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Diffusion coefficients of the surface layers are calculated to investigate
transport properties of the Va(111),Va(001) and Va(011) samples.
The coefficients are found from the particle trajectories,
,
by calculating the average mean square displacement (See Fig 5.22):

(6.10) 
where is a coordinate index, the sum includes atoms in the layer ,
and the angular brackets denote averaging over time from the origin ().
The diffusion coefficients are calculated
separately in the and directions, according to Einstein relation for each layer:

(6.11) 
Figure:
Mean square displacement in the direction of an atom in
the surface layer of Va(111) vs. time.
Note the increased mobility of particles with temperature.

Figure:
Diffusion coefficients of as a function of layer number at temperature T=2200 K.

The diffusion coefficients are larger at the surface region.(See 5.23)
The mobility of the atoms increases with elevation of the
sample temperature and converges to the liquid bulk values. These observations
correlate with the structural variations in the surface region exhibited in the pair
correlation functions, the structural order parameters, and the local density profiles.
The diffusion coefficients of the first crystal layer of the
Va(011) as a function of temperature are shown in Figs. 5.24.
Figure:
Diffusion coefficients of the surface layer of Va(011) vs. temperature in different directions.
Note an anisotropy of the inplane diffusion coefficients :

The diffusion coefficients are different in different directions
for Va(011) and Va(111).
In the course of diffusion an atom jumps from one point (its current position)
to another one (the nearest vacant place on the lattice),
the distance between these two points is termed as jump distance.
This jump distance is larger along the direction than in the direction, because
the nearestneighbor distance is larger in the direction
than in the , i.e. (See Table 5.1).
Hence the diffusion coefficients are larger in the direction .
The diffusion coefficient along the direction is
smaller than along the and directions.
That difference can again be explained by the fact that (See Table 5.1),
and therefore, the jump distance is the smallest along the direction, thus
.
The diffusion coefficients of the least packed Va(111) surface are the largest one.
The diffusion coefficients of the Va(001) are smaller than the Va(111) ones, yet they are larger
than the diffusion coefficients of the close packed Va(011) surface, which are
close to zero even at the elevated temperatures (See Fig 5.25).
Figure:
In plane diffusion coefficients as a function of
temperature for the surface layer of Va(111),Va(001) and Va(011)
calculated for the direction).

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Up: Results: surface melting
Previous: Plane radial distribution function
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