Showing papers on "Nucleation published in 1983"

Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures

Abstract: The dynamics of concentration fluctuations in binary polymer mixtures AB, A and B being long and flexible chains, is studied near the critical point of unmixing. A ‘‘hydrodynamic’’ theory in close analogy to the treatments of Cahn–Hilliard and Cook for the dynamics of unmixing alloys is developed, and its validity is carefully analyzed. It is shown that homogeneous nucleation for long chains is negligible except in a narrow region of volume fraction φ0 near the spinodal curve φs0 of width (φs0−φ0)/φ0∝N−1, where N is the number of subunits of the chains. For N→∞ the spinodal curve hence is well defined, in contrast to mixtures with short‐range forces, and also the linearized theory of spinodal decomposition is predicted to have wider validity. The collective relaxation in the one‐phase region is described by a characteristic time involving the collective diffusion constant Dcoll τq=(Dcoll q2)−1, if the wave vector q is smaller than the inverse correlation length ξ−1coll, while in the range ξ−1coll≪q≪R−1 (R...

Transient nucleation in condensed systems

Abstract: Using classical nucleation theory we consider transient nucleation occurring in a one‐component, condensed system under isothermal conditions. We obtain an exact closed‐form expression for the time dependent cluster populations. In addition, a more versatile approach is developed: a numerical simulation technique which models directly the reactions by which clusters are produced. This simulation demonstrates the evolution of cluster populations and nucleation rate in the transient regime. Results from the simulation are verified by comparison with exact analytical solutions for the steady state. Experimental methods for measuring transient nucleation are assessed, and it is demonstrated that the observed behavior depends on the method used. The effect of preexisting cluster distributions is studied. Previous analytical and numerical treatments of transient nucleation are compared to the solutions obtained from the simulation. The simple expressions of Kashchiev are shown to give good descriptions of the nucleation behavior.

Introduction to the Theory of Metastable and Unstable States

Abstract: A simple model of binary alloys.- Dynamical model of binary alloys.- The classical theory of nucleation.- Field theory of nucleation : Statics.- Field theory of nucleation : Dynamics.- Theories of spinodal decomposition.- Lifshitz-Slyozov late stage growth theory.- Kinetic drumhead model for nonconserved order parameter.- Dynamical scaling.

Kinetic evidence for a monomer activation step in actin polymerization

Abstract: We measured the time course of skeletal muscle actin polymerization at different actin concentrations. In 0.1 M KCl with 1 mM Mg2+, log/log plots of the rate of the early, slow phase of polymerization vs. actin concentration were linear with slopes from 1.0 to 1.3. Computer-assisted calculations of similar curves from theoretical models with different sizes for the nucleus showed that no simple model gave a log/log plot with a slope less than 1.5. Addition of a first-order, monomer activation step before nucleation allowed models of any reasonable nucleus size to have a slope of 1. This is the first evidence that such a step is part of the kinetic pathway for actin polymerization. In 0.1 M KCl with 0.2 mM Ca2+, log/log plots of the rate of the slow phase vs. actin concentration were linear with slopes from 2.0 to 2.5. Monomer activation was not necessary to account for this slope. However, fits of kinetic curves calculated from theoretical models to experimental kinetic curves showed that filament fragmentation was important to achieve a good fit, confirming the finding of Wegner and Savko [Wegner, A., & Savko, P. (1982) Biochemistry 21, 1909-1913]. Our fit procedure also allowed us to estimate the size of the nucleus and the rate constants for activation, nucleation, and fragmentation. In 0.1 M KCl with 1 mM Mg2+, the nucleus was a dimer or trimer, and nucleation was fast. In 0.1 M KCl with 2.0 mM Ca2+, the nucleus was a trimer, and nucleation was slow.

Why large earthquakes do not nucleate at shallow depths

Abstract: Spontaneous rupture models were examined to determine if gradients of average stress-drop and average strength relative to ambient stress account for earthquake nucleation near the base of the seismogenic layer. The frictional strength has been proved to increase with normal stress, which (across a fault) increases with depth in concert with the frictional strength. It is assumed that the large earthquakes occur at a time when the applied stress is equal to the frictional strength. A gradient has been found in frictional strength relative to the ambient stress and the stress-drop with depth. Attention is given to two cases where a circular crack appears, and radiates outward. It is shown that nucleation in the lower part of the seismogenic region will permit growth into a large earthquake, while nucleation in the lower stress-drop regime will encapsulate the crack. It is concluded that only cracks propagating in a high stress-drop regime can move easily into a relatively lower strength region.

The interaction of CO and Pt(100). II. Energetic and kinetic parameters

Abstract: We have investigated the mechanism and driving force of the CO‐induced phase transition of the Pt(100) surface. In a preceding paper, we have concentrated on the mechanism by which CO removes the surface reconstruction. As discussed, the clean reconstructed (hex) surface of Pt(100) is more stable than the unreconstructed (1×1) phase, but if the CO coverage on hex exceeds a small critical value (θ≳0.05) nucleation of (1×1) patches occurs and proceeds until, at θ=0.5, the entire surface has been converted to the (1×1) phase. In this paper we present data which quantitatively describe the energetics of this system. Values for the heats of adsorption of CO on both the reconstructed and unreconstructed phases, as well as values for the preexponential factors for the desorption rates, are determined from quasiequilibrium LEED measurements at different coverages. The difference in the low coverage heats of adsorption of CO on the hex and (1×1) phases (27.5 vs 37.5 kcal/mol) is the driving force in the Pt phase transformation during adsorption. On the other hand, during desorption, the hex phase does not return until the coverage has decreased below 0.3. This measurement allows an estimation of the difference in stability between the clean (1×1) and hex phases: about 9–13 kcal per mole of Pt atoms. The transition between the two phases which are in equilibrium [COgas+hex‐Pt(100) vs COads+(1×1)‐Pt(100)] shows a hysteresis due to kinetic limitations. These kinetic effects are characteristic of a nucleation process involving a critical coverage.

Nucleation and strain relaxation at the InAs/GaAs(100) heterojunction

Abstract: The techniques of molecular beam epitaxy have been used to investigate the nucleation and growth of InAs heteroepitaxial thin films lattice mismatched to GaAs(100) substrates. Our previous observations have been that optimum structural and electrical properties are obtained only if the heteroepitaxial nucleation sequence is carried out under experimental conditions leading to the indium stabilized (4×2) InAs(100) surface reconstruction. In this work, reflection electron diffraction, Auger electron spectroscopy and x‐ray diffraction have been used to determine the InAs(100) surface phase diagram. The InAs/GaAs(100) heterojunction grown by MBE is abrupt and smooth surfaces are obtained only under indium stabilized nucleation conditions. A residual compressive strain at the crystalline interface occurs which is somewhat relieved by a tetragonal distortion in the direction normal to the film plane. Results of investigations by reflection electron diffraction show that the nucleation of InAs/GaAs(100) occurs v...

Microstructural development of sub-eutectoid aged MgO-ZrO2 alloys

Abstract: The microstructural development in fully and partially stabilized MgO-ZrO2 alloys during sub-eutectoid heat treatment at 1100° C, has been studied by optical and electron microscopy and powder X-ray diffraction in order to correlate the observed microstructures with the mechanical properties. The materials used were 14 mol % MgO-ZrO2 (Mg-CSZ) of eutectoid composition and 9 mol % MgO-ZrO2 (Mg-PSZ). In Mg-CSZ the decomposition reaction proceeds almost to completion before the maximum thermal up-shock properties are attained. For the Mg-PSZ material the most significant event leading to the enhanced mechanical properties appears to be the nucleation and growth of a long-range ordered anion vacancy phase within the cubic zirconia matrix. This, in turn, leads to the destabilization of the tetragonal ZrO2 precipitates also present in Mg-PSZ, causing some of them to acquire monoclinic intergrowths whilst others transform to the monoclinic form on cooling. Beyond about 4 h ageing at 1100° C the decomposition product in the grain boundaries began to influence the mechanical properties.

The dependence of magnetic domain structure upon magnetization state with emphasis upon nucleation as a mechanism for pseudo-single-domain behavior

Abstract: The stable carriers of the paleomagnetic record in rocks are commonly fine pseudo-single-domain (PSD) particles between about 1 and 20 μm in diameter. However, the underlying mechanism which determines PSD behavior has previously remained in debate. To study this problem, magnetic domain patterns have been observed with the Bitter method on particles of natural pyrrhotite and intermediate titanomagnetite in various magnetization states, including natural remanent magnetization (NRM), after alternating field demagnetization of the NRM and during high-field hysteresis. From these observations it is evident that two primary mechanisms govern high-field hysteresis behavior: (1) ‘bulk’ pinning of fully developed domain walls by intervening energy barriers, and (2) nucleation, the creation and expansion of walls into the particle volume to produce a fully developed domain structure. These observations demonstrate that nucleation can explain several important aspects of PSD behavior. Typically, multidomain particles are entirely governed by bulk wall pinning, since they readily develop walls whose dimensions are comparable to the particle diameter prior to or upon removal of a strong field. For these grains the average domain wall spacing is relatively insensitive to the particular magnetization state, being approximately proportional to r (r being the grain diameter), in accordance with equilibrium calculations. In contrast, particles that are at least partially controlled by nucleation fail to develop a discernable domain wall structure at saturation remanence. However, these same grains can easily accommodate walls in other magnetization states. It is found that nucleation can involve two physically distinct but sometimes experimentally inseparable processes: (1) initial creation of walls at surface imperfections, and (2) unpinning of minute wall fragments from strong potential energy ‘traps’ near the grain surface. When either process fails, a grain remains locked in a metastable, single-domain-like state at saturation remanence and requires application of a reverse field Hn, called the nucleation field, before walls appear. In pyrrhotite, the probability for nucleation failure rises with decreasing grain size and has been determined through observation to be given by f(w = 0) = 1.2 exp (−0.46 r)r being in micrometers). Such single-domain-like particles can thus contribute substantially to the saturation remanence in the PSD range. The nucleation field determined experimentally for pyrrhotite is given by Hn ≃ 1200/ r Oe. In many fine pyrrhotites, Hn is sufficiently strong to reverse completely the magnetization through a single Barkhausen jump of the nucleated wall. These observations thereby demonstrate that nucleation becomes increasingly more dominant as the particles become smaller, a manifestation of the random distribution of active nucleation sites. Nucleation may therefore account for much of the magnitude and grain size dependence of hysteresis parameters in the PSD range as well as resulting in a gradual transition between multidomain and PSD behavior. Fine particles completely controlled by nucleation during hysteresis behave in a strikingly parallel manner to classical single domains and are therefore quite appropriately described as being pseudo-single-domain.

Theory of the nucleation of multicomponent precipitates

Abstract: The nucleation kinetics of multicomponent precipitates is studied. For this, asymptotic solutions of the corresponding stationary Fokker-Planck equation are derived and analyzed. The nucleation flux in composition space ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}}$ is determined by the reaction rates $R$ of the constituent components (kinetic barrier) and the formation free enthalpy $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}})$ of the precipitates (energetic barrier). If the kinetic barrier is small compared with the energetic one, the nucleation flux goes across the saddle point of $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}})$. For significantly different reaction rates the nucleation flux is bent into the directions of the rapidly reacting components, and the kinetic barrier is controlled by the fastest component $i$ for which $\frac{{\ensuremath{\partial}}^{2}G}{\ensuremath{\partial}{{n}_{i}}^{2}}l0$. If the kinetic and energetic barriers are comparable, the nucleation flux can go across a ridge in the direction of a rapidly reacting component. In this case the nucleation barrier is governed by a balance of the kinetic and the energetic barriers. The condition for this is in approximate agreement with the one suggested by Stauffer and Kiang. As the simplest example for binary nucleation the formation of ideal gas bubbles under gas and vacancy supersaturation is considered to illustrate and test the most important results of the theory.

Homogeneous nucleation rate measurements for water over a wide range of temperature and nucleation rate

Abstract: An expansion cloud chamber was used to measure the homogeneous nucleation rate for water over a wide range of temperature from 230–290 K and nucleation rates of 1–106 drops cm−3 s−1. The comprehensive and extensive nature of this data allows a much more detailed comparison between theory and experiment than has previously been possible. The expansion chamber technique employs continuous pressure measurement and an adiabatic pulse of supersaturation to give the time history of supersaturation and temperature during the nucleation. The resulting drop concentration is determined using photographic techniques. The experimental observations are presented in tabular form and from them an empirical nucleation rate formula is determined: J=S2 exp[328.124−5.582 43T+0.030 365T2−5.0319E−5T3 −(999.814−4.100 87 T+3.010 84E−3 T2)ln−2S], where J is the nucleation rate in units of drops cm−3 s−1. S is the supersaturation ratio and T is the temperature in K.