1.5  Energetics of Solid Surfaces

All surfaces are energetically unfavourable in that they have a positive free energy of formation. A simple rationalisation for why this must be the case comes from considering the formation of new surfaces by cleavage of a solid and recognizing that bonds have to be broken between atoms on either side of the cleavage plane in order to split the solid and create the surfaces. Breaking bonds requires work to be done on the system, so the surface free energy (surface tension) contribution to the total free energy of a system must therefore be positive.

The unfavourable contribution to the total free energy may, however, be minimised in several ways :

  1. By reducing the amount of surface area exposed
  2. By predominantly exposing surface planes which have a low surface free energy
  3. By altering the local surface atomic geometry in a way which reduces the surface free energy

The first and last points are considered elsewhere ( 1.7 Particulate Metals, & 1.6 Relaxation and Reconstruction , respectively ) - only the second point will be considered further here.

Of course, systems already possessing a high surface energy (as a result of the preparation method) will not always readily interconvert to a lower energy state at low temperatures due to the kinetic barriers associated with the restructuring - such systems (e.g. highly dispersed materials such as those in colloidal suspensions or supported metal catalysts) are thus "metastable".

It should also be noted that there is a direct correspondence between the concepts of "surface stability" and "surface free energy" i.e. surfaces of low surface free energy will be more stable and vice versa.

One rule of thumb, is that the most stable solid surfaces are those with :

  1. a high surface atom density
  2. surface atoms of high coordination number

(Note - the two factors are obviously not independent, but are inevitably strongly correlated).

Consequently, for example, if we consider the individual surface planes of an fcc metal, then we would expect the stability to decrease in the order

fcc (111) > fcc (100) > fcc (110)

Warning - the above comments strictly only apply when the surfaces are in vacuum. The presence of a fluid above the surface ( gas or liquid ) can drastically affect the surface free energies as a result of the possibility of molecular adsorption onto the surface. Preferential adsorption onto one or more of the surface planes can significantly alter the relative stabilities of different planes - the influence of such effects under reactive conditions (e.g. the high pressure/high temperature conditions pertaining in heterogeneous catalysis ) is poorly understood.

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