\mathsf{WJ}\_{0}^{\frac{B}{A}}}{nFd\upsilon\_{0}}J\_{0}^{\left(1-\frac{B}{A}\right)}\mathsf{C}$$

Compare with *y* =*mx* + *d*, the equation of a straight line. Where *m* is the slope (also written as *tanφ*), and *d* the intercept:

$$\underbrace{C\left(1-\alpha\right)^{\left(2-\frac{B}{A}\right)}}\_{\text{y}} = \underbrace{\mathcal{W}l\_{0}^{\frac{B}{A}}}\_{\text{u}Fdv\_{0}}J\_{0}^{\left(1-\frac{B}{A}\right)}\left(\frac{1}{k}\right) + \underbrace{\mathcal{W}l\_{0}^{\frac{B}{A}}}\_{\text{u}Fdv\_{0}}J\_{0}^{\left(1-\frac{B}{A}\right)}\underbrace{\mathcal{G}}\_{\text{x}}$$

Thus the slope is simply the coefficient of *C*. ie

$$slope = m = \tan \varphi = \frac{\mathcal{W} \mathcal{J}\_0^{\frac{B}{A}}}{nFd\upsilon\_0} J\_0^{\left(1 - \frac{B}{A}\right)} \tag{4}$$

Equation (5) follows quickly from the logarithm law lg(*PQ <sup>R</sup>*)=lg*P* + *R*lg*Q*.

$$\log\left(\tan\varphi\right) = \log\frac{Wl\_0^{\frac{B}{A}}}{nFd\upsilon\_0} + \left(1 - \frac{B}{A}\right)\lg J\_0 \tag{5}$$

where the slope is giving as (1<sup>−</sup> *<sup>B</sup> <sup>A</sup>* ). The ratio *<sup>B</sup> <sup>A</sup>* of the slope can be pre-determined for fitting the experimental data. This ratio is obtained in the following way:

For coatings produced with different current densities, the plot of *C*(1−*α*) 2− *B <sup>A</sup>* against *C* presents a series of straight lines. The selected *<sup>B</sup> <sup>A</sup>* ratio must converge these lines towards the same point on the *C* –axis i.e., ( *C* = <sup>−</sup> <sup>1</sup> *K* )

The logarithm of slopes of lines lg(tan*φ*) obtained from the graph of *C*(1−*α*) 2− *B <sup>A</sup>* versus *C* plotted against log*J*, i.e., lg(tan*φ*) versus log*J* lies on a straight line. According to Equation (5), the slope of this line is equal to (1<sup>−</sup> *<sup>B</sup> <sup>A</sup>* ). The obtained *<sup>B</sup> <sup>A</sup>* ratio should be equal to the selected one.  

**Figure 5**

**5a and 5b:**

where th experim For coat presents point on The loga plotted a

he slope is g ental data. T tings produ s a series of n the � �axis arithm of sl against ���

giving as �� This ratio is uced with f straight lin s i.e., � � � �

� � � � �. The s obtained in different c nes. The sele

�� �� � nes ������ � �� ��versu o�� � � � �. Th

lopes of lin �**,** i.e., �����

 

**Graphical**

 

ratio � � of th

n the follow urrent den ected � � ratio

he slope can wing way: nsities, the o must conv

n be pre‐det

termined fo

or fitting the

� against � rds the same

ee), 

� �� versus � quation (5) ected one. 

�������� �� lines towar

��������� ording to E l to the sele

**of Ni‐Al co**

**o‐deposition**

**n**

plot of �� verge these 

graph of � ht line. Acc uld be equa

d from the on a straig

 ratio shou

**perimental d**

**deductions**

� �

�� obtained us ��� � lies he obtained

**system**

**representat**

In Fig. 5( is clear toward intersect (a), the exp that experi the same tion with *C* erimental r imental dat point on t *‐*axis is eq results cons ta can be w the �‐axis. qual to −0 idering the well‐fitted o From extra .62. This m � � ratio equ on a series apolation o makes it po ual to 0.24, h of straight of these lin ossible to have been p lines, whic nes, the��� obtain the presented. I ch converge �� point o adsorption t eof nee**Figure 5.** Graphical representation of experimental deductions of Ni-Al co-deposition system In Fig. 5(a), the experimental results considering the *<sup>B</sup> <sup>A</sup>* ratio equal to 0.24, have been presented. It is clear that experimental data can be well-fitted on a series of straight lines, which converge toward the same point on the *C* -axis. From extrapolation of these lines, the <sup>−</sup> <sup>1</sup> *<sup>K</sup>* point of intersection with *C-*axis is equal to −0.62. This makes it possible to obtain the adsorption coefficient value of K.

**tion of exp**

coefficie In Fig. 5 slope of nt value of (b), the log f this line i K. arithm of th s 0.76 and he slopes of so the � � r f the straigh atio is 0.24 ht lines ��� 4. This valu ��� �� is p ue is exactl plotted again ly equal to nst �� � . The the � � value In Fig. 5(b), the logarithm of the slopes of the straight lines lg(tan*φ*) is plotted against lg*J* . The slope of this line is 0.76 and so the *<sup>B</sup> A* ratio is 0.24. This value is exactly equal to the *<sup>B</sup> A* value considered previously for initial curve fitting. Hence, the co-deposition behavior of Ni −Al system is in good agreement with the Guglielmi's model.

19 Composite electroplating is a two-step process according to Guglielmi's model. At first, solid particles during electro-deposition are surrounded with cloud of adsorbed ions, which are weakly adsorbed at cathode surface by van der waals forces. In the second step, the loosely adsorbed particles become strongly adsorbed onto cathode surface by Coulomb force and consequently entrapped within metal matrix. The main drawback of this model is absence of mass transfer effect during electro-deposition process such as the adsorption of ionic species on the particle surface, the nature of particle, the ions to be reduced, the bath components, and the hydrodynamic conditions.

Bonino et., al. in their model uses statistical approach that Gugliemi neglected [35]. The model describes the amount of particles that are likely to be incorporated at a given current density. Mass transport of particles is proportional to the mass transport of ions on the working electrode. Volume ratio of particles in the metal deposit will increase under charge transfer control and decrease under mass transport control.

A widely accepted model is developed by Kurozaki, which includes the transport of solid particles from the solution to the cathode surface by agitation. This model is developed in the following steps:


Particles dispersed in the electrolyte bath are in constant Brownian motion. Whether the particles approach one another, their separation or agglomeration mainly depends on the existing energies between those particles. When attraction energy is larger than repulsion energy, particle agglomeration occurs and when repulsion energy is higher than attraction energy, particle separation occurs. The condition and nature of the system mainly determines the magnitude of net force for the production of agglomerated structures. Therefore, knowl‐ edge of interfacial region attraction is very important in understanding dispersion stability of solid particles with electrolyte.
