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The surface energy is defined as:
                 r=(Eslab(Me-Al)-n(Al)Ebulk(Al)-n (Me )Ebulk(Me)      /2A           (1)
whereEslab(Me-Al) is the total energy of Me-Al slab, while nAl and nMe are the number of Al and doped Me atoms per computational cell, and the and are the reference bulk total energy per atom, respectively. The factor 1/2 takes into account that the top and bottom of the slab are equivalent, and the A is the area of the Me-Al surface.
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p.5 - the authors define their surface energy (equation (1)) by simply dividing the total energy difference by 2. This implies that both surfaces of the slab are equal, and that is presumably not true, sinceone side is relaxed and the other is not. A better way to calculate the surface energy would be to do acalculation on a static 5-layer slab and deduce the "static" surface energy in that manner. The energy
difference in equation (1) could then be adjusted for this static surface energy, and the division by 2 could be eliminated. I wouldn't expect this modification to significantly change the calculated surface energy trends, but it might change the quantitative values to some extent.
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