Crystallization stability during capillary shaping: II. Capillary stability for arbitrary small perturbations

Abstract

The problem of stability of the crystal shape grown from the melt is treated. The contour restricting the cross section of a crystal is subjected to an arbitrary small perturbation that can be expanded in a series over a corresponding set of orthogonal functions. Solution of a linearized two-dimensional capillary equation determines the time dependence of the expansion coefficients. The shape of a cross section is stable if the coefficients of all the expansion terms decrease with time. The analysis shows that, in case of the zero-harmonic stability, the higher harmonics are stable too. A possibility is indicated for the development of a first harmonic instability during the growth of thin fibers. Such an instability, resulting in the crystal bending, has been observed during the growth of sapphire fibers, 300 μm in diameter.