Ostwald Step Rule Research Articles

The crystallization kinetics of amorphous boron

The transition of amorphous boron into the crystalline state has been investigated by differential thermal analysis (DTA) at different heating rates. DTA curves were transformed into transitional kinetic relations using the heat balance equation. Equations for the formation process of α- and β-rhombohedral boron were obtained using differential and integral methods in a least-squares refinement of the experimental kinetic curves with respect to various theoretical models. As a result of the investigation a metastable diagram of elementary boron was constructed, which determines the regions of existence of amorphous and crystalline phases and limits the interval of applicability of Ostwald's step rule.

The Ostwald step rule

L'observation empirique de la cristallisation a partir de solution montre que celle-ci s'effectue par etapes de telles sorte que les phases instables thermodynamiquement apparaissent en premier, suivies des phases thermodynamiquement stables. On montre que cette regle minimise la formation d'entropie

On the role of cubic structure in ice nucleation

To clarify the formation mechanism of snow polycrystals the possibility of formation of a cubic ice embryo is discussed on the basis of the homogeneous nucleation theory for supercooled water formed from ambient water molecules in the phase of supersaturated vapour. In this connection, attention is paid to a finding from a model of broken hydrogen bonds that the plane {111} of a cubic ice crystal has a smaller specific interfacial energy than each of the {0001} or {10ovbar|10} planes of a hexagonal ice crystal. Hence, it follows that a critical cubic embryo has a smaller activation energy than a critical hexagonal embryo below a critical temperature; namely, Ostwald's step rule (Stufenregel) holds for a change from cubic ice to hexagonal ice below a critical temperature. This discussion is reinforced by examining, from the viewpoint of this step rule, the observed misorientation of the c-axis of natural snow polycrystals and the results of experiments using frozen water droplets.

多結晶雪の発生機構

To clarify the formation mechanism of snow polycrystals, which have the misorientation of c-axis at 70.5°, the possibility of formation of a cubic ice nucleus (diamond structure) is discussed on the basis of the homogeneous nucleation theory for supercooled water formed in the phase of supersaturated vapour. From the difference of specific interfacial energy between a hexagonal ice and a cubic ice, it follows that a critical cubic nucleus has a smaller activation energy than a critical hexagonal nucleus below a critical temperature ; namely, Ostwald's step rule (Stufenregel) holds for a change from cubic ice to hexagonal ice below a critical temperature.

Crystallization and phase transformation of sodium orthoferrites

Upon heating mixtures of α-Fe 2O 3 powder in a sodium hydroxide melt at around 200°C, unstable β-NaFeO 2 crystallizes in the first reaction stage and transforms spontaneously to stable α-NaFeO 2. The process is typical of the Ostwald Step Rule. When γ-Fe 2O 3 is used as the starting material, instead of α-Fe 2O 3, stable α-NaFeO 2 always crystallizes out. It was clearly observed that even though the reactions are of the dissolution and recrystallization type, three-dimensional structural relations can be preserved between the reactant and the product crystals. The nucleation mechanism is discussed on the basis of topotaxy.

Crystal nucleation in a three-dimensional Lennard-Jones system. II. Nucleation kinetics for 256 and 500 particles

We have, by molecular dynamics computer simulation, observed homogeneous, spontaneous crystal nucleation in the 256-particle Lennard-Jones fluid at ρ*=0.91, 0.92, and 0.93, and in the 500-particle fluid at ρ*=0.92, 0.93, and 0.94. For the 500-particle system a nuclear region may be identified, and the nucleation and growth processes are found to be temporally separate. In all these events the nucleated phase was a body-centered (nearly cubic) structure. We believe this to be a manifestation of the Ostwald step rule.

The deposition of thin films of gold on cylindrical specimens by sputtering

Molecular dynamics simulations have been performed to explore the crystallization mechanism under rapid cooling for Zirconium that has body-centred cubic (bcc) and hexagonal close-packed (hcp) phases separated at 1136 K. The structural evolution was analysed in terms of the system energy, the pair (and angular) distribution function, and the largest standard cluster analysis. It is found that the critical cooling rate (γc) for vitrification is about 5.0 × 1013 K/s, and the Ostwald's step rule is applied to Zr. Crystallization always takes the pathway of supercooled-liquid (scl) → bcc → hcp, determined by the competition between thermodynamics and kinetics at different conditions. Particularly with γ decrease both the onset temperature of scl → bcc and the maximal number of bcc atoms increase; while both the onset temperature of the bcc → hcp transition and the rate of different crystalline atoms in the final solids are randomly. A rather perfect bcc phase can be obtained at γ < 1.0 × 1012 K/s, however, it is unstable and always transforms to the stable hcp phase under all conditions examined here. In the final solids, most of face-centred cubic (fcc) structures act as the hcp crystalline boundaries not comprises individual fcc phase. These findings are useful for understanding the crystallization of metals, especially for those that have a high-temperature-stabled phase.