Molecular dynamics thesis

4.2 Surface relaxation
Free surfaces can be regarded as very large defects. One clearly noticeable effect of
such a defect is surface relaxation of the first few planes near the surface. For a system
based only on pair potentials this phenomenon is easily explained in fig. 9.
In EAM simulations the situation is more complicated. Omitting the embedding interaction
would result in a lattice constant based purely on pair potentials, omitting the pair potential
would result in a different lattice constant based only on the electron density. In EAM
simulations the lattice constant lies somewhere in between. When a perfect crystal is cut in

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Figure 9. Increasing interatomic distance as a result of removing a
neighbouring third atom. The pair of atoms shows the equilibrium
distance for an isolated system of two atoms. The three interacting
atoms show the decreased equilibrium distance when a third atom
is added to the system due to next-nearest neighbour interactions.
two, the electron density varies, from high values far away from the free surface to low
values at the surface. Depending on this density, the change in lattice constant may be an
expansion or a contraction, because sometimes the effect of ‘cutting’ pair potentials may
dominate (increasing the interatomic distances) and sometimes the decrease in electron
density may dominate (decreasing the distance between atoms through the embedding
interaction). The overall change is usually a contraction. The changes in lattice constant can
be considerable. Figs. 10 to 12 show the lattice constant for planes near the surface of
perfectly flat (100), (110), and (111) surfaces, obtained from the simulations.
Figure 10. Distance between consecutive planes of a (100) surface after relaxation
.
The surface is at plane number 28. The bulk value is 1.5736 Å. In the simulations
each atomic plane contains 196 atoms.
From figs. 10 to 12 it will be clear that near a surface, atoms are not located at regular
distances. Also, diffusion of an atom over a surface can change the equilibrium position of
other atoms. Locally, changes of up to 30 percent of the nearest neighbour distance have
been observed in simulations.

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Figure 11. Distance between consecutive planes of a (110) surface after relaxation
.
The surface is at plane number 20. The bulk value is 2.2254 Å. In the simulations
each atomic plane contains 280 atoms.
Figure 12. Distance between consecutive planes of a (111) surface after relaxation
.
The surface is at plane number 61. The bulk value is 0.9085Å. In the simulations
each atomic plane contains 80 atoms.

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The results above do not all agree with results reported by others. Zeper [12] and
Robbemond and Thijsse [11] found contractions of 2.7 and 2.5 % in the distance between
the first and second atomic planes of the (100) surface and 1.5 and 1.0 % contractions
between the first and second atomic planes of the (110) surface. In the simulations in this
thesis the distance between the first two planes of the (100) surface expands 2.2 % and the
distance between the first two (110) planes contracts 1.1 %. The experimental value
determined by Clarke [13], using LEED, for the (100) surface was a 9.5 % contraction.
Clarke mentions that experimental results may be contradictory. For example, for the W
(100) surface four LEED experiments resulted in contractions of 4.5, 5, 6, and 11 %. Ion
scattering never resulted in a values higher than 6 %. Taking into account that all methods
produce different results (even experiments using the same method and simulations using
the same potentials), it should be concluded that the reliability of the results presented above
is very limited.