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DOE OSTI2022

Hydroxide films on mica form charge-stabilized microphases that circumvent nucleation barriers

Crystal nucleation is facilitated by transient, nanoscale fluctuations that are extraordinarily difficult to observe. Here, we use high-speed atomic force microscopy to directly observe the growth of an aluminum hydroxide film from an aqueous solution and characterize the dynamically fluctuating nanostructures that precede its formation. Nanoscale cluster distributions and fluctuation dynamics show many similarities to the predictions of classical nucleation theory, but the cluster energy landscape deviates from classical expectations. Kinetic Monte Carlo simulations show that these deviations can arise from electrostatic interactions between the clusters and the underlying substrate, which drive microphase separation to create a nanostructured surface phase. This phase can evolve seamlessly from a low-coverage state of fluctuating clusters into a high-coverage nanostructured network, allowing the film to grow without having to overcome classical nucleation barriers.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A 1D Model for Nucleation of Ice From Aerosol Particles: An Application to a Mixed‐Phase Arctic Stratus Cloud Layer

Abstract Mixed‐phase clouds (MPCs) have been identified as significant contributors to uncertainties in climate projections, attributable to model representation of processes controlling the formation and loss of supercooled water droplets and ice particles from the atmosphere. Arctic MPCs are commonly widespread and long‐lived, with sustained ice crystal formation processes that challenge current understanding. This study examines the ice‐nucleating particle (INP) reservoir dynamics governing immersion‐mode heterogeneous freezing in an observed case of Arctic MPCs using a simplified 1D aerosol‐cloud model. The model setup includes prescribed dynamical forcings and thermodynamic profiles, and represents INPs as multicomponent and polydisperse particle size distributions. Diagnostic and prognostic approaches to immersion freezing parameterization are compared, including time‐independent (singular) number‐ and surface area‐based descriptions and a time‐dependent description following classical nucleation theory (CNT). The choice of freezing parameterization defines the size of the INP reservoir. The CNT‐based description yields an orders of magnitude larger INP reservoir than the singular parameterizations, which is the dominant factor for sustained ice crystal formation. The efficiency of the freezing process and cloud cooling are of secondary importance. A diagnostic treatment neglecting INP loss is only accurate when the INP reservoir size is large and INP depletion weak. Since a larger INP reservoir sustains ice crystal formation substantially longer, and ice water path scales with ice crystal concentrations for the conditions considered, resolving the source of differences in INP reservoir dynamics due to model implementation is a high priority for advancing climate model physics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Understanding the Importance of Labile Fe(III) during Fe(II)-Catalyzed Transformation of Metastable Iron Oxyhydroxides

Transformation of metastable Fe(III) oxyhydroxides is a prominent process in natural environments and can be significantly accelerated by the coexisting aqueous Fe(II) (Fe(II) aq ). Recent evidence points to the solution mass transfer of labile Fe(III) (Fe(III) labile ) as the primary intermediate species of general importance. However, a mechanistic aspect that remains unclear is the dependence of phase outcomes on the identity of the metastable Fe(III) oxyhydroxide precursor. Here, we compared the coupled evolution of Fe(II) species, solid phases, and Fe(III) labile throughout the Fe(II)-catalyzed transformation of lepidocrocite (Lp) versus ferrihydrite (Fh) at equal Fe(III) mass loadings with 0.2–1.0 mM Fe(II) aq at pH = 7.0. Similar to Fh, the conversion of Lp to product phases occurs by a dissolution–reprecipitation mechanism mediated by Fe(III) labile that seeds the nucleation of products. Though for Fh we observed a transformation to goethite (Gt), accompanied by the transient emergence and decline of Lp, for initial Lp we observed magnetite (Mt) as the main product. Further, a linear correlation between the formation rate of Mt and the effective supersaturation in terms of Fe(III) labile concentration shows that Fe(II)-induced transformation of Lp into Mt is governed by the classical nucleation theory. When Lp is replaced by equimolar Gt, Mt formation is suppressed by opening a lower barrier pathway to Gt by heterogeneous nucleation and growth on the added Gt seeds. The collective findings add to the mechanistic understanding of factors governing phase selections that impact iron bioavailability, system redox potential, and the fate and transport of coupled elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

How are Heterogeneous Nucleation Rate Observations Influenced by Instrument Resolution?

Experimental measurements of the heterogeneous nucleation rate rely on counting the number of nuclei with time. However, the size of a thermodynamically stable nucleus is often a few nanometers in diameter and is below the resolution of most (in situ) measurement techniques that provide a statistically valid sample. Due to the finite resolution of the instruments and analysis methods, it is challenging to capture the incipient nuclei and the subsequent evolution of nuclei density over time. In this work, we demonstrate the impact of instrument resolution on observed nuclei densities by comparing numerical modeling with experimental results. Further, to achieve this, we implemented heterogeneous nucleation within the pore-scale reactive transport modeling framework using classical nucleation theory (CNT). We compared the modeling results with nucleation rates measured using X-ray nanotomography (XnT) and evaluated how these impact the apparent values of the prefactor and interfacial energy based on CNT and the crystal growth rate. Specifically, we applied a resolution threshold (artificial resolution limit) in the model during nuclei counting to resemble an experimental resolution, ranging from 15 to 500 nm. The findings reveal that the instrument resolution significantly impacts the apparent prefactor and interfacial energy. Both apparent prefactor and interfacial energy decrease with a decrease in the instrument resolution. While deviation in the prefactor due to resolution is anticipated, those in the interfacial energy are unexpected. The approach described here allows one to correct apparent nucleation rates that depend on the instrument’s resolution to derive “intrinsic” CNT parameters for the prefactor and interfacial energy.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Prognostic simulations of mixed-phase clouds with model AC-1D v1.0: the impact of aerosol types and freezing parameterizations on ice crystal budgets

Mixed-phase clouds at high latitudes contribute to the uncertainty in predicting cloud feedbacks and climate sensitivity, mainly due to the complexity of microphysical processes that influence the partitioning between the supercooled liquid and ice phases, and hence, cloud radiative effects on regional scales. Particularly in Arctic mixed-phase clouds, the activation of ice-nucleating particles (INPs) from various aerosol populations remains a leading source of uncertainty. We developed an aerosol-cloud one-dimensional (AC-1D) model, which provides a novel framework to prognostically treat INP and ice crystal budgets while explicitly accounting for polydisperse and multicomponent aerosol that activate INPs following different freezing parameterizations. The AC-1D model is informed by large-eddy simulations to probe the impact of INP representation on predicted ice crystal number concentrations (N i ) and ice crystal budgets in mixed-phase Arctic stratus. We apply three immersion freezing (IMF) parameterizations, two time-independent (singular) and one time-dependent (classical nucleation theory), to predict the evolution of the INP reservoir and resulting ice crystal budget from polydisperse mineral dust, organic (humic-like substances), and sea spray aerosol particle size distributions. Our analysis focuses on how variations in aerosol number concentration and cloud system parameters such as cloud cooling rate, cloud-top entrainment rate, and ice crystal fall speed influence the INP reservoir and ice crystal budgets. Furthermore, this study investigates the competitive ice nucleation dynamics in mixed aerosol environments and provides a process-level quantification of the INP budget terms, which directly controls ice crystal budgets. For all studied case scenarios, the aerosol types and associated particle size distributions significantly impact INP and N i , and the choice between a time-dependent and a singular freezing description yields orders-of-magnitude differences in the predicted INP and N i over the 10 h simulation time, reflecting typical cloud lifetimes. Our results show that the influence of cloud cooling, INP entrainment, and sedimentation varies significantly depending on the chosen freezing parameterization. These findings underscore the critical need for robust IMF parameterizations and precise cloud system observations to enhance the accuracy of models in predicting mixed-phase cloud structure and evolution.

Arctic clouds↗

DOE OSTI2021

The role of precursor decomposition in the formation of samarium doped ceria nanoparticles via solid-state microwave synthesis

The impact on the final morphology of ceria (CeO 2 ) nanoparticles made from different precursors (commercial: cerium acetate/nitrate) and in house: cerium tri(methylsilyl)amide (Ce-TMSA)) via a microwave solid state reaction has been determined. In all instances, powder X-ray diffraction indicated that the cubic fluorite CeO 2 phase (PDF# 04–004-9150, with the space group Fm-3 m) had formed. Scanning electron microscopy (SEM) images revealed spherical nanoparticles were produced from the Ce-TMSA precursor. The commercial acetate and nitrate precursors produced particles with irregular morphology. The roles of the precursor decomposition and binding energy in the synthesis of the nanocrystals with various morphologies, as well as a possible growth mechanism, were evaluated based on experimental and computational data. The formation of spherical shaped nanoparticles was determined to be due to the preferential single-step decomposition of the Ce-TMSA as well as the low activation energy to overcome decomposition. Due to the complicated decomposition of the commercial precursors and high activation energy the resulting particles adopted an irregular morphology. Highly uniform samarium doped ceria (Sm x Ce 1-x O 2-δ ) nanospheres were also synthesized from Ce-TMSA and samarium tri(methylsilyl)amide (Sm-TMSA). The effects of reaction time and temperature, on the final morphology were observed through SEM. The rapid single-step decomposition of TMSA-based precursors as observed through thermogravimetric analysis (TGA) and confirmed through the calculation of potential energy surfaces and binding energies from density functional theory (DFT) calculations, indicated that nanoparticle formation follows LaMer’s classical nucleation theory.

36 MATERIALS SCIENCE↗

NASA NTRS1985

Does nucleation theory apply to the formation of refractory circumstellar grains?

It is pointed out that kinetic factors inherent in cosmic systems will prevent the attainment of an approximate equilibrium precondensation cluster distribution, and that therefore such systems will violate one of the most fundamental assumptions of nucleation theory. More importantly, it is shown that of the 11 refractory metal/metal oxide systems which have been studied experimentally none are consistent with the predictions of either classical nucleation theory or the Lothe-Pound modification. Since no valid method is known by which these deficiencies can be circumvented, it is concluded that nucleation theory cannot be made to work in expanding circumstellar shells. However, a stochastic, kinetic treatment which makes use of experimental and theoretical data for specific refractory systems does appear to be feasible.

Donn, B.↗

DOE OSTI2025

Model form and sensitivity analysis of CALPHAD-based nucleation models in b-stabilized Ti alloys

Accurate prediction of α-phase nucleation and growth in β-stabilized titanium alloys is crucial for designing heat treatments to optimize mechanical properties in additively manufactured lightweight components. Ideally, predictions of nucleation and growth would incorporate both top-down observations of past experimental heat treatments and bottom-up modeling of phase transformations; however, the appropriate method of combining these information sources is not self-evident. Combining top-down and bottom-up information requires a unified form of model that can connect between spatiotemporal scales, as well as sets of fitting parameters that can be identified by each data source. The selection of which parameters to fit to which data source can be made based on expert opinion, or by performing a sensitivity analysis. In solid-solid nucleation, direct observation of the nucleation and growth process is challenging. Most data on the heat treatment-controlled phase transformations are not in-situ. To predict the process and outcome of the nucleation, growth and coarsening of precipitates, theoretical models of the nucleation pathway are used to bridge the gap. Many sources of uncertainty affect the modeling of this nucleation process. It can be influenced by small variations in the thermomechanical processing history, chemical composition, and initial microstructure. If molecular dynamics (MD) simulations are used to determine thermodynamic quantities and inform CALPHAD modeling, additional uncertainty can be introduced and accounted for using Bayesian methods. Top-down uncertainties require additional steps to quantify. The influence of nucleation model form on the sensitivity of predictions to input parameters and physical conditions is the focus of this study. Classical nucleation theory (CNT) allows modeling to formulate the nucleation as homogeneous or, more commonly, heterogeneous. Non-classical nucleation models are also increasingly explored as a means of reconciling top-down and bottom-up data. In this study, the sensitivity of the intragranular nucleation of α in a β-annealed, slow-cooled aging (BASCA) heat treatment of β-stabilized Ti5553 alloy is explored using CNT and both heterogeneous and homogeneous assumptions. The Kampmann-Wagner Numerical model of precipitate nucleation and growth is employed. Using open-source tools (pyCalphad and thermodynamic modeling of TiMo as a surrogate system, a sensitivity analysis is performed to measure variations in key parameters, including chemical driving force, interfacial energy, and diffusivity, as they relate to predictions of precipitate number density. The inclusion of top-down and bottom-up data in selection of nucleation model form is discussed.

Rodriguez Negron, A. M.↗

NASA NTRS1982

Nucleation theory - Is replacement free energy needed?

It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

Doremus, R. H.↗

NASA NTRS2017

A Theory of Immersion Freezing

Immersion freezing is likely involved in the initiation of precipitation and determines to large extent the phase partitioning in convective clouds. Theoretical models commonly used to describe immersion freezing in atmospheric models are based on the classical nucleation theory which however neglects important interactions near the immersed particle that may affect nucleation rates. This work introduces a new theory of immersion freezing based on two premises. First, immersion ice nucleation is mediated by the modification of the properties of water near the particle-liquid interface, rather than by the geometry of the ice germ. Second, the same mechanism that leads to the decrease in the work of germ formation also decreases the mobility of water molecules near the immersed particle. These two premises allow establishing general thermodynamic constraints to the ice nucleation rate. Analysis of the new theory shows that active sites likely trigger ice nucleation, but they do not control the overall nucleation rate nor the probability of freezing. It also suggests that materials with different ice nucleation efficiency may exhibit similar freezing temperatures under similar conditions but differ in their sensitivity to particle surface area and cooling rate. Predicted nucleation rates show good agreement with observations for a diverse set of materials including dust, black carbon and bacterial ice nucleating particles. The application of the new theory within the NASA Global Earth System Model (GEOS-5) is also discussed.

Ice Nucleating particle↗

DOE OSTI2020

Critical nuclei at hetero-phase interfaces

Two-step nucleation, in which a metastable intermediate phase acts as a precursor for nucleating a thermodynamically stable phase, has been widely observed in many materials systems and solid-state reactions. Among the advantages of two-step nucleation is that the stable phase may nucleate heterogeneously at the hetero-phase interface between the original and the precursory phases. Although heterogeneous nucleation (HN) theories for homo-phase grain boundaries and inert surfaces are well established, our understanding of HN at reactive hetero-phase interfaces remains incomplete. This deficiency stems from the discontinuity of the chemical potential driving force across the hetero-phase interface, which profoundly affects the fundamental properties of the nucleus in a way that is not properly accounted for in existing models. In this work, we incorporate these effects to extend the classical nucleation theory to HN at hetero-phase interfaces. Our extended model demonstrates that the nucleus shape along the minimum energy path is strongly size-dependent, and this additional degree of freedom can result in the reduction of the critical nucleus volume and associated activation energy barrier by orders of magnitude relative to conventional predictions. The simulation results are used to construct a sensitivity map in the parameter space of interfacial energy and bulk driving force ratios, which quantifies the difference in nucleation barriers predicted by different models.

36 MATERIALS SCIENCE↗

NASA NTRS2008

Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys

The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Booth-Morrison, Christopher↗

DOE OSTI2020

A Perspective on Multistep Pathways of Nucleation

While views on crystal nucleation throughout the 20th century were dominated by classical nucleation theory (CNT) in which the ordered nucleus forms directly from monomeric species, observations over the past two decades across scientific fields have revealed a plethora of multi-step nucleation processes, often involving more complex species. These processes have come to be known as non-classical, reflecting distinctions from the expectations of CNT. Here I consider the various classes of non-classical nucleation pathways and examine the extent to which they can be easily placed within the framework of CNT modified to include well-understood complexities in the free energy landscape and/or kinetic factors. I highlight recent examples that illustrate these pathways before turning to processes that cannot readily be included in this framework. I conclude by describing future research directions needed to fill the knowledge gaps that prevent the development of quantitative models for multi-step nucleation processes

De Yoreo, James J.↗

DOE OSTI2020

Theoretical insight into thermodynamics of particle-based crystallization

Crystallization process often does not follow the monomer-by-monomer addition pathway, as described by classical nucleation theory. Instead, initial step may involve the formation of larger building blocks, such as crystalline or amorphous nanoparticles, droplets, clusters, complexes or oligomers, which subsequently undergo assembly into a crystal. These multistep crystallization processes are ubiquitous in mineral formation and biomineralization. In materials synthesis utilizing non-classical crystallization pathways is particularly attractive as the restriction on which crystalline faces can grow is lifted in a multistep crystallization process adding to the versatility of materials architectures that can be obtained. Predicting the outcomes of non-classical crystallization through the understanding of the control parameters influencing crystallization pathways is an important and challenging task essential for utilizing the full potential of non-classical crystallization in the design of functional materials. Here, the current status of the development of a predictive theoretical framework for modeling non-classical crystallization is reviewed.

Sushko, Maria L.↗

DOE OSTI2024

Experimental and Computational Studies of Crystal Nucleation in Composition Gradients (Final Report)

The major goals of this project were to develop and validate a predictive nucleation model that incorporates composition gradients and is applicable to a large range of metallic systems which form both stochiometric and non-stochiometric compounds. Computationally we planned to expand the extent of thermodynamics-based theories and lay the groundwork to improve the general understanding and predictive capabilities of the role that gradients play in phase formation, glass formability and stability, and nucleation and growth events. To address these goals, we used Molecular Dynamics (MD) simulations and both isothermal and isochronal nanocalorimetric experiments on amorphous phases with a controlled composition gradient with the hopes of validating and improving the classical nucleation model and its use in solid solutions. While the computations were successful and identified ways to improve the classical nucleation model, the in situ nanocalorimetry studies proved very challenging due to unexpected difficulties in fabricating effective calorimeters and samples. Thus, we could not experimentally validate our predicted influence of composition gradients on nucleation. Nonetheless, important insights were gained and modifications to the classical nucleation theory were suggested.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1982

Ion-induced nucleation in a binary mixture

Recent ion-induced nucleation studies in a binary mixture of H2O and H2SO4 vapors indicate that conventional classical nucleation theories cannot account for the experimentally observed ion-H2O-H2SO4 microcluster spectra. An empirical-analytical, semi-molecular theory of nucleation of a binary mixture of vapors on ions has been developed. This theory includes molecular approach to ion-induced changes in dielectric properties in the immediate neighborhood of an ion core as well as the size dependence of the surface tension of the microcluster. In addition to gaseous sulfuric acid and water molecules, the effect of ion-hydrates and sulfuric acid hydrates has also been considered. This theory is further simplified by using an empirical correction factor for the electrostatic term. This correction factor has been obtained by comparing the simplified model with the molecular dynamics calculations for selected ion hydrate formation. These two theoretical models are then compared with the classical theory for a variety of experimental conditions.

Smith, A. C.↗

DOE OSTI2022

Dynamics of homogeneous cavitation with pressure feedback

Theoretical studies of homogeneous cavitation have largely been based on the classical nucleation theory. However, existing cavitation models cannot adequately describe its dynamics at nanosecond timescale, which has been called for in other fields. We develop a model coupling nucleation kinetics with cavity growth and pressure feedback as saturation mechanisms. Our numerical studies reveal the exponential dependence of cavitation characteristics such as saturation cavity density and most probable cavity radius on model parameters: Tolman length and initial pressure. This work also sheds light on the possibility of accurately determining Tolman length, whose value has a large spread in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗