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Nucleation

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Full-Text Articles in Physics

Kinetic Monte Carlo Simulations Of Quantum Dot Self-Assembly, Matthew Abramson, Hunter J. Coleman, Paul J. Simmonds, Tim P. Schulze, Christian Ratsch Nov 2022

Kinetic Monte Carlo Simulations Of Quantum Dot Self-Assembly, Matthew Abramson, Hunter J. Coleman, Paul J. Simmonds, Tim P. Schulze, Christian Ratsch

Physics Faculty Publications and Presentations

In the Stranski–Krastanov growth mode for heteroepitaxial systems, layer-by-layer growth is followed by the formation and growth of three-dimensional (3D) islands. In this paper, we use a kinetic Monte Carlo method to simulate this growth mode behavior. We present a detailed and systematic investigation into the effects of key model parameters including strain, growth temperature, and deposition rate on this phenomenon. We show that increasing the strain lowers the apparent critical thickness that is defined by the onset of 3D island formation. Similarly, increasing the growth temperature lowers the apparent critical thickness, until intermixing, and the resulting relevance of entropic …


Image Data Analysis And Design Optimization Of The Snowball Chamber, Yujia Huang Dec 2021

Image Data Analysis And Design Optimization Of The Snowball Chamber, Yujia Huang

Legacy Theses & Dissertations (2009 - 2024)

Dark Matter is the invisible massive particle that makes up over 26.8 percent of the mass-energy content of the universe. Weakly Interacting Massive Particles, or WIMPs, are one of the candidates of dark matter particles. Many scientists around the world are trying to figure out how to detect detect dark matter using either indirect search, direct production or direct detection experiments. However, due to the lack of evidence of finding WIMPs in direct detection experiments at a large mass scale, a call for investigating WIMPs at a lower mass range is attracting more attention.


Simulation Analysis Of The Snowball Chamber, Thomas Guile Aug 2021

Simulation Analysis Of The Snowball Chamber, Thomas Guile

Legacy Theses & Dissertations (2009 - 2024)

Dark matter is non-baryonic, weakly interacting matter that makes up nearly 85% of the mass ofour universe, as seen through many different phenomena such as gravitational lensing and flat galactic rotation curves [48]. There are many experiments across the globe that are working to find these dark matter particles, but despite increasing levels of detector sensitivity, dark matter has been difficult to detect. Because of this, it is possible that dark matter has a lower mass than originally predicted. A new detector, the Snowball Chamber, could be used to aid in this search. By using the light molecule of water, …


Multiscale Investigation Of Dropwise Condensation On A Smooth Hydrophilic Surface, Shahab Bayani Ahangar Jan 2021

Multiscale Investigation Of Dropwise Condensation On A Smooth Hydrophilic Surface, Shahab Bayani Ahangar

Dissertations, Master's Theses and Master's Reports

The objective of this work is to identify the fundamental mechanism of dropwise condensation on a smooth solid surface by probing the solid-vapor interface during phase-change to evaluate the existence and structure of the thin film and the initial nucleus that develop during condensation. In this work, an automated Surface Plasmon Resonance imaging (SPRi) instrument with the ability to perform imaging in intensity modulation and angular modulation is developed. The SPRi instrument is used to probe (in three dimensions) the adsorbed film that forms on the substrate during dropwise condensation. SPRi with a lateral resolution of ~ 4-10 μm, thickness …


Thermophysical Properties And Phase Transformations In Metallic Liquids And Silicate Glasses, Daniel Christian Van Hoesen May 2020

Thermophysical Properties And Phase Transformations In Metallic Liquids And Silicate Glasses, Daniel Christian Van Hoesen

Arts & Sciences Electronic Theses and Dissertations

The first quantitative measurements of the electrical resistivity in binary metallic liquids, used to probe local order in the liquid, are reported in this dissertation. The electrical resistivity is very sensitive to short and medium range ordering because the electron mean free path is approximately the same length scale as the atomic spacing. Particular attention is given to the resistivity value at a crossover temperature that, based on molecular dynamics (MD) simulations, is the onset of cooperative motion in liquid alloys. Experimental evidence for the crossover is found in measurements of the shear viscosity, a dynamical property. An indication of …


Studies Of Maximum Supercooling And Stirring In Levitated Liquid Metallic Alloys, Mark Edward Sellers May 2020

Studies Of Maximum Supercooling And Stirring In Levitated Liquid Metallic Alloys, Mark Edward Sellers

Arts & Sciences Electronic Theses and Dissertations

Nucleation—or the formation of some cluster in a medium undergoing a phase transition—is usually the initial step in a phase transition. However, this process is still not fully understood, as outstanding questions related to the role of structure, local order, and diffusion remain unanswered. Systematic supercooling studies on metallic liquids performed using electrostatic and electromagnetic (ESL and EML, respectively) will be presented and discussed within the context of several nucleation theories, such as the Classical Nucleation Theory, Diffuse Interface Theory, and Coupled-Flux theory. To study the role of diffusion on nucleation, studies on the International Space Station using the on-board …


The Impact Of Membrane Tension On Phase Separation And Solid Domain Properties In Model Multicomponent Vesicles, Dong Chen Nov 2014

The Impact Of Membrane Tension On Phase Separation And Solid Domain Properties In Model Multicomponent Vesicles, Dong Chen

Doctoral Dissertations

Multicomponent phospholipid membranes provide an ideal model to study the complex phase behavior of biological membranes. Giant unilamellar vesicles (GUV) formed by mixtures of two or more phospholipids have particular merit as model membranes because of their simplicity, operability, and ease of viewing phase separation and testing membrane mechanics. Until the research in this thesis, biochemistry and biophysical studies of phase separation in phospholipid membranes primarily addressed the influence of membrane composition on the transition temperatures and domain shapes. This thesis focuses on a commonly neglected variable - membrane tension, analogous to pressure in bulk materials, as an important parameter …


The Creation Of 360° Domain Walls In Ferromagnetic Nanorings By Circular Applied Magnetic Fields, Jessica E. Bickel, Spencer A. Smith, Katherine E. Aidala Feb 2014

The Creation Of 360° Domain Walls In Ferromagnetic Nanorings By Circular Applied Magnetic Fields, Jessica E. Bickel, Spencer A. Smith, Katherine E. Aidala

Physics Faculty Publications

Switching behavior in ferromagnetic nanostructures is often determined by the formation and annihilation of domain walls (DWs). In contrast to the more familiar 180° DWs found in most nanostructures, 360° DWs are the proposed transition state of nanorings. This paper examines the formation of 360° DWs created by the application of a circular magnetic field using micromagnetic simulations. 360° DWs form from pairs of canting moments that are oppositely aligned, which each grow to form rotated domains bounded by two 180° DWs and the 180° DWs combine to form 360° DWs. The resulting 360° DWs occur in pairs of opposite …


Dynamic Light Scattering Study Of Hydroxyapatite Formation: Effect Of Osteopontin And Bone Sialoprotein, Maryam Mozaffari Oct 2013

Dynamic Light Scattering Study Of Hydroxyapatite Formation: Effect Of Osteopontin And Bone Sialoprotein, Maryam Mozaffari

Electronic Thesis and Dissertation Repository

Biomineralization is the process by which living organisms synthesize minerals. Some bone-related proteins, such as bone sialoprotein (BSP), have been found to enhance biomineralization, while others, including osteopontin (OPN), act as inhibitors of this process. Dynamic light scattering was used to investigate the effect of several native and recombinant proteins and peptides on the formation and growth of hydroxyapatite (HA) crystals from solutions of Ca2+ and PO43- ions. We studied two isoforms of OPN, the OPN-derived peptides P0, P3, OPAR and pOPAR, and recombinant BSP. X-ray diffraction was used to identify the precipitate as HA crystals. Native …


The Density Factor In The Synthesis Of Carbon Nanotube Forest By Injection Chemical Vapor Deposition, Robert W. Call, C. Read, C Mart, T. C. Shen Jan 2012

The Density Factor In The Synthesis Of Carbon Nanotube Forest By Injection Chemical Vapor Deposition, Robert W. Call, C. Read, C Mart, T. C. Shen

Graduate Student Publications

Beneath the seeming straight-forwardness of growing carbon nanotube(CNT) forests by the injection chemical vapor deposition(CVD) method, control of the forest morphology on various substrates is yet to be achieved. Using ferrocene dissolved in xylene as the precursor, we demonstrate that the concentration of ferrocene and the injection rate of the precursor dictate the CNT density of these forests. However, CNT density will also be affected by the substrates and the growth temperature which determine the diffusion of the catalyst adatoms. The CNT growth rate is controlled by the temperature and chemical composition of the gases in the CVD reactor. We …


Communication: Bubbles, Crystals, And Laser-Induced Nucleation, Brandon C. Knott, Jerry L. Larue, Alec M. Wodtke, Michael F. Doherty, Baron Peters May 2011

Communication: Bubbles, Crystals, And Laser-Induced Nucleation, Brandon C. Knott, Jerry L. Larue, Alec M. Wodtke, Michael F. Doherty, Baron Peters

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Short intense laser pulses of visible and infrared light can dramatically accelerate crystal nucleation from transparent solutions; previous studies invoke mechanisms that are only applicable for nucleation of ordered phases or high dielectric phases. However, we show that similar laser pulses induce CO2bubblenucleation in carbonated water. Additionally, in water that is cosupersaturated with argon and glycine, argon bubbles escaping from the water can induce crystal nucleation without a laser. Our findings suggest a possible link between laser-induced nucleation of bubbles and crystals.


Nucleation, Wetting And Agglomeration Of Copper And Copper-Alloy Thin Films On Metal Liner Surfaces, Stephanie Florence Labarbera Jan 2011

Nucleation, Wetting And Agglomeration Of Copper And Copper-Alloy Thin Films On Metal Liner Surfaces, Stephanie Florence Labarbera

Legacy Theses & Dissertations (2009 - 2024)

One of the key challenges in fabricating narrower and higher aspect ratio interconnects using damascene technology has been achieving an ultra-thin (~2 nm) and continuous Cu seed coverage on trench sidewalls. The thin seed is prone to agglomeration because of poor Cu wetting on the Ta liner. Using in-situ conductance measurements, the effect of lowering the substrate temperature during Cu seed deposition has been studied on tantalum (Ta) and ruthenium (Ru) liner surfaces. On a Ta surface, it was found that lowering the deposition temperature to -65°C increases the nucleation rate of the Cu thin film, and reduces the minimum …


Tensile Strained Island Growth At Step-Edges On Gaas(110), Paul J. Simmonds, M. L. Lee Oct 2010

Tensile Strained Island Growth At Step-Edges On Gaas(110), Paul J. Simmonds, M. L. Lee

Paul J. Simmonds

We report the growth of tensile strained GaP islands on a GaAs(110) surface. Three-dimensional island formation proceeds via a step-edge nucleation process. To explain the dislocation-free nature of these islands, we consider the kinetics of strain relief within the context of a model for dislocation glide as a function of surface orientation and sign of strain.


Scaled Vapor-To-Liquid Nucleation In A Lennard-Jones System, Barbara N. Hale, Mark Thomason Jul 2010

Scaled Vapor-To-Liquid Nucleation In A Lennard-Jones System, Barbara N. Hale, Mark Thomason

Physics Faculty Research & Creative Works

Scaling of the homogenous vapor-to-liquid nucleation rate, J, is observed in a model Lennard-Jones (LJ) system. The model uses Monte Carlo simulation-generated small cluster growth to decay rate constant ratios and the kinetic steady-state nucleation rate formalism to determine J at four temperatures below the LJ critical temperature, Tc. When plotted vs the scaled supersaturation, lnS/[Tc/T-1]3/2, the values of log J are found to collapse onto a single line. A similar scaling has been observed for the experimental nucleation rate data of water and toluene.


Direct Measurements Of Island Growth And Step-Edge Barriers In Colloidal Epitaxy, Rajesh Ganapathy, Mark R. Buckley, Sharon J. Gerbode, Itai Cohen Jan 2010

Direct Measurements Of Island Growth And Step-Edge Barriers In Colloidal Epitaxy, Rajesh Ganapathy, Mark R. Buckley, Sharon J. Gerbode, Itai Cohen

All HMC Faculty Publications and Research

Epitaxial growth, a bottom-up self-assembly process for creating surface nano- and microstructures, has been extensively studied in the context of atoms. This process, however, is also a promising route to self-assembly of nanometer- and micrometer-scale particles into microstructures that have numerous technological applications. To determine whether atomic epitaxial growth laws are applicable to the epitaxy of larger particles with attractive interactions, we investigated the nucleation and growth dynamics of colloidal crystal films with single-particle resolution. We show quantitatively that colloidal epitaxy obeys the same two-dimensional island nucleation and growth laws that govern atomic epitaxy. However, we found that in colloidal …


Dependence Of Domain Wall Structure For Low Field Injection Into Magnetic Nanowires, Andrew Kunz, Sarah C. Reiff Jan 2009

Dependence Of Domain Wall Structure For Low Field Injection Into Magnetic Nanowires, Andrew Kunz, Sarah C. Reiff

Physics Faculty Research and Publications

Micromagnetic simulation is used to model the injection of a domain wall into a magnetic nanowire with field strengths less than the so-called Walker field. This ensures fast, reliable motion of the wall. When the wire is located at the edge of a small injecting disk, a bias field used to control the orientation of the domain wall can reduce the pinning potential of the structure. The low field injection is explained by a simple model, which relies on the topological nature of a domain wall. The technique can quickly inject multiple domain walls with a known magnetic structure.


Bubbling The False Vacuum Away, M. Gleiser, B. Rogers, J. Thorarinson Aug 2007

Bubbling The False Vacuum Away, M. Gleiser, B. Rogers, J. Thorarinson

Dartmouth Scholarship

We investigate the role of nonperturbative, bubble-like inhomogeneities on the decay rate of false- vacuum states in two and three-dimensional scalar field theories. The inhomogeneities are induced by setting up large-amplitude oscillations of the field about the false vacuum as, for example, after a rapid quench or in certain models of cosmological inflation. We show that, for a wide range of parameters, the presence of large-amplitude bubble-like inhomogeneities greatly accelerates the de- cay rate, changing it from the well-known exponential suppression of homogeneous nucleation to a power-law suppression. It is argued that this fast, power-law vacuum decay – known as …


Energy Pathways And Directionality In Deformation Twinning, S. Kibey, J. B. Liu, Duane D. Johnson, H. Sehitoglu Jan 2007

Energy Pathways And Directionality In Deformation Twinning, S. Kibey, J. B. Liu, Duane D. Johnson, H. Sehitoglu

Duane D. Johnson

We present ab initiodensity functional theory calculations of twinning energy pathways for two opposite twinning modes, (111)[112¯] and (111)[1¯1¯2], in fcc materials to examine the directional nature of twinning which cannot be explained by classical twin nucleationmodels or the “twinnability” criterion. By accounting for these energy pathways in a multiscale model, we quantitatively predict the critical twinning stress for the (111)[1¯1¯2] mode to be substantially higher compared to the favorable (111)[112¯] mode (whose predicted stresses are in agreement with experiment), thus, ruling out twinning in the (111)[1¯1¯2] mode.


Local Defect In A Magnet With Long-Range Interactions, Jose A. Hoyos, Thomas Vojta Jan 2007

Local Defect In A Magnet With Long-Range Interactions, Jose A. Hoyos, Thomas Vojta

Physics Faculty Research & Creative Works

We investigate a single defect coupling to the square of the order parameter in a nearly critical magnet with long-range spatial interactions of the form r−(d+sigma), focusing on magnetic droplets nucleated at the defect while the bulk system is in the paramagnetic phase. To determine the static droplet profile, we solve a Landau-Ginzburg-Wilson action in the saddle-point approximation. Because of the long-range interaction, the droplet develops a power-law tail which is energetically unfavorable. However, as long as sigma>0, the tail contribution to the droplet free energy is subleading in the limit of large droplets; and the free energy becomes …


Volumes Of Critical Bubbles From The Nucleation Theorem, Gerald Wilemski Sep 2006

Volumes Of Critical Bubbles From The Nucleation Theorem, Gerald Wilemski

Physics Faculty Research & Creative Works

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V* of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility …


Generalized Planar Fault Energies And Twinning In Cu–Al Alloys, S. Kibey, J. B. Liu, Duane D. Johnson, H. Sehitoglu Jan 2006

Generalized Planar Fault Energies And Twinning In Cu–Al Alloys, S. Kibey, J. B. Liu, Duane D. Johnson, H. Sehitoglu

Duane D. Johnson

We report ab initio density functional theory calculations of generalized planar fault energies of fcc Cu–xAl (x=0, 5.0, and 8.3at.%) alloys. We investigate the effects of substitutional solute Al on the unstable intrinsic γus and twin γutstacking faultenergies (SFEs). Our results reveal an increased tendency of Cu–Al to deform preferentially by twinning with increasing Al content, consistent with experiment. We attribute this mechanical behavior to appreciable lowering of the twinning barrier γut, along with the stable intrinsic and twin SFEs.


Temperature Dependence Of Homogeneous Nucleation Rates For Water: Near Equivalence Of The Empirical Fit Of Wölk And Strey, And The Scaled Nucleation Model, Barbara N. Hale May 2005

Temperature Dependence Of Homogeneous Nucleation Rates For Water: Near Equivalence Of The Empirical Fit Of Wölk And Strey, And The Scaled Nucleation Model, Barbara N. Hale

Physics Faculty Research & Creative Works

It is pointed out that the temperature fitting function of Wölk and Strey [J. Phys. Chem. 105, 11683 (2001)], recently shown to convert the Becker-Döring [Ann. Phys. (Leipzig) 24, 719 (1935)] nucleation rate into an expression in agreement with much of the experimental water nucleation rate data, also converts the Becker-Döring rate into a form nearly equivalent with the scaled nucleation rate model, Jscaled=Joc exp[-16πΩ3(Tc/T-1)3/3(ln S)2]. In the latter expression Joc is the inverse thermal wavelength cubed/sec, evaluated at Tc.


Nucleation Rates Of Water And Heavy Water Using Equations Of State, Abdalla Obeidat, Jin-Song Li, Gerald Wilemski Nov 2004

Nucleation Rates Of Water And Heavy Water Using Equations Of State, Abdalla Obeidat, Jin-Song Li, Gerald Wilemski

Physics Faculty Research & Creative Works

The original formula of Gibbs for the reversible work of critical nucleus formation is evaluated in three approximate ways for ordinary and heavy water. The least approximate way employs an equation of state to evaluate the pressure difference between the new and old phases. This form of the theory yields a temperature dependence for the nucleation rate close to that observed experimentally. This is a substantial improvement over the most commonly used (and most approximate) form of classical theory.©2004 American Institute of Physics.


Nucleation Near The Spinodal: Limitations Of Mean Field Density Functional Theory, Gerald Wilemski, Jin-Song Li Oct 2004

Nucleation Near The Spinodal: Limitations Of Mean Field Density Functional Theory, Gerald Wilemski, Jin-Song Li

Physics Faculty Research & Creative Works

We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory ~GT! of van der Waals and Cahn and Hilliard and mean field density functional theory ~MFDFT!. As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Dg satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the …


Kinetics Of Binary Nucleation Of Vapors In Size And Composition Space, Sergey P. Fisenko, Gerald Wilemski Jan 2004

Kinetics Of Binary Nucleation Of Vapors In Size And Composition Space, Sergey P. Fisenko, Gerald Wilemski

Physics Faculty Research & Creative Works

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different …


Small Angle Neutron Scattering From D2o–H2o Nanodroplets And Binary Nucleation Rates In A Supersonic Nozzle, Christopher H. Heath, Kiril A. Streletzky, Barbara E. Wyslouzil, Judith Woelk, Reinhard Strey Mar 2003

Small Angle Neutron Scattering From D2o–H2o Nanodroplets And Binary Nucleation Rates In A Supersonic Nozzle, Christopher H. Heath, Kiril A. Streletzky, Barbara E. Wyslouzil, Judith Woelk, Reinhard Strey

Physics Faculty Publications

Small angle neutron scattering (SANS) experiments were used to characterize binary nanodroplets composed of D2O and H2O. The droplets were formed by expanding dilute mixtures of condensible vapor in a N2 carrier gas through a supersonic nozzle, while maintaining the onset of condensation at a fixed position in the nozzle. It is remarkable, given the small coherent scattering length density of light water, that even the pure H2O aerosol gave a scattering signal above background. The scattering spectra were analyzed assuming a log-normal distribution of droplets. On average, the geometric radius of the nanodroplets rg was rg=13 (±1) nm, the …


Temperature Dependence Of Droplet Nucleation In A Yukawa Fluid, Jinsong Li, Gerald Wilemski Feb 2003

Temperature Dependence Of Droplet Nucleation In A Yukawa Fluid, Jinsong Li, Gerald Wilemski

Physics Faculty Research & Creative Works

We have studied the temperature dependence of gas-to-liquid nucleation in Yukawa fluids with gradient theory and density functional theory. Each of these nonclassical theories exhibits a weaker (i.e., better) temperature dependence than classical nucleation theory. At fixed temperature, the reversible work to form a critical nucleus found from gradient theory approaches the value given by density functional theory as the supersaturation increases. At high temperatures, the two theories remain quite close over a wide range of vapor densities. As the temperature is reduced, the difference between the two theories increases with decreasing vapor density. Compared to the classical theory we …


Controlling Nucleation And Growth Of Nanodroplets In Supersonic Nozzles, Kiril A. Streletzky, Yury Zvinevich, Barbara E. Wyslouzil, Reinhard Strey Mar 2002

Controlling Nucleation And Growth Of Nanodroplets In Supersonic Nozzles, Kiril A. Streletzky, Yury Zvinevich, Barbara E. Wyslouzil, Reinhard Strey

Physics Faculty Publications

We present the first results for a new supersonic nozzle that decouples nucleation and droplet growth, and closely controls the supersaturation and temperature during nucleation. We characterize the expansions using pressure trace measurements, and the aerosol properties using light scattering and small angle neutron scattering. We show that when nucleation and droplet growth are separated, the aerosol number density decreases, the average particle size increases, and the aerosol can be more monodisperse than that formed in a conventional nozzle. Under these conditions, we can estimate the nucleation rate J as a function of supersaturation S and temperature T directly from …


Oscillons: Resonant Configurations During Bubble Collapse, E J. Copeland, M Gleiser, H R. Müller Jun 1995

Oscillons: Resonant Configurations During Bubble Collapse, E J. Copeland, M Gleiser, H R. Müller

Dartmouth Scholarship

Oscillons are localized, non-singular, time-dependent, spherically-symmetric solutions of nonlinear scalar field theories which, although unstable, are extremely long-lived. We show that they naturally appear during the collapse of subcritical bubbles in models with symmetric and asymmetric double-well potentials. By a combination of analytical and numerical work we explain several of their properties, including the conditions for their existence, their longevity, and their final demise. We discuss several contexts in which we expect oscillons to be relevant. In particular, their nucleation during cosmological phase transitions may have wide-rangingconsequences.


Time Lag In Diffusion-Controlled Nucleation, David Peak Jan 1978

Time Lag In Diffusion-Controlled Nucleation, David Peak

All Physics Faculty Publications

Nucleation occurring in the presence of a dense solvent is accompanied by spatial correlations among the reactant clusters and monomers which affect the aggregation rates. The classical theory of nucleation, which does not take such correlations into account, overestimates the observed nucleation rate and underestimates the time lag in condensed systems. An explicit expression for the time lag in diffusion‐controlled nucleation is derived. Values associated with miscibility gap experiments differ from the classical predictions by factors of 5 to 10.