THE INCORPORATION OF CONVECTION IN 1D MODELS OF FLOAT-ZONE AND TRAVELING SOLVENT TECHNIQUES

In the present paper we develop an analytically solvable 1D model of t he thermal regime of float zone and traveling solvent zone processes w ith the incorporation of the convective transport to heat transfer ins ide the molten zone and with account of the dependence of the temperat ure of the solid/liquid transition on the melt composition. We conside r two limiting cases of convective transport: (i) natural convection a nd (ii) thermocapillar, so-called Marangoni convection. The model matc hes well with two different sets of numerical simulation data. The cal culations are carried out for the specific case of the float zone of L aB6 and the float zone traveling solvent technique of LaB6 in an exces s of La as a solvent. The calculations show that convection transport plays a crucial role in the formation of the temperature regime in the melt. The Marangoni convection is important for the heat transfer in a molten zone of any height while the natural convection is important when the zone height becomes large enough. It is shown that the excess of La leads to a strong decrease of (i) the melting temperature, (ii) the heating power necessary to form the zone of a given height and (i ii) the maximal temperature inside the melt.