Phenomenological parameters constants

To distinguish between simultaneous or only consecutive epimerizations at CHD centers, kinetic experiments based on the four isomers of 1 -methyl-2,3-d2-cyclopropane were designed141. The phenomenological rate constants associated with the various reactions leading from one isomer to another employ subscripts to designate the carbon atom at which an epimerization occurs k, indicates a one-center epimerization at C(/), and /q is used for a two-center epimerization at C(i) and C(J) (Scheme 1). In this case, with all four isomers present in equal concentrations at equilibrium, the time dependence of each is governed by four rate constants kuk2- k2, kl2 = kl2 and /c23. But, at best, only three kinetic parameters may be found experimentally kt, k2i and (k2 + kl2). 

The Curie constant C can be considered a magnetic parameter (MP) associated with the sample. Theory, however, tells us that such a phenomenological parameter could be made of fundamental physical constants and the magnetogyric-ratio parameter g in the following way ... 

The parameters measured in an ultrasonic experiment are the amplimde and phase of the signal. They are determined by attenuation and phase velocity of a wave. In turn, the attenuation and phase velocity are associated with material constants. In our case they are elastic coefficients (or elastic moduli). These constants can be calculated using quanmm-mechanical approach. Finally, we will obtain the expressions for the measured (phenomenological) parameters in terms of the microscopic ones. In the present section we will discuss the basics of the phenomenological elasticity theory and the microscopic description of the Jahn-Teller contribution to the elastic moduli will be discussed later. 

In the remainder of this subsection, the goal is to relate these phenomenological rate constants to more fundamental parameters of the growing oxide layer. Table 7.1 lists the parabolic rate constants for a number of metals oxidized in pure oxygen at 1000°C. 

Dynamic parameters such as diffusion coefficients and the phenomenological rate constant of ion transfer can also be evaluated. 

Ea. corresponds to the stabilization energy. The exchange field is much stronger than the CEF effect. However, in a more advanced approach (see e.g. Stefahski and Kowalczyk 1991) additional CEF parameters 5°, 5°, etc., are involved in a definition of the phenomenological anisotropy constants. In the strong exchange limit valid for the ThMni2-type compounds the anisotropy constants are as follows ... 

Here, gj is the Land6 g factor of the rare-earth ion, jS the Bohr magneton, and Ko the Knight shift due to band paramagnetism only (see section 1.2.1.). The parameter is a phenomenological exchange constant, which enters from the assumed Hamiltonian for the sf exchange interaction,... 

The upper script spec is written in the case of the phenomenological parameters in order to distinguish between these and the physically defined constants B, and co, ... 

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