Nucleation Theory

One of the most striking phenomena in condensed matter physics is the occurrence of abrupt transitions in the structure of a substance at certain temperatures or pressures. These are first order phase transitions, and examples such as the freezing of water are familiar in everyday life. The conditions at which the transformation takes place can sometimes vary. For example, the freezing point of water is not always 0°C, but the liquid can be supercooled considerably if it is pure enough and treated carefully. The reason for this phenomenon is nucleation. This monograph covers all major available routes of theoretical research of nucleation phenomena (phenomenological models, semi-phenomenological theories, density functional theories, microscopic and semi-microscopic approaches), with emphasis on the formation of liquid droplets from a metastable vapor. Also, it illustrates the application of these various approaches to experimentally relevant problems. In spite of the familiarity of the involved phenomena, it is still impossible to calculate nucleation accurately, as the properties and the kinetics of the daughter phase are insufficiently well known. Existing theories based upon classical nucleation theory have on the whole explained the trends in behavior correctly. However they often fail spectacularly to account for new data, in particular in the case of binary or, more generally, multi-component nucleation. The current challenge of this book is to go beyond such classical models and provide a more satisfactory theory by using density functional theory and microscopic computer simulations in order to describe the properties of small clusters. Also, semi-phenomenological models are proposed, which attempt to relate the properties of small clusters to known properties of the bulk phases. This monograph is an introduction as well as a compendium to researchers in soft condensed matter physics and chemical physics, graduate and post-graduate students in physics and chemistry starting on research in the area of nucleation, and to experimentalists wishing to gain a better understanding of the efforts being made to account for their data.

Nucleation is the initial step of every first-order phase transition, and most phase transitions encountered both in everyday life and industrial processes are of the first-order. Using an elegant classical theory based on thermodynamics and kinetics, this book provides a fully detailed picture of multi-component nucleation. As many of the issues concerning multi-component nucleation theory have been solved during the last 10-15 years, it also thoroughly integrates both fundamental theory with recent advances presented in the literature. Classical Nucleation Theory in Multicomponent Systems serves as a textbook for advanced thermodynamics courses, as well as an important reference for researchers in the field. The main topics covered are: the basic relevant thermodynamics and statistical physics; modelling a molecular cluster as a spherical liquid droplet; predicting the size and composition of the nucleating critical clusters; kinetic models for cluster growth and decay; calculating nucleation rates; and a full derivation and application of nucleation theorems that can be used to extract microscopic cluster properties from nucleation rate measurements. The assumptions and approximations needed to build the classical theory are described in detail, and the reasons why the theory fails in certain cases are explained. Relevant problems are presented at the end of each chapter.

An overview of recent developments in the field of first-order phase transitions, which may be considered a continuation of the previous work 'Aggregation Phenomena in Complex Systems', covering work done and discussed since then. Each chapter features a different aspect of the field written by international specialists, and covers such topics as nucleation and crystallization kinetic of silicate glasses, nucleation in concentration gradients, the determination of coefficients of emission of nucleation theory, diamonds from vitreous carbon.

Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation discusses the influence of classical thermodynamics, statistical mechanics, and multistate kinetics on the homogeneous nucleation theory. This book is organized into 10 chapters and begins with a simple model calculation that yields an important insight into the major physical features governing supersaturated vapor condensation. The following chapters explore the development of the theory of equilibrium thermodynamics pertinent to the study of a nucleation phenomena and a postulatory formulation of statistical mechanics and its relation to the calculation of the thermodynamic potentials. The discussion then shifts to a statistical thermodynamics description of an imperfect gas assuming the droplet model of Band-Bijl-Frenkel and to the development of the multistate kinetics of cluster formation. The book also explores the development of the classical Einstein theory for crystalline solids and generalizes this theory for its applications to planar surfaces of microcrystalline clusters. It also presents a comparison of the exact free energies for the microcrystallites with the predictions of the droplet model using the capillarity approximation. Three distinct approaches for calculating the thermodynamic properties of physical clusters are covered in the concluding chapters.

Semiconductor nanostructures such as nanowires are promising building blocks of future nanoelectronic, nanophotonic and nanosensing devices. Their physical properties are primarily determined by the epitaxy process which is rather different from the conventional thin film growth. This book shows how the advanced nucleation theory can be used in modeling of growth properties, morphology and crystal phase of such nanostructures. The book represents a systematic account of modern nucleation theory in open systems, nanostructure nucleation and growth mechanisms, and possibilities for tuning the nanostructure properties to the desired values.

Nucleation has been the subject of intense research because it plays an important role in the dynamics of most first-order phase transitions. The standard theory to describe the nucleation phenomena is the classical nucleation theory (CNT) because it correctly captures the qualitative features of the nucleation process. However potential problems with CNT have been suggested by previous studies. We systematically test the individual components of CNT by computer simulations of the Ising model and find that it accurately predicts the nucleation rate if the correct droplet free energy computed by umbrella sampling is provided as input. This validates the fundamental assumption of CNT that the system can be coarse grained into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Employing similar simulation techniques, we study the dislocation nucleation which is essential to our understanding of plastic deformation, ductility, and mechanical strength of crystalline materials. We show that dislocation nucleation rates can be accurately predicted over a wide range of conditions using CNT with the activation free energy determined by umbrella sampling. Our data reveal very large activation entropies, which contribute a multiplicative factor of many orders of magnitude to the nucleation rate. The activation entropy at constant strain is caused by thermal expansion, with negligible contribution from the vibrational entropy. The activation entropy at constant stress is significantly larger than that at constant strain, as a result of thermal softening. The large activation entropies are caused by anharmonic effects, showing the limitations of the harmonic approximation widely used for rate estimation in solids. Similar behaviors are expected to occur in other nucleation processes in solids.

This book represents a detailed and systematic account of the basic principles, developments and applications of the theory of nucleation. The formation of new phases begins with the process of nucleation and is, therefore, a widely spread phenomenon in both nature and technology. Condensation and evaporation, crystal growth, electrodeposition, melt crystallization, growth of thin films for microelectronics, volcano eruption and formation of particulate matter in space are only a few of the processes in which nucleation plays a prominent role. The book has four parts, which are devoted to the thermodynamics of nucleation, the kinetics of nucleation, the effect of various factors on nucleation and the application of the theory to other processes, which involve nucleation. The first two parts describe in detail the two basic approaches in nucleation theory - the thermodynamic and the kinetic ones. They contain derivations of the basic and most important formulae of the theory and discuss their limitations and possibilities for improvement. The third part deals with some of the factors that can affect nucleation and is a natural continuation of the first two chapters. The last part is devoted to the application of the theory to processes of practical importance such as melt crystallization and polymorphic transformation, crystal growth and growth of thin solid films, size distribution of droplets and crystallites in condensation and crystallization. The book is not just an account of the status quo in nucleation theory - throughout the book there are a number of new results as well as extensions and generalisations of existing ones.