Transition-pathway models of atomic diffusion on fcc metal surfaces. I. Flat surfaces

Numerical calculation of minimum-energy paths and activation energy barriers for various atomic diffusion processes on fcc metal surfaces are presented. The computational method employed is the action-derived molecular dynamics that searches the approximate Newtonian trajectory on potential-energy surfaces. The minimization of a modified action, which facilitates the conservation of total energy and the control of kinetic energy, enables us to find efficiently the minimum-energy paths of complex microscopic processes. Diverse diffusion mechanisms on flat fcc substrates are investigated in this first part of the series. More complicated systems including surface steps are simulated in paper II.

Figure 1

Three flat surfaces of the fcc structure for diffusion simulations. From top to bottom: (001), (111), (110), surfaces.

Figure 2

(Color online) Models used in one atom diffusion on the (001) surface. Adatom diffusion model (left) and vacancy diffusion model (right).

Figure 3

(Color online) Basic diffusion pathways on the (001) surface. Hopping (top row) and exchange (bottom row) pathways. Each row proceeds from left to right.

Figure 4

Diffusion pathways of a single adatom on the (111) surface. Positions of local minima and diffusion paths.

Figure 5

Diffusion pathways of a single adatom on the (110) surface.

Figure 6

(Color online) Multiple-exchange diffusion process on the Cu(001) surface. Nine snapshots along the diffusion pathway (top panel, proceeding from left to right and from top to bottom) and its energy profile (bottom panel).

Figure 7

(Color online) A vacancy diffusion on the (001) surface. “Hopping” type (top row), “hurdling” type (middle row), and “kicking out” type (bottom row). Each row proceeds from left to right.

Figure 8

(Color online) Pathway snapshots of two-adatom diffusion on the (001) surface. Hopping direction is normal to the linear shape (top row). Hopping direction is parallel to the linear shape (middle row). Exchange pathway (bottom row). Each row proceeds from left to right.

Figure 9

(Color online) Pathway snapshots and energy profile of four-adatom diffusions by exchange. Exchange of linear shape tetramer (a) and exchange of rectangular shape tetramer (b). Each row proceeds from left to right. Energy profiles of linear shape (c) and rectangular shape (d).