Chemistry of Microstructure and Nanostructure

Potentials or gradients in concentration or other driving forces determine the direction of the reactions. If the potentials are low and the mobility of the atoms is high enough, potentials affect rates. These effects have been well studied and dominate the formation of solids if it takes place under conditions not far removed from thermodynamic equilibrium, e.g., the growth of single crystals from a melt or from solution. 

In many if not most formation processes diffusion is rate- and shapedetermining, in which case the reaction path of the process rather than the driving forces determines the result. Diffusion of reactants may introduce fractality and fractal processes on fractal surfaces (see below). If diffusion is rate-limiting when solids are formed the temporal fluctuations are frozen in spatial structures. The direction of transport of the atoms or energy during the formation of the solid introduces anisotropy in the solid products. 

Time modulation of the process conditions during synthesis (or adding impurities) is used to control the microstructure and the composition of phases in the material. 

Examples of morphology control during synthesis can be found throughout this book. 

Generally, neither the form nor the size of crystallites is the result of equilibrium during formation. The existence of grain boundaries already implies an absence of equilibrium because they represent extra energy. The grain size and form depend on the history of the solid and on the rates at which the different faces grow. 

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