The Structure of a Crystalline Surface

A crystal is surrounded at equilibrii n by flat, atomically smooth, low-index faces or, in Frank s classification, by singular faces. These faces in equilibrium forms are defined by the Gibbs definition of the equilibrium form requiring a minimum of the surface free energy of the crystal at constant volume (see Section 5.1). 

The Surface Roughness Adatoms, Steps, and Kink Positions 

Now it is also understandable that the exchange of kink atoms with the ambient phase can be used for the definition of the equilibrium, because it requires the same Gibbs free energy per atom as the average disintegration free energy of the crystal per atom, i.e., just equal to the chemical potential of the crystalline phase. 

One cannot, however, mechanically transfer the problem of crystal-vapor equilibrium to the case of electrocrystallization. In the first case t)k is obtained from the sublimation energy (f)k = Gs/Na, or from the energy of interaction (Ai between first neighbor atoms and the number of first neighbors of a kink atom (e.g., six, as in the case of a fee or hep crystal (f)k = Sif/i). In the second case, however, charge transfer across the electric field of the double layer as well as the ion-solvent interaction have to be also considered. 

According to Kaischew the frequencies of deposition and dissolution of atoms on/from a site i of the crystal surface are given for the case of electrocrystallization by 

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