Electric Conduction in crystalline oxides

The Oxyde S Cristal flaxes, when they are stoechiometric, are electric Isolant S: they can be described like ic crystals quasi Ion (close relations of the salt S), the loads are related to the atoms and are not mobile. The electric insulating are besides frequently Céramique S or Verre S (let us note however that ceramics all is not of oxides, and that glasses are solid but amorphous oxides).

However, the variations with stoichiometry give rise to specific defects which allow an electric conduction.

; Prérequis

to read the articles

* Crystallography

* specific Defect ;

* Notation of Kröger and Vink ;

* Diffusion ;

* Law of Ohm .

Ionic and electronic conductivity

The electric current can result from the movement of two types of loads:

the Ion S (Anion S and Cation S): the migration of the ions involves the displacement of the associated load;
electronic loads: free electrons and holes of electron.

The displacement of the ions can be done in two manners:

is the ions slip between the “fixed” ions of the network, one speaks about “interstitial” movement;
is it exists a gap in network (a missing ion), an ion of the network can then “jump” in the empty position; one speaks about “lacunar” movement.

The transported load is not the load of the ion itself, but the difference between the load of the ion and the load which one would have if the network were perfect at this place, which one calls the “effective load”.

For example: in Al₂O₃ alumina, the ion aluminum in the network has a load 3+; the “natural” load of an aluminum site is thus 3+. So now the site is occupied by an ion of iron Fe²⁺ in substitution, then the site is in deficit of positive load; its effective load is thus -1. In the Notation of Kröger and Vink, one notes this “Fe_Al'”. Thus, a displacement of the positive ion Fe^{2+ corresponds in fact to the displacement of a negative charge in the network.}

An interstitial position is empty in a perfect crystal, its “natural” load is thus null. In this case, the effective load of the site is the real load of the species which occupies it.

A free electron or a hole of electron is considered in interstitial position. Their displacement follows a traditional Loi of Ohm. They can however be captured by an ion and modify the local load, for example:

M_M + e' → M_M'

they move then with the ion.

The displacement of the ions can be the only fact of thermal agitation; one speaks then about “diffusion”, the generated electric current being a consequence of this migration. But displacement can also be created by

a chemical Gradient of Potentiel;
a Potential gradient of electrostatic (tension).

Variation with stoichiometry

Let us consider an element M, and this element M_NO₂ oxidizes it. One can describe it like a salt

(M^{Z +}_N, O^2-₂).

The variation with stoichiometry can come from two factors: thermodynamic balance with the atmosphere and the doping.

Thermodynamic balance with the atmosphere

The oxide and the reduced element are in balance following the reaction of Oxydation

N M + O₂ ↔ M_NO₂

according to the Pressure partial of Dioxygène and the temperature, balance moves on a side or other. Under the conditions where the oxide is stable, one will have variations with stoichiometry, the formula of becoming oxide:

M_n-xO₂ : the oxide is known as “overdrawn in cation”;
M_n+xO₂ : the oxide is known as “surplus in cation”;
M_NO_{2- there}: the oxide is known as “overdrawn in anion”;
M_NO_{2+ there}: the oxide is known as “surplus in anion”.

Doping

The oxide can contain foreign elements. These elements can be:

of the impurities, introduced involuntarily into the present or manufactoring process in the natural product;
of the voluntary additions to modify the oxide reaction of.

These impurities can slip between the ions of the network, they are then known as “interstitial”, or peeuvent to replace atoms of the network, they are then known as “in substitution”.

The doping elements can introduce a nonnull effective load. This creation of load will allow an electric conductivity, either in ionic form, or in electronic form, by collecting electrons of other sites (thus creating holes of electron), or in “emitting” free electrons.

Laws phenomenologic of conduction

If one subjects oxide to an electric tension, the nonnull relative loads are put moving. By doing this, that creates a gradient of concentration, that the diffusion tends to level. If there is a stationary mode, one can describe this movement in a total way - statistics - by the Loi of Nernst-Einstein:

v_i = \ frac {D_i F_i} {kT}

where

v_i is the mean velocity of the species I considered;
D_i is the Coefficient of diffusion of this species I in the crystal;
F_i is the electrostatic Force to which the species I is subjected;
K is the Boltzmann constant;
T is the absolute Température.

This law is similar to a fluid Frottement (effect Parachute): speed, in stationary mode, is proportional to the force.

One can thus connect the electric Conductivité local σ_I due to the species I with the coefficient of diffusion:

\ sigma_i = \ frac {D_i z_i^2e^2 c_i} {kT}

where

z_i is the effective load of the species I (many loads);
E is the Elementary charge;
c_i is the concentration of the species I at the place considered.

Total electric conductivity σ is the sum of electric conductivities for each species:

σ = ∑_I σ_I

See too

Internal bonds

Corrosion at high temperature

Theory of the kinetics of oxidation of Semiconductor Wagner

Random links: