Popov K.I., Djokic S.S., Grgur B.N. Fundamental Aspects of Electrometallurgy

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Chapter 2

and on the cathode (Cu)

According to the rule derived in the conclusion from section 2.3.1, on the

anode the oxygen evolution reaction will occur, and on the cathode copper

ions will be reduced to the metal phase, because the most positive catodic

reaction can be neglected due to the low oxygen concentration in the

electrolyte solution. Hence the reaction:

will take place at the anode and the reaction

at the cathode.

Obviously, the minimum external cell voltage for electrolysis to occur in

this case is 0.893 V.

The overall reaction in the cell is

It follows from the Eq. 2.14 that in a cell with an insoluble anode the

concentration of depositing ions decreases and the hydrogen ion concentra-

tion increases during electrolysis.

2. Definitions, Principles and Concepts

The mechanism of the extraction of metals from ionic solutions and the

essenc

of the electrowinning process are well explained by Eq. 2.14.

2.3.3

A cell with a soluble anode

In the cell:

the following reactions are possible on the anode (Cu):

and on the cathode (Au):

Hence, the reaction

occurs on the anode, and

at the cathode, and so the composition of the electrolyte solution remains

constant if the anode is made of pure copper and oxygen is removed from

the solution. The lowest cell voltage at which electrolysis can start in this

cell is zero.

Chapter 2

It is obvious that electrorefining processes are based on electrolysis in

cells with soluble anodes.

2.3.4

Current efficiency

Metal deposition can be accompanied by any other cathodic reaction,

most frequently hydrogen evolution.

This leads to the situation in which metal is deposited but metal

deposition uses only a part, of the total current, I, through the cell. The

current efficiency

indicates which part of the total current is used for the deposition of metals.

It is a very important parameter of an electrodeposition process

2.3.5

Faraday’s law

Faraday’s law relates the quantity of electricity passed through the cell

and the quantity of chemical substances which react on the electrodes. It

states that the mass of metal, m, electrodeposited on the cathode is given by

where / is the total current, t is the deposition time, M is the molar mass of

the deposited metal, is the current efficiency and nF is the number of

Faradays per mole of consumed ions. It follows from Eq. 2.16 that can be

easily determined by measuring the electrodeposited mass of metals and

supplied quantity of electricity

1,2

2.3.6

The current density – overpotential relationships

2.3.6.1 Basic equations

The most complete discussion of the current density – overpotential

relationship was given by Bockris

. The approach suitable for use in metal

electrodeposition will be given here.

The general form of current density – overpotential relationship in

electrodeposition of metals for the reaction

2. Definitions, Principles and Concepts

taking cathodic current density and overpotential as positive, is given by

where is the exchange current density and is the activity of the oxidized

(O) or reduced (R) state at a current density j and is the activity in the

equilibrium state.

On the other hand

and

where and are the cathodic and anodic transfer coefficient, and

corresponding Tafel slopes and is the overpotential and

and

The ratio of the activities for the cathodic reaction may be written as:

where is the limiting diffusion current density and for the reverse anodic

reaction as:

Chapter 2

taking into account the Kelvin term which becomes appreciable at low values

of electrode radii

. In Eq. 2.23 is the surface energy, V is the molar volume of

the electrodeposited metal and is the radius of the electrode. Eq. 2.23 is

valid for two electron reactions

, other possibilities are discussed in Ref. 7.

For a spherical electrode Eq. 2.17 can be written as:

where

where is the bulk concentration and D diffusivity coefficient of a

depositing ions.

A somewhat modified Eq 2.25 is necessary for an understanding of

electrodeposition on the tip of dendrites inside the diffusion layer of a

macroelectrode, especially in the case of electrodeposition at a periodically

changing rate

7-9

For sufficiently large to make surface energy term negligible Eq. 2.25

can be rewritten in the form:

For a sheet electrodes and sufficiently large spherical electrodes Eq. 2.25

becomes:

2. Definitions, Principles and Concepts

where

and is the diffusion layer thickness

2.3.6.2 Some approximations

Equation 2.27 is valid generally but it is more convenient to use some

approximative relations derived from them, so for flat surface if

Eq. 2.28 can be rewritten in the form:

which becomes

at very low overpotentials by expanding the exponential terms in Eq. 2.31

and retaining the two terms of expansion of each exponential terms, if

and

where is a the symmetry factor.

When

the relation:

Chapter 2

is valid.

For

Eq. 2.28 can be rewritten in the form:

which is valid if Eqs. 2.33 and 2.34 are valid and finally, if

Eq. 2.39 becomes

The range of validity of Eqs. 2.31 and 2.32, 2.36 and 2.37 and 2.38 and

2.39 and 2.43 can be easily determined from and plots. The

equations 2.36 and 2.37 are valid from the beginning to the end of Tafel

linearity (Tafel line). At lower overpotentials, Eqs. 2.31, and 2.32 are valid

If Eq. 2.28 becomes:

2. Definitions, Principles and Concepts

and at higher ones, Eq. 2.38, 2.39 and 2.43. In the Fig. 2.5 the simulated

polarization curve for cathodic metal electrodeposition together with the

Tafel plot and the range of validity of mentioned equations are shown.

Usually, in electrochemistry the marked regions are called: 1 and 2-

activation controlled region, 3- mixed activation-diffusion controlled region,

4- pure diffusion controlled region.

2.3.7

The cell voltage

It is to be noted that the difference of cathodic and anodic overpotentials

is the sum of their absolute values. Hence, if anode overpotential is

considered in the anode Tafel region the absolute values of overpotentrials

and current density should be used, and equation

is valid.

There are not mass transport limitations in anodic dissolution of metals

and there is not equation analoguous to Eq. 2.39.

20 Chapter 2

It is now possible to define the cell potential in electrolysis. The cell

voltage U of a driven electrochemical cell is given by:

where E is the equilibrium potential difference between the anode and the

cathode, and are the absolute values of the anodic and cathodic over-

potentials respectively,

is the current, and is the sum of the Ohmic

resistance of the electrolyte, electrodes, contacts and connecting wires.

2.3.8

Specific energy consumption

The electrical work W required to deposit a quantity m of metal on the

cathode is given by:

On the other hand, the quantity of deposited metal and the required

quantity of electricity for deposition are related by the equation:

By combining Eq. 2.16 with Eq. 2.46, the specific energy consumption,

w, is then given by:

The specific energy consumption, w, is the most important energetic

parameter in metal electrowinning and electrorefining technologies.

2.4

SOME ASPECTS OF

ELECTROCRYSTALLIZATION

Figure 2.6 shows the originally published in-situ STM images of copper

clusters which were formed during electrodeposition on Au(111) substrate

The top image shows the gold substrate at a potential positive of the

Nernst potential for bulk copper deposition. This area of the surface is

2. Definitions, Principles and Concepts

characterised by two atomically smooth terraces separated by a monoatomic

high step edge. Upon stepping the electrode potential to a value negative of

the Nernst potential, distinctive copper clusters form at the step edges. By

contrast, the terraces in Fig 2.6b remain free from copper clusters. The

clusters are seen to grow from Fig. 2.6b to the subsequent image 2.6c. These

STM images are a visual verification of the important role which defects can

play in the initial stages of electrocrystallization. Clearly, they are in good

accordance with the textbook model of Kossel and Stranski

3,10

. Nucleation

occurs preferentially at the step edges, where an ad-atom is more high

coordinated with the surface than an ad-atom on the atomically flat surfaces.

The energetics of copper nucleation on flat gold terraces are clearly less

favorable, occurring only at longer times or higher overpotentials

Hence, the monoatomic high step edges, the microsteps, are required for

continuos metal electrocrystalization. Possible sources of microsteps on a sur-

face are shown in Figs. 2.7 and 2.8, i.e. the low-index planes, two dimensional

nuclei, emergent screw dislocations and indestructible reentrant groves.

7,11