2.4 Chemical Reactivity 21 precisely, when atoms cluster together to form the new phase, they begin to create an interface between themselves and their surrounding medium, which costs energy A , where A is the area of the cluster's surface, equal to .4 / 1=3 .3nv/ 2=3 , where n is the number of atoms in the cluster. At the same time each atom contributes to the (nega- tive) cohesive energy of the new phase, equal to nv1G, where 1G is the difference in the free energies (per unit volume) between the uncondensed and condensed phases, the latter obviously having the lower energy. Summing these two contributions, at first the energy will increase with increasing n, but ultimately the (negative) cohesive energy of the bulk will win. Differentiating with respect to n and looking for maxima yields n D 32 3 . 3v.1G/ 3 (2.6) The critical nucleation size can lay reasonable claim to be considered as the bound- ary of the nanoscale from the mechano-chemical viewpoint. At least it represents a discontinuity qua crossover point. The critical nucleus size represents the bound- ary between "surface dominated" (an unstable state) and "bulk dominated" (a stable state).