The Growth of Crystals of Low Supersaturation

Growth of low energy planes of perfect crystals at low supersaturation requires two-dimensional nucleation. The formation energy of nuclei of i atoms may be written G’( = -ikT In cc+G,(i), where G( is the saturation ratio. An atomistic evaluation of G,, for a simple model, is in good agreement with the classical form G,(i) = iiD’, with a constant edge energy coefficient b’, even for very small i. /I’ includes entropy terms and is significantly lower than the unmodified edge energy coefficient b when /l/kT < 5. The evaluation /3 1: 1-2~1 where % is the latent heat, or enthalpy of solution, and c is the surface energy (with c z A/6 and /? ‘v 21./3 on low energy planes) is a useful first approximation for any crystal. j? is the primary material parameter for twodimensional nucleation (2DN) and also for screw disclocation growth (SDG) of imperfect crystals. When B/kT > 10, which is typical of growth from the vapour on low energy planes, 2DN is slower than SDG for c( 2 lOand is negligible for CC y 2. When /l/kT < 8, which is typical of melt growth, 2DN is faster than SDG at moderate supersaturation and lower at low supersaturation. When B/kT Q 2, B’ 0 and growth by either mechanism is unimpeded at all supersaturations. For 2DN growth, simple crystal forms with only low energy planes are expected when growth is impeded; the occurrence of other crystal faces indicates SDG.