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[MIS12-P03] Conversion of crystal phase by temperature cycling
Keywords:Phase conversPhase conversion, Temperature cycling, Cluster, Solution growth
Materials have some crystal structures. The crystal structure of the most stable state is unique and other structures are metastable thermodynamically. Even if the metastable crystal appears temporarily, that is well known as the Ostwald’s step rule, the large stable crystal forms in equilibrium.
We demonstrate a numerical calculation for the conversion from stable crystals to metastable crystals in a solution with a periodic change of temperature. The generalized Becker-Doering model is introduced. The ordinary Becker-Doering model is described for a nucleation phenomenon and includes the monomer incorporation to crystals. Our model includes the cluster incorporation to crystals of the same phase. Two parameters distinguish the phases in this model: solubility and surface tension. We set the solubility of the metastable phase as larger than that of the stable phase and the surface tension of the metastable phase is equal to that of the stable phase for simplicity. Thus, in the nucleation process from supersaturation, the metastable phase does not appear based on the Ostwald’s step rule, even temporarily. We apply the periodic change of the temperature modulation to this system. The values of the solubilities and the surface tensions vary with the temperature.
When the amount of the metastable crystals in the initial state is larger than that of stable crystals in the initial state, it is possible that metastable crystals eat up the stable crystals completely. The difference between the mass of stable crystals and that of metastable crystals is amplified exponentially. This feature is similar to the Viedma ripening, which is complete chiral symmetry breaking in crystal distribution of chiral crystals. We make a conversion diagram with the initial mass difference and the solubility ratio, and found a jump of the boundary. From the detailed analysis, the metastable phase cannot exist stably even under temperature modulation below a certain solubility ratio. The subcritical pitch fork bifurcation is realized.
We demonstrate a numerical calculation for the conversion from stable crystals to metastable crystals in a solution with a periodic change of temperature. The generalized Becker-Doering model is introduced. The ordinary Becker-Doering model is described for a nucleation phenomenon and includes the monomer incorporation to crystals. Our model includes the cluster incorporation to crystals of the same phase. Two parameters distinguish the phases in this model: solubility and surface tension. We set the solubility of the metastable phase as larger than that of the stable phase and the surface tension of the metastable phase is equal to that of the stable phase for simplicity. Thus, in the nucleation process from supersaturation, the metastable phase does not appear based on the Ostwald’s step rule, even temporarily. We apply the periodic change of the temperature modulation to this system. The values of the solubilities and the surface tensions vary with the temperature.
When the amount of the metastable crystals in the initial state is larger than that of stable crystals in the initial state, it is possible that metastable crystals eat up the stable crystals completely. The difference between the mass of stable crystals and that of metastable crystals is amplified exponentially. This feature is similar to the Viedma ripening, which is complete chiral symmetry breaking in crystal distribution of chiral crystals. We make a conversion diagram with the initial mass difference and the solubility ratio, and found a jump of the boundary. From the detailed analysis, the metastable phase cannot exist stably even under temperature modulation below a certain solubility ratio. The subcritical pitch fork bifurcation is realized.