T. V. Savina

On a minimal element for a family of bodies producing the same external gravitational field

A minimal element, mother body, for a family of bodies producing the same external gravitational field is the body in the family, whose support has Lebesgue measure zero and satisfies some additional requirements. The finite algorithm of constructing mother bodies in is suggested. The local structure of mother bodies near singular points of continued logarithmic potential is investigated in generic positions.

The effect of surface stress and wetting layers on morphological instability in epitaxially strained films

This paper investigates effects of surface stress and wetting layers on the morphological instability of a growing epitaxially strained dislocation-free solid film. Linear stability analysis of the planar film shows that the film, unstable due to lattice mismatch, is affected differently by surface stress for a film under compression than for one under tension and depends on whether the relative stiffness of the film to the substrate is less than or greater than (1−2ν)−1; here ν is Poisson’s ratio. The presence of a wetting layer has the capacity to substantially stabilize the planar film. The critical thickness of the film below which the film is stable depends on the bulk elastic properties of film and substrate and increases with increase of the wetting potential.

Suppressing morphological instability via feedback control

Abstract This paper theoretically investigates the possibility for feedback control of morphological instability of the melt/crystal interface during the directional growth of a binary crystal from its melt. The control method involves applying external heating within the melt in the vicinity of the melt/crystal interface, with the heating parameters depending, through the control loop, on the morphology of the solidification front. Linear stability analysis of the corresponding mathematical problem is performed, accounting the solute diffusion in the melt, the thermal diffusion in crystal and melt, the latent heat release, as well as the effects of the constitutional undercooling and melt/crystal interfacial tension. Neutral stability curves are plotted and it is shown that the chosen feedback control approach can substantially increase the threshold for onset of morphological instability. The dependence of feedback control improvement on parameters characterizing the external melt heating as well as on the physico-chemical parameters of the system, is investigated. Finally, the feedback-induced oscillatory instabilities are analyzed, and it is shown that they can be suppressed by an appropriate choice of the control parameters.

Feedback control of morphological instability

A possibility for a feedback control of morphological instability of the interface of a binary crystal growing from its melt in directional solidification process is theoretically investigated. As a feedback control method external melt heating in the vicinity of the melt/crystal interface is considered, with the heating parameters depending, through the control loop, on the morphology of the solidification front perturbations. Linear stability analysis of the corresponding mathematical problem is performed taking into account solute diffusion in the melt, thermal diffusion in crystal and melt, latent heat, as well as the effects of the constitutional undercooling and the melt/crystal interfacial tension. Neutral stability curves are plotted and it is shown that the chosen feedback control can substantially increase the threshold value of the morphological number above which the morphological instability occurs. Dependence of the feedback control effect on the parameters characterizing the external melt heating, as well as on the physico-chemical parameters of the system, is analyzed.

Thermionic emission microscopy of scandium thin film dewetting on W(100)

Scandium thin films of 5-30 nm thickness deposited on clean W(100) surfaces de-wet from the tungsten surface when heated to temperatures < 0.5 Tmelt. The dewetting temperature and the resulting droplet size are a function of the initial scandium film thickness.Scandium thin films of 5-30 nm thickness deposited on clean W(100) surfaces de-wet from the tungsten surface when heated to temperatures < 0.5 Tmelt. The dewetting temperature and the resulting droplet size are a function of the initial scandium film thickness.