The theory of the instability of a planar interface in a process of the phrase transformation

The theory of the instability of a planar interface during an isothermal phase transformation is developed. It is shown that for large times only perturbations with large wave length are essential. The amplitude of the deviation from a planar interface grows with time as an exponent, the argument of which is proportional to $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ instead of the usual simple exponential law.