Aspectos laborales

The initial oxidation of a bare metal surface is generally understood to begin with the adsorption of O2 gas, which subsequently dissociates into adsorbed atomic oxygen (O

(ads)) [4-5]. The O (ads) atoms then covalently bond to adjacent metal atoms, weakening the attachment of the latter to the metal crystal. This is followed by the place exchange of a metal and an O2- ion at the metal/gas interface resulting in the formation of the first one or two monolayers of oxide (see Figure 1.1(a)). The formation of thin passive films beyond the place exchange process can be described using either inverse logarithmic, direct logarithmic or parabolic rate laws [4-10]. Typically, the logarithmic mechanisms best describe film formation at low temperature, while the parabolic law better models oxide growth at higher temperatures. The transition temperature from logarithmic growth to parabolic growth is ambiguous and dependent on the metal being oxidized.

The theory of inverse logarithmic kinetics was first suggested by Mott [6] and Mott and Cabrera [7]. They proposed that, at low temperatures oxidation was driven by the tunnelling of electrons from the metal to O (ads) species at the surface. This

tunnelling of electrons produces an electric field, in which ions are mobile, resulting in the thickening of the oxide with time (see Figure 1.1(b)). The potential across the oxide is assumed to be constant and as a result the strength of the field diminishes with time. Oxidation is terminated when the electric field is no longer strong enough to support ion migration. The integrated form of the inverse logarithmic rate equation is shown below [8]:

1 x =−

kT

qaVlnt+C

1.1

where x is the oxide thickness, k represents Boltzmann’s constant, T is the reaction temperature, q is the ionic charge, a is equal to half of the ion jump distance, V is the potential across the oxide, t is the exposure time, and C is a constant.

The inverse logarithmic theory was unable to accurately model the low

temperature oxidation of all metal surfaces. As a result, the direct logarithmic kinetic model was later proposed by Eley and Wilkinson [4]. As with the inverse logarithmic mechanism, oxidation is driven by ion migration in an electric field created by tunnelling electrons. In this model the electric field, not the potential, across the oxide film is assumed to be constant and oxide growth continues until the potential can no longer support ion migration. The direct logarithmic rate equation is presented below in its integrated form [4]:

x = RT

γ lnt+C'

1.2

where x represents the film thickness, R is the universal gas constant, T is the reaction temperature, γ is the observed increase in activation energy as the oxide film thickens, t is

the exposure time and C′ is a constant.

At elevated temperatures the oxidation of metal surfaces tends to follow parabolic kinetics as described by Wagner [7,11-13]. The Wagner model assumes that the oxide formed is compact and adherent, the reaction rate is controlled by either cation or anion diffusion through the film, thermodynamic equilibria are established at both the

metal/oxide and oxide/gas interfaces, thermodynamic equilibrium also exists throughout the film, and the oxide formed only deviates slightly from stoichiometry. For oxides in

which cations are the mobile species diffusion is driven along the metal chemical potential gradient across the film. Conversely, for oxides in which anion diffusion dominates, the driving force of the reaction is proportional to the O2 chemical potential

gradient. In both cases, as the film thickens, the rate of oxidation decreases until the reaction terminates. The full integrated parabolic kinetic rate equation is shown below [7,11-13]:

x = C”t1/2 1.3

where x represents the film thickness, C” is the parabolic rate constant and t is the exposure time. The parabolic rate constant is dependent on the volume of the oxide present per metal atom, the diffusion coefficient and the concentration of mobile species.

Metal oxides can generally be grouped into three different classes; p-type, n-type and amphoteric semi-conductors [13]. During the growth of a p-type oxide a small number of cation vacancies and electron holes are created within the oxide lattice (cation deficient). In p-type oxides the mobile species are cations, which migrate/diffuse through lattice defect sites such as vacancies and/or grain boundaries to the oxide/gas interface where they react with O2. In the case of NiO, defect formation involves the creation of a

Ni2+ vacancy at the oxide/gas interface and, in order to balance charge, two neighbouring Ni2+ atoms each lose an electron forming two Ni3+ (electron holes). Conversely, n-type oxides can be grouped into two classes. In the first class oxidation proceeds via the migration of free electrons and excess metal ions through interstitial lattice positions in the oxide, while in the second class film growth proceeds via the formation of anion vacancies (anion deficient) and anion migration. In the former case the oxide grows at

Figure 1.1: The mechanism for the oxidation of a metal (M) surface exposed to O2

gas. The initial place exchange reaction resulting in the first layers of oxide is shown in (a). The continuous growth of a film following logarithmic or parabolic kinetics beyond the place exchange process is shown in (b). The vacancies ( ) present within the film provide pathways for ion migration.

M

M

M

M

O

O

Metal

M

O

M

O

O

M

O

M

Metal

O

M

M

M

M

O

Metal

O

O

M

M

M

M

O

δ

δ

Metal

O

a) Place exchange model

O- _O- Metal Oxide Ions O- _O- Metal Oxide e-

the oxide/gas interface while in the latter case oxidation occurs at the metal/oxide

boundary. Some oxides such as Cr2O3 are known as amphoteric and will exhibit either p-

type or n-type characteristics depending on the reaction conditions. For example at low O2 pressures Cr2O3 behaves like a cation excess n-type semiconductor, while at higher O2

activities it exhibits p-type properties.

Oxide film growth on metal surfaces exposed to aqueous solutions is best described using the Point Defect Model (PDM) proposed by Macdonald et al. [14-15]. A simplified version of the PDM is presented in Figure 1.2 for a MO type oxide. This model is similar to the direct logarithmic mechanism proposed by Eley and Wilkinson [4], in which the electric field across the film is assumed to be constant. In simplified terms, film growth proceeds via the dissolution of metal cations (M2+→ M2+(aq)) at the oxide/solution

interface. This introduces cationic vacancies (VM2-) to the film similar to the p-type oxide

growth discussed earlier. These vacancies will migrate in the electric field towards the oxide/metal interface where they are filled with metal cations (M2+) produced at the metal surface. The oxidation of metal atoms at the metal surface introduces oxygen vacancies (VO2+) to the oxide which will diffuse towards the oxide/solution interface. At the

film/electrolyte boundary adsorbed H2O and/or dissolved O2 gas are reduced creating O2-

anions, destroying the anionic vacancies. In the PDM model the film behaves like an electronically doped semi-conductor due to the presence of the cationic and anionic vacancies. More recently, the PDM has been expanded by Bojinov et al. to include film properties such as capacitance, resistance, thickness and conductivity in the theoretical calculations [16-17]. The model of Bojinov et al. is termed the Mixed Conduction Model (MCM).

Figure 1.2: Simplified diagram of the PDM model showing the major cationic, anionic and vacancy species involved in the growth of an MO type oxide during reaction with a H2O molecule.

O2- M M2+ e- V_M2- V_O2+ V_M2- Metal Oxide M2+ Solution V_O2+ M2+ (aq)+ 2e- M M2+ e- Metal Oxide Solution V_M2- VM2- VO2+ Metal Oxide Solution VO2+ Metal Oxide Solution H2O + 2e-→O2-+ 2H+