An analysis of and a model for spiral growth of Czochralski-grown oxide crystals with high melting point

The spiral morphology of Czochralski-grown high melting point oxides is an unwanted phenomenon because it diminishes the yield of useful material. We differentiate in our analysis of the spiral growth between (1) the growth conditions for spiral growth (boundary conditions) and (2) the events, which can trigger the onset of spiral growth. We present a detailed description of spiral growth (3), which is based on dominating radiative heat transport and the loss of the rotational symmetry of the melt meniscus. Once the symmetry breaking of cylindrical morphology has taken place, an asymmetric cooling of the meniscus of the crystal will enhance this event and the centre of the crystal interface will grow out of the crystal rotation axis. The rotation of the out-of-centre-interface on the melt surface further deforms the meniscus azimuthally by viscous shear. This leads to the beginning of spiral growth. In later growth stages, the asymmetric ("spiral") cooling of the melt meniscus by the already grown spiral crystal above it is the main driver for the spiral growth. Our model description is supported by experimental results. We present a simplified quantitative model (4) in which the last complete spiral terrace is influencing the radiative cooling of the melt meniscus of the next growing spiral terrace. The model is based on sole radiative heat exchange between adjacent terraces and predicts a nonlinear dependence of the distance A of the spiral terraces on the pulling speed v(z), namely A=const.circle dot v(z)(1/2). This dependence indicates the trend, which was found experimentally. We propose the spiral growth of some high melting point oxides to be a kind of self-organisation. (C) 2011 Elsevier B.V. All rights reserved.