Characterization of shape and heat flow in melt-grown crystals by an affective seed radius

Abstract

The shape of the liquid-solid interface of crystals grown from the melt by heat removal through a seed in fixed position can be described by an ellipsoid of rotation, having a linear eccentricity equal to the seed radius R. This statement is derived from the equation of heat flow and proper boundary conditions. This prediction is tested experimentally by growing KCl crystals and observing their shapes. The measured linear eccentricity R * = √ (a 2 - b 2) ( a = crystal radius, b = crystal length), is in general not equal to R. R * is interpreted as an effective seed radius characterizing the heat flow conditions of the system. R * was found to be independent of the actual seed radius R for KCl crystals grown in air and increases linearly with the crystal radius. Here the convection of the gas ambient acts as effective seed. Its radius R * approaches R if the crystals are grown at pressures below 50 Torr.