Page 106 - Science at the nanoscale

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June 9, 2009
Surfaces at the Nanoscale
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The surface atom on the {100} facet
would have four bonds broken, ch05
1 2
γ = x x ε 4 x 2
2 a
4ε
γ =
a 2
Figure 5.2. Schematic of a “new” {100} surface, showing four broken
bonds for the red coloured surface atom. The broken bonds are illustrated
by the green coloured balls in the front unit cell.

Cube {100} Dodecahedron{110} Octahedron {111}

Figure 5.3. Forms or shapes of crystals are determined by the surround-
ing facets.

observed crystals thus often have simple shapes bounded by low
index surfaces.
Thermodynamically, the equilibrium shape of a crystal is
determined by considering the surface energies of all facets. Typ-
ically, a crystal surrounded by {100} facets will adopt the form of
a cube, whereas one with {111} or {110} facets will have the form
of an octahedron or dodecahedron (Fig. 5.3). This general guide-
line, however, may not be applied to nano-sized crystals that are
grown through kinetically-controlled routes.

5.1.3 Lowering of Surface Energy

We often observe that liquid water forms spherical droplets on
a substrate. This is a spontaneous behavior as the spherical
shape minimizes the total surface area and hence the free energy.
Thermodynamically, a material object is stable when in a state of