Morphological instability of the solid-liquid interface and the supersaturation gradient in crystal growth from a high-temperature solution

The problem of morphological instability is considered within the framework of linear perturbation theory for the particular case of growth of LaB6 crystals from high-temperature solution in excess of La and B with account of the actual liquidus Lines on the relevant phase diagram of Storms and MuelIer, J. Phys. Chem. 82, 51 (1978), and Otani et al., J. Cryst. Growth 100, 658(1990). Stability is shown to be determined by the interplay of the concentration gradient which causes instability, and the thermal effect associated with heat transfer from the solidification interface combined with the slope of the liquidus line, which inhibits instability. The thermal-kinetic effect is shown to be negligibly small for the temperature of solidification in the range 2500-2900 K. An increase in the excess of La or B solvent is shown to cause a transition from stability to instability due to (i) a sharp increase in the concentration gradient and (ii) a decrease in the temperature of the solidification interface and associated decrease in the heat transfer flux from the interface into the growing crystal, and in the derivative of the equilibrium concentration versus the solidification temperature. It is shown that the breakdown of morphological instability may take place under growth conditions without onset of increasing supersaturation in front of the solidification interface if the heat conductance of the liquid is smaller than that of the solid phase.