Phase first kind

Electrodes such as Cu VCu which are reversible with respect to the ions of the metal phase, are referred to as electrodes of the first kind, whereas electrodes such as Ag/AgCl, Cl" that are based on a sparingly soluble salt in equilibrium with its saturated solution are referred to as electrodes of the second kind. All reference electrodes must have reproducible potentials that are defined by the activity of the species involved in the equilibrium and the potential must remain constant during, and subsequent to, the passage of small quantities of charge during the measurement of another potential. 

In all these cases the support has a dramatic effect on the activity and selectivity of the active phase. In classical terminology all these are Schwab effects of the second kind where an oxide affects the properties of a metal. Schwab effects of the first kind , where a metal affects the catalytic properties of a catalytic oxide, are less common although in the case of the Au/Sn02 oxidation catalysts9,10 it appears that most of the catalytic action takes place at the metal-oxide-gas three phase boundaries. 

Depending on electrolyte composition, the metal will either dissolve in the anodic reaction, that is, form solution ions [reaction (1.24)], or will form insoluble or poorly soluble salts or oxides precipitating as a new solid phase next to the electrode surface [reaction (1.28)]. Reacting metal electrodes forming soluble products are also known as electrodes of the first kind, and those forming solid products are known as electrodes of the second kind. 

The phase AE in Fig. 2.17 which extends to the value 6 = 45.7° corresponds to a first-kind ground state. In the angle Grange of 45.7 to 90°, a second-kind ground state is realized, at 8= 90° it coinciding with the ground state of free quadrupoles on a square lattice. 

This is called a point-spread function, because it describes how what should be a point focus by geometrical optics is spread out by diffraction. The expression in the curly brackets is the one that is of interest. The other terms are phase and overall amplitude terms, as are usual with Fraunhofer diffraction expressions. The function Ji is a Bessel function of the first kind of order one, whose values can be looked up in mathematical tables. 2Ji(x)/x, the function in the curly brackets, is known as jinc(x). It is the axially symmetric equivalent of the more familiar sinc(x) = sin(x)/x (Hecht 2002), the diffraction pattern of a single slit, usually plotted in its squared form to represent intensity. Just as sinc(x) has a large central maximum, and then a series of zeros, so does jinc(x). Ji(x) = 0, but by L Hospital s rule the value of Ji(x)/x is then the ratio of the gradients, and jinc(0) = 1. The next zero in Ji(x) occurs when x = 3.832, and so that gives the first zero in jinc(x). This occurs at r = (3.832/n) x (q/2a)Xo in (3.2), which is the origin of the numerical factor in (3.1). 

Patterns of the second type are obtained when clean tips are exposed to various gases or when volatile substances are sublimed onto them, and are the result of work-function changes due to chemisorption. These will be discussed in the next section. Patterns of the first kind are due to relatively nonvolatile impurities like carbon, silicon, or (under certain conditions) oxygen. These patterns show their characteristic form only after heating of the tip to fairly high temperatures, 700 to 1500 K, and can be most easily explained as the result of overgrowths or surface phases of... 

In this context, it is again advisable to distinguish between rate constants of the first and second kind. kp, as introduced in Eqn. (6.41), obviously is the rate constant k of the first kind. It describes the growth of phase p when all the other phases form simultaneously. The rate constant kf] of the second kind describes the growth of phase p from phases (p- 1) and (p+ 1) only. 

Explicit expressions for the ratio (k /k ) of a multiphase reaction product layer have been presented in the literature, see, for example, [H. Schmalzried (1981)]. If k(2) of the second kind, which depends only on the properties of phase p, is calculated or measured for every phase p individually, it is possible to derive (from all NiiP, A p, and the molar volumes Vp) the rational rate constant k p] of the first kind, and thus eventually k in Eqn. (6.41). 

Figure 12-1. Phase diagram of first kind. Phase boundaries are schematically plotted for the intensive variable 02 as a function of 0,. 0,...

This paper by Ya.B. helped lay the foundation for the study of the kinetics of phase transitions of the first kind. It considers the fluctuational formation and subsequent growth of vapor bubbles in a fluid at negative pressures. It is assumed that the fluid state is far from the boundary of metastability and that the volume of the bubbles formed is still small in comparison with the overall volume of the fluid. The first assumption ensures slowness of the process the time of transition to another phase is large compared to the relaxation times of the fluid per se. This allows the application of the Fokker-Planck equation in the space of embryo dimensions to describe the growth of the embryos. 

The course of the process at a later stage, where the second assumption is not satisfied, was studied by I. M. Lifshitz and V. V. Slezov.1 The kinetics of phase transitions of the first kind near absolute zero, where fluctuations have a quantum character, were described by I. M. Lifshitz and Yu. M. Kagan2 and by S. V. Iordanskii and A. M. Finkelshtein.3 In these works the ideas of Ya.B. s paper also play an important role. 

Reference electrodes can be classified into several types (1) electrodes of the first kind a metallic or soluble phase in equilibrium with its ion... 

Below the T0 temperature fullerite has simple cubic lattice (set), above this temperature it has face-centered cubic lattice (feel) and in the area of T0 temperature the first-kind phase transition from sc phase to fee phase occurs. The orientation ordering takes place in fullerite that was experimentally studied in papers [6-11] and at 260 K the fee lattice was formed from the simple cubic one due to this orientation ordering. The orientation ordering is defined not only by temperature, but by pressure as well [12]. 

Equation (9.32) is a linear Fredholm integral equation of the first kind. It is also known as an unfolding or deconvolution equation. One can preanalyze the data and try to solve this first-kind integral equation. Besides the complexity of this equation, there is a paucity of numerical methods for determining the unknown function / (h) [208,379] with special emphasis on methods based on the principle of maximum entropy [207,380]. The so-obtained density function may be approximated by several models, gamma, Weibull, Erlang, etc., or by phase-type distributions. 

The first kind of development (being continuous or single-phased) is an evolutionary precondition for the second one (which is two-phased or discontinuous), and this suggested that there might have been a transition from the first to the second developmental strategy in the history of life. Such a transition, incidentally, could well correspond to the Cambrian explosion, i.e. to the appearance of all known animal phyla in a geologically brief period of time. 

While actual chemical events involved in nucleation and crystal growth are not known a phenomenological treatment (gives some insight. Willard Gibbs (9J considered processes of phase separation of two extreme kinds. In the first, fluctuations in concentration occur which are minute in volume but large in extent of departure from the mean (the case of binodal phase separation). In the second the volume of the fluctuation is large but the deviation from the mean for the solution is minute (responsible for spinodal phase separation). In nucleation of zeolites one is conerned only with fluctuations of the first kind. 

The temperature dependence of A-site Jahn-Teller distortions has also been discussed by Kanamori (322). The phase transition in this case is of the first kind. Comparison of theory and experiment for CuCr204 is shown in Figure 54. 

The solid-phase synthesis of peptide aldehydes can be carried out from either protected amino aldehydes or common protected amino acids. While the first kind of method requires prior synthesis of a convenient aldehyde derivative, in the second type the final cleavage of the product is performed in the presence of a reducing reagent. 

---