Anderson/Stuart model

The first term corresponds to its energy in the stable lattice position, and the second term, to the energy in the saddle point position. Ze and are the charges on the cation and the oxygen ion respectively, r and are the corresponding radii of the ions and X is the distance between the two equivalent sites. is obtained using an equation from continuum mechanics. 

G is the shear elastic modulus, is the doorway radius in the normal state. AS assumed that the covalency of bonding between the carrier atom and oxygen reduces the magnitude of the coulomb energy and introduced a correction term, y. The final AS expression for activation barrier is given 

Most importantly this model considers the equivalent site to which the Li ion jumps as a vacancy. It has also brought out clearly the importance of polarization terms in determining the energetics of ion migration in glasses. Similar conclusions were arrived at by Elliott (1994) 

---

Figure 6.01. A pictorial view of the Anderson-Stuart model. (After Martin and Angell, 1986).

M. Strpmme Mattsson, G. A. Niklasson, and C. G. Granqvist [1997] Diffusion of Li, Na and K in Fluorinated Ti Dioxide Films Applicability of the Anderson-Stuart Model, J. Appl. Phys. 81, 2167-2172. 

One of the advantages of the DCR model is that it provides an expression for s which rationalizes its temperature variation. However, the DCR model is based on the same assumptions as those made in Anderson-Stuart (1954) and Charles (1961) models to describe non-local and local... 

A number of variations for E have been offered since the original Anderson and Stuart model was first proposed. While these models... 

Electrolyte models. Assuming dissociation of the donor salt in the glass matrix, there is either a complete dissociation (strong electrolyte, Anderson-Stuart modeF°) or incomplete dissociation (weak electrolyte, Ravaine-Souqueti model) and the cations usually move in the matrix. 

A recent example of a chemical study showing how strain effects could be important in an enzymatic reaction, dealt with the hydrolysis of benzaldehyde di-t-butyl acetal [18] (Anderson and Fife, 1971b). As shown by a Stuart-Briegleb model, substantial ground-state strain is present which would be partially relieved in the... 

The problems of parametric estimation and model identification are among the most frequently encountered in experimental sciences and, thus, in chemical kinetics. Considerations about the statistical analysis of experimental results may be found in books on chemical kinetics and chemical reaction engineering [1—31], numerical methods [129—131, 133, 138], and pure and applied statistics [32, 33, 90, 91, 195—202]. The books by Kendall and Stuart [197] constitute a comprehensive treatise. A series of papers by Anderson [203] is of interest as an introductory survey to statistical methods in chemical engineering. Himmelblau et al. [204] have reviewed the methods for estimating the coefficients of ordinary differential equations which are linear in the... 

---