Constant-phase-element concept

The concept of fractals was introduced for electrochemical impedance by Le Mehaute and coworkers [319, 320] and later developed by Nyikos and Pajkossy [317, 321-328]. They showed that the fractal geometry of a blocking interface leads to constant phase element behavior, Eq. (8.6). 

The position of Ti and Zr is again important in this context. While the b.c.c. phase in these elements has long been known to indicate mechanical instability at 0 K, detailed calculations for Ti (Petty 1991) and Zr (Ho and Harmon 1990) show tiiat it is stabilised at high temperatures by additional entropy contributions arising from low values of the elastic constants (soft modes) in specific crystal directions. This concept had already been raised in a qualitative way by Zener (1967), but the... 

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