Paper Information

Citation: Ghaleb, D. (1984). Diffusion of adatom dimers on (111) surface of face centred crystals: A molecular dynamics study. Surface Science, 137(2), L103-L108. https://doi.org/10.1016/0039-6028(84)90515-6

Publication: Surface Science 1984

What kind of paper is this?

Discovery (Translational Basis)

This paper applies a computational method (Molecular Dynamics) to observe and characterize a physical phenomenon: the specific diffusion mechanisms of adatom dimers on a crystal surface. It focuses on the “what was found” (simultaneous multiple jumps) rather than proposing a new algorithm or theoretical proof.

Based on the AI for Physical Sciences Paper Taxonomy, this is best classified as $\Psi_{\text{Discovery}}$ with a minor superposition of $\Psi_{\text{Method}}$ (approximately 80% Discovery, 20% Method). The dominant contribution is the application of computational tools to observe physical phenomena, while secondarily demonstrating MD’s capability for surface diffusion problems in an era when the technique was still developing.

What is the motivation?

The study aims to investigate the behavior of adatom dimers in an intermediate temperature range ($0.3T_{m}$ to $0.6T_{m}$). At the time, Field Ion Microscopy (FIM) provided data at low temperatures ($T \le 0.2T_{m}$), and previous simulations had focused on single adatoms or different surfaces (like (110) or (100)). The authors sought to compare dimer mobility with single adatom mobility on the (111) surface, where single adatoms move almost like free particles.

What is the novelty here?

The core contribution is the observation of simultaneous multiple jumps for dimers on the (111) surface at intermediate temperatures. The study reveals that:

  1. Dimers migrate as a whole entity, with both atoms jumping simultaneously
  2. The mobility of dimers (center of mass) is very close to that of single adatoms in this regime, contrasting with the expectation that larger clusters might be significantly slower

What experiments were performed?

The authors performed Molecular Dynamics (MD) simulations of a face-centred cubic (fcc) crystallite:

  • System: A single crystallite of 192 atoms bounded by two free (111) surfaces
  • Temperature Range: $0.22 \epsilon/k$ to $0.40 \epsilon/k$ (approximately $0.3T_m$ to $0.6T_m$)
  • Duration: Integration over 50,000 time steps
  • Comparison: Results were compared against single adatom diffusion data and Einstein’s diffusion relation

What were the outcomes and conclusions drawn?

  • Mechanism Transition: At low temperatures ($T^*=0.22$), diffusion occurs via discrete single jumps where adatoms rotate or extend bonds. At higher temperatures, the “multiple jump” mechanism becomes preponderant.
  • Migration Style: The dimer migrates essentially by extending its bond along the $\langle 110 \rangle$ direction.
  • Mobility: The diffusion coefficient of dimers is quantitatively similar to single adatoms.
  • Qualitative Support: The results support Bonzel’s hypothesis of delocalized diffusion involving energy transfer between translation and rotation, though the statistical sample was too small to confirm the coupling function definitively.

Reproducibility Details

Data (Simulation Setup)

The “data” in this context is the configuration of the physical simulation.

Visualization of argon dimer on fcc(111) surface
Initial configuration showing two adatom dimers on an fcc(111) surface. The crystallite consists of 192 atoms with periodic boundary conditions in the x and y directions.
ParameterValueNotes
Particles192 atomsSingle fcc crystallite
Dimensions$4[110] \times 4[112]$Thickness of 6 planes
BoundaryPeriodic (x, y)Free surface in z-direction
Initial StateDimer on neighbor sitesStarts with 2 adatoms

Algorithms

The simulation relies on standard Molecular Dynamics integration techniques.

  • Integration Scheme: Central difference algorithm (Verlet algorithm)
  • Time Step: $\Delta t^* = 0.01$ (reduced units)
  • Total Steps: 50,000 integration steps
  • Dimer Definition: Two adatoms are considered a dimer if their distance $r \le r_c = 2\sigma$

Models (Analytic Potential)

The physics are modeled using a classic Lennard-Jones potential.

Potential Form: (12, 6) Lennard-Jones

Parameters (Argon-like):

  • $\epsilon/k = 119.5$ K
  • $\sigma = 3.4478$ Å
  • $m = 39.948$ a.u.
  • Cut-off radius: $2\sigma$

Evaluation

Metrics used to quantify the diffusion behavior:

MetricFormulaNotes
Diffusion Coefficient$D = \langle R^2 \rangle / 4t$Calculated from Mean Square Displacement of center of mass
Trajectory AnalysisVisual inspectionCategorized into “fast migration” (multiple jumps) or “discrete jumps”

Hardware

  • Specifics: Not specified in text
  • Scale: 192 particles for 50k steps is extremely lightweight by modern standards (seconds on a modern CPU), though it required mainframe resources in 1984

Citation

@article{ghalebDiffusionAdatomDimers1984,
  title = {Diffusion of Adatom Dimers on (111) Surface of Face Centred Crystals: A Molecular Dynamics Study},
  author = {Ghaleb, Dominique},
  year = {1984},
  journal = {Surface Science},
  volume = {137},
  number = {2},
  pages = {L103-L108},
  doi = {10.1016/0039-6028(84)90515-6}
}