Nonlinear theory of autooscillations of quasiplanar interface during directional solidification

Abstract

Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of small partition coefficient the full problem is reduced to the system of two ordinary differential equations describing the interface motion in terms of its velocity and position coordinate. The type of the oscillatory instability bifurcation is studied in detail in different limits. For the subcrytical bifurcaton relaxation interface oscillations are analyzed analytically and numerically. We show that these oscillation exibit a number of anomalous properies. In particular, such oscillations can be weakly- or strongly-dissipative depending on the physical parameters and the amplitude of the strongly-dissipative oscillations is determined not only by the form of the corresponding nullcline but also by the behavior of the system for small values of the interface velocity. Characteristic parameters of the superlattice occuring in the growing crystal are estimated.