Jump processes in surface diffusion - Bilkent University - Faculty of ...

54 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) 39–61
Fig. 43. Schematic of possible atom jumps on W(110) plane.
Fig. 45. Displacement distribution of Pd adatom on W(110) plane at 210
K [122]. Double/single jump rate β/α is 0.12, δ y /α is 0.11.
Fig. 44. Dependence of the diffusivity of single Pd adatom on W(110) upon
the reciprocal temperature [122]. Data corrected for edge effects as well as for
migration during transients.
and horizontal jumps, which is huge. It has been possible to
derive a significant energy difference between the two kinds of
jumps.
Oh et al. [123] also examined the self-diffusion of tungsten
atoms on W(110), and surprisingly found behaviour similar to
that of palladium. At 365 K, the distribution yielded β/α =
0.22, δ x /α = 0.36, and δ y /α = 0.43. Half of the transitions
now were long jumps. Of particular interest are the vertical δ y
and horizontal δ x transitions. It is not yet clear how they take
place, but they can be envisioned as starting as jumps in the
〈111〉 direction, which are then deviated either toward the x- or
y-axis.
Although long jumps had now been found for a variety
of atoms in both one- and two-dimensional diffusion, nothing
was known about the rates of these transitions. This matter
was tackled by Antczak [124]. In 2004 she examined in detail
the distribution of displacements of tungsten atoms on W(110)
Fig. 46. Arrhenius plot for diffusivities of W atom on W(110) along 〈100〉 and
〈110〉 direction [124]. Best fit is obtained with a straight line.
over a range of temperatures and with very good statistics of
1200 observations. From an Arrhenius plot of the diffusivities,
in Fig. 46, she obtained straight lines, indicating a barrier
of 0.92 ± 0.02 eV for diffusion along 〈100〉 and much the
same barrier of 0.93 ± 0.01 eV along 〈110〉. Again there
were no indications in the diffusivity of anything to suggest
contributions from long jumps. However, the distribution of
displacements at elevated temperatures clearly showed such
transitions, as is evident from Fig. 47. It must be noted that at
these high temperatures significant displacements occur during
the temperature rise before the diffusion interval and during the
fall at the end. The distribution of displacements during these
temperature transients therefore has to be determined and is
also shown in Fig. 47. The final rates were obtained using the
relation
r = Rt − r ot o
t e
(9)