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Pattern Formation via BLAG

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

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  1. Pattern Formation via BLAG Mike Parks & Saad Khairallah

  2. Outline • Simulate laboratory experiments • If successfully simulated, proceed to new computer experiments.

  3. Phase 1: Deposition Gold particles incoming onto the surface from a heat source The particles will not move much at T=20K Xenon Substrate T=20K

  4. Phase 2: Desorbtion Xenon particles desorbing Gold particles walk randomly With a sticking probability of one they form clusters when colliding Thin xenon film acts as timer Substrate T>20K

  5. Final State: Clusters Final Equilibrium State: clusters on substrate (abrupt interface) Substrate T>>20K

  6. 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

  7. 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.

  8. - - - - + + + + …our contribution: • Charge the particles • Apply electric field perturbation Uniform E

  9. Simulation • 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.

  10. 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

  11. The SIMULATIONS Performed • Uncharged particles: mimic experiment • Charged particles: uniformly distributed • Charged particles with uniform electric field: weak and strong

  12. Results (Uncharged) Initial Configuration Final Configuration

  13. Power Law Dependence(uncharged) Experiment: 1.9 +/- 0.3 Simulation: 2.00 +/- 0.03 Agreement!

  14. Fractal Dimension(uncharged) Agreement!

  15. 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.

  16. Results (Charged Particles) Final Configuration

  17. Fractal Dimension(charged plus charged with e-field) Fractal: New results. We see same dimension as with no charging.

  18. Power law : Size~t2

  19. Interpretation… 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

  20. Interpretation… • 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?

  21. 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

  22. 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.

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