Experimental measurements of colloidal crystallization in a wide range of volume fractions of charged particles were performed to investigate the liquid−metastable−stable transition process. To fit the obtained experimental data, we developed a theoretical model to formulate the kinetics of the concurrent liquid− metastable and metastable−stable transitions. This model is wellsupported by our observations. We found that when the ratio of the metastable−stable transition rate to the liquid−metastable rate is very large, the metastable state can become undetectable, although it still exists, offering a possible explanation for very few exceptions to Ostwald's step rule.
■ INTRODUCTIONColloidal crystallization has attracted a great deal of attention as a model system for mimicking the atomic or molecular counterparts, and also for assessing the validity of classical crystal growth theories.1−5 Understanding the nature of the structural evolution during nucleation and growth is still a fundamental and challenging issue in condensed-matter science.6,7 One of the major relevant topics is Ostwald's step rule, 8 first proposed in 1897 as an empirical rule, stating that in general it is not the most stable, but the least stable, polymorph that crystallizes first.However, Ostwald's step rule is not yet a universal law for two reasons. First, there are exceptions (although very few) to the rule. Second, an undisputed theoretical basis for the rule has not been formulated successfully. Over the past 100 years, various attempts were made to reach the goal, but none of them were successful. In 1978, on the basis of the mean-field treatment, Alexander and McTague 9 published their striking result predicting that a body-centered cubic (bcc) structure should be formed first regardless of whether a more thermodynamically stable one exists, as long as the first-order nature of the transition from the liquid is not too distinct. Since then, a great deal of research attention has been devoted to finding the existence of the metastable bcc phase in various systems.10,11 Among these efforts, our previous studies focused more on the issues of the structural evolution in colloidal crystallization. 12,13 We quantitatively demonstrated bcc's formation and face-centered cubic (fcc)'s growth at the expense of metastable bcc, confirming the existence of the metastable bcc phase. However, determining how to explain the exceptions to the step rule is still an interesting issue. To explore this more deeply, we conducted a series of experiments in an extended range of volume fractions, Φ, covering the phase behavior involved in entire liquid−metastable−stable (L−M−S) transitions. To fit the obtained experimental data, we also proposed a new theoretical model and found that the model fits the data very well.Analyzing our experimental data with an appropriate theoretical model is critical for a better understanding of the phase transition kinetics. Dating back to 1940s, the Kolmogorov, Mehl, Johnson, and Avrami (KMJA) phenomenological mo...