Migration energy barrier

Fig. 1. STM images resolving (a) the hexagonal atomic structure of the close-packed fcc(lll) surface and (b) the anisotropic fcc(llO) surface of Ag. The surface unit cells and high symmetry directions are marked, (c) Schematic one-dimensional potential energy surface experienced by a simple individual adsorbate along a high-symmetry surface direction (Em migration energy barrier ICf, bonding energy a surface lattice constant).

To obtain a solid with a high conductivity, it is clearly important that a large concentration, c, of mobile ions is present in the crystal [Eq. (6.1)]. This entails that a large number of empty sites are available, so that an ion jump is always possible. In addition, a low enthalpy of migration is required, which is to say that there is a low-energy barrier between sites and ions do not have to squeeze through bottlenecks. Hence the structure should ideally have open channels and a high population of vacancy defects. 

Figure 10.10 Energy barrier for the migration of an ion in the presence of an external field.

Much of the quantitative information in this paper is derived from first-principles calculations based on density functional theory (DFT). Experimentally it is difficult to determine ion migration paths and energy barriers along migration paths in structural transformations such as from i-LiJV[n02 to 5-LiMn204. Examining the atomic-scale ionic movements that could occur in such a transformation using first-principles calculations can therefore be informative. 

Figures 3 and 4 show the energy barriers calculated for Mn and Co movements out of a TM layer octahedron and into the Li/vacancy layer of the layered a-NaFe02-type structure (recall that the TM cations have to migrate into the Li/vacancy layer for the transformation to spinel). The cation positions used in these calculations follow the Oh Oh (Figure 3) and Oh Oh (Figure 4) type paths shown in Figure 2.

In contrast, 1-phenylethylidene (74), which can undergo 1,2-hydrogen migration to form styrene (75), was found to be thermally stable in argon or xenon matrix at 10 K. The carbene decay to give styrene only when warming to 65 K in xenon matrix (Scheme 9.18). From the disappearance rate constant for 74, a energy barrier... 

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