The role of surface and volume diffusion in the growth of TGS single crystals

Msasurements of the growth rates of {110} and {001} faces of triglycinsulphate (TGS) as functions of supersaturation of the solution are analyzed on the basis of the surface-diffusion model of Burton, Cabrera and Frank. Approximate values of the free activation energies of dehydratation, surface diffusion and incorporation of TGS molecules into the crystal lattice are determined. It is shown that surface diffusion is responsible for the low growth rate of {001} faces; in the case of {110} faces, this mechanism is less important at higher values of supersaturation than volume diffusion. This fact is discussed on the basis of results obtained from measurements of the influence of hydrodynamical conditions on the growth of the prismatic {110} faces of TGS crystals.List of symbols T temperature - k Boltzmann constant - KT/h atomic frequency factor - a shortest distance between growth units in the crystal - x ₀ distance between nearest kinks in a step on the surface - x _s mean quadratic displacement of growth units on the surface - volume of the growth unit in the crystal - unit free energy of the growth unit in the crystal - N ₀ number of growth units in the solution per unit volume - N _s0 number ot growth units in the adsorbed layer per unit volume - thickness of the volume-diffusion layer - thickness of the adsorbed layer of growth units on the crystal surface - d characteristic length in semi-empirical formulas for determination of - c ₀ retardation factor in the case ofx _s x ₀ - retardation factor which depends on the rate of penetration of growth units into kinks in the crystal surface, and expresses deviations from the ideal BCF function - number of active growth spirals - G _h activation free energy of dehydratation - G _a activation free energy of desorption - G _s activation free energy of surface diffusion - G _k activation free energy of penetration of growth units into kinks in the crystal surface - D _v volume-diffusion coefficient - D _s surface-diffusion coefficient - Re Reynolds number - Sc Schmidt number - Gr Grashoff number - C first constant in the BCF function - ₁ second constant in the BCF function - mean distance between equilibrium positions of growth units in the adsorbed layer