Crystallography and Energetics of Ideal Surfaces

Our endeavor to uncover the energetic features of surfaces begins with a pair potential description. For convenience, we leave the specific details of the pair potential unspecified, noting only that the total energy of the solid is written as 

One of the key linkages between continuum and microscopic descriptions of interfaces is the notion of an interfacial energy. Though the use of such energies is by now entirely routine, nevertheless, this exemplifies the type of information passage that is one of the hallmarks of multiscale modeling. Note that from the perspective of the continuum mechanics of materials with interfaces, the total energy is often written in the form 

Note that in deducing this result we have not allowed for the possibility of structural relaxations that might occur for surface and near-surface atoms. 

The type of calculation illustrated above can be elaborated by appeal to more sophisticated descriptions of the total energy. Regardless of choice of energy function, the fundamental concept is embodied in eqn (9.5). In preparation for our discussion of surface reconstructions, we will generalize the description given above to the case of pair functionals such as the embedded-atom method. We adopt 

Following the discussion from chap. 4, recall that within a pair functional description the energy takes the form, 

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