CRYSTAL GROWTH LAWS AND MECHANISMS FROM THE SHAPES OF CRYSTAL SIZE DISTRIBUTIONS

Two crystal growth laws can be distinguished by their effects on the shapes of crystal size distributions (CSDs):

(1) X_j+1=X_j + k_j;

(2) X_j+1=X_j + k_jX_j.

X_j is the crystal diameter after j time steps, and k_j is approximately constant for all crystals for a given time step. The first growth law is termed constant growth, or size-independent growth, because all crystals grow by the same amount during a given time interval. Eq.(2) describes proportionate growth, or size-dependent growth, because a crystal's linear growth rate will increase in proportion to its size. Calculations indicate that Eq.(2), and by analogy Eq.(1), are approximations, because k_j may contain randomness, wherein the constants are replaced by random numbers that vary between certain limits.

Growth by Eqs.(1) and (2) can be distinguished by the development of distinctly different CSDs. Constant growth causes the absolute size difference between crystals in a CSD to be maintained, whereas proportionate growth causes the relative size difference to be maintained. Therefore, growth by Eq.(1) leads to a decrease in the log-based variance (beta²) of a CSD, whereas beta² remains constant during growth by Eq.(2).

Given these relationships, we tested the hypothesis that the mechanism for growth by Eq.(1) is related to the supply of reactants to crystal surfaces by diffusion, whereas that for growth by Eq.(2) is related to supply by advection. K-alum and calcite crystals were grown under static and stirred conditions. For both mineral systems, the tendency was for constant growth (Eq.1) to occur in the static experiments, whereas proportionate growth (Eq.2) was evident with stirring. Investigations of the shapes of natural CSDs indicate that proportionate growth (Eq.2) is by far the more common growth law, thereby suggesting that advection, rather than diffusion, dominates in the supply of reactants to mineral surfaces.