1)      The VO2(B) structure was built in Materials Studio with the following parameters and atomic positions: a = 12.03 Å, b = 3.693 Å, c = 6.42 Å, and β = 106.6°, and the space group is C2/m.

2)      A supercell measuring A1, B2, and C1 was then constructed.

The supercell measures 12.090 x 7.404 x 6.433 Å (β = 106.6°). CASTEP Energy analysis is run on this cell (bulk).

3)      The supercell was then cleaved at the (010) using the ‘Cleave Surface Tool’.

The cell used has a u-vector, which spans the distance from the origin to the point A, with length 6.433 Ǻ (001). The cell is also defined by a v-vector, which is from the origin to the point B, its length is 11.963 Ǻ (101). The vectors u and v are separated by an angle γ = 75.58°.  

4)      After cleaving the plane, a vacuum slab of thickness 10 Angstroms was added in the B-direction.

5)      The CASTEP Calculation was then run, with constraints, according to the following input parameters:

In these calculations, 2 k-points were used. Cut off energy was 300 eV. After finding the energies of the bulk and surface, the surface formation energy can be calculated. The surface formation energy is the energy required to create the surface. The surface energy is the change in energy from bulk to the surface divided by the area of each surface. The energy at the surface (SE) can be calculated thus:

SE = (Esurface - N*(Ebulk/n))/(2*A)

where N is the number of atoms in the Surface cell,

n is the number of atoms in the bulk cell,

and A is the area of the surface.

The surface area for this system can be found in this manner:

(uXv) = |u|*|v| * sin(θ)

The problem is that when I use these methods I always end up with energy values that seem unreliable. Does anyone have any alternatives or suggestions for calculating the facet energy.