Mass transport of adsorbates near a discontinuous structural phase transition

We study the mass transport dynamics of an adsorbed layer near a discontinuous incommensurate striped-honeycomb phase transition via numerical simulations of a coarse-grained model focusing on the motion of domain walls rather than individual atoms. Following an initial step profile created in the incommensurate striped phase, an intermediate hexagonal incommensurate phase nucleates and grows, leading to a bifurcation into two sharp profiles propagating in opposite directions as opposed to broad profiles induced by atomic diffusive motion. Our results are in agreement with recent numerical simulations of a microscopic model as well as experimental observations for the Pb/Si(111) adsorbate system.

Figure 1

Phase diagram showing the striped incommensurate phase (SI), honeycomb incommensurate phase (HoI), and the coexistence region (dark area) in the range ${\rho }_h<\overline{\rho }<{\rho }_s$. L corresponds to a uniform phase without domain-wall patterns.

Figure 2

Domain-wall patterns corresponding to the (a) honeycomb incommensurate phase and (b) striped incommensurate phase. The dark areas correspond to domain-wall regions where the phase field $\rho (x,y)$ is closest to its minimum value.

Figure 3

Snapshots of the density field when a “hole,” namely, a circular region of radius $R=40dx$ (white circle) with an average density $\overline{\rho }=0.6<{\rho }_h$, is introduced in the stripe phase, for increasing times: (a) $t=0$, (b) $t=6$, (c) $t=9$, (d) $t=21$, (e) $t=78$, and (f) $t=126$ in units of $4.8\times {10}^{5}dt$. The initial striped phase has an average density of $\overline{\rho }=0.98$ and $\overline{\rho }=0.951$ after introduction of the hole.

Figure 4

Radius of the expanding SI-HoI interface as a function of time (in units of $4.8\times {10}^{5}dt$) for initial stripe phases with different average densities $\overline{\rho }$, for a hole of radius $R=20dx$.

Figure 5

Snapshots of the density field for increasing times when the average density after introducing a hole with density $\overline{\rho }=0.8$ is inside the coexistence region. The average density of the initial striped phase is $\overline{\rho }=0.945$, and $\overline{\rho }=0.934$ after the introduction of the hole. (a) $t=4$, (b) $t=21$, and (c) $t=126$ in units of $4.8\times {10}^{5}dt$.

Figure 6

Snapshots of the density field with quenched disorder inside the hole for increasing times: (a) $t=5$, (b) $t=8$, (c) $t=21$, (d) $t=42$, (e) $t=72$, and (c) $t=126$ in units of $4.8\times {10}^{5}dt$. Average density of the initial striped phase is $\overline{\rho }=0.98$, and $\overline{\rho }=0.943$ after the introduction of the hole with density $\overline{\rho }=0.5$. The disorder strength here is $\mathrm{\Delta }=0.08$.