McNabb-Foster equation

Pyun etal. [18,82-84] have suggested that this abnormal behavior in CTs involving the inflexion point could be reasonably explained in terms of the difference in the kinetics of lithium deintercalation from two different lithium deintercalation sites having different activation energies for lithium deintercalation. The McNabb-Foster equation [101, 102] was modified to satisfy spherical symmetry and to represent the coexistence of two different types of trap site, and was also used as a governing... 

From the numerical solution to the modified McNabb-Foster equation, the anodic CTs determined at the potential jumps of 0.3, 0.2, and 0.05 V (versus Li/Li+) to various lithium extraction potentials Fext are illustrated in Figure 5.19a-c. The anodic CTs theoretically calculated based upon the modified McNabb-Foster equation, along with the cell-impedance-controlled constraint in Figure 5.19a-c, almost coincide with experimental CTs (see Figure 5.18a-c). This strongly indicates that the appearance of an inflexion point in the CT is due to the lithium deintercalation from two different kinds of sites with clearly distinguishable activation energies. 

Vc) = 0 (D diffusion coefficient, c H-atoms per unit volume ), is limited to some rare cases (e.g. to steels with saturated traps resulting from low density of defects or high H-content). In fact, a source term must be added to the right side of the equation, which was firstly developed by McNabb and Foster, (McNabb Foster, 1963), and later by Oriani assuming local equilibrium, (Oriani, 1970). Thus, the following equations hold for diffusion of hydrogen under the presence of local stress fields (c << 1), (Serebrinsky et al., 2004) ... 

A general model for hydrogen diffusion with reversible trapping was formulated by McNabb and Foster [103]. The general diffusion equation can be written as... 

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