Nucleation thermodynamics

Chemical vapor deposition (CVD) of thin solid films from gaseous reactants is reviewed. General process considerations such as film thickness, uniformity, and structure are discussed, along with chemical vapor deposition reactor systems. Fundamental issues related to nucleation, thermodynamics, gas-phase chemistry, and surface chemistry are reviewed. Transport phenomena in low-pressure and atmospheric-pressure chemical vapor deposition systems are described and compared with those in other chemically reacting systems. Finally, modeling approaches to the different types of chemical vapor deposition reactors are outlined and illustrated with examples. 

Nucleation thermodynamics were published by Ginns in 1928 based upon his work at the end of the last century. Volmer and Weber (1926) indicated that the growth and decay of clusters of molecules played a major role in nucleation kinetics. The most recent reviews of hydrate nucleation are by Kashchiev and Firoozabdi (2002a,b). 

Keywords crystallization, crystal growth, nucleation, thermodynamics, nano-ciystals... 

In theoretical studies on diamond nucleation, thermodynamic theory, homogeneous and heterogeneous chemical kinetics, classical nucleation theory, adsorption-desorption kinetics and equilibrium have been considered to predict preferential conditions for diamond nucleation and growth. A narrow range of conditions, such as pressure (supersaturation), temperature,... 

Let us now discuss the principles of nucleation thermodynamics in relation to a number of particular examples illustrating the formation of a new phase within a metastable initial phase. 

In case of liquid marbles, the observed deformation may very possibly be explained on the basis of Marangoni convection and preferred nucleation. Thermodynamically, because only the bottom layer of particles are directly cooled by the cold substrate, heterogeneous nucleation is... 

Other nucleation thermodynamic parameters such as the interfacial energy between Ndl23 or Y123 and melt, metastable zone width, Gibbs free energy, critical nucleation radii etc. were estimated by Paul et al. (1999, 2000) using classical nucleation theory. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

In this chapter we have shown that diffusive transformations can only take place if nuclei of the new phase can form to begin with. Nuclei form because random atomic vibrations are continually making tiny crystals of the new phase and if the temperature is low enough these tiny crystals are thermodynamically stable and will grow. In homogeneous nucleation the nuclei form as spheres within the bulk of the material. In... 

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Here the nucleation barrier AO is the excess thermodynamic potential needed to form the critical embryo within the uniform metastable state, while the prefactor Jq is determined by the kinetic characteristics for the embryo diffusion in the space of its size a. Expressions for both AO and Jo given by Zeldovich include a number of phenomenological parameters. 

Later on Cahn and Hilliard presented some thermodynamic estimates for the nucleation of liquid in vapour. Values of AO and the composition profiles c(r) of the embryos have been estimated using the mean-field and gradient expansion approximations for the free energy functional F c(7 ). A number of qualitative features in variation... 

Although the Langelier index is probably the most frequently quoted measure of a water s corrosivity, it is at best a not very reliable guide. All that the index can do, and all that its author claimed for it is to provide an indication of a water s thermodynamic tendency to precipitate calcium carbonate. It cannot indicate if sufficient material will be deposited to completely cover all exposed metal surfaces consequently a very soft water can have a strongly positive index but still be corrosive. Similarly the index cannot take into account if the precipitate will be in the appropriate physical form, i.e. a semi-amorphous egg-shell like deposit that spreads uniformly over all the exposed surfaces rather than forming isolated crystals at a limited number of nucleation sites. The egg-shell type of deposit has been shown to be associated with the presence of organic material which affects the growth mechanism of the calcium carbonate crystals . Where a substantial and stable deposit is produced on a metal surface, this is an effective anticorrosion barrier and forms the basis of a chemical treatment to protect water pipes . However, the conditions required for such a process are not likely to arise with any natural waters. 

Part of the gas can escape from the solution at a specific concentration and a fixed temperature, as the pressure level falls to under P < Pg. This takes place in two phases appearance of nuclei, and growth of bubbles of the free gas phase. Thermodynamic conditions for stable nucleation are formulated in [1], They are analogous to the conditions for starting the boiling of low-molecular liquids. The following changes take... 

A drastic departure from nucleation theory was made by Sadler [44] who proposed that the crystal surface was thermodynamically rough and a barrier term arises from the possible paths a polymer may take before crystallizing in a favourable configuration. His simulation and models have shown that this would give results consistent with experiments. The two-dimensional row model is not far removed from Point s initial nucleation barrier, and is practically identical to a model investigated by Dupire [35]. Further comparison between the two theories would be beneficial. 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

In aggregate nucleation the oligomers reversibly associate with each other until the aggregate reaches a critical size above which it is thermodynamically stable and continues to grow. 

Such effects are observed inter alia when a metal is electrochemically deposited on a foreign substrate (e.g. Pb on graphite), a process which requires an additional nucleation overpotential. Thus, in cyclic voltammetry metal is deposited during the reverse scan on an identical metallic surface at thermodynamically favourable potentials, i.e. at positive values relative to the nucleation overpotential. This generates the typical trace-crossing in the current-voltage curve. Hence, Pletcher et al. also view the trace-crossing as proof of the start of the nucleation process of the polymer film, especially as it appears only in experiments with freshly polished electrodes. But this is about as far as we can go with cyclic voltammetry alone. It must be complemented by other techniques the potential step methods and optical spectroscopy have proved suitable. 

The MD simulations provided the necessary thermodynamic information to obtain the equilibrium configurations of the films. Often the deposition process will produce films which are not in the equilibrium configuration, and then the problem is to determine the stablity of these films against changes in morphology. Here simulations can also be helpful, since data on the surface energies and chemical potentials of strained films can be used to calculate the probability of cluster nucleation, using classical nucleation theory. 

Transfomation from a meta-stable phase, such as supersaturated solution, to a thermodynamically more favorable phase requires first the crystal nucleation of a germ of the new phase. According to the classical nucleation theory, the volume nucleation rate J (cm" sec ), describing the number of nuclei(i.e., a critical germ) formed per volume per time, is given by ... 

In this work, we developed the safeguard active-set method by modifying the active-set method for thermodynamic equilibrium in order to include the classical nucleation theory. At tn, assume that the partition ( (r ), M(t ), N(t ) and the crystallization time tciyst(t ) forM(t ) are known. For a new feed vector and RH at Vu compute W(tn+i), M(t i), N(t + )) and tciyst(t +i) as follows ... 

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