The Slow Precipitation of Sparingly-soluble Metal Salt Powders from Aqueous Solution: Mathematical Relations for the Kinetics of the Crystal Growth Processes in Different Types of Precipitation

The following types of slow precipitation, of sparingly-soluble metal salts from aqueous solution, have been analysed: precipitations without an induction period – (i) with very few microcrystallites or seeds, (ii) with microcrystallites and first/second order surface or diffusion rate-controlled growth, (iii) with very many microcrystallites; precipitations with significant induction periods – (i) with very few microcrystallites or seeds, (ii) with microcrystallites and first/second order surface or diffusion rate-controlled growth, (iii) with very many microcrystallites. Generally, in the early stages of precipitation, growth rates depend on the rate of addition of metal salt ions to the system and on the rate constant for crystal growth; in this stage, rates increase from low values to optimum values: in the later stages of precipitation, the metal salt ions are used up as rapidly as they are added to the system and growth rates then depend only on the rate of addition and on the number of microcrystallites or seeds; in this range, rates gradually decrease to low values. Mathematical relations, for the variation of crystal size with precipitation time at different stages of growth, have been derived for each of the above types of precipitation.