Crystal growth thermodynamic driving force

Supersaturation is the thermodynamic driving force for both crystal nucleation and growth and therefore, it is the key variable in setting the mechanisms and rates by which these processes occur. It is defined rigorously as the deviation of the system from thermodynamic equilibrium and is quantified in terms of chemical potential,... 

Because of the importance of microstructure on dielectric and ferroelectric properties, the transformation pathway associated with conversion of the amorphous film into the crystalline state has been studied extensively. The basic mechanism involved is one of nucleation and growth, although the formation of intermediate phases that can impact the thermodynamic driving forces associated with the transformation frequently occurs. " Another key aspect of CSD films is that crystallization occurs well below the melting point of the materials. Therefore, compared to standard mixed-oxide processing of bulk materials, the thermodynamic driving forces associated with the transformation are much greater and the kinetics of mass transport are much less. 

The ideas described previously for understanding film morphology in terms of the local equilibrium and in terms of the surface tension are useful, but film growth occurs far from equilibrium (ex vi termini). Thus, kinetic processes control the details of film growth and the final film morphology. According to the paper by Burton, Cabrera, and Frank [13], the kinetic rates and processes are controlled by the thermodynamic driving force Ap, defined as the positive difference between the chemical potential of a molecule in the vapor phase and that in the crystal phase. 

The thermodynamic driving force of crystal growth lies in the metastable equilibrium at the interface of solid and Uquid and is dictated by the degree of... 

Fig. 1. Illustration of the classical thermodynamic driving force for zeolite crystallization. As crystallization occurs, the solution composition falls between the gel solubility and the crystal solubility. Zeolite crystal growth stops when sufficient material has been deposited to reduce the solution concentration to the zeolite equilibrium level...

The crystalline nature of the fibers in SMGs means that the formation of fibers in such a material can be controlled thermodynamically as in a conventional crystallization system. The driving force for the formation of new phases (e.g., fibers/crystals) is determined by the difference between the chemical potentials / mother / crystal e growth Unit in the mother and the crystalline phases. The chemical potential A/r is defined as [20]... 

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