Kinetics of Macrostep Under Diffusion and Thermal Interactions in Stagnant Media

TL;DR

This paper analyzes the stability of macrostep trains during crystal growth in stagnant media, considering diffusion and thermal interactions, revealing conditions under which step trains are stable or unstable based on geometric and physical parameters.

Contribution

It provides a theoretical analysis of step stability in crystal growth influenced by diffusion and thermal effects, extending understanding of macrostep kinetics in stagnant environments.

Findings

Equidistant step trains are unstable when the riser angle exceeds π/3 in solution growth.

Thermal interactions stabilize step trains for riser angles less than π/2 in melt growth with equal thermal conductivities.

Heat transfer through crystals stabilizes step trains at all riser angles.

Abstract

The step motions considered are those in which crystallization is controlled by a single diffusion process, either the substance diffusion for growth from solution or the flow of latent heat from the step for growth from melt. Quasi-static diffusion nearby two parallel steps and nearby a train of parallel steps is considered. Terraces and step risers are assumed flat with arbitrary angles between them. Flux of the crystallizing substance to the crystal or the heat sources on the crystal surface are nonvanishing on the step risers only. Kinematics of the steps under the diffusion interaction is investigated, when velocities of the steps are controlled by the supersaturation at the feet of the steps. For the solution growth it is shown that an equidistant train of steps is unstable against to doubling of period, i.e. neighbouring steps are attracted, when the angle of the riser is more than $\pi/3$. The diffusion interaction stabilizes the train of gently sloping steps. For the melt growth at equal thermal conductivities of the crystal and of the melt, the thermal interaction stabilizes the train of steps without overhanging when the riser angle is less than $\pi/2$. If the heat transfers through the crystals, then the equidistant train is stable at all riser angles.