A Chemical Crystal-Forming System. Hierarchy of Limiting Principles of Thermodynamics

Crystal growth in a heterohomogeneous chemical system can be described phenomenologically on the basis of the limiting principle of nonequilibrium thermodynamics. However, the existence of two mutually exclusive principles—maximum (Ziegler’s principle) and minimum (Prigogine’s principle) of entropy production density—creates a problem in thermodynamic analysis of real crystallization processes. As a result of experiments, the crystallization conditions for four calcium phosphate phases—monetite, brushite, octacalcium phosphate, and hydroxyapatite—in a closed solution–gel chemical system have been established, and a mathematical model of formation of an amorphous phase of calcium phosphate, serving as a precursor for crystalline phases, has been proposed. Three stages of system development are observed. The thermodynamic systems whose development obeys the Ziegler’s and Prigogine’s principles, are implemented at three characteristic scale levels: for a diffusion column of full volume; for the edge section of the Lisegang strip or the surface of a growing crystal with a boundary zone having a thickness of no more than 0.5 mm; and for the contact region of metastable and stable structural varieties of phosphate crystals up to 10 µm thick. The development times of quasi-closed and open systems range from 1 h to several days.