Crystal lattice, activation barrier

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

In a subsequent study, NoorBatcha et al. varied the valence-force parameters used for the lattice interactions to evaluate the effect of the vibrational properties of the crystal on diffusion characteristics. Using three sets of lattice potential parameters, they determined a range of effective activation barriers for diffusion of 3.63 kcal/mole to 7.47 kcal/mole on the Si(001) surface. This range encompasses the experimental estimate of 4.6 kcal/mole for the Si(lll) surface, and further suggests this value as the more accurate experimental estimate. 

It is well known that the surface orientation of crystals and imperfections in the surface, like grain boundaries or dislocations, affect largely the reaction rates at electrodes made of metals or semiconductors. Such effects are most pronounced in those reactions where atoms leave their position in a crystal lattice or have to be incorporated into such one. These processes are connected with activation barriers which are particularly high for semiconductors where the chemical bonds between the components of the crystal lattice are highly directed and localized. If we consider photoelectrochemical reactions at semiconductors we have additionally to discuss the influence of these factors on light absorption and its consequences. 

Gerasimov et al. have reported that poly-p-PDA Et is obtained quantitatively at 170 - 4.2 K and that the activation energy is 1600 300 eal/mol at 170 - 100 K and close to zero (<20 cal/mol) at 90 — 4.2 K, respectively. From the outstanding reactivity of p-PDA Et at an extremely low temperature, the barrier to the reaction in the monomer crystals has been attributed to the force of the crystal lattice and classified into the region of negative values of the potential energy. In addition the observed induction period at 4.2 K has been attributed to the growth period of crystal defects (see Sect. IV.a.) In the case of DSP, quantitative conversion of monomer to polymer crystals has been achieved by photoirradiation at — 60°C26). 

Desolvation. As discussed in Section 3.2, solute molecules or ions can be solvated, which means that one or more solvent molecules are associated with the solute. This is especially true for ions or ionized groups in aqueous solutions the solvation (in this case hydration) then is due to ion-dipole interactions, which are fairly strong, particularly for positive groups (cations). Before an ion can be incorporated into a crystal lattice, desolvation has to occur. This implies a temporary increase in free energy, causing an activation barrier for crystallization. This will slow down the crystallization rate. 

An X-ray crystallographic study (50) revealed a D3 conformation for trans, trans,trans-, 5,9-cyclododecatriene (25) in the crystal lattice. A dynamic NMR study was carried out, and gave the free energy of activation as 8.6 kcal/mol for the interconversion between the enantiomeric D3 conformers, while a force-field calculation (51) gave 9.5 kcal/mol for this energy barrier. 

Because solid-state diffusion is a hopping process that requires the moving atoms to overcome an activation barrier as they squeeze through the crystal between lattice sites, the hopping rate (and hence the diffusivity) is exponentially temperature dependent ... 

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