Va. Shklovskij et Vn. Ostroushko, NONLINEAR RESONANCE STUDY OF THE PERIODIC MOTION OF THE EXPLOSIVE CRYSTALLIZATION FRONT IN GLASSES, Physical review. B, Condensed matter, 53(6), 1996, pp. 3095-3106
The theoretical treatment of self-sustained periodic motion of the exp
losive crystallization (EC) front in a thin amorphous film is presente
d. The main attention is given to the study of nonlinear resonance phe
nomena occurring due to the presence of a small external periodic pert
urbation with the frequency being in the vicinity of the ordinary or p
arametric resonance. Weakly anharmonic oscillations of the EC front ve
locity are considered with the Van der Pole method, and the expression
s for the limit cycle amplitude in the case of free and forced oscilla
tions are derived. Depending on the values of kinetic and thermophysic
al parameters of the model, different kinds of resonance curves (ie.,
front oscillation amplitudes versus frequency detuning) are obtained a
nd analyzed. Our predictions may be tested experimentally by monitorin
g the explosive growth rate using the modulation of laser intensity or
employing amorphous films with thickness periodicity. It is also show
n 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 thickness) so that the region of
stable EC regimes becomes substantially more limited.