Non stoichiometric surfaces: stability and thermodynamics

Scientific problem

We consider an oxide of chemical formula AmOn, in chemical equilibrium with an atmosphere containing O₂, H₂ or H₂O, the oxide slab contains N_A metal atoms at chemical potential µ_A, N_O oxygen atoms at chemical potential µ_O and N_H hydrogen atoms at chemical potential µ_H.

We can defines the surface excesses in oxygen and hydrogen

The surface enery (slab geometry, hence TWO surfaces) can be written as

As we try to simulate a real surface, i.e in equilibrium with its bulk, we have to take into account the following constraint

Some manipulations and approximations later leads to

This last equation forms the basis of the methodology. The surface free energy is a function of both oxygen and hydrogen chemical potentials (things are a bit more complicated in presence of water, but not fudamentally different).

Surfaces with different stoichiometry, and hence differrent excesses, will have different chemical potential dependencies. Therefore, the most stable surface will depend on the chemical potentials conditions. These in turn depend on the temperature and partial pressures (through the ideal gas approximation)

Non stoichiometric surfaces and Grid Computing

The sampling of a large number of surfaces is well adapted to high-throughput approaches as each surface is fully independant. It is only at the processing stage (here phase diagram drawing) that the information is collected together.

Examples

As a first example, we look at he phase diagram of the basal surface of alumina. Despite having simulated 18 different stoichiometries, only two appear to be stable under a realistic range of chemical potentials. In effect, in presence of a lot of water, the surface O saturate their electronic layer by bonding with an H as do the surface Al, but with an OH. No different oxydation states for Al are observed (as in the case of Ce₂O₃ for instance)

Fig. 1: Alumina (0001) surface

Tthe reference chemical potentials need not to be limited to oxygen or hydrogen, as can be seen on this preliminary investigation of a much more relevent mineral, CaCo3. This phase diagram is much richer than for alumina. Depending on the temperature and partial pressures of Co2 and H2O, many different stoichiometry become stable. (It is not the aim of this page to dicsuss the details of this study, actually performed by a colleague not linked to the eMinerals group, but using our tools.)

Fig. 2: Calcite (104) surface

Credits

This work was carried out by Arnaud Marmier and Steve Parker (Bath).