Lattice effects in crystal evaporation (original) (raw)
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Asymptotic analysis and numerical simulations of atomic steps on crystalline surfaces
2004
We study atomic steps on surfaces of crystals. The crystals under consideration are called "unorthodox" since their atomic steps show increasing oscillations for decreasing temperatures. Using a physical model for the shape of atomic steps on the surface of these crystals we perform numerical simulations for terrace-and island-like shapes of atomic steps. Moreover we use the Γ-limit approximation of the model to compare its solutions with experimental data and derive information on the temperature dependence of the relevant physical constants. This method may prove useful also in other physical problems with multiple scales.
Revisiting step instabilities on crystal surfaces. Part II: General theory
Journal of The Mechanics and Physics of Solids, 2021
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on stability of different mechanisms and their interplay: elastic step-step interactions, the Schwoebel barrier, and the chemical coupling of the diffusion fields on adjacent terraces. In this second part, we present a stability analysis of the general problem without recourse to the quasistatic approximation. This analysis reveals the existence of a supplementary mechanism, which we label the "dynamics effect" as it follows from accounting for all the convective and transient terms in the governing equations. This effect can be stabilizing or destabilizing depending on the ratio of step attachment/detachment kinetics to terrace diffusion kinetics. Further, we find that this dynamics effect remains significant in the slow deposition/evaporation regime, thereby invalidating the classical postulate underlying the quasistatic approximation. Finally, revisiting experiments of crystal growth on Si(111)-7×7 and GaAs(001), our analysis provides an alternative explanation of the observed step bunching, one that does not require the mechanisms previously invoked in the literature.
From atoms to steps: The microscopic origins of crystal evolution
Surface Science, 2014
The Burton-Cabrera-Frank (BCF) theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-onsolid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model.
Non-universal equilibrium crystal shape results from sticky steps
Journal of physics. Condensed matter : an Institute of Physics journal, 2011
The anisotropic surface free energy, Andreev surface free energy and equilibrium crystal shape (ECS) z = z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with 'sticky' steps, i.e. steps with a point-contact-type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of 'step droplets' (bound states of steps) (n(p)) using the Monte Carlo method, where p = (∂z/∂x,∂z/∂y) and (·) represents the thermal average. Using the resul...
Fluctuations of steps on crystal surfaces
Computer Physics Communications, 2002
Fluctuations of isolated and pairs of ascending steps of monoatomic height are studied in the framework of SOS models, using mainly Monte Carlo techniques. Below the roughening transistion of the surface, the profiles of long steps show the same scaling features for terrace and surface diffusion. For a pair of short steps, their separation distance is found to grow as t 1/3 at late stages. Above roughening, simulational data on surface diffusion agree well with the classical continuum theory of Mullins.
Nonlinearity, 2020
We study a 4th order degenerate parabolic PDE model in 1 dimension with a 2nd order correction modeling the evolution of a crystal surface under the influence of both thermal fluctuations and evaporation/deposition effects. First, we provide a non-rigorous derivation of the PDE from an atomistic model using variations on Kinetic Monte Carlo rates proposed by the last author with Weare (PRE, 2013). Then, we prove the existence of a global in time weak solution for the PDE by regularizing the equation in a way that allows us to apply the tools of Bernis-Friedman (JDE, 1990). The methods developed here can be applied to a large number of 4th order degenerate PDE models. In an appendix, we also discuss the global smooth solution with small data in the Weiner algebra framework following recent developments using tools of the second author with Robert Strain (IFB, 2018).
Relaxation of surface profiles by evaporation dynamics
Physical Review B - PHYS REV B, 1997
We present simulations of the relaxation towards equilibrium of one-dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and Tang that allows for temperature-dependent next-nearest-neighbor interactions. For the step geometry the results at T=0 agree well with the t1/4 prediction of continuum theory for the spreading of the step. In the case of periodic profiles we modify the mobility for the tips of the profile and find the approximate solution of the resulting free boundary problem to be in reasonable agreement with the T=0 simulations.
Condensation and Crystal Nucleation in a Lattice Gas with a Realistic Phase Diagram
Entropy, 2022
We reconsider model II of Orban et al. (J. Chem. Phys. 1968, 49, 1778–1783), a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: Upon closer inspection, the alleged liquid–vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier relative to crystal nucleation from the “liquid”.
Physica A-statistical Mechanics and Its Applications, 2001
In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step-edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting crossover phenomena are identified. Simulational results are compared, especially, to those of continuum theories and random walk descriptions.