Long jumps in one-dimensional surface self-diffusion: Rebound transitions

The diffusivity as well as the distribution of displacements of tungsten atoms have been examined on the W(211) plane. An Arrhenius plot of the diffusivity does not indicate long jumps, but the distributions of displacements at $T⩾300\mathrm{K}$ show both double transitions between sites two spacings apart, as well as single jumps; double jumps have a high activation energy, $E_{\beta }=1.44\pm 0.13\mathrm{eV}$. At temperatures $T>320\mathrm{K}$, atom motion over the surface is entirely by longer transitions. Most interesting is the fact that the sum of all measured jump rates does not agree with expectations, indicating for the first time that rebound transitions, in which jumping atoms immediately return to the origin, are significant.

Figure 1

(Color online) Arrhenius plot for the diffusivity of tungsten atoms on W(211) surface in the temperature range $T=260–325\mathrm{K}$. Inset: Possible Arrhenius plot for the three highest temperatures. Characteristic values derived from this plot are comparable to those for double transitions.

Figure 2

Distribution of displacements of a tungsten atom in a W(211) channel $\sim 17$ atomic spaces long at a temperature $T=295\mathrm{K}$. Distribution determined in experiment is shown in black, the Monte Carlo best fit appears striped. Only single transitions can be identified.

Figure 3

Distribution of displacements for W atom on W(211) plane at a temperature $T=300\mathrm{K}$. A small number of double transitions is detected for the first time.

Figure 4

Distribution of displacements for W on W(211) at $T=325\mathrm{K}$. Double transitions have increased significance, but there are no triple jumps. Inset shows the distribution of displacements for transitions occurring during warming and cooling sample to $T=325\mathrm{K}$.

Figure 5

(Color online) Temperature dependence of single jumps $\alpha$. A diminution of single jump rate due to increase in number of double transitions is observed. Arrhenius line and diffusion characteristics are based on low temperature rates only.

Figure 6

(Color online) Semilogarithmic plot for the temperature dependence of double jump rate $\beta$. A much higher activation energy and frequency prefactor is found for double jumps than for single transitions.

Figure 7

(Color online) Arrhenius plot for the sum of single plus double transition rates vs reciprocal temperature. The line and characteristic values are for low temperature single jump rates. A deviation at higher temperatures is clear. Inset: schematic of jumps predicted on W(211) in investigated temperature range.