Static stability of menisci in detached Bridgman growth

摘要

A static stability analysis is performed for the menisci that form above the crystal-crucible gap during detached Bridgman growth. The sign of the second variation of the potential energy against admissible meniscus shape perturbations is considered as the stability criterion. Parameters governing the stability are the pressure differential across the meniscus, the Bond number, the crystal radius, the growth angle between the crystal and melt, and the contact angle between the melt and the crucible. The effects on stability of confined gases adjacent to the meniscus are also examined. Axisymmetric as well as non-axisymmetric perturbations are investigated. Axisymmetric perturbation modes require coupling to the meniscus that exists at the top of the melt to ensure melt volume preservation. Both rough and microscopically smooth interior crucible surfaces, corresponding to pinned and unpinned states, are considered. Pinning extends the parameter range over which menisci are stable. The symmetry of the least stable perturbation mode depends on the Bond number and whether the menisci are pinned. For Bond numbers equal to zero, corresponding to zero gravity conditions, all menisci are statically stable.