Ostwald Step Research Articles

New metastable form of ice and its role in the homogeneous crystallization of water.

The homogeneous crystallization of water at low temperature is believed to occur through the direct nucleation of cubic (Ic) and hexagonal (Ih) ices. Here, we provide evidence from molecular simulations that the nucleation of ice proceeds through the formation of a new metastable phase, which we name Ice0. We find that Ice0 is structurally similar to the supercooled liquid, and that on growth it gradually converts into a stacking of Ice Ic and Ih. We suggest that this mechanism provides a thermodynamic explanation for the location and pressure dependence of the homogeneous nucleation temperature, and that Ice0 controls the homogeneous nucleation of low-pressure ices, acting as a precursor to crystallization in accordance with Ostwald's step rule of phases. Our findings show that metastable crystalline phases of water may play roles that have been largely overlooked.

Diversity of transition pathways in the course of crystallization into ice VII

We report various types of pathways emerging in the course of freezing into a high pressure ice VII by large-scale molecular dynamics (MD) simulations at 10 GPa, 425 K. Some trajectories showed an apparently stepwise transition via the unique metastable "phase" in accordance with Ostwald's step rule. The metastable structure was identified as one of the tetrahedrally close-packed structures having the nature of a rotator phase (plastic phase). The unit cell consists of 21 water molecules that has not yet been reported by simulation or by experiments. Structure analysis of numerous trajectories reveals that the nucleation of ice VII easily occurs at the grain boundaries of the metastable embryos, known as epitaxy-mediated transformation in line with Ostwald's step rule. The size of the grain boundaries is thus responsible for the lifetime of the metastable phase. On the other hand, once the embryo of ice VII appears prior to that of the metastable phase in liquid, direct transition to ice VII takes place. We also show that the plastic behavior of the metastable phase is not uniform but is sensitive to the interaction strength of adjacent molecules and the local structure, thus we call "partially plastic ice".

Role of epitaxy-mediated transformation in Ostwald's step rule: a theoretical study

Crystallization following Ostwald's step rule is given theoretical consideration on the basis of the classical nucleation and growth theory. Conditions for homogeneous 3D nucleation of the thermodynamically metastable crystal, for that of the stable crystal, and for co-precipitation of them are derived from comparison of induction periods for nucleation and steady state nucleation rates of both crystal phases. It is shown that if the surface free energy of a critical 3D nucleus of the metastable phase is small enough and its shape is less anisotropic, homogeneous 3D nucleation of the metastable phase rather than the stable phase dominates. After nucleation, the metastable phase should undergo transformation to the stable phase. In addition to two familiar types of transformation, solvent-mediated transformation and direct transformation, we propose a new type of transformation, epitaxy-mediated transformation, which is induced by heterogeneous nucleation and growth of the stable phase on the preexistent crystal of the metastable phase. The general conditions for three competitive processes, growth of the metastable phase, solvent-mediated transformation and epitaxy-mediated transformation, are obtained on the assumption that transformation and growth proceed by 2D nucleation. The result shows that except for the case of co-precipitation, 3D nucleation of the stable phase in solvent-mediated transformation is possible only near or below the equilibrium concentration for the metastable phase. Also, the smaller edge energy of a 2D nucleus of the stable phase and its less anisotropy are more advantageous to epitaxy-mediated transformation. Epitaxy-mediated transformation sometimes results in a polycrystal whose arrangement of components is dominated by the symmetry of the metastable phase. In parallel, heterogeneous nucleation on the metastable phase can act as a trigger of direct transformation, as transformation proceeds from the surface to the center of the crystal.

Phase and morphological transitions of titania/titanate nanostructures from an acid to an alkali hydrothermal environment

A systematical investigation was established to uncover the phase transition of titania/titanate nanostructures in acidic and alkaline media. X-ray diffraction was used to identify the phase composition and phase transition behavior, and field emission scanning electron microscopy was employed to elucidate the morphological transitions of the titania/titanate products, which resulted in the determination of a phase and morphological transition diagram of titania/titanate nanostructures in connection with the acid/alkali concentrations. The crystal growth of rutile nanorods and anatase nanoparticles was proposed following Ostwald's ripening mechanism, but crystal growth of brookite and titanate products should follow another formation mechanism according to Ostwald's step rule, which reveals the phase transitions from layered structure to brookite, dititanate or trititanate under hydrothermal treatment. The anatase samples and anatase–rutile composite obtained in 0.1 M HCl exhibited excellent photocatalytic activities in the photodegradation experiments of methyl orange, salicylic acid and phenol solution under UV irradiation.

Selection mechanism of polymorphs in the crystal nucleation of the Gaussian core model

The principle of polymorph selection upon crystal nucleation is one of the fundamental problems in crystallization. Recently we found that for hard spheres the crystal polymorph is already selected by locally favoured packing symmetry in a metastable supercooled state. Here we study whether this scenario is also valid for soft spheres. To do so, we investigate the homogeneous nucleation process of the Gaussian core model (GCM) in supercooled states by means of Monte Carlo computer simulations. We use bond orientational order parameters, which characterize local packing symmetries, to follow the formation of solid nuclei and to distinguish between different polymorphs. We concentrate on two state points, at low and high pressure respectively, for which macroscopic thermodynamics dictates the formation of the different polymorphs (fcc and bcc crystals respectively). We show that the nucleation of the different crystalline structures does not follow Ostwald's step rule of crystallization, and that, despite the underlying phase diagram, the bcc phase is always favoured. In analogy to hard sphere systems, we find a new criterion for polymorph selection: crystallization occurs in precursor regions of high bond orientational order, and the crystal which first nucleates is the one that has the closest symmetry to these ordered regions in the supercooled state.

Reaction coordinates for the crystal nucleation of colloidal suspensions extracted from the reweighted path ensemble

We study the mechanisms of the homogeneous crystal nucleation from the supercooled liquid to the crystal phase in the Gaussian core model for colloidal suspensions with the aim to find optimal reaction coordinates. We introduce a set of novel collective variables based on the local structure of particles. By applying likelihood maximization of the committor function for the reweighted path ensemble constructed by replica exchange transition interface sampling, we select the optimal reaction coordinates from the set of collective variables. We find that the size of the cloud of prestructured particles surrounding the crystalline nucleus enhances the description of the transition. Further, we show that the rearrangement of the inner core of the nucleus according to Ostwald's step rule is a separate process, independent of the growth of the nucleus.

Kinetics Study of Crystallization with the Disorder–bcc–fcc Phase Transition of Charged Colloidal Dispersions

Structure transformation (disorder-bcc-fcc) in charged colloidal dispersions, as a manifestation of the Ostwald's step rule, was confirmed by means of reflection spectrum (RS) measurements in our previous study. By taking advantage of a reflection spectrum containing plenty of information about the crystallization behaviors, time-dependent changes of parameters associated with the crystal structure and composition during the disorder-bcc-fcc transition are reported by treating the data from RS in this article. In addition, Avrami's model is adopted to analyze the transition process and investigate the transition rate. On the basis of the above investigations, associated kinetic features of crystallization with the disorder-bcc-fcc transition are described.

Size-dependent growth of polymorphs in nanopores and Ostwald's step rule of stages

More than 100 years after Ostwald postulated his step rule of stages, predictive understanding as to early crystallization stages of polymorphic materials is still premature. We studied crystallization of the polymorphic pharmaceutical acetaminophen in nanoporous glasses as a model for early stages of bulk crystallization since the surface energy significantly contributes to the total Gibbs free energy of nanosized crystals in both cases. Systematic studies of transitions between different polymorphs inside nanoporous glasses show that the thermodynamic stability of the polymorphs depends on the crystal size. Accordingly, the transient occurrence of different polymorphs during crystal growth in bulk systems can be related to surface energy contributions to the total Gibbs free energy of the developing crystals. In nanosized early-stage crystals with high surface-to-volume ratios other polymorphs may be stable than in large crystals with low surface-to-volume ratios. Improved control of the crystallization of polymorphic materials by imposing well-defined confinement is a promising strategy to tailor release of polymorphic drugs and to optimize optical, electronic, magnetic and ferroelectric properties of polymorphic materials.

Formation of an fcc phase through a bcc metastable state in crystallization of charged colloidal particles

By in situ monitoring structural changes with the reflection spectrometer during the colloidal crystallization, we present direct experimental evidence of liquid-bcc-fcc phase transition in crystallization of charged colloidal particles, as a manifestation of the Ostwald's step rule. In addition, the lifetime of the bcc metastable structure in this system decreases significantly with increasing particle volume fraction, offering a possible explanation for "exceptions" to the step rule.

Motif Reconstruction in Clusters and Layers: Benchmarks for the Kawska–Zahn Approach to Model Crystal Formation

A recently developed atomistic simulation scheme for investigating ion aggregation from solution is transferred to the morphogenesis of metal clusters grown from the vapor and layers deposited on a substrate surface. Both systems are chosen as benchmark models for intense motif reorganization during aggregate/layer growth. The applied simulation method does not necessarily involve global energy minimization after each growth event, but instead describes crystal growth as a series of structurally related configurations which may also include local energy minima. Apart from the particularly favorable high-symmetry configurations known from experiments and global energy minimization, we also demonstrate the investigation of transient structures. In the spirit of Ostwald's step rule, a continuous evolution of the aggregate/layer structure during crystal growth is observed.

Phase transition and morphological evolution of titania/titanate nanomaterials under alkalescent hydrothermal treatment

A systematic morphological phase diagram of titania/titanate was determined by the most important synthesis parameters of reaction temperature and NaCl concentration via a facile one-step alkalescent approach. X-Ray diffraction and Raman spectroscopy were used to generally assess the phase composition and crystallite size of different titania/titanate samples, which were also used to investigate the phase transition behavior in connection with the synthesis parameters. Scanning/transmission electron microscopy was employed to characterize the morphology, size, and lattice plane, and to further elucidate the morphological evolution of the resulting products. According to the Ostwald's step rule, a phase transition mechanism was proposed based on our current systematic experimental results, which reveals the phase transitions from layered hydrogen titanate to anatase or brookite under hydrothermal treatment. The brookite–anatase composite exhibited excellent photocatalytic activity in the photodegradation of methyl orange, phenol and salicylic acid solution under UV irradiation.

Strategy for control of crystallization of polymorphs

The controlling factor and mechanism of the crystallization of polymorphs were investigated in various systems; i.e. amino acids, inorganic compounds (calcium carbonate), pharmaceuticals and inclusion compounds. The controlling factor depends on the systems (compounds and solvents and additives) and the crystallization methods (cooling crystallization, reactive crystallization and anti-solvent crystallization). The controlling factors for each system were found and a schematic diagram was shown. The mechanism of each controlling factor was investigated and some rules were found. It appears that the establishment of “Ostwald's step rule” depends on the systems. In the cooling crystallization of amino acids (L-glutamic acid and L-histidine), the “Ostwald's step rule” cannot be observed; however, in the crystallization of BPT esters, it is clearly established. The difference of the temperature effect between L-glutamic acid and L-histidine polymorphs may be related to the difference of the molecular conformation between the polymorphs. In the reactive crystallization of calcium carbonate polymorphs, the concentration (supersaturation) of reactant solutions, the mixing rate of the solutions, pH, stirring rate and temperature were found to be the controlling factors for the morphology and the crystallization behavior of polymorphs. As for the effect of additives it should be noted that the additive affects not only one polymorph, but on each polymorph. Then, knowing the relative effect of additives on each polymorph is important for the control. The growth kinetics of polymorphs of L-glutamic acid and the mechanism of morphology change of each polymorph were examined in the presence of L-phenylalanine (as an additive) with batch crystallization and the single crystal method. The growth rate model including the additive concentration was proposed for each polymorph and the method of the selective crystallization of the polymorphs by controlling the supersaturation and the additive concentration was also indicated. In anti-solvent crystallization of pharmaceuticals (BPT) it was shown that the addition rate of anti-solvent, initial concentration of solute and temperature are the controlling factors. With the increase of the addition rate the water composition in the nucleation zone increases, resulting in the preferential crystallization of the hydrate crystals. The transformation from BH to A form was observed, however, the transformation rate increased with a decrease in the water addition rate. It is that even when none of the A form was detected by XRD a small amount of fine crystals (A form) is included within the BH crystals and act as seed crystals for the transformation. Furthermore, the change in the molecular structure is related with a dynamic change of the polymorphic crystallization behavior as observed in L-Glu and L-His systems. The dependence of the polymorphic crystallization behavior on the molecular structure was systematically investigated using the newly synthesized BPT esters. It appeared that the conformational flexibility, the size of alkyl group of the esters and the presence of functional group influences the formation of hydrogen bond and the polymorphism. The solvent effect on the polymorphism was also examined in relation to the molecular structure. The functionality of clathrate crystals and the separation efficiency of isomers by clathrate crystals depend on their polymorphic crystallization behavior. The mechanism of the molecular recognition for the guest isomers by the host molecule is clarified. It was also elucidated that the release process of a guest biocide molecule from clathrate crystals includes polymorphic transformation.

Formation and Evolution of Metastable bcc Phase during Solidification of Liquid Ag: A Molecular Dynamics Simulation Study

On the basis of the quantum Sutton-Chen potential, the rapid solidification processes of liquid silver have been studied by molecular dynamics simulation for four cooling rates. By means of several analysis methods, the competitions and transitions between microstructures during the cooling processes have been analyzed intensively. It is found that there are two phase transitions in all simulation processes. The first one is from liquid state to metastable (transitional) body-centered cubic (bcc) phase. The initial crystallization temperature T(ic) increases with the decrease of the cooling rate. The second one is from the transitional bcc phase to the final solid phase. This study validates the Ostwald's step rule and provides evidence for the prediction that the metastable bcc phase forms first from liquid. Further analyses reveal that the final solid at 273 K can be a mixture of hexagonal close-packed (hcp) and face-centered cubic (fcc) microstructures with various proportions of the two, and the slower the cooling rate is, the higher proportion the fcc structure occupies.

Effect of the Alkyl Group in BPT-Esters on the Polymorphic Crystallization Behavior

Effect of the alkyl group of the ester in polymorphic crystallization was investigated by a rapid cooling method in ethanol solutions using BPT methyl ester [Me-est: methyl 2-(3-cyano-4-(2-methylpropoxy)-phenyl)-4-methyl-thiazole-5-carboxylate] and BPT isobutyl ester [i-But-est: 2-methylpropyl 2-(3- cyano-4-(2-methylpropoxy)-phenyl)-4-methyl-thiazole-5-carboxylate]. The crystallization of Me-est resulted in only one crystal form at every initial concentration. On the other hand, in the crystallization of i-But-est at high initial concentrations, metastable A form first appeared, and then the subsequent transformation to the stable B form occurred. At low initial concentrations, the stable form directly crystallized. Such behavior of i-But-est supports Ostwald's step rule, and it is similar to that obtained previously for BPT propyl ester. Crystallographic analysis indicated that the Me-est crystal is constructed by the sheets of a dimer that are formed by the two hydrogen bonds between the molecules. On the other hand, metastable i-But-est crystal is constructed by stacking the zigzag sheets of the molecules, and the stable i-But-est crystal is formed by stacking two types of layers. These results indicate that even a small change in molecular structure gives rise to a large difference in the polymorphic crystallization behavior and crystal structure.

Negative creep of metallic glasses as an externally-catalyzed dissipative structure within Ginzburg–Landau kinetics

Negative creep concerns annealing temperatures of metallic glasses approaching ambient where normal densification is negligible but negative dimensional change is dramatically catalyzed by a LeChatelier-like load perturbation and initially accelerated against the load by temperature and load increase. This obtains on the isotherm up to the load point and time increment where normal creep in the opposite direction begins to counter the anomalous effects. The proposed dissipative structure is based upon strain as a global average order parameter satisfying the postulated time-dependent Ginzburg–Landau (TDGL) equation and applied to Cu 60Zr 40 at 473 K. This serves as the Euler–Lagrange equation corresponding to the experimentally verified Ostwald's Step Rule which subsumes autonomous selection for near reversibility and minimum dissipation or equivalent high free energy configurations en route to equilibrium thus sustaining the G–L postulate. This quench-induced self-organizing phenomenon can be conceived as a continuous stroke potential energy-increasing heat engine driven by the quenched-in thermal energy.

Long-Lived Metastable bcc Phase during Ordering of Micelles

We report a metastable bcc phase that intervenes between a disordered micellar suspension and an fcc crystal in a block copolymer solution. Upon heating, the metastable bcc phase nucleates first, and then transforms over the course of hours to the stable fcc phase. At still higher temperatures, the fcc phase transforms to an equilibrium bcc phase. These results constitute an interesting experimental manifestation of Ostwald's step rule, and also support recent theory and simulation results whereby bcc nucleates more readily from a melt of spheres.

Proposal of Atomic Models for Formation Process of Carbonitride W(C,N) Synthesized by Normal- and High-pressure Methods

The syntheses of new mono-carbonitrides of W and/or Mo, i.e., W(C, N), Mo(C, N) and (W, Mo)(C, N), which are thermodynamically unable to be generated by using gas of normal pressure, have been succeeded by the authors by using CH4+NH3 mixed gas of normal pressure (normal-pressure method) and C powder+nitrogen gas of high pressure (high-pressure method). The formations of these mono-carbonitrides as well as of general compounds by those methods have been explained by applying traditional Ostwald's step rule and virtual-pressure concept for normal-pressure method, and Le Chatelier's principle for high-pressure method, respectively. These explanations, however, are based only on the macroscopic level, but not on the atomic level.In this paper, we newly proposed atomic models for the formation process of W(C, N) in both normal- and high-pressure methods, mainly based on the previous experimental results. The models include the concepts of nascent atoms and nitrogen molecular cluster in supercritical fluid, etc., respectively.

Mechanism of Formation of Amorphous Silica Inclusion in Silicon Deoxidized Copper

To investigate the formation mechanism of secondary amorphous silica inclusion in iron and copper, silicon-deoxidation experiment of copper at 1 423 K was performed. In the copper quenched into water after deoxidation, three types of secondary amorphous silica inclusions (pinecone-like inclusion, gourd-shaped inclusion and network-like inclusion) were observed. In the copper cooled ultra-rapidly, fine spherical inclusion and coral-like inclusion, which were secondary and amorphous, were observed. The experimental temperature of 1 423 K is not only 573 K lower than the melting point of silica 9) but also 20 K lower than the glass transition temperature of silica (1 443 K 10) ). Therefore, the presence of secondary amorphous silica inclusion should be strong evidence of the formation of liquid silica during cooling of the copper without temperature rise. It would also support the formation of secondary liquid silica inclusion in the iron alloy. Consideration based on Ostwald's Step Rule indicated that liquid silica inclusion could be formed from the supersaturated state of copper.

Control of Polymorphism in Crystallization of Amino Acid

AbstractThe crystallization mechanism and the controlling factors in the crystallization of amino acid polymorphs were investigated. It was demonstrated that the effect of supersaturation (Ostwald's step rule) was not observed for systems of either L‐Glutamic acid (α, β) or L‐Histidine (A, B). The intensive effect of temperature was shown in the crystallization of L‐Glutamic acid (L‐Glu) polymorphs, however, no temperature effect was observed in the case of L‐Histidine (L‐Hist)polymorphs. It was suggested that such a difference could be related to the difference of the molecular conformation between the polymorphs, and the contribution of the conformers in the solutions to the nucleation process of L‐Glu polymorphs. The growth of both L‐Glu polymorphs (α and β) appeared to be due to the nuclei‐above‐nuclei mechanism. With these results, temperature and supersaturation appeared to be the basic important controlling factors (the primary factors) of polymorphism. Solvents and additives (the secondary factors) also have an influence on polymorphism. The influence of ethanol compositions on the crystallization of L‐His polymorphs (A and B) was observed, and demonstrated that the solvent effect is very kinetic, i.e. the nucleation and growth rate of the A form are suppressed with an increase in the ethanol composition. The effects of L‐Phenylalanine as an additive on the crystallization and transformation rates were shown in batch crystallization. The effect of L‐phenylalanine on the growth rate and morphology of L‐Glu polymorphs was also examined using the single crystal method in a flow system. The relationship between the additive concentration and the growth rate of each polymorph was expressed by the proposed equation. The importance of the kinetics of the crystallization for control of the polymorphic crystallization was demonstrated. The supersaturation needed for control of the selective crystallization of the polymorph was also calculated. From these results the controlling factors for the crystallization of polymorphs have been classified in order to clarify their complex interrelationship.

Thermodynamic Analysis on Metastable Alumina Formation in Aluminum Deoxidized Iron Based on Ostwald's Step Rule and Classical Homogeneous Nucleation Theories.

A mechanism for the formation of unstable alumina (δ, y, and κ-alumina) in Al-deoxidized iron has been investigated on the basis of Ostwald's Step Rule and two homogeneous nucleation theories. The two homogeneous nucleation theories include a simplified theory in widespred use and the other is a modified theory in which the Gibbs free energy change of the parent iron phase is taken into consideration. Comparison of the chemical potential of various aluminas from the standpoint of the Ostwald's Step Rule showed that the unstable alumina could form from the liquid iron alloy supersaturated with oxygen. Moreover, the rule revealed that there is a possibility of liquid alumina formation. The two homogeneous nucleation theories also proved the possibility of the formation of unstable and liquid alumina. The latter nucleation theory indicated the easier nucleation of liquid and unstable aluminas than that for α-alumina from the liquid iron containing oxygen contents in excess of the critical value of nucleation at 1 873 K. In contrast, nucleation was rare for oxygen contents less than the critical point at 1 873 K. However, unstable alumina can be formed during cooling and solidification since the oxygen contents of the critical point decreases with temperature decrease. When iron solidifies whilst in the supercooled condition, the nucleation rates of unstable and liquid alumina can be accelerated as a result of the oxygen enrichment at the solidifying front. The authors propose a mechanism of the network-like or coral like inclusion formation by taking into consideration of the liquid alumina formation.