Non-random Nucleation Research Articles

Non-Random Island Nucleation in the Electrochemical Roughening on Pt(111).

Many chemical surface systems develop ordered nano-islands during repeated reaction and restoration. Platinum is used in electrochemical energy applications, like fuel cells and electrolysers, although it is scarce, expensive, and degrades. During oxidation-reduction cycles, simulating device operation, nucleation and growth of nano-islands occurs that eventually enhances the dissolution. Preventing nucleation would be the most effective solution. However, little is known about the atomic details of the nucleation; a process almost impossible to observe. Here, we analyze the nuclei-distance distribution mapping out the underlying atomic mechanism: a rarely observed, non-random nucleation takes place. Special, preferential nucleation sites that a priori do not exist, develop initially via a precursor and eventually form a semi-ordered Pt-oxide structure. This precursor mechanism seems to be general, possibly explaining also the nano-island formation on other surfaces/reactions.

Evaluation of static recrystallization and grain growth kinetics of hot-rolled AZ31 alloy

The static recrystallization/grain growth kinetics of the AZ31 (Mg-3Al-1Zn, wt%) alloy were investigated employing Vickers microhardness and electron backscatter diffraction (EBSD) measurements. The AZ31 alloy was subject to a hot-rolling for 70% of thickness reduction and then annealed at various temperatures (150°C, 250°C, and 350°C) from 5 min to 24 h. First, the static recrystallization kinetics were analysed by means of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The results showed that the recrystallization occurred under two regimes both involving their own Avrami exponent/ activation energy. In regime I, the Avrami exponent was found in the range of 1.5-0.35 depending on the annealing temperature and activation energy of 74.1±5.7 kJ×mol-1. In regime II, an identical value of Avrami exponent was found (0.1-0.2) and a very low activation energy of 14.8±0.7 kJ×mol-1 was found for all annealing conditions. Non-random nucleation sites such as shear bands were considered as the main factor responsible for the deviation from the JMAK model. Moreover, the grain growth kinetics was well fitted by the general equation where . Accordingly, Qg = 109± 0.2 kJ×mol-1 which is median between grain boundary diffusion and bulk diffusion values for Mg and its alloys. The derived activation energies were discussed in terms of influencing factors such as solute drag, formation of basal texture, and microstructural heterogeneities like shear bands and twinning.

Kinetics and phase formation during crystallization of Hf64Cu18Ni18 amorphous alloy

ABSTRACT In this work, crystallization kinetics and phase formation of the Hf64Cu18Ni18 glassy ribbon were studied. It was observed that the ribbon crystallizes via two exothermic peaks. Further, the activation energy (E a) corresponding to each peak was calculated by Kissinger and Augis–Bennett methods. These methods showed nearly similar values of E a. The crystallization product of ribbon was identified by X-ray diffraction and discussed in view of prediction using the CALculation of PHAse Diagram (CALPHAD) approach. The identified phases indicate that the HfNi and Hf2Cu, Hf2Ni are formed after the first and second exothermic crystallization peaks, respectively. Further, the Avrami exponent (n) was calculated as 1.2 and 1.4 for the first and second crystallization peaks, respectively. Avrami exponent values show that crystallization takes place at non-random nucleation sites with either one or two-dimensional growth.

Effect of Silicon, Manganese and Heating Rate on the Ferrite Recrystallization Kinetics

This study presents the effects of silicon (Si) and manganese (Mn) concentration and of heating rate on the ferrite recrystallization kinetics in seven model alloys with different Si and Mn concentrations, which are of relevance for the development of Advanced High Strength Steels (AHSS). The recrystallization kinetics were studied with in-situ 2D X-ray Diffraction (2D-XRD) and ex-situ microstructure observations using Scanning Electron Microscopy (SEM). The experimentally observed differences in the recrystallization start temperature (Ts), dependent on the Si and Mn concentrations and the heating rate, can be described by combining the non-isothermal JMAK-model with a modified version of Cahn's solute drag model. The modified Cahn model takes into account - in an approximate manner - that the interaction energy of the solute atoms with the grain boundary depends on the Si and Mn concentrations in the boundary and the Wagner interaction parameters. The collective contribution of the Si and Mn atoms to the increase in the Ts with respect to the reference alloy (without Si and with very little Mn) is higher than would be expected from the simple addition of the effects of the Si and Mn concentrations alone. This means that the interaction between Si and Mn atoms leads to an additional increase in Ts, i.e. a coupled solute drag effect. For the later stages of recrystallization, we have studied the change in the number density and the growth rates of the recrystallizing grains using SEM. The observations show non-random nucleation, early impingement of the grains in the normal-direction and non-constant growth rates of recrystallizing grains.

Nonrandom γ-TuNA-dependent spatial pattern of microtubule nucleation at the Golgi.

Noncentrosomal microtubule (MT) nucleation at the Golgi generates MT network asymmetry in motile vertebrate cells. Investigating the Golgi-derived MT (GDMT) distribution, we find that MT asymmetry arises from nonrandom nucleation sites at the Golgi (hotspots). Using computational simulations, we propose two plausible mechanistic models of GDMT nucleation leading to this phenotype. In the "cooperativity" model, formation of a single GDMT promotes further nucleation at the same site. In the "heterogeneous Golgi" model, MT nucleation is dramatically up-regulated at discrete and sparse locations within the Golgi. While MT clustering in hotspots is equally well described by both models, simulating MT length distributions within the cooperativity model fits the data better. Investigating the molecular mechanism underlying hotspot formation, we have found that hotspots are significantly smaller than a Golgi subdomain positive for scaffolding protein AKAP450, which is thought to recruit GDMT nucleation factors. We have further probed potential roles of known GDMT-promoting molecules, including γ-TuRC-mediated nucleation activator (γ-TuNA) domain-containing proteins and MT stabilizer CLASPs. While both γ-TuNA inhibition and lack of CLASPs resulted in drastically decreased GDMT nucleation, computational modeling revealed that only γ-TuNA inhibition suppressed hotspot formation. We conclude that hotspots require γ-TuNA activity, which facilitates clustered GDMT nucleation at distinct Golgi sites.

Progress in characterizing submonolayer island growth: Capture-zone distributions, growth exponents, & hot precursors

In studies of epitaxial growth, analysis of the distribution of the areas of capture zones (i.e. proximity polygons or Voronoi tessellations with respect to island centers) is often the best way to extract the critical nucleus size i. For non-random nucleation the normalized areas s of these Voronoi cells are well described by the generalized Wigner distribution (GWD) Pβ(s) = asβ exp(-bs2), particularly in the central region 0.5 < s < 2 where data are least noisy. Extensive Monte Carlo simulations reveal inadequacies of our earlier mean field analysis, suggesting β = i + 2 for diffusion-limited aggregation (DLA). Since simulations generate orders of magnitude more data than experiments, they permit close examination of the tails of the distribution, which differ from the simple GWD form. One refinement is based on a fragmentation model. We also compare island-size distributions. We compare analysis by island-size distribution and by scaling of island density with flux. Modifications appear for attach-limited aggregation (ALA). We focus on the experimental system para-hexaphenyl on amorphous mica, comparing the results of the three analysis techniques and reconciling their results via a novel model of hot precursors based on rate equations, pointing out the existence of intermediate scaling regimes between DLA and ALA.

Electrochemical growth of nickel nanoparticles on carbon nanotubes fibers: Kinetic modeling and implications for an easy to handle platform for gas sensing device

An insight into the nucleation and growth mechanisms involved in the electrodeposition process of Ni nanoparticles is reported for macroscopic fibers consisting of aligned single wall carbon nanotubes (SWCNT). Electrochemical, micro-structural and Raman spectroscopy analyses have been utilized to investigate the electroactivity and the structure of the pristine and metal-decorated fibers. The study has pointed out the electrochemical properties of the bare fibers as electrode substrate and has highlighted the higher reactivity of these systems compared to conventional carbon microfibers toward metal electrodeposition phenomena.Theoretical approaches previously developed for modeling metal electrocrystallization have been employed for describing the experimental current transients. The impact of non-random nucleation and anisotropic shape of nuclei on the kinetics has been taken into account by introducing a phenomenological parameter in the equation for the time-dependent current density.It was found that an instantaneous nucleation process is responsible for a fast and efficient growth of Ni clusters on SWCNT fibers surface, which rules the formation of a hybrid metal-carbon nanostructures material with a high manageability and a potential wide field of application.The pristine SWCNT fibers have proven to be an interesting platform for the assembly of an easy to handle gas sensor device. The present results show that the decoration with the nickel nanoparticles represents an efficient strategy to produce an active hybrid material with enhanced gas sensing properties.

Nanocrystallization in spark plasma sintered Fe48Cr15Mo14Y2C15B6 bulk amorphous alloy

Spark plasma sintering (SPS) is evolving as an attractive process for the processing of multi-component Fe-based bulk amorphous alloys and their in-situ nanocomposites with controlled primary nanocrystallization. Extended Q-range small angle neutron scattering (EQ-SANS) analysis, complemented by x-ray diffraction and transmission electron microscopy, was performed to characterize nanocrystallization behavior of SPS sintered Fe-based bulk amorphous alloys. The SANS experiments show significant scattering for the samples sintered in the supercooled region indicating local structural/compositional changes associated with the profuse nucleation of nanoclusters (∼4 nm). For the samples spark plasma sintered near and above crystallization temperature (&amp;gt;653 °C), the SANS data show the formation of interference maximum indicating the formation and growth of (Fe,Cr)23C6 crystallites. The SANS data also indicate the evolution of bimodal crystallite distribution at higher sintering temperatures (above Tx1). The growth of primary nanocrystallites results in impingement of concentration gradient fields (soft impingement effect), leading to non-random nucleation of crystallites near the primary crystallization.

Phase-field modelling of microstructural evolution in primary crystallization

One of the main routes to obtain nanostructured materials is through the primary crystallization of metallic glasses. In such transformations, crystallites with a different composition than the amorphous precursor grow with a diffusion-controlled regime. Particle growth is slowed and eventually halted by the impingement between the concentration gradients of surrounding particles. Primary crystallization kinetics is not well described by the KJMA equation, and this fact was generally ascribed to both the soft-impingement effect and the non-random nucleation. However, recent phase-field simulations showed that the underlying physical reason is the change in the local diffusion properties of the amorphous precursor due to the variation of the composition during the transformation. The kinetics of primary crystallization is thus well described by considering a diffusion coefficient of the slowest diffusing species dependent on the local concentration. The nanostructure developed in such transformations is a key point to explain the macroscopic properties of these materials. In this work the grain size distributions obtained in realistic phase-field simulations of transformations with continuous nucleation and both constant and variable diffusion coefficient are presented. The obtained distributions are analyzed and the physical mechanisms responsible of their different features are recognized.

Impingement factor in the case of phase transformations governed by spatially correlated nucleation

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory fails to treat nonrandom nucleation and overgrowth processes. However, the very tractability of their solution in describing experimental data caused researchers to slightly modify KJMA's differential equation so as to extend the applicability of the model. In doing this a phenomenological parameter is introduced, named as the impingement factor. Here we analyze, in depth, the limits within which the phenomenological approach is suitable for sidestepping the difficulty of nonrandom nucleation. In particular we tackled two cases: instantaneous cluster growth where cluster overgrowth prevails and the constant nucleation rate of spatially correlated nuclei according to the hard-core model. In the last part of the paper we show that Avrami's general set theory is equivalent to the statistical mechanics of rigid disks. This permits a deeper appreciation of the KJMA theory and the nonrandom nonsimultaneous kinetics.

A New Approach on the Modelling of Isothermal Recrystallisation in Cold Rolled Ferritic Steels: An Application to Back-Annealing of Low Carbon Sheet Steels

A new approach on the modelling of isothermal recrystallisation in cold rolled ferritic steels based on Avrami equation is presented here. The new model corrects some of the fundamental shortcomings of the classical JMAK modelling, such as non-random (clustered) nucleation and decreasing grain growth velocity. It is shown that the new model successfully predicts the recrystallisation degree of the deformed material during an isothermal annealing, depending on the cold rolling grade and annealing conditions. Finally, an application for back annealed cold rolled steels is illustrated. [doi:10.2320/matertrans.MRA2008149]

Impingement function for nucleation on non-random sites

Many kinetics theories assume that nucleation of a new phase takes place on sites that are randomly located within the parent matrix. In practice, however, nuclei form at non-random sites. These sites could be situated, for example, on grain boundaries or within a heavily deformed grain or deformation band. Applying formal kinetics theories to reactions in which sites are non-randomly located may result in erroneous values calculated for microstructural quantities such as the number of grains per unit of volume, and for kinetic quantities such as the interface velocity. Non-random sites pose particularly difficult problems because formal kinetic equations might still fit measured data even when the nucleation sites are non-random, as will be demonstrated in this study. Therefore, measurement of additional parameters that are able to detect non-randomness, such as the contiguity function recommended by Vandermeer, becomes mandatory. In this work, the concept of an “impingement function” is introduced. Our impingement function aims at replacing the usual relationship between the extended and real volume fractions when nucleation takes place at non-random sites. Knowledge of this impingement function allows treating non-random nucleation sites in a manner that parallels the approach used for random sites. The impingement function by its own definition is directly related to impingement and can be seen both as a fundamental description of non-randomly located nuclei and a factor that relates kinetic properties of extended quantities to the kinetic properties of their corresponding real quantities. The new methodology was tested with the help of cellular automata computer simulation. The analysis of computer simulated data showed that the impingement function was much more sensitive to underlying non-randomness than the contiguity. Even when the non-randomness was apparently not so severe, the impingement function was able to show that impingement was significantly different from the random case.

On the validity of Avrami formalism in primary crystallization

Calorimetric data of primary crystallization is usually interpreted in the framework of the Kolmogorov [Dokl. Akad. Nauk SSSR 1, 355 (1937)], Johnson and Mehl [Trans. AIME 135, 416 (1939)], and Avrami [J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941)] (KJMA) theory. However, while the KJMA theory assumes random nucleation and exhaustion of space by direct impingement, primary crystallization is usually driven by diffusion-controlled growth with soft impingement between the growing crystallites. This results in a stop of the growth before the space is fully crystallized and induces nonrandom nucleation. In this work, phase-field simulations are used to check the validity of different kinetic models for describing primary crystallization kinetics. The results show that KJMA theory provides a good approximation to the soft-impingement and nonrandom nucleation effects. Moreover, these effects are not responsible of the slowing down of the kinetics found experimentally in the primary crystallization of glasses.

Microstructural implications of non-random nucleation protocols in nanocrystallized metallic glasses

Macroscopic properties of nanocrystallized metallic glasses are dependent of their nanostructure. The knowledge of the crystallization kinetics and its effect on the nanostructure are then essential in designing production and annealing protocols. Deviations from the Avrami kinetics in many of such systems are often interpreted in terms of either non-random nucleation or soft impingement due to overlapping concentration gradients. In this work, simple simulations of non-random nucleation processes allow us to evaluate the main features of both kinetic parameters and the nanostructure. It is shown that although non-random nucleation highly affects the nanostructure, it has a small effect on the transformed fraction evolution. Consequently, the decreasing Avrami exponents often reported in primary crystallization of metallic glasses have to be associated to a time dependent growth rate. Moreover, as similar kinetic behaviors are observed for different nucleation and growth protocols the understanding of the kinetics-nanostructure relationship becomes fundamental in studying such systems.

Phase transition kinetics in the case of nonrandom nucleation

A theoretical model is developed for describing phase transition kinetics occurring by nucleation and growth processes. The model treats the case of spatially correlated nuclei and applies to any kind of nucleation function. A stochastic approach is employed that gives the fraction of transformed phase as a function of a series in terms of the m-dots correlation functions. Truncation of the expansion up to the second order in the correlation functions leads to an analytical solution. Computer simulations based on the hard core model have been also performed confirming the goodness of the analytical approach.

Non-random nucleation and the Avrami kinetics

Abstract The theory available for obtaining the time evolution of the transformation for a nucleation and growth process, the well-known Kolmogorov-Johnson-Mehl and Avrami kinetic equation, is not accomplished for non-random nucleation processes. However, non-random nucleation protocols are very common; for example in first-order phase transitions where position-dependent nucleation protocols arise from the modification of the nucleation rates in the regions around the growing grains. The present paper attempts to study the effect of these position-dependent nucleation protocols in the overall kinetics of the transformation. Monte Carlo simulations of such processes are performed, and the deviations of the resulting kinetics of the transformation from the Avrami equation are analysed in detail. Consideration of the different effects resulting from the nucleation protocol allows us to model the transformation. A modified Avrami equation is obtained and compared with Monte Carlo simulations, giving excellen...

Kinetic simulation of primary transformations in glassy alloys

The kinetic processes of primary transformations have recently been modelled using the Avrami formalism and a mean field hypothesis [D. Crespo, T. Pradell, M.T. Clavaguera-Mora, N. Clavaguera, Phys. Rev. B 55 (1997) 3435]. However, the importance of several of the factors influencing the transformation has not been studied. In particular, the lack of randomness in the nucleation rate induced by the change in the untransformed matrix concentration has never been evaluated. This factor is of interest because non-random nucleation has been described in the literature as one of the main factors responsible for deviations from the Avrami kinetics. In this work, a kinetic Monte Carlo simulation of a primary transformation is presented. The simulation attempts to account for both the reduction in the nucleation and growth rates and the non-randomness in the nucleation protocol, due to the changes in the untransformed matrix along the transformation. The effects on the predicted time-dependent transformed fraction as well as on the microstructure are shown.

Modeling of Non-Random Nucleation Protocols

AbstractNon random nucleation processes are a subject of much interest in the study of first order phase transformations. However, the theory available to obtain the time evolution of the transformation for a nucleation and growth process, the well known Kolmogorov, Johnson-Mehl and Avrami kinetic equation (KJMA), is not accomplished if the nucleation process is nonrandom. Therefore, KJMA does not give an adequate description of the transformation kinetics.In the present paper, a non-random nucleation protocol resulting from a reduced nucleation rate due to the nearby presence of other growing grains is considered. Monte-Carlo simulations of such processes are performed, and the deviations from the Avrami kinetics observed are analyzed in detail.

X‐ray investigation of the mechanisms of phase transformations in single crystals of ZnS, ZnxCd1−xS, and ZnxMn1−xS (II). Comparison of observed and calculated diffraction effects

AbstractThe experimentally observed intensity profiles recorded from ZnS, ZnxCd1−xS and ZnxMn1−xS crystals at different stages of the 2H‐3C and 2H‐6H transformations are compared with those computed theoretically from the three parameter model in the previous paper. It is found that the 2H‐3C and 2H‐6H transformations occur by the nonrandom nucleation of deformation faults. The probability of the growth of a nucleus is much greater than that of the creation of a fresh nucleus. At least two different fault probabilities have therefore to be employed in computing the diffraction effects in each case. The transformation behaviour of ZnxCd1−xS and ZnxMn1−xS crystals is strongly influenced by variations in stoichiometry (x). Large values of x (x &gt; 0.95) favour the 2H‐3C transformation, whereas smaller values (x ≦ 0.94) favour the formation of the 6H phase. A comparison of the calculated and observed intensity distributions indicates that in some crystals the 2H‐3C and 2H‐6H transformations occur simultaneously in different regions of the same single crystal.

An X-ray diffraction study of faulting in single crystals of cubic ZnS grown from the vapour phase

Abstract An X-ray diffraction study is made in order to determine the nature of stacking faults present in vapour-grown cubic ZnS crystals, as well as in cubic crystals obtained by solid-state transformation from the 2H phase by thermal annealing. For this the point intensity distribution along the 10.L reciprocal lattice row of both kinds of disordered 3C crystals was recorded on a single-crystal diffractometer. The observed intensity profiles are found to be asymmetrically broadened and do not show any peak shifts, indicating that stacking faults present in both as-grown and annealed crystals are predominantly twin faults distributed randomly. The experimentally obtained intensity profiles are compared with those calculated theoretically for a random distribution of twin faults. The experimental results indicate (i) that the disordered 3C structures result by solid-state transformation of the 2H phase during the cooling of the growth furnace (ii) that they contain a random distribution of twin or growth faults and (iii) that the 2H-3C transformation in ZnS occurs by the non-random nucleation of deformation faults, occurring preferentially at two layer separations.