Nonlinear resonance study of the periodic motion of the explosive crystallization front in glasses

Abstract

The theoretical treatment of self-sustained periodic motion of the explosive crystallization ͑EC͒ front in a thin amorphous film is presented. The main attention is given to the study of nonlinear resonance phenomena occurring due to the presence of a small external periodic perturbation with the frequency being in the vicinity of the ordinary or parametric resonance. Weakly anharmonic oscillations of the EC front velocity are considered with the Van der Pole method, and the expressions for the limit cycle amplitude in the case of free and forced oscillations are derived. Depending on the values of kinetic and thermophysical parameters of the model, different kinds of resonance curves ͑i.e., front oscillation amplitudes versus frequency detuning͒ are obtained and analyzed. Our predictions may be tested experimentally by monitoring the explosive growth rate using the modulation of laser intensity or employing amorphous films with thickness periodicity. It is also shown that inclusion of the results of dynamic stability analysis changes the steady-state EC stability diagram in the (T s ,d) plane ͑T s is the substrate temperature and d the film thickness͒ so that the region of stable EC regimes becomes substantially more limited.

Explosive Crystallization in Thin Amorphous Layers on Heat Conducting Substrates

“…This is in contrast to any formulation in terms of a local heat transfer coefficient, which is often found in the literature, e.g. in Geiler et al (1986); Grigoropoulos et al (2006); ; Kurtze (1986); Shklovskij & Ostroushko (1996). It is also at odds with a more general polynomial relationship between heat loss and temperature, as reported in Ma et al (1990).…”

“…This influence is examined e.g. in Geiler et al (1986); Grigoropoulos et al (2006); ; Kurtze (1986); Rogers et al (2006); Shklovskij & Ostroushko (1996). The heat loss can even lead to the explosive crystallization process dying out (Heinig & Geiler, 1986;Provatas et al, 1996).…”

“…Specifically, the influence of heat loss into the substrate on the explosive crystallization process is examined in detail. Often, inclusion of heat loss is realized semi-empirically using an apparent heat transfer coefficient (Geiler et al, 1986;Grigoropoulos et al, 2006;Kurtze, 1986;Shklovskij & Ostroushko, 1996). In contrast, the present work derives the equations governing heat conduction into the substrate from first principles, avoiding the use of an empirical heat transfer coefficient.…”

“…It is often assumed in the literature -e.g. in Grigoropoulos et al (2006); ; Kurtze (1986); Shklovskij & Ostroushko (1996) -that the heat loss into the substrate can be described by a local heat transfer coefficient (see also section 5.2.2). If that were the case, a constant temperature would require a constant rate of crystallization, i.e.…”

Influence of heat conducting substrates on explosive crystallization in thin layers

“…A thorough investigation of various instabilities, cf. [37][38][39][40][41][42], is certainly desirable. The present analysis as well as previous theoretical work, e.g.…”