Zener mechanism

Use the Zener mechanism to explain the magnetoresistance of the doped lanthanum manganate perovskites... 

However, the mobile or localized behaviour of the electrons changes so dramatically with only minor changes in the stoichiometry (Figure 7.11) that the Zener mechanism is thought to be too simple. It also fails to explain the magnetoresistance in compounds in which there are no Jahn-Teller distorted ions. 

A With thallium trivalent, manganese must be present as Mn". This is not a Jahn-Teller ion, since there are three d-electrons, one each for the set of d-orbitals, and so the Zener mechanism would not explain the magnetoresistance of this compound. 

For example, the ZN theory, which overcomes all the defects of the Landau-Zener-Stueckelberg theory, can be incorporated into various simulation methods in order to clarify the mechanisms of dynamics in realistic molecular systems. Since the nonadiabatic coupling is a vector and thus we can always determine the relevant one-dimensional (ID) direction of the transition in multidimensional space, the 1D ZN theory can be usefully utilized. Furthermore, the comprehension of reaction mechanisms can be deepened, since the formulas are given in simple analytical expressions. Since it is not feasible to treat realistic large systems fully quantum mechanically, it would be appropriate to incorporate the ZN theory into some kind of semiclassical methods. The promising semiclassical methods are (1) the initial value... 

Figure 3. Initial vibrational state specified cummulative reaction probabilities for v = 2. Dashed line exact quantum mechanical numerical solution. Solid hue TSH results with use of the Zhu-Nakamura formulas. Dash-dot hue TSH results with use of the Landau-Zener formula. Taken from Ref. [50].

Stresses can can be concentrated by various mechanisms. Perhaps the most simple of these is the one used by Zener (1946) to explain the grain size dependence of the yield stresses of polycrystals. This is the case of the shear crack which was studied by Inglis (1913). Consider a penny-shaped plane region in an elastic material of diameter, D, on which slip occurs freely and which has a radius of curvature, p at its edge. Then the shear stress concentration factor at its edge will be = (D/p)1/2.The shear stress needed to cause plastic shear is given by a proportionality constant, a times the elastic shear modulus,... 

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... 

In the case of semiconductors, the idea of electron tunneling has been used by Zener [42] to describe the so-called interband tunneling. Such tunneling represents one of the possible mechanisms of semiconductor breakdown. To understand the nature of interband tunneling, we shall first follow Ziman [43] and consider the one-dimensional motion of an electron in a separate band under the influence of an electric field. If we use the scheme of repeated bands, then the electron motion in momentum space is an up and down motion along the OABC periodic curve (Fig. 16). In the coordinate space, the electron, starting from point O, accelerates then slows down as it approaches point A here, the direction of the motion is changed to the... 

Fig. 10.5 Energy level diagram showing the mechanism by which an n = 20 atom is ionized by a microwave field of 700 V/cm amplitude. An atom initially excited to the 20d state is brought to the point at which the n = 20 and 21 Stark manifolds intersect. At this point the atom makes a Landau-Zener transition, as shown by the inset, to the n = 21 Stark manifold and on subsequent microwave cycles makes further upward transitions as shown by the bold arrow. The process terminates when the atom reaches a sufficiently high n state that the microwave field itself ionizes the atom. This occurs at point B in this example (from...

The contribution of the thermoelastic effect to energy dissipation in solids under transient or cyclic deformation was first studied by Zener and shown to account for mechanical relaxation peaks in some metals. 

To understand the factors that are important in controlling the rates of ET reactions, it is best to refer to a specific theoretical model [35]. Choosing a model defines terms and allows us to analyze the results of experiments in precise ways. There are two main types of models classical and quantum mechanical. One way of smoothly moving from the use of a classical to a quantum mechanical model is provided by semiclassical (Landau-Zener) ET theory [36-38]. At high temperature, quantum mechanical models become equivalent in most respects to semiclassical ones. Thus the appropriate choice of model depends on the type of ET reaction that we are interested in studying. Ones in which the electron donor and acceptor have strong electronic interaction with each other prior to the ET event are well described by a classical model. In these systems an ET reaction always proceeds to products if the reactants reach the top of the reaction barrier (strong-... 

Although, AE is not generally equal to AG° unless the frequencies of the reactant and product are the same, this assumption is almost universally made. With this assumption classical Marcus ET theory combined with a quantum mechanical (Landau-Zener) treatment of the barrier crossing also yields Eq. (4) [2,36-39]. This derivation of Eq. (4) is called semiclassical ET theory, and therefore in the rest of this paper Eq. (4) will also be referred to as the semiclassical rate expression or the semiclassical model. 

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