2000/05/26 by Klaus Kassner, Chaouqi Misbah, Kassner, Klaus +8
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0005476
40 pages, 12 figures, submitted to Phys. Rev. E
arxiv created 2000/05/26 · openalex publication_date 2000/05/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the Grinfeld instability. Moreover, we use our approach to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by comparison with a sharp-interface simulation. We then investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wavenumbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion.