Search

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)-7x7 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.

Epitaxial growth on a surface vicinal to a high-symmetry crystallographic plane occurs through the propagation of atomic steps, a process called step-flow growth. In some instances, the steps tend to form close groups (or bunches), a phenomenon termed step bunching, which corresponds to an instability of the equal-spacing step propagation. Over the last fifty years, various mechanisms have been proposed to explain step bunching, the most prominent of which are the inverse Ehrlich-Schwoebel effect (i.e., the asymmetry which favors the attachment of adatoms from the upper terrace), elastically mediated interactions between steps (in heteroepitaxy), step permeability (in electromigration-controlled growth), and the chemical effect (which couples the diffusion fields on all terraces). Beyond the discussion of the influence of each of these mechanisms taken independently on the propensity to bunching, we propose a unified treatment of the effect of these mechanisms on the onset of the bunching instability, which also accounts for their interplay. This is done in the setting of the so-called quasistatic approximation, which by permitting mostly analytical treatment, offers a clear view of the influence on stability of the combined mechanisms. In particular, we find that the Ehrlich-Schwoebel effect, elastic step-interactions and the chemical effect combine in a quasi-additive fashion, whereas step permeability is neither stabilizing nor destabilizing per se but changes the relative influence of the three aforementioned mechanisms. In a companion paper, we demonstrate and discuss the importance of another mechanism, which we call the dynamics effect, that emerges when relaxing the simplifying but questionable quasistatic approximation.

Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between mechanical, thermal and electromagnetic effects will consequently arise and a consistent multiphysics modeling approach is required for the motors' design. Typical simulations-the bulk of which are presented in the electrical engineering literature-involve a stepwise process, where the resolution of Maxwell's equations provides the Lorentz and magnetic forces which are subsequently used as the external body forces for the resolution of Newton's equations of motion. The work presented here proposes a multiphysics setting for the boundary value problem of electric motors. Using the direct approach of continuum mechanics, a general framework that couples the electromagnetic , thermal and mechanical fields is derived using the basic principles of thermodynamics. Particular attention is paid to the derivation of the coupled constitutive equations for isotropic materials under small strain but arbitrary magnetization. As a first application, the theory is employed for the analytical mod-eling of an idealized asynchronous motor for which we calculate the electric current, magnetic, stress and temperature fields as a function of the applied current and slip parameter. The different components of the stress tensor and body force vector are compared to their purely mechanical counterparts due to inertia, quantifying the significant influence of electromagnetic phenomena.