Phase second kind

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

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. 

The second kind of interaction takes place between solids and as a pure solid phase interaction, does not release any C02. 

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. 

Electrodes of the second kind. These electrodes consist of three phases. The metal is covered by a layer of its sparingly soluble salt, usually with the character of a solid electrolyte, and is immersed in a solution containing the anions of this salt. The solution contains a soluble salt of this anion. Because of the two interfaces, equilibrium is established between the metal atoms and the anions in solution through two partial equilibria between the metal and its cation in the sparingly soluble salt and between the anion in the solid phase of the sparingly soluble salt and the anion in solution (see Eqs (3.1.24), (3.1.26) and (3.1.64)). 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

Anodic oxidation often involves the formation of films on the surface, i.e. of a solid phase formed of salts or complexes of the metals with solution components. They often appear in the potential region where the electrode, covered with the oxidation product, can function as an electrode of the second kind. Under these conditions the films are thermodynamically stable. On the other hand, films are sometimes formed which in view of their solubility product and the pH of the solution should not be stable. These films are stabilized by their structure or by the influence of surface forces at the interface. 

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. 

Ternary derivatives of the Th6Mn23 type are the (second kind derivative) Mg6Cui6Si7-type phases (also described as G phases). 

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 7-6. a) Schematic A-B-O phase diagram of the second kind (/i0//VB) and possible oxidation reaction paths involving (A, B) alloy and oxide compounds, b) Corresponding reaction paths (NB( )) in real space at time t. 

Figure 9-3. TWo schematic phase diagrams of the second kind (logp0 vs. yB = ArB/(NA + zVB) for an A-B-0 system. Reaction paths for internal oxidation are indicated.

Figure 9-5. Schematic phase diagram of second kind (logp0i vs. yB = NB/(NA+NB) for an A-B-O system. Reaction path for internal reduction is indicated.

Figure 9-14. a) Possible reaction path during interdiffusion m the quasi-binary AO-BO system, plotted into a phase diagram of the second kind. The initial couple is (A,B)0 and (A,B)0". b) Real-space presentation of the processes occurring at different times during interdiffusion. 

Let us consider the high temperature reduction of oxide solid solutions as discussed in Chapter 9. The overall reaction reads (A, B) O + H2 = A + BO + H20. We conclude from Figure 11-10 a that the receding phase boundary is always morphologically unstable, in accordance with Figure ll-5b (see also [D.P. Whittle (1983)]). There is yet a second kind of instability involved in the oxygen activity change at the... 

This typical application of the second kind is the Gibbs Phase Rule (for inert systems). This rule is often stated merely for systems with only two external coordinates (n = 2, e.g., xt = P,x2 = T). There must then be no internal partitions within the system, nor may it, for instance, contain magnetic substances in the presence of external magnetic fields. 

Views of the second kind had been adopted by Larmor and Debye,7 who conceived the quantum of action h as an elementary domain of finite extension in the space of phases intervening in the computation of the probability W(E) for the energy density to have the value E. 

Properties of the Ideal Reference Electrode. An ideal reference electrode should show the following properties (1) it should be reversible and obey the Nemst equation with respect to some species in the electrolyte (2) its potential should be stable with time (3) its potential should return to its initial value after small currents are passed through the electrode (no hysteresis) (4) if it is an electrode of the second kind (e.g., Ag/AgCl), the solid phase must not be appreciably soluble in the electrolyte and (5) it should show low hysteresis with temperature cycling. 

Electrodes of the second kind These consist of three phases. A metal is covered by a layer of its sparingly soluble salt, and immersed in a solution containing the anion of this salt. The Ag/AgCl/Ch and Hg/Hg2Cl2/Cl electrodes referred to above are of this type. 

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