Kinetics of crystalline transformations involving nanoparticles

In a previous section we showed that, for nanoparticles, the ktable phase can depend upon the crystal size (also see Navrotsky, this volume). Thus, it follows that a crystal could switch from one polymorph to another as it grows. Furthermore, the phase transformation (or reaction) mechanism may be particle size-dependent. This could arise 

Much of the work to date on particle size effects on phase transformation kinetics has involved materials of technological interest (e.g., CdS and related materials, see Jacobs and Alivisatos, this volume) or other model compounds with characteristics that make them amenable to experimental studies. Jacobs and Alivisatos (this volume) tackle the question of pressure driven phase transformations where crystal size is largely invariant. In some ways, analysis of the kinetics of temperature-motivated phase transformations in nanoscale materials is more complex because crystal growth occurs simultaneously with polymorphic reactions. However, temperature is an important geological reality and is also a relevant parameter in design of materials for higher temperature applications. Thus, we consider the complicated problem of temperature-driven reaction kinetics in nanomaterials. 

For reasons noted above, titania (Ti02) has been a popular experimental model system for investigating the fundamental ways in which crystal size alters thermally-driven reactions. Also, temperature leads to rapid coarsening and phase transformations that modify the utility of nanoparticle titania for commercial applications. 

First we consider the transformation mechanism of anatase to rutile in order to determine the reason for the dependence of the transformation rate on particle size. Penn and Banfield (1998 1999) showed that the oriented assembly of nanoparticles to form larger crystals (see below for details) is accompanied by formation of twins that introduce new atomic arrangements at particle-particle interfaces. In the case of anatase, a 112 twin represents a slab of brookite and thus, a structural state intermediate between anatase and rutile. Penn and Banfield (1999) proposed that the activation barrier for rutile nucleation is lowered by the presence of these twins. Simultaneously, it was noted that the transformation of anatase to rutile in air (Gribb and Banfield 1997) and under hydrothermal conditions (Penn and Banfield 1999) rarely generates partially reacted crystals, suggesting a high activation barrier for rutile nucleation but rapid rutile growth. 

Once initiated, a cascade of atomic displacements and distortions occurs, converting anatase to rutile. Thus, it appears that the transformation rate is limited by the nucleation rate, which is increased by an increase in the number particle-particle interfaces, thus a decrease in particle size. Zhang and Banfield (1999) extended this more generally to particle-particle contacts. 

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