Ostwald Step Rule Research Articles

Energetic clues to pathways to biomineralization: precursors, clusters, and nanoparticles.

Nanoparticle and nanocluster precursors may play a major role in biomineralization. The small differences in enthalpy and free energy among metastable nanoscale phases offer controlled thermodynamic and mechanistic pathways. Clusters and nanoparticles offer concentration and controlled transport of reactants. Control of polymorphism, surface energy, and surface charge on nanoparticles can lead to morphological control and appropriate growth rates of biominerals. Rather than conventional nucleation and growth, assembly of nanoparticles may provide alternative mechanisms for crystal growth. The Ostwald step rule, based on a thermodynamic view of nucleation and growth, is supported by the observation that more metastable phases tend to have lower surface energies. Examples from nonbiological systems, stressing the interplay of thermodynamic and kinetic factors, illustrate features potentially important to biomineralization.

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.

Reaction sequences occurring in dense Li-doped sialon ceramics: influence of temperature and holding time

Spark Plasma Sintering (SPS) has been used to consolidate a lithium-doped duplex α–β sialon with the overall composition Li0.5Si9.5Al2.5O2.0N14. The kinetics of densification has been studied, and the phase transformation, reactions and grain growth occurring in the dense compacts upon further heat treatment have been investigated. Two sources of Si3N4 powders were used, namely α- and β-Si3N4. Green bodies heated at a rate of 100 °C min−1 yielded fully dense compacts at 1450 °C (α-Si3N4) and 1500 °C (β-Si3N4) without holding, and these compacts consisted mainly of a locally formed liquid and precursor Si3N4 particles. Upon further heating it was observed that α-sialon is formed initially, irrespectively of whether α-Si3N4 or β-Si3N4 powder is used as Si3N4 source; and when α-Si3N4 is used as starting powder, almost monophasic α-sialon compacts are formed before any transformation to β-sialon takes place on further heating. When β-Si3N4 is used as starting powder the formation of β-sialon is kinetically promoted, and compacts containing α-sialon, β-sialon and β-Si3N4 are obtained before the equilibrium phase assemblage is reached, i.e. a lithium-doped duplex α–β sialon ceramic. These observations can be interpreted in terms of the Ostwald step rule. Grain growth does not occur until the equilibrium phase assemblage has been established. The separation of grain growth from densification and phase transformation has implications for preparing Si3N4-based nano-ceramics and provides possibility for further studies of the kinetics of grain growth in Si3N4-based ceramics.

Weathering of Chlorite: II. Reactions and Products in Microsystems Controlled by Solution Avenues

AbstractWeathering of chlorite adjacent to macro- and micro-passages (fissures) in regolith units has been studied to determine the alteration mechanisms and products and compare them to those that prevail at a distance from the open passages. The micro-fissures in the saprolith units evolve as a function of weathering with an increase in micro-fissure density and their infilling with ferriargillans corresponding to an increase in weathering intensity. In the saprock and saprolite units, goethite-rich bands with surrounding reddish haloes invade the chlorite adjoining the micro-fissures. In the reddish haloes surrounding the goethite bands and fissures, the phyllosilicates alter to an intimate mixture of goethite, kaolinite, feroxyhyte and halloysite with the possible nanoscale presence of other fine-grained iron aluminosilicates such as hisingerite and smectite. In the fine saprolite, the weathering products after original chlorite adjoining the micro-fissures bearing ferriargillans, alter directly to ferriargillan products — kaolinite and goethite. The lack of orientation of the products with the parent phyllosilicates indicates the operation of a dissolution-precipitat ion mechanism which is in contrast to the topotactic alteration mechanism functioning at a distance within the phyllosilicate grain assemblage. The differences in alteration mechanisms and products of chlorite weathering in different microsites suggest the rate of weathering of chlorite can differ in microsites within individual regolith units. The presence of fine-grained metastable products in the form of feroxyhyte and halloysite adjoining the fissures suggests an Ostwald Step Rule sequence during alteration of phyllosilicates with rapid oxidation of Fe and the presence of Si in the microsite considered the main factor favoring fine-grained metastable products.

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.

X-ray diffraction studies on nitric acid dihydrate

Amorphous nitric acid hydrates in the concentration range 25 to 50 mol% HNO3 were prepared by low-temperature quenching of the respective HNO3/H2O aerosols. Subsequently, a properly selected thermal treatment enabled the phase distribution of two thermodynamically stable (NAM, β-NAT) and three metastable phases (α-NAD, β-NAD, α-NAT) to be determined between 180 and 232 K by X-ray powder diffractometry. The intriguing phase distribution of the two nitric acid dihydrates was interpreted on the basis of the classical nucleation theory and Ostwald's step rule using known crystallographic data on α- and β-NAD.

Comparison of Evolution of Trioctahedral Chlorite/Berthierine/Smectite in Coeval Metabasites and Metapelites from Diagenetic to Epizonal Grades

AbstractThe evolution of texture, structure and chemical composition of chloritic clays in coeval pairs of metabasites and metapelites of a prograde sequence from the Bükk Mountains has been investigated using electron microscopy techniques. Samples are from the Bükkium (innermost Western Carpathians, Hungary) that underwent Alpine metamorphism, ranging from late diagenesis to epizone for pelites and from prehnite-pumpellyite to greenschist facies for the metabasites.Although bulk-rock compositions, textures and primary minerals are different, chlorite evolved at similar rates in coeval metabasites and metasediments, but along different paths. The principal similarities in the prograde sequence are a decrease in the percentage of interstratified material in both dioctahedral and trioctahedral phyllosilicates and increase in thicknesses of chlorite and illite crystallites. The principal difference is in the type of interstratification in chlorite, with berthierine in metapelites, and smectite (saponite) in metabasites, although smectitic mixed layers also occur in the former. The evolution of trioctahedral phyllosilicates is marked by a decrease in the number of mineral species with increasing grade, chlorite, sensu stricto, being the only trioctahedral mineral at higher grades. This is consistent with the trend in reaction progress where both metastable systems (metabasites and metapelites) tend toward the same end-member, thermodynamically stable chlorite, as well as texture (crystal size), and where all intermediate states are metastable, and determined by the Ostwald step rule.

Ostwald's step rule and hyperthermodynamics: examples from decomposition in gold-nickel

The classical free-energy minimum and Gibbs' topological Phase Rule have explicit counterparts in isothermal dissipative phase space as exhibited within the kinetics of autonomous microstructure formation, in part attributable to the kT/2 of equilibrium fluctuation free energy per atom degree of freedom which is inherited by the kinetic state. The near-reversible modulated decomposition and subsequent decoherency followed by coarsening in Au-Ni alloys is examined within this and other analogues of the minimum free energy requirement. This observed sequence for T<T c is contrary to the original conclusion that there is a unique transition to a lamellar near-equilibrium state. Furthermore, equilibrium empirical studies have indicated that Ll 2 ordering of the form Ni 3X with X:Ni lattice parameter ratios > 1.12 excludes the appearance of such a compound since this ratio is 1.15. On the other hand, our observations identify Ni 3Au superlattice satellites in modulated alloys at 773K consistently suggesting a dynamical selection to higher free energy trajectories in accord with Ostwald's Step Rule. Van Santen proved this to be corollary to the Onsager-Prigogine Principle of Minimum Dissipation (PMD) and states that where distinct isothermal patterning sequences are feasible nature selects a sequence passing near reversibly through high free energy states rather than decaying directly to the ground state. The Step Rule as a theorem in irreversible thermodynamics is also activated by the time-dependent Ginzburg-Landau equation in contrast to the extra-constrained free energy trajectories associated with the Cahn-Hilliard equation in application to double well decomposition. This article reports the multi-faceted empirical high free energy sequence of states in the decomposition of Au-Ni which strongly supports Ostwald's insight as an extension of the concept of hyperthermodynamics through optimality of the dissipation.

Structure and Thermal Stability of the New Intermetallics MgPd2, MgPd3, and Mg3Pd5 and the Kinetics of the Iodine-Catalyzed Formation of MgPd2

Three new binary intermetallics in the palladium-rich part of the magnesium–palladium system have been identified and characterized by combining preparative methodologies with powder X-ray diffraction techniques and thermochemical analyses. MgPd2 decomposing in the solid state at 628(2)°C adopts a Co2Si-type structure: space group Pnma, a=5.4421(2), b=4.1673(2), c=8.0129(3) Å. MgPd3 crystallizes in a Al3Zr-type structure: space group I4/mmm, a=3.92263(7), c=15.6527(4) Å. It decomposes in a peritectoid reaction at 704(2)°C. The kinetics of the iodine-catalyzed synthesis of MgPd2 have been studied. The reactions seem to follow Ostwald's step rule. Four intermediate phases were identified, among them was Mg3Pd5, a previously unknown phase with a Ge3Rh5-type structure: space group Pbam, a=5.427(2), b=10.588(5), c=4.1304(12) Å.

Formation of nm-Size Dispersoids from Supersaturated Solid Solutions of Aluminium

The principles are discussed which control the formation of ultra fine heterogeneous microstructures from supersaturated solid solutions of Al-alloys. The role of defects in nucleation of metastable or stable phases is emphasized with respect to the formation of dispersoids of nano-sized particles, which in turn cause maximum hardening. Finally, a + /-rule (atomic size ratios) and an extended version of Ostwald's step rule are applied as gidelines for obtaining this objective.

Ostwald step rule in films of metastable nanocrystalline alloys Fe-C prepared by pulsed plasma vaporization

Ferromagnetic nanocrystalline Fe(C) films were prepared by pulsed plasma vaporization. A comprehensive investigation of the structure and magnetic properties made it possible to identify the type of short-range order here and to establish the sequence of structural states occurring in these films in the process of thermal relaxation: fcc-Fe(C)→hcp-Fe(C)→bcc-Fe+C. On the basis of an analysis of the metastable phase diagrams using Ostwald’s rule, it is shown that the observed scenario of the structural transformations in these metastable nanocrystalline alloys Fe(C) is a natural phenomenon.

Evidence for aqueous clusters as intermediates during zinc sulfide formation

Using zinc sulfide as an example, we demonstrate a plausible stepwise process for the formation of minerals from low temperature aqueous solutions. The process occurs with the formation of soluble complexes that aggregate into soluble rings and clusters. The final moiety in solution has a structure similar to the moiety in the first formed solid, which is a restatement of the Ostwald step rule. Titrations of aqueous Zn(II) with bisulfide indicate that sulfide clusters form at concentrations of 20 μM (or less) of metal and bisulfide. Precipitation does not occur according to voltammetric measurements using a mercury electrode and UV-VIS (ultra-violet to visible) spectroscopic data. UV-VIS data and filtration experiments indicate that the material passes through 0.1 μm Nuclepore and 1000 dalton filters. The complexes form rapidly (kf > 108 Ms−1), are kinetically inert to dissociation and thermodynamically strong. Although a neutral complex of 1:1 (ZnS) empirical stoichiometry initially forms, an anionic complex with an empirical 2 Zn:3 S stoichiometry results with continued addition of sulfide. Gel electrophoresis confirms the existence of a cluster that is negatively charged with a molecular mass between 350 and 750 daltons. On the basis of known mineral and thiol complex structures for these systems, a tetrameric cluster unit of Zn4S6(H2O)44− is likely. Molecular mechanic calculations show that this cluster is structurally analogous to ZnS minerals (particularly sphalerite) and is a viable precursor to mineral formation and a product of mineral dissolution.The formation of Zn4S6(H2O)44− can occur from condensation of Zn3S3(H2O)6 rings, which are neutral molecular clusters. The Zn atoms on one Zn3S3(H2O)6 ring combine with the S atoms on another Zn3S3(H2O)6, to lead to higher order clusters with loss of water. The Zn4S64− species form by the cross-linking of two neutral Zn3S3 rings by added sulfide; thus a Zn–S–Zn bridge forms across the rings with subsequent rearrangement and condensation to Zn4S64−; this combination results in a sphalerite-like cluster. If the rings condense without additional sulfide, a wurtzite-like structure could form. All condensations result in sulfide displacement of water from Zn to form Zn–S bonds. Water loss is an example of an entropy-driven process, which leads to a more favorable thermodynamic process. These clusters would be resistant to oxidation by O2. Voltammetric experiments indicate neutral and anionic clusters for Zn and agree with ion chromatographic data from the sulfidic waters of the Black Sea.

準安定相の析出と溶液媒介相転移のカイネティクス

This study summarizes the principal factors on nucleation, growth and polymorphic transformation termed “solution-mediated phase transformation” of some thermodynamically metastable phases in nature. The formation of the metastable phases occurring occasionally in hydrothermal deposits and sedimentary rocks is explained by the empirical Ostwald step rule, where the surface free energy and degrees of supersaturation are important factors. Transformation from a metastable phase to a stable polymorph in a solution can be kinetically analyzed by the relative rates of dissolution and growth of the two phases. The solubility of opal-CT as an example of metastable phase is usually higher than that of quartz as the stable phase, but this relation reverses in the case of nm-size grains according to the mesoscopic effect. In the latter case both solubilities of opal-CT and quartz become distnctly higher, and so the polymorphic relation among the silica minerals in nature is inferred to be in accordance with the Ostwald step rule. In contrast to solid-state transformation, metastably crystallized wurtzite appears to transform readily into stable sphalerite under hydrothermal conditions. This suggests that the solution-mediated transformation can be rapidly attained as compared with the solid-state transformation, showing that the dissolution-precipitation mechanism is predominant in the low-temperature polymorphic transformations.

Homogeneous nucleation and the Ostwald step rule

We compare the pathways for homogeneous nucleation in a number of different systems. In most cases, the simulations show that the nucleation pathways are markedly different from what is assumed in classical nucleation theory. We find that homogeneous nucleation exhibits, at the microscopic level, features that were formulated over a century ago by Ostwald to account for the nucleation of metastable bulk phases. We observe that the structure of the precritical nuclei may differ qualitatively from that of (post)critical nuclei. Surprisingly, in the interface of the larger nuclei, traces of the structure of the smaller nuclei survive.

TEM study of progressive alteration of igneous biotite to kaolinite throughout a weathered soil profile

TEM characterization of progressive alteration of igneous biotite to kaolinite throughout a weathered soil profile was carried out to study the mechanisms of the reaction from biotite to kaolinite. A biotite-like phase with d (001) ≅ 10.5 Å but with a higher Al/Si ratio and lower Fe, Mg, and K contents forms as a first, intermediate alteration product of igneous biotite. This phase is referred to as altered biotite. Two different alteration mechanisms are responsible for the altered biotite-kaolinite reaction: (1) reaction of one layer of altered biotite to form two layers of kaolinite and (2) transition of one layer of altered biotite to one layer of halloysite, which subsequently reacted to form one layer of kaolinite. Metastable intermediate altered biotite and halloysite form at low temperatures, where reactions are sluggish, as consistent with the Ostwald step rule, and in direct contrast to equivalent reactions at high temperatures.

Range of metastability of tetragonal zirconia in some rare earth doped zirconia fibers

Studies on the thermal treatment of amorphous zirconia (gel, precipitate, etc.) have shown that its conversion to crystalline forms usually starts around 400±500 8C [1±4], and that the precise temperature of conversion may vary with the composition (e.g. the type and amount of cationic dopants, hydroxyl content). It has been reported by various workers [2± 4] that the product of this initial crystallization is a metastable tetragonal (t) phase, not the thermodynamically stable monoclinic (m) phase. Further, it has been shown that this metastable t-phase persists, even at higher temperatures within the stability range of the m-phase before ®nally converting to the latter. Thus, for an undoped zirconia gel, crystallization mainly to the t-phase was observed at 400 8C, and t! m conversion at 1000 8C [4]. Generally speaking, this follows Ostwald's step rule [5]. In addition, the apparent stabilization of t-ZrO2 at low temperatures has been explained to be a function of structural similarities of an amorphous phase with the t-phase [3], crystallite size [6], effect of strain [5] etc., apart from the presence of ionic impurities (as mentioned previously). Naskar and Ganguli [7] recently studied the crystallization behavior of rare earth (RE) doped zirconia gel ®bers that were obtained by spinning doped zirconium acetate sols. They showed (Fig. 1) that the metastable t-phase obtained from ZrO2RE2O3 gel ®bers yields partially or fully to the mphase at higher temperatures as a function of the size of the cationic dopant (2 mol % rare earth oxide in each case). Fig. 1 indicates that although all the dopant cations yielding t-ZrO2 were larger in size than Zr4‡ (La . Pr . Nd . Sm . Gd . Dy . Zr), the larger cations among them yielded the phase with progressively shorter thermal ` stability'' ranges. On

Disequilibrium during metamorphism: the role of nucleation kinetics

Abstract The sluggishness of nucleation, one of the most poorly understood and least-discussed processes involved in mineral reactions, is an important cause of disequilibrium during metamorphism. Both field-based and experimental petrological studies show that metastable phases can persist far from equilibrium on long time scales because the stable phases are unable to nucleate. This behaviour applies not only to solid-solid reactions but also to some dehydration and melting reactions. Although the degree of overstepping required for nucleation during polymorphic phase transformations is relatively small (2–4 kbar on an experimental time scale), nucleation can be much more sluggish for reactions involving two or more product phases. When reactions occur at conditions of large overstepping due to delayed nucleation, reaction rates can be very fast because of the effect of the large free energy change on growth kinetics. Under these circumstances, new metastable phases may form instead of the stable mineral assemblage, as predicted by the Ostwald step rule. Such metastable phases can persist during metamorphism, even during high-strain ductile deformation and fluid influx, but without any obvious texture evidence to indicate that they are metastable.

天然における準安定相の生成と消滅

Formation of a thermodynamically metastable phase instead of a stable phase during crystallization has been interpreted by the Ostwald step rule. The rule was applied to natural crystallization of minerals in complex systems in the present paper. Phase transition from a metastable to stable phases and/or two dimensional nucleation of a stable phase on a pre-existing metastable phase are possible during growth of a metastable phase. Disappearence of a metastable phase is therefore strongly related to these processes, resulting in the formation of complex textures in grown crystals. The complex texture in cordierites from hornfels was then interpreted based on the growth and transformation of a metastable phase.