Repetitorium der Logik

On the Application of the Kramers‐Kronig Relations to Evaluate the Consistency of Electrochemical Impedance Data

“…The "inconsistency factor" f accounts for the direction of change of E; the value of E decreases with time when f < 0, and increases when f> 0. N represents the number of cycles used to make measurement at a given frequency It is well known that amorphous metal-metalloid alloys with a certain amount of chromium have extremely high corrosion resistance in neutral and acidic solutions (1)(2)(3)(4)(5)(6)(7)(8). Such a high corrosion resistance of amorphous alloys has been thought to be due to their chemical homogeneity and high passivating ability of amorphous alloys (3): amorphous alloys are free of defects such as grain boundaries and dislocations, and of compositional fractuation formed by solid-state diffusion, Such a chemical homogeneity assists the formation of a uniform passive film on amorphous alloys.…”

“…The addition of molybdenum to amorphous iron-chromium-metalloid alloys further improves the corrosion resistance (4)(5)(6)(7)(8). When sufficient amounts of chromium and molybdenum are added, the amorphous iron-metalloid alloys passivate spontaneously even in hot concentrated hydrochloric acid (5)(6)(7)(8).…”

“…The addition of molybdenum to amorphous iron-chromium-metalloid alloys further improves the corrosion resistance (4)(5)(6)(7)(8). When sufficient amounts of chromium and molybdenum are added, the amorphous iron-metalloid alloys passivate spontaneously even in hot concentrated hydrochloric acid (5)(6)(7)(8). It is also well known that the addition of molybdenum to stainless steels increases the corrosion resistance, especially resistance to occluded cell corrosion (9)(10)(11).…”

“…It has been suggested that the Kramers-Kronig (KK) relations can be employed to evaluate and analyze complex impedance data of electrochemical systems (1)(2)(3). These equations, developed for the field of optics, constrain the real and imaginary components of complex physical quantities for systems that satisfy the conditions of causality, linearity, stability, and finite impedance values at the frequency limits of zero and infinity (4)(5)(6). Bode (7) extended the concept to electrical impedance, and has tabulated various forms of these equations.…”

Measurement Models for Electrochemical Impedance Spectroscopy: I . Demonstration of Applicability

“…Zr(to) = Zr(| + -~ x 2 w2 dx [2] provide a relationship between the real and imaginary components of impedance [Zr(~) and Zi(to), respectively] that hold under the assumptions of stability, causality, and linearity (3)(4)(5)(6). Lack of consistency with the Kramers-Kronig relations in electrochemical systems can often be attributed to failure of the stability criterion.…”