Local Nucleation Rates Research Articles

Strengthening Cu-containing high entropy alloys through ultrasonic solidification constructed heterostructures

The solidification process of FeCoNiCu1.5Al0.2 high-entropy alloy (HEA) with two FCC phases was modulated by three-dimensional (3D) ultrasounds with 20 kHz frequency and 22 μm amplitude. The statically solidified alloy was composed of a primary γ1 phase growing into coarse dendrites and a Cu-rich γ2 phase dispersed in interdendritic spacings. Once 3D ultrasounds were applied, the primary γ1 phase was refined into small equiaxed grains and the secondary γ2 phase was distributed around their grain boundaries. Based on the estimation of local sound pressure and undercooling, as well as acoustic spectra examination, it is concluded that transient cavitation was the dominant reason for the formation of tiny equiaxed γ1 phase by remarkably increasing local nucleation rate, which also promoted the generation of connected γ2 phase together with acoustic streaming effect. The yield strength, ultimate strength and total elongation for ultrasonically solidified alloy sample were simultaneously enhanced by 73 %, 54 % and 13 %, which were up to 605 MPa, 845 MPa and 35 % respectively. According to LUR tests and dislocation characterization, both hetero-deformation induced (HDI) strengthening and grain refinement strengthening contributed to the increase of yield strength, while the former mainly enhanced ultimate strength and ductility synergistically. This indicates that 3D ultrasonic solidification provides an effective approach to overcoming the strength-ductility trade-off for Cu-containing HEAs.

An atomistic theory of nucleation: Self-organization via non-equilibrium work and fluctuations

Insights from non-equilibrium statistical mechanics, highlighting the role of work and fluctuations at the microscale, are applied toward the development of a fundamental, rigorous and purely atomistic theory of nucleation. Nanoscale fluctuations in order, density and heat influence the local nucleation rate by orders of magnitude, necessitating their inclusion through a modern approach. Coarse-graining over the underlying Hamiltonian dynamics allows derivation of a microscale expression for the nucleation rate in terms of a classical path integral over far from equilibrium trajectories and their associated work. Second law violating states at the microscale, as found from the dynamics of small critical nucleation clusters, contribute exponentially to the observable macroscale nucleation rate.

Derivation and validation of a simplified analytical mass transfer model of the laminar co-flow tube for nucleation studies

A laminar co-flow tube is a device recently developed by the present team to study the formation of aerosol particles in atmospherically relevant vapor mixtures. The device employs isothermal mutual diffusion of vapors in two merging laminar gas flows, each saturated with a different vapor. The main quantity of interest, namely, the nucleation rate at which aerosol particles are formed at given temperatures and vapor concentrations, is not measured directly. Therefore, a mass transfer model is needed to evaluate the local nucleation rate and local concentrations obtained from measured integral quantities the flow rates and vapor concentrations at the inlets and the number concentration of generated aerosol particles at the tube outlet. This article presents the derivation and testing of an analytical simplified mass transfer model in which the diffusion problem is solved with approximations for simplification. The purpose of the simplified model is to provide a tool suitable for experimental design and evaluation of results that does not require lengthy computations and transparently shows the effects of the main parameters. By idealizing the velocity field in the co-flow section as plug flow and neglecting axial dispersion, the governing equations of mass transport reduce to a 1D unsteady diffusion problem in cylindrical coordinates moving with the fluid. Such a simplified model has an analytical solution in the form of an infinite series. The simplified mass transfer model is tested for particle formation in the sulfuric acid-water system. New experimental data for particle formation at temperatures of 15 ∘C and 27 ∘C at a relative humidity of 0.38 and various sulfuric acid concentrations are provided as a basis for testing. The results of the model are compared with numerical Computational Fluid Dynamics (CFD) simulations of the full mass and momentum transfer problem. The appropriate choice of plug-flow velocity for the analytical model is discussed. In this connection, hydrodynamics in the undeveloped region of the co-flow are described in detail. Based on the hydrodynamic entrance length, two essential fluid flow regimes are identified. The model results and CFD simulations show a nucleation zone with a shape resembling a candle flame located in the central part of the laminar co-flow tube, with a maximum nucleation rate at the tube axis. The main quantitative characteristics of the particle formation evaluated with the help of the simplified model and with CFD simulations are compared. It turns out that, especially when choosing the plug-flow velocity appropriately, the difference between the numerical CFD model and the simplified analytical model is less than the experimental uncertainty of the measured data. This justifies the application of the simplified mass transfer model for the purpose of quantitative evaluation of experiments with the laminar co-flow tube. This article presents new details of the mass transfer processes and evaluation procedures for the novel experimental device exemplified with a new set of experimental data for particle formation in a sulfuric acid-water system.

Measuring the activation energy barrier for the nucleation of single nanosized vapor bubbles

Heterogeneous bubble nucleation is one of the most fundamental interfacial processes that has received broad interest from diverse fields of physics and chemistry. While most studies focused on large microbubbles, here we employed a surface plasmon resonance microscopy to measure the nucleation rate constant and activation energy barrier of single nanosized embryo vapor bubbles upon heating a flat gold film with a focused laser beam. Image analysis allowed for simultaneously determining the local temperature and local nucleation rate constant from the same batch of optical images. By analyzing the dependence of nucleation rate constant on temperature, we were able to calculate the local activation energy barrier within a submicrometer spot. Scanning the substrate further led to a nucleation rate map with a spatial resolution of 100 nm, which revealed no correlation with the local roughness. These results indicate that facet structure and surface chemistry, rather than geometrical roughness, regulated the activation energy barrier for heterogeneous nucleation of embryo nanobubbles.

(Invited) Tracking Hydrodynamic Signatures of Metal Nucleation Events Via Lateral Molecular Force Microscopy

The direct visualization of local events leading to the formation of a critical nucleus remains as one of the most formidable challenges in electrodeposition. Recently, state-of-the-art video-rate scanning tunnelling microscopy has been able to follow lateral growth of Bi deposits with exquisite atomic resolution [1]. However, strong local potential bias between tip and substrate often leads to ‘shielding effects’, significantly decreasing local nucleation rates. Substrate-tip interactions in conventional atomic force microscopy also have a strong effect in local nucleation rate. In this contribution, we shall demonstrate a new approach to monitor individual nucleation events based on tracking local perturbations of hydration shells employing high-speed lateral molecular force microscopy (HS-LMFM). A unique optical feedback mechanism lies at the center of the operating mode of HS-LMFM [2,3]. Under this configuration, the position of a vertically oriented probe (VOP) is tracked by measuring the scattering of the evanescent wave of a laser impinging under total internal reflection from the back of an optically transparent electrode. As the tip approaches the surface oscillating close to its resonant frequency, the oscillation frequency is affected by the visco-elastic properties of the various hydration layers. Changes in the VOP oscillations are optically detected by the scattering evanescent field. This approach enables monitoring interaction with individual hydration layers simultaneously with, but independent of, the optical feedback. In these experiments, the tip is positioned at a distance in which shear force interactions with hydration layers of an In-doped SnO2 electrode (approximately 2.9 nm roughness level) become negligible [4]. As nucleation events are triggered, the hydration layers around individual nuclei move into a detectable range of the VOP, leading to changes in the oscillation frequency. Shear force maps uncover a highly dynamic landscape prior to the formation of stable nucleus. At constant potential, the stochastic formation and dissolution of nuclei can be observed in the sub-second time scale. The growth of a stable nucleus is also followed in real-time, illustrating the potential of this technique for probing complex phase formation phenomena at electrode surfaces. References Matsushima, H. et al. Faraday Discuss. 193, 171-185 (2016).Fletcher, J. M. et al. Science 340, 595-599 (2013).Antognozzi, M. et al. Nat. Phys. 12, 731-735 (2016).Harniman, R.L. et al. Nat. Commun. 8, 971 (2017)

Phase-field simulation of nucleation and growth of M23C6 carbide and ferromagnetic phases during creep deformation in Type 304 steel

Abstract A phase-field method was applied to the simulation of simultaneous nucleation and growth of both M23C6 carbide and ferromagnetic α phases during the creep process in Type 304 steel. Nucleation events of these product phases were explicitly introduced through a probabilistic Poisson seeding process based on local nucleation rates that were calculated as a function of local concentration. The defect energy of the creep dislocations near the carbides, which increases during creep, was integrated into the nucleation driving force for the α phase. The simulation used in this study accurately reproduced changes in the amounts of the precipitated phases as a function of creep time. Furthermore, we examine the effect of the dislocation density on precipitation of the α phase, and show that the phase-field method is useful for examining the stochastic and kinetic phenomenon of phase transformation.

Convective effect on the microstructure evolution during a liquid-liquid decomposition

The microstructure evolution during a liquid-liquid phase transformation was calculated. The effect of convections on the microstructure development was investigated. The results demonstrate that the convective flow against the solidification direction causes an increase in the local nucleation rate. Convections lead to a more nonuniform distribution of the minority phase droplets (MPDs) in the melt. They cause an increase in the size of the largest MPDs and are against the obtaining of the immiscible alloys with a well dispersed microstructure.

Multistep Crystal Nucleation: A Kinetic Study Based on Colloidal Crystallization

Crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), plays a key role in biomineralization and protein crystallization. MSC has attracted much attention in the past decade, but a quantitative understanding of it has so far not been available. The major challenge is that the kinetics governing the nucleation of crystals occurring in the metastable amorphous precursor remains unclear. In this study, the kinetics of MSC is addressed experimentally. Most importantly, a mathematical method is developed to calculate the local nucleation rate of the crystals in the amorphous precursor, which is not accessible to conventional methods. This local nucleation rate is critical to the understanding of MSC, but it has never been dealt with experimentally because of the difficulties of in situ observation. With the local crystal nucleation rates, the supersaturation for crystallization and the crystal-liquid interfacial free energy in the amorphous precursor are evaluated.

Homogeneous nucleation rate measurements of 1-propanol in helium: The effect of carrier gas pressure

Kinetics of homogeneous nucleation in supersaturated vapor of 1-propanol was studied using an upward thermal diffusion cloud chamber. Helium was used as a noncondensable carrier gas and the influence of its pressure on observed nucleation rates was investigated. The isothermal nucleation rates were determined by a photographic method that is independent on any nucleation theory. In this method, the trajectories of growing droplets are recorded using a charge coupled device camera and the distribution of local nucleation rates is determined by image analysis. The nucleation rate measurements of 1-propanol were carried out at four isotherms 260, 270, 280, and 290 K. In addition, the pressure dependence was investigated on the isotherms 290 K (50, 120, and 180 kPa) and 280 K (50 and 120 kPa). The isotherm 270 K was measured at 25 kPa and the isotherm 260 K at 20 kPa. The experiments confirm the earlier observations from several thermal diffusion chamber investigations that the homogeneous nucleation rate of 1-propanol tends to increase with decreasing total pressure in the chamber. In order to reduce the possibility that the observed phenomenon is an experimental artifact, connected with the generally used one-dimensional description of transfer processes in the chamber, a recently developed two-dimensional model of coupled heat, mass, and momentum transfer inside the chamber was used and results of both models were compared. It can be concluded that the implementation of the two-dimensional model does not explain the observed effect. Furthermore the obtained results were compared both to the predictions of the classical theory and to the results of other investigators using different experimental devices. Plotting the experimental data on the so-called Hale plot shows that our data seem to be consistent both internally and also with the data of others. Using the nucleation theorem the critical cluster sizes were obtained from the slopes of the individual isotherms and compared with the Kelvin prediction. The influence of total pressure on the observed isothermal nucleation rate was studied in another experiment, where not only temperature but also supersaturation was kept constant as the total pressure was changed. It was shown that the dependence of the nucleation rate on pressure gets stronger as pressure decreases.

Spatial distribution of nuclei inhibition of local nucleation rates by the most influential neighbours

The effects of nearest neighbours on the local nucleation rates and on the spatial distribution of electrodeposited nuclei growing under diffusion control have been analysed. Based upon the Dirichlet tessellation procedure, a systematic criterion is developed for selecting for each site on the surface its natural neighbours, i.e. those nuclei whose diffusional fields are not screened by other nuclei. Through computer simulations, the combined effect of the natural neighbours on the local nucleation rate at a site, or that of only the most influential neighbour, as well as the resulting spatial distributions of nuclei, are analysed. Comparison with experimental results shows that the effect of the most influential neighbour determines the spatial distribution of nuclei. It is also shown that the spatial distribution of nuclei does not depend on the detailed dependence of the local nucleation rate on the radial distance to its most influential or natural neighbours, as long as their propagation occurs with the same time-dependence.