S.J. Liu

Schwoebel-Ehrlich barrier: from two to three dimensions

The Schwoebel-Ehrlich barrier—the additional barrier for an adatom to diffuse down a surface step—dictates the growth modes of thin films. The conventional concept of this barrier is two dimensional (2D), with the surface step being one monolayer. We propose the concept of a three-dimensional (3D) Schwoebel-Ehrlich barrier, and identify the 2D to 3D transition, taking aluminum as a prototype and using the molecular statics method. Our results show that: (1) substantial differences exist between the 2D and 3D barriers; (2) the transition completes in four monolayers; and (3) there is a major disparity in the 3D barriers between two facets; further, alteration of this disparity using surfactants can lead to the dominance of surface facet against thermodynamics.

Monte Carlo simulation of pulsed laser deposition

Using the Monte Carlo method, we have studied the pulsed laser deposition process at the submonolayer regime. In our simulations, dissociation of an atom from a cluster is incorporated. Our results indicate that the pulsed laser deposition resembles molecular-beam epitaxy at very low intensity, and that it is characteristically different from molecular-beam epitaxy at higher intensity. We have also obtained the island size distributions. The scaling function for the island size distribution for pulsed laser deposition is different from that of molecular-beam epitaxy.

Interatomic potentials and atomistic calculations of some metal hydride systems

The effective interatomic pair potentials for Ti, Zr, Hf, V, Nb, Ta and their hydrides are obtained by inverting the ab initio cohesive energy curves based on the lattice inversion method, and then the inverted pair potentials are used to calculate the mechanical and thermal properties of these hydrides.

Phonon dispersions and elastic constants of Ni3Al and Möbius inversion

Abstract The Mobius inversion formulation corresponding to inequally weighted summations for solving some three-dimensional lattice problems introduced by Chen et al. [Phys. Lett. A 184 (1994) 347] has been used for the first time to obtain the pair potentials for fcc and L12 structures. The derivation is exact for radial potentials not only between identical atoms, but also between distinct atoms. We have tested this formulation for Ni3Al using the empirical total energy function in the Rose model. The phonon dispersions and the elastic constants have been evaluated based on our calculated pair potentials and the results are in good agreement with the experimental data. This method shows a convenient route from electronic structure. calculation or empirical formula of binding energy curve to mechanical properties of materials. It also indicates the potential application of the number theory method to condensed matter physics.

Mobius transform and inversion from cohesion to elastic constants

Elastic constants have been calculated for the FCC metals Cu, Al and Ni using the Mobius transform and a short-range three-body potential correction. Unlike a previous calculation based only on pair potentials, the result is in good agreement with experiment since the restriction of the Cauchy relation has been removed. More importantly, it shows the potential application of the Mobius-inversion method for evaluating interatomic potentials from ab initio electronic structure calculations.

Modified Möbius inversion transform and phonon dispersion relations for copper

Abstract A new method to calculate the phonon dispersion relations is presented in this paper. By using the Mobius-converted pair potential and a simplified three-body potential the phonon dispersion relations are calculated in three directions with a very simple procedure. The results for copper are in good agreement with experiments. Of more importance, it indicates the potential application of the Mobius method to different physical problems.

Diffusion of clusters down (111) aluminum islands

Abstract The key factor determining nucleation processes and faceting in homoepitaxial growth as well as texture competition is the mobility of adatoms and small clusters across step edges and facets. Using a combination of molecular dynamics and ab initio calculations, we investigate the mechanisms of small clusters (dimer and trimer) diffusion down the aluminum (1xa01xa01) surface. In this paper we report results of molecular dynamics studies. Our study shows that the clusters dissociate at the step-edge of compact islands. As a result, the clusters diffuse down the step by an exchange mechanism with a small or medium Schwoebel barrier. The mechanism of this down-diffusion/dissociation is discussed and the corresponding energetics are calculated using the molecular statics method. We find a large anisotropy between the barriers at the two types of 〈1 1 0〉 oriented steps.

Perturbation series solution of the Fokker-Planck equation

An approximate procedure is presented for the evaluation of the so-called perturbation series solution for the temporal evolution of the Fokker-Planck equation. The transient phenomena near or at the point of instability in the double stable symmetrical potential case are discussed in detail. The evaluated results are satisfactory.