Conventional Nucleation Theory Research Articles

SAXS study on crystallization of an amorphous Pd76Au6Si18 alloy

The crystallization behaviour of an amorphous Pd76Au6Si18 alloy has been investigated mainly by means of small angle X-ray scattering measurements. The amorphous alloy crystallized to form MS-I phase with composition Pd78Au22 in the amorphous matrix, which later crystallized as MS-II. The crystallization kinetics of MS-I phase were analysed in the framework of conventional nucleation theory. It was suggested that the considerable number of nuclei of MS-I phase had been already formed in the as-quenched specimen and the remaining nucleation attained within the short period of isothermal ageing. The remarkable increase of the scattering intensity corresponded to the growth of MS-I phase, the kinetics of which were found to be controlled by the diffusion mechanism. The interdiffusion constant was obtained fromD=6.0×1015 exp (−420 kJ mol−1/RT) m2 sec−1, which agreed fairly with the reported values.

A molecular theory of crystal nucleation from the melt

We construct a molecular theory for the homogeneous nucleation of crystals from pure liquids by combining an order parameter theory of freezing with a square gradient approximation for the nonlocal dependence of free energy on density. We show the results of our theory for the free energy, radius, and shape of crystal nuclei as a function of supercooling, and compare with the conventional nucleation theory based on the capillarity approximation. We argue that the simple picture given by the conventional approach is qualitatively reasonable, although calculated values of the liquid–solid surface free energy may be inaccurate. We point out some of the limitations of our approach and stress the need for additional structural data on supercooled liquids.

Time-Resolved, Laser-Induced Phase Transformation in Aluminum

ABSTRACTThe technique of picosecond electron diffraction is used to time resolve the laser-induced melting of thin aluminum films. It is observed that under rapid heating conditions, the long range order of the lattice subsists for lattice temperatures well above the equilibrium point, indicative of superheating. This superheating can be verified by directly measuring the lattice temperature. The collapse time of the long range order is measured and found to vary from 20 ps to several nanoseconds according to the degree of superheating. Two interpretations of the delayed melting are offered, based on the conventional nucleation and point defect theories. While the nucleation theory provides an initial nucleus size and concentration for melting to occur, the point defect theory offers a possible explanation for how the nuclei are originally formed.

Effects of temperature and helium on void formation in self-ion irradiated aluminum

High-purity aluminum was irradiated with 9 MeV aluminum ions at several temperatures in the range 25–125°C, both with and without pre-injected helium. The aluminum ion irradiation doses ranged from 0.2 to 20 dpa. Void swelling in the temperature range studied was found to occur only when the aluminum contains helium gas, and as little as 0.1 appm helium is sufficient to nucleate a substantial void population. In the absence of helium, even doses of 20 dpa do not result in void formation. The void number density and size follow the general trends in conventional nucleation theories, and are similar to trends observed in nickel and stainless steels. The microstructure quite often contained heterogeneous distributions of void stringers, suggesting nucleation of voids on dislocations.

Photoinduced nucleation of supersaturated vapors in the presence of carbon disulfide

With illumination by ultraviolet light in the 280-390-nm wavelength region, copious nucleation is observed in supersaturated vapors containing carbon disulfide. This photoinduced nucleation cannot be explained by conventional nucleation theories nor by the photochemistry of C${\mathrm{S}}_{2}$. We suggest that the nucleation is initiated by the clustering of photoaffected C${\mathrm{S}}_{2}$ molecules, and that these molecules may be stable complexes formed by an interaction of the photoexcited C${\mathrm{S}}_{2}$ and host vapor molecules.

Heterogeneous nucleation of damage in crystalline silicon with picosecond 1.06-μm laser pulses

The heterogeneous nature of the nucleation and growth of damage induced by ;picosecond Nd:YAG laser pulses in single-crystal silicon has been demonstrated. A damage kinetic model analogous to the conventional theory of nucleation and growth is used to analyze experimental results. The analysis shows that the damage kinetics has a critical dependence on the incident intensity.

Kinetics of nucleation in near-critical fluids

A simple set of rate equations is proposed to describe nucleation and growth of droplets in metastable, near-critical fluids. These equations are used in conjunction with steady-state nucleation theory to compute completion times for phase separation in binary mixtures. Reexamination of available experimental data provides little if any evidence for the major failure of conventional nucleation theory that has been postulated on the basis of these data.

Nucleation near a critical temperature

In this paper we extend the conventional theory of nucleation to take in the effects of excluded-volume interference between the precritical droplets present prior to phase transformation. It is shown that, close to the critical point, the effect of excluded volume is to cause a sizable increase in the surface free energy of the critical nucleus. A corresponding increase in the barrier to nucleation explains the large undercoolings achieveable experimentally in this region. Our results are compared with recent experimental measurements of Heady and Cahn and favorable agreement is found.

Nucleation of electrically charged droplets

The presence of a finite electric potential in many nucleation environments is discussed. It is contended that this potential introduces a nontrivial modification in the conventional nucleation theory. (AIP)

Colloidal plasmas in space: some aspects of condensation and growth of solids

The abundant occurrence of colloidal plasma clouds in the observable universe is reviewed, and the possible locales of condensation of cosmic solids identified. The physical properties of the condensation environment and the thermal physics of the plasma-cluster medium are outlined. In the light of these discussions, an attempt is made to identify the salient features of the processes of nucleation and growth in space. It is suggested that the conventional nucleation theory is inadequate when applied to the tenuous, partially excited, partially ionized multispecies cosmic vapor phase, and that studies relying on the physics of progressive molecule growth in such environments hold promise of understanding the process of transition of a cluster from the size of a few atomic mass units through the macromolecular range into what may be characterized as the bulk condensed phase.

Formation of atmospheric ultrafine particles and ions from trace gases

Firstly, the importance of ultrafine particles in the atmospheric aerosol is reviewed. Based on conventional nucleation theory, it is shown that water vapor alone cannot initiate the formation of such particles. We consider a mixture of water vapor and sulfuric acid and, pursuant to a discussion of theoretical results obtained by various writers, we consider the case under atmospheric conditions. We demonstrate that this leads to orders of magnitude which compare with the results of simulation experiments now under way. Secondly, we study the mobility spectrum of atmospheric ions, based on mobility mass correlations, and we demonstrate that Thomson's conventional theory, calling upon only the presence of water vapor in the atmosphere, does not allow for the interpretation of the atmospheric ions' mobility spectrum observed in our experiment. This spectrum is qualitatively interpreted by generalizing the theory of Thomson and by introducing in it the simultaneous presence of water vapor and sulfuric acid.

On the composition of nuclei in binary systems

It is shown that some past thermodynamic treatments of the so-call ’’classical’’ nucleus for nucleation in a liquid–liquid miscibility gap have neglected certain important terms. These occur in the chemical potential and are associated with the dependence of interfacial tension on composition. A careful thermodynamic development is presented which yields the more complete result. In 1959 Cahn and Hilliard (CH) presented a thermodynamic theory for the nucleus based on the use of ’’gradient’’ terms in the interfacial transition zone in place of the conventional interfacial tension. The properties of their nucleus differed appreciably from those of what they termed the ’’classical’’ nucleus in connection with which more conventional interfacial concepts are used. For example, at the spinodal, the CH nucleus has no free energy of formation and is of infinite size with a composition infinitesimally different from that of the parent solution while the ’’classical’’ nucleus requires finite free energy, has finite size, and a composition close to that of one branch of the coexistence curve. There are many other differences. However, when the ’’classical’’ nucleus is subjected to the complete thermodynamic treatment it assumes all of the features of the CH nucleus, and proves to be essentially equivalent. Since the CH method and the classical have certain complementary features, one or another is the most useful depending on the problem involved. Both Heady and Cahn (HC) and Sundquist and Oriani (SO) have performed experiments which indicate that the conventional theory of nucleation fails for supercoolings within a miscibility gap. Although the analysis in this paper indicates that their estimates of the thermodynamic properties of the nucleus, from experimental data, via the so-called ’’tangent rule’’ may be incomplete, the more precise free energy barrier is found to be even smaller than their estimate, thus adding strong support to their claim that the conventional theory fails.

Nucleation in a nonuniform vapor

Conventional nucleation theory describes nucleus formation in a uniform vapor as the addition or loss of single molecules from clusters of a given size. However, under nonuniform conditions, clusters can also be removed by diffusing away from the region of interest. Although there are many practical situations in which nucleation does occur under nonuniform conditions, the conventional theory cannot account for the loss of clusters by diffusion. It is therefore the purpose of this paper (1) to formulate a new theory which does include loss by diffusion and (2) to make a quantitative study of the diffusion effect in order to delineate the range of conditions under which it becomes important. The new theory is derived in the context of a typical diffusion cloud chamber by considering the diffusion loss from the narrow slab where nucleation occurs. The supersaturations which give rise to a unit steady rate of nucleation are then compared with and without the diffusion term for model compounds under a variety of conditions. These quantitative studies on typical model compounds show that the diffusion effect first becomes important for vapor pressures as low as 10−8 torr. Thus, in the cloud chamber, nonuniformities do not cause serious errors. More importantly, in polluted atmospheres, even very low concentrations of vapors of involatile organic substances (e.g., sulfinic acids) can nucleate and give rise to the particulate matter commonly found in photochemical smog.

A Possible Mechanism for Contact Nucleation

A contact nucleation mechanism is suggested, by which ice embryos formed on a nucleus in vapor are able to nucleate supercooled water on contact. Using conventional nucleation theory, the activity of a contact nucleus is calculated as a function of the contact angle of ice on the nucleus in vapor, and as a function of nucleus size. It is predicted that the threshold supercooling required for deposition nucleation should be about 2.3 times as great as that required for contact nucleation (for nuclei >0.1 μm radius), and this prediction is found to be in reasonable agreement with the limited experimental evidence. A relation between the deposition and contact nucleus concentrations in air samples is predicted.

Investigation of metastable states and nucleation in the kinetic Ising model

The relaxation of a two-dimensional Ising ferromagnet after a sudden reversal of the applied magnetic field is studied from various points of view, including nucleation theories, computer experiments, and a scaling theory, to provide a description for the metastable states and the kinetics of the magnetization reversal. Metastable states are characterized by a "flatness" property of the relaxation function. The Monte Carlo method is used to simulate the relaxation process for finite $L\ifmmode\times\else\texttimes\fi{}L$ square lattices ($L=55, 110, 220 \mathrm{and} 440, \mathrm{respectively}$); no dependence on $L$ is found for these systems in the range of magnetic fields calculated. The metastable states found for small enough fields terminate at a rather well-defined "coercive field," where no singular behavior of the susceptibility can be detected, within the accuracy of the numerical calculation. In order to explain these results an approximate theory of cluster dynamics is derived from the master equation, and Fisher's static-cluster model, generalizing the more conventional nucleation theories. It is shown that the properties of the metastable states (including their lifetimes) derived from this treatment are quite consistent with the numerical data, although the details of the dynamics of cluster distributions are somewhat different. This treatment contradicts the mean-field theory and other extrapolations, predicting the existence of a spinodal curve. In order to elucidate the possible analytic behavior of the coercive field we discuss a generalization of the scaling equation of state, which includes the metastable states in agreement with our data.

Nucleation of voids in irradiated metals

Conventional nucleation theory cannot properly be applied to the process of co-precipitation of vacancies and interstitials into voids. A proper formalism is developed herein and utilized to derive an expression for the void nucleation rate under these conditions. Although such a system is of a higher degree of irreversibility than those considered by Volmer and by Becker, the resulting rate equations are superficially similar. In the present case, however, the activation barrier is a function of the defect mobilities, hence is not the customary free energy of activation.

Treatment of droplike clusters by means of the classical phase integral in nucleation theory

The “translation” inconsistency in the theory of nucleation is discussed in historical perspective. A theory is then developed, beginning with the classical phase integral, which not only allows all approximations to be well defined, but also leads to the most “natural” droplike model for the cluster. The theory makes it possible to apply, in a consistent manner, the thermodynamics of curved surfaces or, alternatively, moleculardynamic numerical computation schemes to the evaluation of the partition function of the cluster. If the cluster is treated as a macroscopic drop (having the free energy of a macroscopic drop), the result for the distribution of clusters differs in only a minor way from that prescribed by the conventional theory of nucleation. It is concluded that for liquid nuclei the conventional theory is consistent, but that a replacement factor may be necessary for solid nuclei. In general, however, the major problems confronting the theory involve the precise evaluation of the work of cluster formation.

Resolution of the Translation—Rotation Paradox in the Theory of Irreversible Condensation

In this paper it is shown that the Lothe and Pound correction to nucleation theory based upon the introduction of translational and rotational partition functions for individual drops does not arise. The error originates in the improper assumption that the free energy assigned to a drop, in the conventional theory of nucleation, corresponds to that for a drop whose center of mass is stationary.

Crystallization Kinetics in High Polymers. I. Bulk Polymers

The rates of crystallization of five polymers, poly-(ethylene oxide), poly-(decamethylene adipate), and three poly-(N,N′-sebacoyl piperazine)'s differing in molecular weight, have been observed dilatometrically at various temperatures ranging from 5.5 to 24° below the respective melting points Tm. The crystallization isotherms are remarkably reproducible, and the previous thermal history above the melting point is without effect provided that melting is completed before the crystallization experiment is begun. The crystallization isotherms display induction periods. The very large temperature coefficients observed are uniform throughout the crystallization process, i.e., isotherms at different temperatures are superimposable by rescaling the time. It is inferred from this and other evidence that steady-state nucleation and growth occur simultaneously throughout the process. The results are satisfactorily interpreted by applying conventional nucleation theory and assuming that nuclei grow at rates proportional to their surface areas. The treatment resembles that applied to crystallization in metals. Spherical and disk-shaped nuclei are considered, but the data do not discriminate between them. An extension of the theory accounts for the maximum commonly observed in the crystallization rate as the temperature is decreased below the range of the present measurements.