Construction of metastable zone width prediction models and process optimization for ammonium dihydrogen phosphate crystallization

To achieve precise control of industrial crystallization processes and enhance product quality and production efficiency, in this study, the aqueous solubility and saturated solution density of the target substance were first systematically determined within 308.15-338.15 K, and the Apelblat equation, Van′t Hoff equation, and polynomial equation were employed for thermodynamic correlation of the solubility data. The results showed that the Apelblat equation had the smallest error and optimal precision （fitting coefficient: 0.999 64）; the calculated dissolution enthalpy and entropy were 11.265 0 kJ·mol⁻¹ and 14.872 6 J·mol⁻¹·K⁻¹, respectively, confirming the dissolution process as endothermic and non-spontaneous. Subsequently, the effects of cooling rate and stirring rate on the metastable zone width （MSZW） were investigated, and the Nývlt theory, self-consistent Nývlt-like theory, and 3D nucleation theory model were applied for MSZW prediction and comparative analysis. It was found that increasing temperature, decreasing cooling rate, or increasing stirring rate significantly narrowed the MSZW, and the self-consistent Nývlt-like theory model exhibited the best predictive performance and applicability （fitting coefficient: 0.9）. Finally, a quantitative correlation between MSZW, saturation temperature, and cooling rate was constructed based on this model, providing critical theoretical basis and data support for the optimal design of industrial crystallization process parameters （e.g., cooling program, stirring intensity）.