Zener element

A three-parameter model, the Zener element or standard linear solid (SLS), has been used to represent viscoelastic behavior in certain solids. Two equivalent forms of the SLS are ... 

Another model consisting of elements in series and parallel is that attributed to Zener. It is known as the Standard Linear Solid and is illustrated in Fig. 2.41. The governing equation may be derived as follows. 

The probability P in equations (61) and (62) may be related to the electronic coupling matrix element through equation (63) by application of the Landau-Zener model ... 

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... 

The earliest derivation of was made by Zener (1955) who postulated that the effect of an alloying element was proportional to its effect on Tc. With the assumption that 6Tc/6x is a constant, it is then possible to write ... 

These monolayers provide a significant opportunity to compare the extent of electronic communication across the p3p bridge when bound to a metal electrode as opposed to being coupled to a molecular species, e.g. within a dimeric metal complex. Electronic interaction of the redox orbitals and the metallic states causes splitting between the product and reactant hypersurfaces, which is quantified by HabL the matrix coupling element. The Landau-Zener treatment [15] of a non-adiabatic reaction yields the following equation ... 

The recently available spectroscopic data and the RKR potentials of the alkali hydrides allow us to determine the "experimental" values of the parameters relevant to the transition probability of the charge transfer processes. In the Landau-Zener model these parameters are the energy gap between the and X S adiabatic potentials at the avoided crossing distance and the coupling matrix elements. In this paper the coupling matrix elements are evaluated in a two-state ionic-covalent interaction model. The systema-tic trends found in the alkali hydride series for their X e potentials are presented. This leads to a simple model for the ionic potentials. 

In the avoided crossing region the experimental RKR potential of the state and the "essentially experimental" potential of the state are used to determine the crossing distance R(- and the coupling matrix element T -. in the two state approximation. These quantities are relevant to the evaluation of the total charge transfer cross section at high energy (e.g. in the Landau-Zener model). 

What is commonly called the three-element standard, or simply the standard solid (or Zener s solid), is a combination of either a Kelvin-Voigt element in series with a spring or, alternatively, a Maxwell element in parallel with a spring (see Fig. 10.6). The strain response of the first model to the stress input CT = cjoH(t) can be written as... 

From now on we will assume that we are dealing with a set of two crossing diabatic states for all R and an interaction matrix element Hl2(R) = <(/>, Hel 02), at least at R = Rc. In the next section we will discuss the well-known Landau-Zener-StUeckelberg (henceforth abbreviated as LZS-) model in order to solve the coupled equations (4). 

Slater4 has constructed a similar table, based, however, on Zener s variation-method calculations for the first ten elements (Sec. 316). His screening constants are meant to be used in... 

The nuclear frequency is related to the solvent and inner-shell reorganization energies as well as the corresponsing vibration frequencies. The electronic factor can be described on the basis of the Landau-Zener framework and is related to the electronic coupling matrix element... 

Another model, attributed to Zener, consists of three elements connected in series and parallel, as illustrated in Figure 3.15, and known as the standard linear solid. Following the procedure already given, we derive the governing equation of this model ... 

The Zener diode appears to be the simplest element able to fulfill this task. 

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