Influence of Environment on Surface Structure

The surface free energy, y, is just the free energy for the reaction of Equation 8.32 per unit surface area of the slab. If a slab simulation geometry gives two surfaces of area S  

To link this definition of surface energy to calculations on relaxed slabs we now make the assumption that the entropy in the slab and bulk oxide free energy terms can be neglected. Then the surface energy based on calculated quantities 

For example the standard energy of formahon of the oxide is the energy for the reaction  

Since the metal will usually have a standard state which is solid the values and gA can be obtained from extrapolahon of DFT optimization calculations. Accurate values of AG (A 0 ) are tabulated for the common oxides [56], for example the value for AI2O3 is -1576 kj moh and so Fquahon 8.38 provides a route to gA without explicit calculahons on O2. 

Equation 8.38 also sets the lower limit of the range of values accessible for go since reduction of the oxide will occur spontaneously into the pure metal and dioxygen gas if the free energy for Equahon 8.37 is positive. This means for a stable oxide  

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