On the capillary stability of the crystal–crucible gap during dewetted Bridgman process

Abstract On the physical point of view, the dewetting phenomenon is governed by the Young–Laplace capillary equation through the Laplace ( La ) and Bond ( Bo ) non-dimensional numbers. Other relevant parameters are the contact angle of the liquid on the crucible wall, θ c , and the growth angle of the solidified material, α e . In practice two different cases, θ c + α e θ c + α e ≥180°, should be considered, as they lead to different behaviors. For studying the dependence of the crystal–crucible gap ( e ) on the main parameters of the process, the non-dimensional Young–Laplace equation has been solved numerically in the axi-symmetric case and for various values of the parameters, the results are presented in term of abacuses. These calculations allowed plotting a diagram giving the values of Laplace's number as a function of the crucible radius, that furthermore fulfill the capillary stability criteria of the crystal diameter.