Lattice defects diffusion constants

It has been shown that the accurate measurement of the diffusion constant ), combined with such measurements as electrical conductivity and quantity of non-stoichiometry as functions of temperature and oxygen pressure, afford us significant knowledge on lattice defects. 

Defect diffusion traditionally is treated as a process in continuum medium. However, discreteness of the crystalline lattice becomes important in particular situations, e.g., when defect recombination occurs in several hops (nearest neighbour recombination) [3, 4] or even for nearest-site hops of defects if their recombination is controlled by the tunnelling whose probability greatly changes on a scale of lattice constant [45, 46],... 

Finally, for the kinetics of lamella thickening it is essential to know the lattice resistance to the motion of dispiration loops. This has been estimated by Reneker and Mazur (1983) to be describable by a diffusion constant 1 x 10 cm /s at 343 K. They consider that dispiration loops are likely to have a thermal equilibrium concentration of roughly one defect per molecule stem in a lamella, or a linear concentration of roughly 10 m ... 

Later on [87, 88] it was observed by STM that ion bombardment of the Pt25Ni7s(l 11) surface leads to the formation of a pattern of shallow ditches (some 0.2-0.5 A deep) that have been attributed to the dislocations generated by the lattice mismatch of the top layers and the bulk ones. The top layers are enriched in Pt by ion bombardment and hence have a different lattice constant. These dislocations in sputtered alloys may provide diffusion pipes for implanted atoms to reach the surface. Diffusion of metal atoms in the surface region at relatively low temperatures has however been proven to be related to the presence of defects, such as the pinholes observed by STM at the Co/Cu( 100) interface [89]... 

Here gp is the Gibbs free energy to form a vacancy, k is the Boltzmann constant, and T is the temperature. Diffusion in a crystal lattice occurs by motion of atoms via jumps between these defects. For example, vacancy diffusion - the most common mechanism in close-packed lattices such as face-centered cubic fee) metals, occurs by the atom jumping into a neighboring vacancy. The diffusion coefficient, D, therefore will depend upon the probability that an atom is adjacent to a vacancy, and the probability that it has sufficient energy to make the jump over the energy barrier into the vacancy. The first of these probabilities is directly proportional to c,. and the... 

KNs. The d.c. electrical conduction of KN3 in aqueous-solution-grown crystals and pressed pellets was studied by Maycock and Pai Verneker [127]. The room-temperature conductivity was found to be approximately 10" (ohm cm) in the pure material. Numerical values for the enthalpies of migration and defect formation were calculated from ionic measurements to be 0.79 0.05 and 1.43 0.05 eV (76 and 138 kJ/mole), respectively. In a subsequent paper [128], the results were revised slightly and the fractional number of defects, the cation vacancy mobility, and the equilibrium constant for the association reaction were calculated. The incorporation of divalent barium ions in the lattice was found to enhance the conductivity in the low-temperature region. Assuming the effect of the divalent cation was to increase the number of cation vacancies, the authors concluded that the charge-carrying species is the cation, and the diffusion occurs by means of a vacancy mechanism. 

Above Tg, chain defects like kinks can diffuse from the amorphous parts into the crystallites, so that we have an equilibrium defect concentration at each temperature. Below Tg, this defect concentration is a constant. This leads to the two different slopes below and above Tg in Fig. 18. Below Tg, the influence of defects is weaker, which results in a lower slope of the curve. The frequency shift is correlated to the thermal expansion of the corresponding lattice parameter, here the a axis. This is discussed in more detail in Ref. 22. 

Except for perovskite-type oxides with small lattice constants, that is, short oxygen separations, reorientation of protonic defects (rotational diffusion) is generally fast, and proton transfer is the rate limiting process. According to the above described interactions, the activation enthalpy of the latter exhibits contributions from the compression of the OH/O separation and elongation of the B/O and O/H bond. Not only symmetry reduction of the average structure, but also local symmetry perturbations, for example, by acceptor dopants, may significantly reduce the mobility of protonic defects [212]. 

Polycrystalline oxide was prepared by sintering, and was used for O diffusion experiments that involved gas-phase analysis. Lattice-constant measurements confirmed the stoichiometric nature of the sample. Although Si was present in the specimens as an impurity, it was considered that point defects were not created by the Si, because both Si and Ce had the same valence. The O diffusivity could be described by ... 

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