Transition Zone Theory Compared to Standard Models: Reexamining the Theory of Crystal Growth from Melts

Abstract

Ideas proposed at the beginning of the 20th century to describe the temperature dependence of crystal growth rates have become accepted as the “standard model.” Specifically, it was proposed that rates are controlled by a thermodynamic driving force, liquid/solid interfacial surface energy requires crystal growth to occur at step or kink sites, and particle diffusion/viscous relaxation also controls the rate of growth. However, as described in this article, these underlying assumptions are inconsistent with the fact that crystal growth from supercooled melts is microscopically irreversible, and the well-known fact that short- and intermediate-range order in melts and crystals is essentially equivalent, precluding the existence of sharp interfaces and the need for material diffusion. By contrast, we recently introduced the Transition Zone Theory of crystallization, TZTc, a condensed matter analogue of Eyring’s transition state theory that uses Kauzmann’s conception of configurational entropy and Adam and Gibbs’ ideas of cooperativity to describe the ensemble characteristics governing crystal growth rates. Here, the TZTc model is applied to the same sets of inorganic oxides and organic molecules that were used to evaluate the apparent decoupling of viscosity from the standard model, as well as to several other materials. Without exception, the TZTc model provides a superior fit to temperature-dependent crystal growth-rate data. With a single model accurately describing diverse crystallizing systems, the three parameters extracted from TZTc, for the first time, provide a platform with which to compare and contrast chemical/physical factors that influence crystallization reactions.

Indomethacin: The Interplay between Structural Relaxation, Viscous Flow and Crystal Growth

“…An alternative revision of the u kin -η decoupling was provided by Schmeltzer et al [ 76 ], who introduced a decoupling temperature T d , below which the decoupling between the diffusion and viscosity occurs, with the decoupling exponent being temperature dependent (a qualitatively similar finding was recently obtained for amorphous selenium [ 77 ]). An interesting alternative to the above-mentioned standard models for crystal growth is the approach of Martin et al [ 78 ], who introduced the “transition zone theory” based on the cooperating ensemble of structural entities driving the mechanistic formation of the crystalline phase.…”

“…The concept of cooperating regions (as introduced in [ 78 ] for the description of the crystal growth) can also qualitatively be applied to explain the fourth mutual relationship in the present discussion: that between the structural relaxation and crystal growth. Over the past years, such a correlation has been suggested based on the structural behavior related to the distribution of the relaxation times (expressed by β in the TNM model) within the concept of cooperatively rearranging regions [ 79 ].…”

Kinetic Behavior of Quaternary Ammonium Hydroxides in Mixed Methane and Carbon Dioxide Hydrates

“…This behavior was also reported in earlier studies, which indicate that sufficient subcooling temperature is required for efficient nucleation [ 43 , 44 ]. Also, in a subcooling temperature system, the hydrate nucleation and formation behavior has been proven to be controlled by the activation barrier of the system [ 45 ]. Thus, at higher subcooling temperature there is a large negative entropy of activation which causes the hydrate to form faster and grow more compared to systems at lower subcooling [ 45 ].…”

“…Also, in a subcooling temperature system, the hydrate nucleation and formation behavior has been proven to be controlled by the activation barrier of the system [ 45 ]. Thus, at higher subcooling temperature there is a large negative entropy of activation which causes the hydrate to form faster and grow more compared to systems at lower subcooling [ 45 ]. The induction time results suggest that all of the QAHs considered were able to work as kinetic inhibitors.…”

“…The RIP induction time data also show the influence of subcooling. At the higher subcooling temperature of 274.0 K, the RIP induction times values of the QAHs are observed to be higher than at 277.0 K. This is due to the large negative entropies of activation generated at, the higher temperature [ 45 ].…”