Nucleation Rate Theory Research Articles

Nucleation Rate Theory for Coordination Number: Elucidating Water-Mediated Formation of a Zigzag Na2SO4 Morphology.

Predicting and controlling nanostructure formation during nucleation can pave the way to synthesizing novel energy materials via crystallization. However, such control over nucleation and crystallization remains challenging due to an inadequate understanding of critical factors that govern evolving atomistic structures and dynamics. Herein, we utilize coordination number as a reaction coordinate and rate theory to investigate how sodium sulfate, commonly known as a phase-change energy material, nucleates in a supersaturated aqueous solution. In conjunction with ab initio and force field-based molecular dynamics simulation, the rate theoretical analysis reveals that sodium sulfate from an initially dissolved metastable state transits to a heterogeneous mixture of prenucleated clusters and finally to a large cylindrical zigzag morphology. Measurements of Raman spectra and their ab initio modeling confirm that this nucleated morphology contains a few waters for every sulfate. Rate processes such as solvent exchange and desolvation exhibit high sensitivity to the evolving prenucleation/nucleation structures, providing a means to distinguish between critical nucleation precursors. Desolvation and forming the first-shell interionic coordination structure via monomer-by-monomer addition around sulfates are found to explain the formation of large nuclei. Thus, a detailed understanding of the step-by-step structure formation across scales has been achieved. This can be leveraged to predict nucleation-related structures and dynamics and potentially control the synthesis of novel phase-change materials for energy applications.

Bidirectional polymorphic conversion by focused femtosecond laser irradiation

We present bidirectional polymorphic conversion of L-phenylalanine by focused femtosecond laser irradiation. When the femtosecond laser beam is focused at an air/solution interface of its unsaturated solution, the plate-like anhydrous crystals are generated from the laser focus. This crystal nucleation is realized by local concentration increase achieved by femtosecond laser trapping, which is the first demonstration of femtosecond laser trapping-induced crystallization. Furthermore, the whisker-like monohydrate crystals are produced by continuing the femtosecond laser irradiation on the surface of the plate-like crystals. On the contrary, when a focused femtosecond laser irradiation is applied to the whisker-like monohydrate crystals, the plate-like crystals are formed, meaning that an unstable phase is successfully produced from a stable phase. The dynamics and mechanism of the bidirectional polymorphic conversion are explained from the viewpoint of the nucleation rate theory considering solution concentration around the surface of laser-induced cavitation bubbles.

Modeling layered crystal growth at increasing supersaturation by connecting growth regimes

Mechanistic modeling facilitates rational crystallization engineering and design space screening. For an accurate model, the dominant growth mechanism operating on each face must be determined, which is highly dependent on supersaturation. Considering the case of centrosymmetric growth units, we developed and connected existing mechanistic expressions for spiral and two‐dimensional‐nucleation growth regimes, through application of stationary nucleation rate theory. Our approach enables calculation of crossover supersaturations and forms a framework to model the specific mechanism operating on each face under given crystallization conditions. Increasing supersaturation can change the crystal morphology; as face families switch growth mechanisms, they may grow out of the steady‐state shape, or influence its aspect ratio. Application of the model to naphthalene, biphenyl, pentaerythritol and β‐HMX shows the ability to capture experimentally observed examples of such supersaturation‐dependent crystal habits. This methodology broadens the applicability of mechanistic crystal growth modeling to include higher‐supersaturation industrial processes. © 2017 American Institute of Chemical Engineers AIChE J, 63: 1338–1352, 2017

On the nucleation rate for the solidification of metals

The classical homogeneous nucleation rate theory for the solidification of metals has been in use for over 50 years, but it is almost universally used incorrectly. Because of this, solid–liquid surface energies calculated from nucleation rate theory are also incorrect. Herein, the correct usage of the homogeneous nucleation rate equation for the solidification of metals is presented. It is shown that because of the assumption of thermodynamic equilibrium, the homogeneous nucleation rate cannot be accurately calculated but is likely in the range 1012–1014s−1. Also, it is shown that the homogeneous nucleation temperature for a pure metal is essentially a material property. Calculations for the solidification of pure Ni are included.

Justification of biexponential rate law of spreading over heterogeneous and rough surfaces

Both surface roughness and chemical heterogeneity can be viewed as surface energy fluctuations acting as energy barriers for the three phase contact (TPC) line motion. This viewpoint provides a way to obtain the TPC line propagation rate as a function of the TPC contact angle in the frame of either nucleation rate theory or Eyring's absolute rate theory. In this study, a general biexponential rate law is deduced, and the wetting kinetic characteristics are related to statistical characteristics of the surface chemical heterogeneity and roughness, experimentally available from surface image analysis. A step mechanism for TPC line propagation is proposed; the barrier for a step is due to solid surface roughness and liquid surface corrugation, and the absolute frequency of steps is estimated through the dispersion relation of the capillary waves at the liquid surface. The free energy vs. TPC contact angle diagram of a randomly rough surface is deduced and found to be very similar to Dettre–Johnson's diagrams of periodically rough surfaces. The TPC propagation rate law is generally asymmetric, in accordance with the available experimental data. A comparison with experimental dynamic contact angle hysteretic curves gives reasonable values of the model's parameters.

Development of a Versatile Kinetic Monte Carlo Code to Simulate Physical Processes in Thin Film Nucleation and Growth

Thin film development and nanoscale oxidation studies have been of great interest recent years. Nucleation rate theory[1‐3] has been successfully used to describe metal heteroepitaxy [4] and qualitatively explained the initial stage of oxidation behavior[5]. To further quantitative understanding of these nano‐scale processes and the morphology evolution in general gas‐metal reactions and thin film development, a powerful simulation tool is urgently needed. The Thin Film Oxidation (TFOx) model is an atomistic Kinetic Monte Carlo (KMC) model, which has been developed of this purpose. The TFOx model includes all of the relevant microscopic processes in thin film growth. It simulates various steps and phenomenon during thin film development, which includes deposition, decomposition, adatom diffusion, nucleation, adatom desorption, island growth and et.al. TFOx has a large amount of input parameters compared to other KMC models to assure the realistic and accuracy, which also makes itself a versatile tool of studying the thin film development. Some application of TFOx in simulating the Cu (100) oxidation behavior will also be discussed in this paper.

A Model for Particle Dissolution and Precipitation in HSLA Steels

Precipitation of carbonitrides has been studied in as-cast slabs of one Nb and one Nb and Ti containing HSLA steel. The precipitates have been quantified using LOM and TEM. The measured size and number distributions was then compared to model calculations of precipitate nucleation and growth using estimates of the cooling rates in the austenitic range (1490oC to 800oC) during casting. Both average size and number distributions could be modelled with good agreement using identical model parameters (except for individual diffusion coefficients for the participating species). The model is based on classic nucleation rate theory and a quasistationary approximation for growth of spherical particles. Local equilibrium is assumed at the phase boundary.

Nucleation and growth of Pd clusters on (001) SrTiO3: Determination of diffusion and adsorption energies from cluster densities

The nucleation and the growth of Pd on (001) SrTiO3 surfaces were studied by scanning tunneling microscopy. Between 500 and 700°C the Pd nucleated as three-dimensional clusters on the (001) SrTiO3 surface. The condensation regime for the nucleation of Pd clusters on SrTiO3 could be confined by Auger electron spectroscopy and transmission electron microscopy investigations. An approximation of Venables’s nucleation rate theory [J. A. Venables, Philos. Mag. 27, 697 (1973)] was used which holds for the initially incomplete and complete regimes of condensation. With this approximation, we could simultaneously extract the activation energies for the diffusion and adsorption, Ed and Ea, of Pd atoms on the (001) surface of SrTiO3. The results are compared with other metal-oxide systems, and some general trends of the nucleation behavior of metal clusters on oxide surfaces are discussed.

Quantitative characterization of the Al nanoclustering induced by H interaction with Si(1 0 0)c(4 × 12)-Al surface phase

Abstract Self-organized formation of Al nanoclusters (i) induced by interaction of atomic hydrogen with the Si(1 0 0) c (4 × 12)-Al surface and (ii) in the course of Al deposition onto the Si(1 0 0) c (4 × 12)-Al surface has been quantitatively characterized using scanning tunneling microscopy measurements of the Al nanocluster number density. The obtained data have been evaluated within the framework of nucleation rate theory. In the case of Al nanoclustering upon Al deposition at 350–600 K, the changeover of the critical cluster size has been revealed at about 500 K. In the case of H-induced nanoclustering at 400–650 K, the changeover of the rate-limiting process has been detected at about 550 K, namely, at lower temperatures the rate-limiting process is the H-induced detachment of Al atoms from the Si(1 0 0) c (4 × 12)-Al phase, while at higher temperatures this is a competition between H adsorption and desorption at the surface. Activation energy of surface diffusion of Al atoms on the Si(1 0 0) c (4 × 12)-Al surface has been found to be 0.99 eV. Activation barrier for Al detachment from the Si(1 0 0) c (4 × 12)-Al has been estimated to be 1.53 eV.

Strangeness nucleation in neutron star matter

We study the transition from npe-type nuclear matter (consisting of neutrons, protons, and electrons) to matter containing strangeness, using a Walecka-type model predicting a first-order kaon-condensate phase transition. We examine the free energy of droplets of K matter as the density, temperature, and neutrino fraction are varied. Langer nucleation rate theory is then used to approximate the rate at which critical droplets of the new phase are produced by thermal fluctuations, thus giving an estimate of the time required for the new (mixed) phase to appear at various densities and various times in the cooling history of the protoneutron star. We also discuss the famous difficulty of ``simultaneous weak interactions'' which we connect to the literature on nontopological solitons. Finally, we discuss the implications of our results to several phenomenological issues involving neutron star phase transitions.

In-Situ UHV Tem Investigations of the Initial Oxidation Stage of Copper Thin Films

ABSTRACTThe nucleation and growth of Cu2O due to oxidation of Cu(001) films were monitored at various temperatures and oxygen partial pressures. For all examined temperatures and pressures, Cu2O islands were observed to form epitaxially with respect to the copper film. The nucleation of these oxide islands was homogeneous –no clear evidence was observed for either steps or dislocations being preferential nucleation sites. Based on this data, we have developed a semiquantitative model of the initial oxidation stage where the dominant mechanism for transport, nucleation and growth of oxide islands is oxygen diffusion on the Cu surface. We are presently comparing our experimental data with nucleation rate theory, where the predictions qualitatively describe our observations, but not quantitatively.

Ctivation Energies Of Interstitial Oxygen Diffusion In Silicon Containing Hydrogen

AbstractThe activation energies of interstitial oxygen diffusion in silicon containing hydrogen were derived from the results obtained from thermal donor generation experiments using numerical fitting based upon the classical nucleation rate theory and the time-dependent reduction of interstitial oxygen concentration resulting from oxygen aggregation. By using a new thermal equilibrium concentration of hydrogen at a pressure of 1 atm of 2×1021 exp(- 1.75 eV/kT), and the expression for the dependence of hydrogen thermal equilibrium concentration on the partial pressure P given as P0.65 times the hydrogen thermal equilibrium concentration at a pressure of 1 atm, the correlation between the activation energies of interstitial oxygen diffusion and hydrogen saturation is observed to be linearlogarithmic. In the hydrogen saturation range between 103 and 106, the activation energies of interstitial oxygen diffusion are estimated to be between 0.03 and 0.21 eV lower than the normal value of 2.53 eV. This implies that enhanced oxygen diffusion may occur primarily under hydrogen saturation conditions.

Numerical Simulation of Point Defect Distributions in a Growing Czochralski Silicon Crystal in Response to an Abrupt Change in the Growth Conditions

AbstractNumerical simulation of point defect distributions in a growing Czochralski silicon crystal with an abrupt change in the crystal growth rate from 1.0 to 0.4 mm/min was performed. The result was fitted to the experimental data for the flow pattern defects obtained from a crystal grown under simulated conditions. From the simulation result, it was observed that the axial temperature distribution shifts slightly upwards as a result of the growth rate reduction. Based upon the argument that the flow pattern defects are of vacancy-type, it is proposed that the generation rate of the flow pattern defects during crystal growth can be described by the classical nucleation rate theory proposed by Becker [Proc.Phys.Soc., 52, 71(1940)]. In addition, it is suggested that the vacancy concentration in the flow pattern defects depends upon the reaction time between the silicon interstitials and the flow pattern defects and thus the crystal growth rate.

Toward a molecular theory of vapor-phase nucleation. I. Identification of the average embryo

A statistical-mechanical theory of vapor-phase nucleation is developed which improves on that introduced by Reiss, Katz, and Cohen (RKC), and revised by Reiss, Tabazadeh, and Talbot (RTT) by identifying a physical embryo appropriate to the nucleation process. Put in the simplest manner, the goals of this paper are (1) to define embryos in such a manner that their thermodynamic properties can be easily calculated by means of computer simulation; (2) to define embryos in such a manner that (ideally) they can be used as entities in terms of which the systematic exact evaluation of the classical phase integral can be performed, and the equilibrium distribution of embryos therefore determined. This model of a pre-nucleating embryo prevents redundant counting of configurations in the partition function needed to derive the metastable equilibrium distribution of embryos. The embryo definition does not artificially constrain the molecules within the embryo, but remains only a procedural device for organizing the counting. The present treatment also resolves a problem not noticed by RTT involving an inconsistency concerning dimensions in their theory. Using the embryo definition the metastable equilibrium distribution of embryos is derived. Finally, a brief discussion of how the distribution can be used in a theory of nucleation rate is provided. Work is presently under way on the rate theory.

Hydrates in supersaturated binary sulfuric acid–water vapor: A reexamination

The influence of hydrates formation on the energetics of nucleation has been reexamined. The distribution Nh of hydrates containing one acid molecule and h water molecules has been calculated as a function of the relative humidity and acid vapor concentration. A new formula giving the reversible work required to form a droplet has been derived. Hydrate formation can exert an appreciable effect on the energetics of nucleation in the H2SO4–H2O system and must be included in any theory of nucleation rate.

A statistical treatment of nucleation rates in boron thin films

A nucleation rate theory for boron films was developed using a statistical approach based on a critical nucleus model. Due to the unique bonding in boron, and its charge to size ratio, two center and three center bonding plays a dominant role in the formation of condensed nuclei. By proper choice of the ratio between two and three center bonding a critical nucleus consisting of 12 boron atoms linked together in an icosahedral structure appears to be a reasonable structure. Reduced nucleation parameters are then calculated to indicate stable growth regions. The statistical methods employed yield nucleation rates which are consistent with independently determined experimental parameters.

A model for the simultaneous heterogeneous and homogeneous nucleation of gas bubbles

Electron microscope observations of cavities in steels have shown that they are often associated with microstructural features as well as occurring randomly in the matrix. Previous theoretical studies of gas bubble nucleation have concentrated on either homogeneous or heterogeneous nucleation. In the present work we extend the homogeneous nucleation rate theory for rare gases in solids to include, for the first time, the competitive mechanism of heterogeneous nucleation. The model indicates that the temperature dependence of the bubble density varies as the binding energy between a trap and a single gas atom is changed, and provides an interpretation of the high Arrhenius energy found from observed cavity densities.

Nucleation and growth of an epitaxial monolayer of Cd on Ge(111): A simultaneous RHEED–molecular-beam study

The nucleation and growth of an epitaxial monolayer of Cd on Ge(111) was studied by simultaneously employing RHEED and the mass spectrometric molecular beam (MSMB) technique. The MSMB spectra are discussed in terms of the atomistic rate theory of nucleation and the correlation between structures and spectra is presented. The results suggest that a convention of nucleation rate theory, that growing clusters act as monomer capture centers which increase in capture efficiency with time, does not hold at submonolayer coverages for this system. A model where capture efficiency decreases with cluster size is considered and from this model an estimate of the heat of adsorption and the activation energy for diffusion of monomers is obtained. Independent of the model we find that the nucleation process precedes the epitaxial alignment of clusters.

On the atomistic theory of nucleation rate

The atomistic nucleation theory has been extended and generalized. A new criterion has been proposed for a comparison of the theory with experimental results. The data of Walton, Rhodin and Rollins as well as the data of Poppa have been analyzed.