The precipitation of calcium carbonate powders from aqueous solution with slow development of supersaturation. Induction periods, crystal numbers and final sizes

The precipitation of calcium carbonate was studied by slow addition of anion solution to excess cation solution and by slow mixing of equivalent cation land anion solutions at 20 °C: the final solute concentrations ( C fin were varied from 0.01 to 0.75 mole 1 −1 while the rates (R) of addition of ions were varied from 0.06 to 6 · 10 −3 ion 1 −1 sec −1 . At first, mainly heterogeneous nuclei formed continuously during induction periods; then, as the metal salt concentration in solution increased, some more heterogeneous nuclei formed but homogeneous nucleation soon predominated. The second nucleation process probably attained its maximum rate when the metal salt concentratio in solution reached its maximum value ( C max) and then probably terminated quite rapidly. Some further nuclei also formed during the growth process when crystal growth was prolonged. The final nucleus numbers (N) (and thence the crystal numbers) for slow precipitations from dilute solutions were then rather higher than the optimum number N ∞ (het) of heterogeneous nuclei in the solution; nucleus numbers then increased with increasing maxing rate according to the relations\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {N = N\infty \left({{\rm het}} \right) + N,R^{0.9} } \hfill & {\left({{\rm in solutions with excess cation}} \right),} \hfill \\ {N = N\infty \left({{\rm het}} \right) + N,R^{1.8} } \hfill & {\left({{\rm in equivalent solutions}} \right).} \hfill \\ \end{array} $$\end{document} . These numbers were similar to those noted for rapid precipitation – onto homogeneous nuclei – from calcium carbonate solutions of concentrations somewhat lower than the C max values. The final average crystal lengths of any precipitate then generally varied with mixing rate according to the relations,\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c}{l_{{\rm fin}} = {{l_1 } \mathord{\left/ {\vphantom {{l_1 } {R^{0.3} }}} \right. \kern-\nulldelimiterspace} {R^{0.3} }}} \hfill & {\left({{\rm in solutions with excess cation}} \right),} \hfill \\ {l_{{\rm fin}} = {{l_1 } \mathord{\left/ {\vphantom {{l_1 } {R^{0.6} }}} \right. \kern-\nulldelimiterspace} {R^{0.6} }}} \hfill & {\left({{\rm in equivalent solutions}} \right).} \hfill \\ \end{array} $$\end{document} . where l 1 values increased with (C fln ) 0.33 .