Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions

Abstract

Experimental observations show that the gap between the sample and the crucible, commonly obtained after solidification in microgravity, is remarkably stable. With the aim to understand the reason of this stability, the dewetting phenomenon is studied by Lyapunov's method. After a short review of the existing mechanisms leading to dewetting, the open smooth crucible configuration is chosen as the most representative. The analytical stability analysis, taking into account geometrical and thermal effects, performed under some boundary heat transfer approximations, shows that, in most cases, the dewetting process is intrinsically stable.

Dewetted Bridgman crystal growth: practical stability over a bounded time period in a forced regime

“…1; see also [10][11][12]14]. This is an over-specified boundary-value problem which has no solution for arbitrary p and h. The main objective, formulated in terms of p, is to find the range of p and h for which the above problem has an approximate solution, i.e.…”

“…where t denotes the time, n is the number of unknown functions (which depends on the crystallization technique), c denotes a set of crystallization parameters (thermophysical and other constants of the substance being crystallized, see for example [4,7,11,12,[18][19][20][21]), (i 1 , . .…”

“…19-167] to numerical solutions of discretized partial differential equations [8,9]. On this basis, several papers have been devoted to the study of the stability of dewetting, all based on Lyapunov's theory as usually applied to crystal growth [7]: simple approaches considering only the capillary effect [10,11] as well as more thorough analyses taking into account coupling between capillarity, heat transfer, and pressure fluctuations [12,13]. However, such analyses consider the stability on an infinite time period and do not allow studying the time scale of perturbation recovery, nor the acceptable amplitude of the perturbations.…”

Thermodynamics of (Ga, In)‐Sb‐O‐Si and impact on dewetting process

“…It is in fact the controlling parameter in the process, which can be monitored by an external gas circuit [4] or by changing the temperature of the gases at the hot and cold sides [5]. Dynamic stability analyses of the process [2,[6][7][8][9][10][11] predict that it is stable if the inequality θ + α > 180° (1) is satisfied, which means that the meniscus is convex (seen from the gas, figure 1-I). This has been verified experimentally in the case of the growth of gallium antimonide in silica crucibles, and it was shown that the gap between the crystal and the crucible, of the order of some tens of micrometers, remains constant on several centimetres [12][13][14].…”

Comment on the paper “Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions”

“…The paper [1] presents a study of the stability of the dewetting phenomenon under microgravity conditions, in the frame of Lyapunov's stability theory. A more thorough investigation of this problem reveals that the presented study is valid only in the case where the liquid meniscus (the liquid free surface at the level of the solid-liquid interface) is fixed at a point on the crucible wall, for example because of sharp roughness or chemical heterogeneities on the crucible wall.…”