Showing papers on "Nucleation published in 1988"

A discretized population balance for nucleation, growth, and aggregation

Abstract: The population balance for batch aggregation of particulate suspensions is recast in a form that may be solved simply and accurately. The transformed equation is deduced with the introduction of only one additional parameter, which is found to be a constant for all cases. The transformed equation is tested by comparison with some analytical solutions with which it is found to be in excellent agreement. In particular, the equation is shown to predict correctly the rate of change of total particle number and volume. Compatible descriptions of linear growth and nucleation are developed with similar success. The method is then applied to modeling the in vitro growth and aggregation of kidney stones (calcium oxalate monohydrate crystals). It is found that these phenomena are well described by McCabe's ΔL law, a size-independent coalescence kernel, and first-order kinetics. Simulated particle size distributions and their moments are in excellent agreement with the experimental results.

Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization

Abstract: Crystal-size in crystalline rocks is a fundamental measure of growth rate and age. And if nucleation spawns crystals over a span of time, a broad range of crystal sizes is possible during crystallization. A population balance based on the number density of crystals of each size generally predicts a log-linear distribution with increasing size. The negative slope of such a distribution is a measure of the product of overall population growth rate and mean age and the zero size intercept is nucleation density. Crystal size distributions (CSDs) observed for many lavas are smooth and regular, if not actually linear, when so plotted and can be interpreted using the theory of CSDs developed in chemical engineering by Randolph and Larson (1971). Nucleation density, nucleation and growth rates, and orders of kinetic reactions can be estimated from such data, and physical processes affecting the CSD (e.g. crystal fractionation and accumulation, mixing of populations, annealing in metamorphic and plutonic rocks, and nuclei destruction) can be gauged through analytical modeling. CSD theory provides a formalism for the macroscopic study of kinetic and physical processes affecting crystallization, within which the explicit affect of chemical and physical processes on the CSD can be analytically tested. It is a means by which petrographic information can be quantitatively linked to the kinetics of crystallization, and on these grounds CSDs furnish essential information supplemental to laboratory kinetic studies. In this three part series of papers, Part I provides the general CSD theory in a geological context, while applications to igneous and metamorphic rocks are given, respectively, in Parts II and III.

Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization II: Makaopuhi lava lake

Abstract: Crystal size distribution (CSD) theory has been applied to drill core samples from Makaopuhi lava lake, Kilauea Volcano, Hawaii. Plagioclase and Fe-Ti oxide size distribution spectra were measured and population densities (n)were calculated and analyzed using a steady state crystal population balance equation: n=n0 exp(-L/Gτ). Slopes on ln(n) versus crystal size (L) plots determine the parameter Gτ, a. product of average crystal growth rate (G) and average crystal growth time (τ). The intercept is J/G where J is nucleation rate. Known temperature-depth distributions for the lava lake provide an estimate of effective growth time (τ), allowing nucleation and growth rates to be determined that are independent of any kinetic model. Plagioclase growth rates decrease with increasing crystallinity (9.9−5.4×10−11 cm/s), as do plagioclase nucleation rates (33.9−1.6×10−3/cm3 s). Ilmenite growth and nucleation rates also decrease with increasing crystallinity (4.9−3.4 ×10−10 cm/s and 15−2.2×10−3/cm3 s, respectively). Magnetite growth and nucleation rates are also estimated from the one sample collected below the magnetite liquidus (G =2.9×10−10 cm/s, J=7.6×10−2/cm3 s). Moments of the population density function were used to examine the change in crystallization rates with time. Preliminary results suggest that total crystal volume increases approximately linearly with time after ∼50% crystallization; a more complete set of samples is needed for material with <50% crystals to define the entire crystallization history. Comparisons of calculated crystallization rates with experimental data suggests that crystallization in the lava lake occurred at very small values of undercooling. This interpretation is consistent with proposed thermal models of magmatic cooling, where heat loss is balanced by latent heat production to maintain equilibrium cooling.

The formation of quasi-icosahedral spiral shell carbon particles

Abstract: A simple, new, carbon nucleation scheme has been developed which results in quasi-single crystal particles of concentric, spiral-shell internal structure and overall quasi-icosahedral shape. Intermediates consisting of curved graphitic networks and overall growth controlled by epitaxy are key factors in the scheme which also produces buckminsterfullerene, C60B, as an inert by-product. The scheme which explains, for the first time, the occurrence of polyhedral carbonaceous particles may also apply to soot and circumstellar dust formation.

Precipitation of the δ-Ni 3 Nb phase in two nickel base superalloys

Abstract: The precipitation of the equilibrium δ-Ni3Nb phase has been studied in two niobium bearing nickel base superalloys—INCONEL 718 and INCONEL* 625—both of which are hardenable by the precipitation of the metastableγ″-Ni3Nb phase. The morphology and the distribution of precipitates have been examined and the crystallographic orientation relationship between the austenite and theδ phases has been determined. The nucleation of theδ phase at stacking faults within pre-existing δ" precipitates has been discussed.

Nonclassical nucleation theory for the gas-liquid transition

Abstract: We use density functional methods to develop a new nonclassical theory for the homogeneous nucleation of the gas to liquid phase transition. The extent of agreement between our results and the classical prediction of Becker, Doring, and Zeldovich is strongly dependent on the range of the attractive potential which we employ. We show that our predictions are consistent with experimental data using cloud chambers, and we suggest several directions in which experimentalists might look in order to find nonclassical effects. In particular, we suggest that cavitation (gas bubble formation in a liquid subjected to tensile stress) should nucleate at a significantly greater rate than that predicted by classical theory.

Nucleation of a new phase from the interaction of two adjacent phases: Some silicides

Abstract: The reactions of metal layers with their silicon substrates resulting in the formation of various silicides are considered generally not only as phenomena common to all diffusion couples where new phases are formed, but also as typical of all transitions from two to three phases. The conditions under which such transitions will display the same characteristics as encountered in the usual one-to-two phase transitions (condensation, crystallization, boiling) are analyzed by comparison to the classical theory of nucleation. Because of the lack of knowledge about the exact values of the relevant parameters, the discussion is carried out mostly in descriptive thermodynamic terms. Although nucleation effects are analyzed in general terms, the main focus of attention is a class of reactions where nucleation dominates the formation of a new phase; a salient feature of these reactions is the absence of any equilibrium temperature, although the nucleation temperatures are relatively well defined within narrow limits. Nucleation effects are correlated to such material characteristics as the stability of the nucleated phases, and to such kinetic characteristics as the sequence of phase formation. The modification of the energy levels of the different phases brought about by stress, ion bombardment, or the replacement of usual phases by metastable ones, are considered with respect to their effect on nucleation processes. The nearly total absence of literature references to nucleation in metal-metal diffusion couples is discussed with respect to some specific aspects of the metal-silicon reactions.

Structural instability and relaxation in liquid and glassy phases near the fragile liquid limit

Abstract: We consider two sorts of structural instability of glassy substances, each of which may be released by a relaxation process with its own characteristic relaxation time, and specific kinetic features. The first of these is the instability against relaxation out of the amorphous state into the crystalline state, while the second is the instability against relaxation within the amorphous state itself. The latter may often involve relaxation out of a homogeneous amorphous phase into a two-phase amorphous structure, but we will not specifically consider this liquid-liquid phase separation process here. In most glasses, the former (which is no more than the characteristic nucleation time) is much longer than the latter time. However, there are important classes of glasses, for instance the metallic glasses, in which the former is in fact the shorter time, a fact which is responsible for the inability to observe the glass transition phenomenon in such substances. In this paper we will be considering the relation between these two times and the specific kinetics of each. The nucleation time has been the subject of theoretical developments over a number of decades, and details will be omitted in order to concentrate on experimental studies of this phenomenon. We will described briefly the recently developed DSC techniques for determining the classical time-temperature-transformation curves for a variety of supercooled liquids, and the relation of these to the nucleation curves. The relaxation process within the amorphous state, which can be observed for cases where the nucleation time is relatively long, has a number of features which currently lack a complete explanation. In most cases the relaxation process is non-Arrhenius in its temperature dependence, nonexponential in its time dependence, and nonlinear in its structural state dependence. Some examples taken from glasses at the “fragile” edge of the deduced viscosity-temperature pattern for glassforming liquids are dealt with in detail, and the distinction between shear stress relaxation and thermodynamic stress relaxation is made. The possibility that near T g the latter relaxation time remains Vogel-Fulcher in form with T 0 ≡ T K (the Kauzmann temperature), in contrast with the common observations for (the decoupled) shear relaxation, is raised. Strong support for this notion is found in the current “specific heat spectroscopy” results of Nagel and co-workers. Microscopic relaxation processes, as observed using spectroscopic probes and neutron scattering techniques, are reviewed, and the difference in non-exponentiality from macroscopic relaxation are examined in the light of current theories. Finally, secondary relaxations in ionic and molecular glasses, and their relation to the fastest of all glassy state relaxation processes, the tunnelling modes (TLS), are briefly considered.

Dynamics of Growth of Silica Particles from Ammonia-Catalyzed Hydrolysis of Tetra-ethyl-orthosilicate

Abstract: The NH3-catalyzed formation of colloidal silica particles from tetra-ethyl-orthosilicate (TEOS) in methanol and ethanol is studied by means of light scattering and Raman spectroscopy. We find that the growth is characterized by an incubation period after which no significant nucleation takes place. The particles have uniform, non-fractal structure and show low polydispersity. In the presence of excess water, the rate-limiting step is the hydrolysis, which is a first-order process in the orthosilicate concentration. © 1988 Academic Press, Inc.

Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization

Abstract: Crystal size distributions (CSDs) measured in metamorphic rocks yield quantitative information about crystal nucleation and growth rates, growth times, and the degree of overstepping (ΔT) of reactions during metamorphism. CSDs are described through use of a population density function n=dN/dL, where N is the cumulative number of crystals per unit volume and L is a linear crystal size. Plots of ln (n) vs. L for olivine+pyroxene and magnetite in high-temperature (1000° C) basalt hornfelses from the Isle of Skye define linear arrays, indicating continuous nucleation and growth of crystals during metamorphism. Using the slope and intercept of these linear plots in conjunction with growth rate estimates we infer minimum mineral growth times of less than 100 years at ΔT<10° C, and nucleation rates between 10−4 and 10−1/cm3/s. Garnet and magnetite in regionally metamorphosed pelitic schists from south-central Maine have CSDs which are bell-shaped. We interpret this form to be the result of two processes: 1) initial continuous nucleation and growth of crystals, and 2) later loss of small crystals due to annealing. The large crystals in regional metamorphic rocks retain the original size frequency distribution and may be used to obtain quantitative information on the original conditions of crystal nucleation and growth. The extent of annealing increases with increasing metamorphic grade and could be used to estimate the duration of annealing conditions if the value of a rate constant were known. Finally, the different forms of crystal size distributions directly reflect differences in the thermal histories of regional vs. contact metamorphosed rocks: because contact metamorphism involves high temperatures for short durations, resulting CSDs are linear and unaffected by annealing, similar to those produced by crystallization from a melt; because regional metamorphism involves prolonged cooling from high temperatures, primary linear CSDs are later modified by annealing to bell shapes.

Heterogeneous and epitaxial nucleation of protein crystals on mineral surfaces.

Abstract: Fifty different mineral samples were tested as potential heterogeneous or epitaxial nucleants for four commonly crystallized proteins. It was found, by conventional protein crystallization techniques, that for each protein there was a set of mineral substrates that promoted nucleation of crystals at lower critical levels of supersaturation than required for spontaneous growth. Numerous examples, involving all four proteins, were observed of modification of crystal habit and, in some cases, unit cell properties promoted by the presence of the mineral nucleants. In at least one case, the growth of lysozyme on the mineral apophyllite, it was shown by lattice analysis and x-ray diffraction that the nucleation and growth of the protein crystal on the mineral was likely to involve a direct lattice match.

Channel formation in Pb-Sn, Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH 4 CI-H 2 O

Abstract: The formation of segregation channels during the unidirectional solidification of base chilled ingots has been studied as a function of composition in binary Pb-Sn and Pb-Sb and ternary Pb-Sn-Sb alloys. The patterns of channel distribution were characterized in the binary and ternary systems and are described as functions of temperature gradients, growth rates, dendrite spacings, and interdendritic permeabilities. Channels appear to nucleate at random across a dendritic front and subsequently to interact as they propagate, decreasing in density across the front. Assuming that the interdendritic spacing is the characteristic distance for a liquid perturbation, yields critical effective Rayleigh numbers which lie within a factor of x40 for both metallic and aqueous systems. This correlation is close, considering the sensitivity to any assumed dimension and the range of material properties involved, and is taken to support a model for channel nucleation occurring close to the dendritic growth front.

Diamond crystal growth by plasma chemical vapor deposition

Abstract: We have grown diamond crystals and polycrystalline diamond films from CH4/H2/O2 gas feeds in a simple, high‐power density, 2450‐MHz discharge tube reactor. Single‐crystal growth rates over 20 μm/h have been achieved. The material has been analyzed using Raman spectroscopy, Auger spectroscopy, and x‐ray diffraction. Control of nucleation is a major problem for growing sound films, and the high temperatures currently required for growth will limit applications. Oxygen additions were necessary to deposit diamonds over the range of feed composition we studied.

Homogeneous Nucleation Rate for Highly Supercooled Cirrus Cloud Droplets

Abstract: A mixed-phase hydrometer growth model has been applied to determining the nucleation mode and rate responsible for the glaciation of a highly supercooled liquid cloud studied jointly by ground-based polarization lidar and aircraft in situ probes. The cloud droplets were detected at the base of an orographically induced cirrus cloud at temperatures between −34.3° and −37.3°C. The vertical distribution above cloud base of two independent data quantities, the aircraft-measured water and ice particle concentrations and the lidar linear depolarization ratio, have been compared to model predictions for both the homogeneous and heterogeneous drop-freezing. modes. It is concluded that, although activated ice nuclei may have contributed to the glaciation of the cloud, homogeneous nucleation was the dominant mode. Accordingly, a homogeneous nucleation rate ∼106 times greater than that predicted by classical theory, but ∼103 times less than laboratory measurements would suggest is found to be appropriate at...

The kinetics of ferrite nucleation at austenite grain boundaries in Fe-C alloys

Abstract: The nucleation kinetics of grain boundary allotriomorphs of proeutectoid ferrite at austenite grain faces have been measured in three high purity Fe-C alloys as a function of isothermal reaction time and temperature. Several correction techniques, including discrimination between different nucleation sites and the effect of carbon diffusion fields on further nucleation of ferrite, were incorporated into a stereological procedure utilizing the SchwartzJSaltykov size distribution analysis. This analysis enabled the number of ferrite particles per unit unreacted grain boundary area to be obtained as a function of isothermal reaction time, and thus the time-dependent nucleation kinetics to be obtained as a function of temperature and carbon concentration. These rates were then compared with those predicted by classical heterogeneous nucleation theory using various models for the critical nucleus. It was concluded that viable critical nuclei must have predominately low energy interphase boundaries. Only a very small fraction of the austenite grain face area appears to be capable of supporting nucleation.

Supercooling and nucleation of silicon after laser melting

Abstract: Bulk nucleation of crystalline Si at a supercooling of 505 K was observed following pulsedlaser-induced melting of thin films. If the nucleation was homogeneous, the estimated nucleation rate of ${10}^{29}$ events/${\mathrm{m}}^{3}$ \ifmmode\cdot\else\textperiodcentered\fi{} s implies a liquid-Si-crystalline-Si interfacial energy of 0.34\ifmmode\pm\else\textpm\fi{}0.02 J/${\mathrm{m}}^{2}$. In addition, observation of crystalline nucleation bounds the interface energy between amorphous Si and liquid Si to be g 0.20 J/${\mathrm{m}}^{2}$. This laser melting technique is applicable to nucleation studies in a wide variety of materials.

Electrodeposited Cu‐Ni Textured Superlattices

Abstract: Artificially layered materials of alternating 2–3 nm thick copper and nickel layers have been produced by electrodeposition on oriented single‐crystal copper substrates. X‐ray diffraction examination of thin layers chemically removed from the substrate showed that a coherent, relatively homogeneous coating, with a strong epitaxial relationship, had been produced. In particular, artificially layered Cu‐Ni alloys displaying a textured [110] orientation were obtained by electrodeposition. Noncoherent nucleation leads to the presence of various amounts of randomly oriented alloy grains on all substrates but, in particular, for the [100] orientation.

Transformation Kinetics of Diphasic Aluminosilicate Gels

Abstract: The formation of mullite in diphasic aluminosilicate gels of stoichiometric composition was studied by quantitative X-ray diffraction (QXRD) and electron microscopy (AEM and SEM). The transformation is preceded by an incubation time which is apparently an activated process with an activation energy of 236 ± 15 kcal/(g·mol) (∼987 ± 63 kJ/(g·mol)). Microscopic observations show that mullitization occurs via nucleation and growth as a mechanism either interface-controlled or controlled by short-range diffusion near the interface. The kinetic time exponent (n), determined by microstructural and QXRD observations, is close to 1.3. The transformation kinetics involve a nearly constant nucleus density, and time-dependent growth rate for nearly spherical grains. A linear time-temperature-transformation diagram is observed.