Environment from the Molecular Level
A NERC eScience testbed project
Non stoichiometric surfaces: stability and thermodynamics
We consider an oxide of chemical formula AmOn, in chemical equilibrium with an atmosphere containing O2, H2 or H2O, the oxide slab contains NA metal atoms at chemical potential µA, NO oxygen atoms at chemical potential µO and NH hydrogen atoms at chemical potential µH.
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.
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
This work was carried out by Arnaud Marmier and Steve Parker (Bath).