On the theory of transient nucleation at the intermediate stage of phase transitions

The evolution of a system of growing aggregates in a macroscopically homogeneous medium with account of both the reduction in metastability and the continuing initiation of new nuclei is studied. The corresponding integro-differential model describing the intermediate stage of phase transitions is solved analytically for arbitrary nucleation kinetics and growth rates of nuclei. An exact solution of the Fokker–Planck equation is found with allowance for the diffusivity along the axis of nucleus radii. In limiting cases of purely kinetic and mixed kinetic-diffusion rates of crystal growth for a special form of diffusivity, the obtained solutions transform to earlier known expressions.     

On a reconsideration of classical nucleation theory

A correct account of the collective motion of a cluster does not require the Lothe-Pound correction; furthermore, this correction is shown to contradict the laws of thermodynamics.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

Classical nucleation theory with a tolman correction

The effect of the Tolman correction for the surface tension of small droplets on the classical Becker-Doering theory of nucleation is studied near the critical temperature T_c. Also a generalization of the kinetic prefactor is studied together with this correction. No qualitative change in the very small slope of the curve of the reduced supercooling as a function of (1–T)/T _c at constant nucleation rates was found.The Center for Polymer Studies is supported in part by grants from ARO, ONR, and NSF.     

Breakdown of classical nucleation theory near isostructural phase transitions

We report simulations of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model. We argue that the observed behavior is due to the surface stress of the crystal nuclei. The observed effect highlights a general deficiency of the most frequently used thermodynamic theories for crystal nucleation. Surface stress should lead to an experimentally observable expansion of crystal nuclei of colloids with short-ranged attraction and of globular proteins.     

On the existence of a nonuniform spin-isospin ordered phase in high-density neutron matter

Using a Jastrow-like correlated wavefunction and a realistic two-body interaction, the energy per particle of neutron matter has been evaluated both in the normal uniform phase and in a π⁰-condensed phase exhibiting one-dimensional density fluctuations and spin-isospin order. The numerical results indicate that the standard configuration is energetically favored, even at very high densities.     

Mean-field nucleation theory with nonlocal interactions

Mean-field nucleation theory has for a long time been successfully used to extract microscopic parameters from island density data in growth experiments. However, it produces grossly incorrect results when used to analyze weakly corrugated systems, where adsorbate interactions cannot be neglected. Here, a mean-field theory that includes nonlocal adsorbate interactions is developed and successfully tested against kinetic Monte Carlo growth simulations for a realistic adsorbate system.     

Decline of nucleation in the heating process with a high heating rate

The effect of the heating rate on the nucleation of metallic glass in a rapid heating process starting from the glass transition temperature is investigated. The critical nucleus radius increases with the increase of the temperature of the undercooling liquid. If the increment rate of the critical nucleus radius, owing to the heating process, is higher than the growth rate of the nuclei, the nuclei generated at the low temperature will become the embryos at the high temperature. This means that the high heating rate can make no nucleation happen in the heating process. In consideration of the interfacial energy, the growth rate of the nuclei increases with the increase of their size and the growth rate of the critical nucleus is zero. Thus, the lower heating rate can also make the nuclei decline partially. Finally, this theory is used to analyze the nucleation process during laser remelting metallic glass.     

On the problem of the consistency of the high-temperature precipitation model with the classical nucleation theory

The adequacy of the model of high-temperature precipitation in dislocation-free silicon single crystals to the classical theory of nucleation and growth of second-phase particles in solids has been considered. It has been shown that the introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to explain the precipitation processes occurring in the high-temperature range and thus extend the theoretical basis of the application of the classical nucleation theory. According to the model of high-temperature precipitation, the smallest critical radius of oxygen and carbon precipitates is observed in the vicinity of the crystallization front. Cooling of the crystal is accompanied by the growth and coalescence of precipitates. During heat treatments, the nucleation of precipitates starts at low temperatures, whereas the growth and coalescence of precipitates occur with an increase in the temperature. It has been assumed that the high-temperature precipitation of impurities can determine the overall kinetics of defect formation in other dislocation-free single crystals of semiconductors and metals.     

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.     

On the description of isothermal phase transformations in binary alloys

Two effects are considered to influence the time dependence of the transformed volume in a binary alloy: a) the impingement effect (IE), takes into account the mutual impingement of the growing particles and b) the impoverishment effect (PE), which considers the decrease of driving forces and the increase of the diffusion paths in the approximation of an impoverishing matrix. Combining both effects growth equations are obtained analogous toJohnson-Mehl-Avrami only for one-dimensional growth.     

New theory of nucleation

New distributions are obtained in classical statistical physics; these distributions explain some old experiments.     

On the conformal transformations of metrics in Rosen's bimetric gravitation theory

The conformal transformations of the background metric are considered and the transformed expressions of the gravitational energy and of the gravitational field equations are obtained. The conditions of conservation of the nongravitational energy are formulated with respect to the transformed metric. Then the background and the physical metrics are both subjected to transformations and the relationship between the corresponding conformal factors analyzed, particularly in the case of conserved nongravitational energy.     

Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters. Received: 18 August 1999 / Published online: 14 October 1999     

Relativistic backward-wave tube with nonuniform phase velocity of the synchronous harmonic

We have investigated the possibility of increasing the efficiency of a moderately relativistic backward-wave tube (BWT) by longitudinal modification of the phase velocity profile of the synchronous (−1) spatial harmonic. We have shown theoretically that the efficiency of oscillators with a nonuniform electrodynamic system may reach 60% in the approximation of a near zero space-charge field. We have found that the use of nonuniform periodic structures leads to reduction of the critical value of the space-charge field, and also impairment of the adaptive properties of the device. In our experiments, we have realized backward-wave oscillators (BWO) with 40% efficiency and microwave radiation power of 500 MW. Institute of High-Current Electronics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 56–61, December, 1996.     

On the theory of phase interaction of modes

The selfoscillatory lasing operating modes of lasers are investigated in the presence of phase coupling between modes. The small-parameter method is used to find the conditions of existence and form of the time-periodic solution in the lowest approximation. Stable periodic solutions correspond to selfoscillatory operating modes; unstable periodic solutions characterize the finite dimensions of the domain of attraction of the stable stationary operating mode and indicate under certain conditions the existence of selfoscillatory operating modes of another type. The specific calculations apply to the theory of nonlinear phase interaction of angular oscillation modes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 43–50, January, 1972.     

Canonical transformations in a higher-derivative field theory

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiralgauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.     

On the mean-field theory of the metal-insulator phase transition

Two mean-field models describing the metal-insulator phase transition are studied. In the model due to Keldysh and Kopaev (1964) different effective masses in the valence and conduction bands are considered and in the model due to Mattis and Langer (1970) the exact s.c. and b.c.c. densities of states are taken into account. It is shown that these modifications do not change the qualitative features of the phase diagrams. In each case a special attention is paid to the domain of the degenerate semiconductor, which has been of primary interest in many attempts to explain conjectured enhancement of superconductivity in systems undergoing dielectric transition.     

On the multidimensional theory of the first-order phase transitions

Multidimensional theory of first-order phase transitions in the vicinity of a one-dimensional saddle point is considered. Transformations of the variables describing new-phase nuclei are suggested; these transformations allow one to completely separate the variables in the Fokker-Planck equation and reduce the problem to a one-dimensional one. The distribution function and the nucleation rate are found for both stationary and non-stationary nucleation stages. As an illustration, the problem of boiling of a volatile liquid is considered in the case where new-phase nuclei are characterized by two parameters.