Nucleation and growth of Ta oxide in nonstationary thermal field—III. Self-organized structures controlled by convection

Abstract

Oxidation of Ta in the temperature field linearly increasing with the heating rate β (50 K min −1 ⩽ β ⩽ 80 K min −1), was studied. Since the increasing temperature at this β-scale soon reaches T ⩾ 1000 K, the growing Ta oxide layer is transformed into the liquid state. A vertical thermal gradient establishes convection structures of liquid Ta oxide in the regular form (cells, rolls, cells+rolls) and in the irregular form (turbulent convection). These structures have been studied on the basis of weekly nonlinear convection theory. Turbulent convection structures (irregular island-like structures) have been identified as Mandelbrot fractals and simulated by using f c = z 2+ c and f c = z 4+ c functions. The origin of the irregular (fractal)—nowhere differentiable—basin boundaries has been interpreted on the basis of chaotic forcing of a one parameter bistable system.