A NUMERICAL-ANALYSIS OF DENDRITIC AND CELLULAR ARRAY GROWTH - THE SPACING ADJUSTMENT MECHANISMS

A numerical model has been used to describe the steady and the non-steady growth of array cells and dendrites in a moving linear temperature field. It was found that the four parameter numerical results could be approximated by a single parameter for a wide range of growth conditions. The practical limitation on array spacing is discussed and the upper and lower spacing limits have been modelled numerically. A new easily formulated criterion for the lower array spacing limit is deduced. The models predict a small range of stable spacings for cells and a separate range for dendrites. Cells are found to be present at low and very high velocities with dendrites at intermediate velocities. The numerical model correctly predicts the absolute stability limit and the onset of constitutional undercooling. The agreement with experiment is generally good provided anisotropy in surface energy is included. The calculated tip radii for dendrites were found to be close to that predicted by the "marginal stability condition" over the complete range of steady state array spacings and so cannot be used to select the operating array spacing. For cells the calculated tip radii was different from that predicted by the "marginal stability condition", but it is shown that the condition could be used to select a very approximate growth spacing.