Transient behaviour of surface supersaturation caused by an abrupt change in bulk supersaturation

• Published in: Surface science 2001-11, Vol.494 (2), p.60-74
• Main Author: Rak, Mirosława
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Crystallization; Diffusion; Exact sciences and technology; Growth; Growth kinetics; Materials science; Methods of crystal growth; physics of crystal growth; Models of surface kinetics; Numerical analysis; Phase interfaces; Physics; Solid–liquid interfaces; Supersaturation; Surface diffusion; Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation; Vicinal single crystal surfaces
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/S0039-6028(01)01478-9

The transient behaviour of the surface supersaturation, caused by an abrupt (stepped) change in bulk supersaturation from one constant value σ 0 to another σ 1, is studied with the use of the surface diffusion theory of Burton, Cabrera and Frank (BCF). The presented analytical solution of the time-dependent BCF equation takes into account a phenomenological coefficient Λ s describing the kinetics of growth unit exchange between the step edge and the adsorbed layer. It is shown that the solution can be approximated by a simple expression, which enables an easy estimate of the time t s required to attain the steady-state value of the surface supersaturation. The time t s is independent of the difference between values σ 0 and σ 1 but it increases with increasing coefficient Λ s or increasing interstep distance. On the other hand, the average rate of change in the surface supersaturation during the transient state is determined neither by the coefficient Λ s nor by the interstep distance but it is proportional to the difference between values of σ 0 and σ 1 of bulk supersaturation.