Nucleation Induction Time Research Articles

Induction time for crystal growth

Abstract An expression is derived for the induction time for crystal growth. It is shown that this induction time is not uniquely determined, and is dependent on experimental conditions. Induction time for crystal growth, unlike the induction time for nucleation, becomes unbounded if defined rigorously.

Induction time analysis of nucleation and crystal growth in di- and metasilicate glasses

Abstract The nucleation and crystallization kinetics in three glasses with stoichiometric composition Li2O·2SiO2, Na2O·2CaO·3SiO2 and 2Na2O·CaO·3SiO2 are investigated by determining the nucleation and crystal growth rates and the corresponding induction times. An analysis of the induction times for crystal growth and nucleation indicates that in the two soda-lime metasilicate glasses nucleation and crystallisation of the crystals occur subsequently, i.e., no time lag exists between the two experimentally determined induction times. By contrast with this absence of a time lag, a considerable time lag appears in the case of lithium disilicate, indicating a metastable phase formation and probably compositional changes during crystallisation in this early stage. Transmission electron microscopy shows that a metastable phase (denoted by transient-phase) occurs in the early stage which is totally dissimilar to lithium disilicate and which acts as a precursor to the equilibrium crystallisation of lithium disilicate. This two-stage process leads to the conclusion that the theory of homogeneous nucleation cannot be applied to the Li-disilicate melt.

Rapid precipitation of biochemicals

The production of uniform fine crystalline particles is highly desirable for pharmaceutical products in order to enhance stability and dissolution rates and, thereby, to favour high bioavailability. Precipitation under high-supersaturation conditions favours nucleation over growth processes and will result in smaller particles. Little fundamental information is available on the kinetics of nucleation and growth of organic compounds when precipitated under high-supersaturation conditions by the addition of a non-solvent. In order to accurately measure such rapid kinetics a technique for rapid mixing prior to any nucleation events is required. The authors report the use of a grid mixing device with a mixing time of less than 3 ms to measure the nucleation and growth rates of L-asparagine and lovastatin when precipitated by non-solvents at high supersaturation ratios. Nucleation induction times as small as 60 ms are observed, and the growth of asparagine at high supersaturation is found to be described by the same rate law as previously determined at low supersaturations.

Temperature dependence of protein solubility — determination and application to crystallization in X-ray capillaries

A scintillation method was developed for determinations of the temperature dependence of the solubility, and of nucleation induction times of proteins, in 50–100 μl volumes of solution. Solubility data for lysozyme and horse serum albumin were obtained for various combinations of pH and precipitant concentrations. These data and the nucleation induction information were used for dynamic crystallization control, that is, for the controlled separation of nucleation and growth stages. Individual lysozyme and horse serum albumin crystals were grown in 15–20 μl solution volumes contained in X-ray capillaries.

Revival of the Induction Time Concept in the Theory of Polymer Crystallization

To monitor early stages of spherulite growth, a microscopical method has been worked out based on the photometrical measurement of the intensity of depolarized light during isothermal crystallization. Application of the technique to polypropylene yields the evidence of existence of nucleation induction time which reflects the processes taking place prior to the onset of spherulite growth, viz. the formation of stable crystal nuclei. Using the method, it is possible to evaluate also systems with a dispersed phase, the interfacial relations being reflected in the induction time of the nucleation on the surface of the dispersed phase. Application to the model PP/carbon fibres system yields differing results for carbon fibres of various provenance and of various properties.

Breakdown of Passive Film on Copper in Bicarbonate Solutions Containing Sulfate Ions

The formation, breakdown, and composition of the surface films formed on a copper rotating disk electrode at 25°C were studied by potentiodynamic and potentiostatic pulse measurements. The present results explain the nature of the pit initiation process, especially some characteristic values of pitting phenomena such as the critical breakdown potential and the induction time for pit nucleation on passive copper in contact with bicarbonate solution, , containing aggressive sulfate ions. It was found that the critical breakdown potential, , and the inhibition potential, depend on the concentration of the aggressive anion A and inhibitor anion I according to the equations: and . The critical potentials are explained by the adsorption of sulfate anions on the metal surface and their competition with the inhibitor. On the basis of the experimentally obtained dependencies for the critical breakdown potential and induction time on halide concentration and potential, respectively, the various theories for pit initiation on a passive metal in contact with a solution containing aggressive ions were tested. The experimental data are analyzed in terms of the point defect model, the 2‐D nucleation and growth model, and the sulfate nuclei model for passivity breakdown. The validity of the particular models is discussed. Numerical analysis enabled the evaluation of several unknown parameters which are characteristic for the models proposed.

Transient nucleation induction time from the birth–death equations

For the set of finite-difference equations of Becker–Döring an exact formula for the induction time, which is expressed in terms of rapidly convergent sums, is presented. The form of the result is particularly amenable for analytical study, and the latter is carried out to obtain approximations of the exact expression in a rigorous manner and to assess its sensitivity to the choice of the nucleation model. The induction time, tind, is found to be governed by two main nucleation parameters, Φ*/kT, the normalized barrier height, and g*, the number of molecules in the critical cluster. The ratio of these two parameters provides an assessment of the importance of discreteness effects. We study the exact expression in both the continuous (g*→∞) and the asymptotic (Φ*/kT→∞) limits. Asymptotic results for tind are compared with those previously reported from simulation studies as well as with tind obtained numerically from the exact expression in the present study. Also, the accuracy of the Zeldovich equation, which is produced in the continuous limit, is discussed for several nucleation models.

Breakdown of the Passive Film on Polycrystal and Single Crystal (100) Nickel by Chloride

Chloride ion‐induced breakdown of the passive films on polycrystal and single‐crystal (100) nickel surfaces was studied in terms of the film breakdown potential and induction time as a function of chloride concentration. The film was grown in a deaerated chloride‐free borate buffer solution at to a constant thickness of 4.5 mC/cm2, and and were determined potentiodynamically and potentiostatically, respectively, after injecting chloride ion into the solution. The film breakdown potential was found to increase linearly with the potential scan rate, and the critical pitting potential (the breakdown potential at zero scan rate) decreased linearly with . The presence of grain boundaries on the polycrystal surface decreases the intercept of the relationship slightly, but did not significantly change the slope. The intercepts are higher than most of the values reported in the literature, although the slope is similar to previously found values. The induction time for pit nucleation on the two crystal forms for was found to decrease with increasing potential. The experimental data are analyzed in terms of the halide nuclei and point defect models for passivity breakdown.

Computer simulation of nucleation and crystal growth

The computer simulations of four crystallization phenomena: three- and two-dimensional nucleation, expansion of a monomolecular layer and crystal growth, are described in detail. They are based on the same molecular model as used in the classical theory of Volmer and others. The dependence of nucleation frequencies and rates of growth on supercooling is of the same order as in the classical theory. Their dependence on the interfacial free energy parameter is significantly different, large deviations being observed at low values of this parameter. Nuclei as defined in the classical theory do not show up in the simulations. Crystal growth appears to be controlled by successive initiations of monomolecular layers (the degree of supercooling not being small) if an initiation frequency is taken into account that follows from the simulation of secondary nucleation. Deviations arise at low values of the interfacial free energy parameter, where the growth face appears to be rough, whereas it is smooth at high values of this parameter. Induction times in the systems studied are negligible. Potential induction times for secondary nucleation are too small to influence rates of crystal growth. The simulation model allows many alterations and the building-in of various constraints. The method, therefore, seems appropriate for the study of various kinds of growth and adsorption phenomena.

On some probabilistic aspects of the nucleation process

Nucleation is a random phenomenon. The analysis of the expressions giving the time-dependence of the probability of formation of at least one (P⩾1), two (P⩾2), etc, nuclei makes it possible to assess the role of transient effects in nucleation kinetics as well as to evaluate the parameters of the process. Experiments on the electrolytic nucleation of mercury and cadmium on platinum are carried out by means of the double pulse potentiostatic technique ensuring reproducible working conditions and a precise control of the factors governing the deposition process. It is shown that the distribution of the number of the deposited nuclei as well as the P⩾m(t) plots (t = time) obtained are in good agreement with formal probabilistic considerations. The P⩾1(t) functions are S-shaped over the whole interval of variation of the overvoltage (equivalent to the supersaturation) which is an important indication of the non-steady state character of the process of electrolytic nucleation within the studied time intervals. A semianalytical procedure is developed to calculate stationary nucleation rates and induction times (in the sense of Zeldovich) from the experimental results. The outlined probabilistic approach may prove very useful in situations in which the time-dependence of the mean number of the nuclei formed at constant supersaturation is not available experimentally.

Determination of critical pitting potentials of stainless steels in aqueous chloride environments

A new method for determining the critical pitting potentials, E c, of stainless steels in aqueous chloride environments has been developed. The technique has the advantage of defining a discrete value of E c which is dependent only on the composition and structure of the metal and the test environment. The irreproducibility of E c measurements frequently discussed in corrosion literature is readily explained on the basis of these new measurements. Experimental data are presented for Fe-Cr and Fe-Cr-Mo alloys in a hot sea-water environment. These data suggest that the passivity of the alloys is attributable to an adsorbed layer on the metal surface, and that further film growth merely influences the induction time for pit nucleation.

Heterogeneous Nucleation of Bi and Ag on Amorphous Substrates (In Situ Electron Microscopy Studies)

Quantitative measurements of the kinetics of nucleation in some simple substrate-overgrowth systems have been made using improved in situ electron microscopy techniques. The nucleation of bismuth and silver on evaporated carbon and the nucleation of bismuth on evaporated SiO substrates were studied as a function of substrate temperature and impinging flux. The results were analyzed in terms of the phenomeno-logical theory of nucleation and in terms of Walton's atomistic model of condensation from the vapor phase. Both theoretical concepts led to specific conclusions concerning such nucleation parameters as the number of atoms in the critical nucleus n* and the free energy of desorption ΔGdes. The substrate temperature and impingement flux dependence of the maximum number of deposit particles that can be accommodated on the substrate surface were determined and tentatively interpreted on the basis of nucleation-limited surface migration. Some nucleation induction time observations were made and were related to the clustering kinetics of adatoms, the growth process of individual nuclei, and the instrumental limitations of the detection method.

Role of Kinetics in Early Diagenesis of Carbonate Sediments: ABSTRACT

Because most modern carbonate sediments are a mixture of several metastable carbonate phases, studies of such deposits necessarily represent instantaneous observations of disequilibrium systems which may be undergoing slow but significant change. Conventional thermodynamic (equilibrium) models may be of little value in interpreting such observations, but kinetic and steady-state models promise to afford a clearer understanding of depositional and early diagenetic processes in natural environments. End_Page 633------------------------------ Reaction rates for a wide variety of reactions involving carbonate phases and aqueous solutions have been investigated by monitoring pH changes as the reactions proceed. Rate constants are available for the escape of CO2 from solution, for the dissolution of a wide range of calcium and calcium-magnesium carbonate minerals, and for growth rates of aragonite and calcite. Preliminary studies of nucleation energy and nucleation induction time have been carried out, but these studies have limited applicability to natural systems where abundant nuclei already are available. In certain cases where carbonate deposition is assumed to occur, tetracycline marking techniques have been employed to test the validity of the kinetic models. On the basis of the experimental results, kinetic theory allows the following predictions: (1) in the presence of organisms, surface waters will appear oversaturated with respect to both CO2 and dissolved carbonates during daylight hours; (2) the composition of a solution in contact with mixed carbonate phases will be determined by the more rapid of the simultaneous dissolution and precipitation reactions, with dissolution generally being the controlling process; and (3) in the absence of a continuing supply of metastable phases, equilibration will be approached more rapidly by the removal of metastable phases (either by solution or by replacement) and much more slowly by interstitial carbonate precipitation. Each of these observations is supported by field evidence. The observations made suggest the need for caution when applying the results of field study of modern carbonate environments to the interpretation of ancient carbonate rocks. End_of_Article - Last_Page 634------------