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Pattern Formation via BLAG. Mike Parks & Saad Khairallah. Outline. Simulate laboratory experiments If successfully simulated, proceed to new computer experiments. Phase 1: Deposition. Gold particles incoming onto the surface from a heat source. The particles will not move much at T=20K.

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Pattern formation via blag

Pattern Formation via BLAG

Mike Parks & Saad Khairallah


  • Simulate laboratory experiments

  • If successfully simulated, proceed to new computer experiments.

Phase 1 deposition
Phase 1: Deposition

Gold particles incoming onto the surface from a heat source

The particles will not move much at T=20K




Phase 2 desorbtion
Phase 2: Desorbtion

Xenon particles desorbing

Gold particles

walk randomly

With a sticking


of one they

form clusters

when colliding

Thin xenon film

acts as timer



Final state clusters
Final State: Clusters

Final Equilibrium State:

clusters on substrate

(abrupt interface)



Control parameters
Control Parameters

  • Parameters for Cluster Creation:

    • The thickness of the xenon layer acts as a timer

    • Sticking probability coefficient ~1 (DLCA)

    • Surface coverage

    • External potential (???)

  • No need to satisfy thermodynamics constraints:

    • surface free energy and the three growth modes

Results to simulate
Results to simulate…

  • Weighted cluster size grows as S~t2

  • Density decays as N~t-2.

  • Fractal dimension according to DLCA size ~ (average radius)^Dimension.

Our contribution









…our contribution:

  • Charge the particles

  • Apply electric field perturbation

Uniform E


  • Start with uncharged particles interacting on a square lattice with Lennard-Jones potentials.

  • When two atoms become adjacent, they bond to form a cluster.

  • Update simulation time as

    t = (# Atoms Moved)/(# Atoms),

    i.e. diffusion does not depend on time.

  • Simple metropolis algorithm

    No KMC:

  • We are not describing the dynamics on the surface.

  • Pattern formation via BLAG does not depend on time explicitly.

Implementation issues
Implementation Issues:

  • Need to efficiently determine when to merge clusters

  • Use bounding boxes on clusters and check for adjacent atoms only when boxes overlap

  • Linked-cell method implemented for L-J potentials

The simulations performed

  • Uncharged particles: mimic experiment

  • Charged particles: uniformly distributed

  • Charged particles with uniform electric field: weak and strong

Results uncharged
Results (Uncharged)

Initial Configuration

Final Configuration

Power law dependence uncharged
Power Law Dependence(uncharged)


1.9 +/- 0.3


2.00 +/- 0.03


Fractal dimension uncharged
Fractal Dimension(uncharged)


Modification add charge
Modification : Add Charge

  • Add a positive or negative charge of magnitude 1.6e-19 Coulombs to all atoms, such that the net charge is zero.

  • Distribute the charged particles uniformly over the lattice.

  • Clusters that form as to have no net charge interact only with L-J potential.

Results charged particles
Results (Charged Particles)

Final Configuration

Fractal dimension charged plus charged with e field
Fractal Dimension(charged plus charged with e-field)


New results. We see same dimension as with no charging.

Power law size t 2
Power law : Size~t2


The effect of charging subsides according to coverage:

  • Fast decay if high coverage:

    particles neutralize each other quickly

  • Slow decay if low coverage:

    particles neutralize each other slowly


  • When charging effect subsides fast, L-J takes over giving close results to exp.

  • When charging effect subsides slow, Coulomb potential acts longer altering results from exp..

  • So what does the electric field do?

Electric field effect
Electric Field Effect…

  • The electric field accelerates the process of particles neutralizing each other making the charge effect decay fast.

  • We expect L-J to dominate on the long run

  • Hence results closer to experiment

Future work
Future work…

  • The model, DLCA based on sticking probability coefficient ~1: so change that number allowing for non-sticking collisions.

  • Have a metallic substrate to alter the potential with an image potential

  • Apply varying electric field

  • More complicated: 3D clusters.