Constrained metastable structure

In a reactional medium (such as water, for several materials), the competition between dissolution and reprecipitation renders this interpretation more complex. Even though the main ideas remain valid, the first stages of the formation of a crystal may be the coalescence of two fairly large clusters, eliminating water, protons, and OH groups from the surface [2,94]. This step - often referred to as poly condensation [43,100] - has no clear activation energy and may differ significantly from classical nucleation. Hence, a conclusion dictated by conunon sense may hold true in some cases the metastable structure of the nanoparticle comes from a memory of the precursor or, in the case of amorphous nanoparticles, the precursor nanostructure constrains the atoms in positions such that crystallization is impossible. 

However, it is believed that the area in which sol-gel preparation is going to make the most significant impact is multicomponent systems because of the following specific advantages of the sol-gel approach (i) the ability to control structure and composition at a molecular level (ii) the ability to introduce several components in a single step (hi) the ability to impose kinetic constrains on a system and thereby stabilize metastable phases and (iv) the abihty to fine-time the activation behavior of a sample and thereby trace the genesis of active species [32]. 

One must keep in mind that a 2D-crystal is always metastable and if allowed, will grow into a 3D-crystal. In other words, the greater the thickness is allowed, the lower-energy structures can be found. Thus, 2D-crystals give an example of constrained optimization, where the final results are determined by the constraint. 

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