Enthalpy for migration

The activation energy for self-diffusivity of the Ag cations by the interstitialcy mechanisms is the sum of one-half the Frenkel defect formation enthalpy and the activation enthalpy for migration,... 

A [1,3]- or [1,5]-H shift is formally required for the rearrangement of 162 to benzene (Scheme 6.40). Quantum-chemical calculations predict that the hydrogen atom migrates in two steps, that is, in consecutive [1,2]-H shifts, with the species 177 being the intermediate, which has to be described either as a diradical [117] or a car-bene [116, 117]. The experimental activation enthalpy for the conversion of 176 into benzene [112] was correctly simulated by the energy of the transition state separat-... 

With decreasing temperature, as we have seen, the intrinsic defect population decreases exponentially and, at low T, extrinsic disorder becomes dominant. Moreover, extrinsic disorder for oxygen-based minerals (such as silicates and oxides) is significantly alfected by the partial pressure of oxygen in the system (see section 4.4) and, in the region of intrinsic pressure, by the concentration of point impurities. In this new region, term Qj does not embody the enthalpy of defect formation, but simply the enthalpy of migration of the defect—i.e.,... 

The 1,3-silyl migrations from C to C occurred with inversion of configuration at silicon and with a rather high activation enthalpy for the 1,3-silyl migration of a-methylallyltrimethylsilane studied by Kwart and Slutsky, AH =47.7 kcalmol-1 and AS = —6.2 calmol-1 K-1297. On the other hand, 1,3-silyl migrations in ketosilanes... 

Calculate the migration enthalpy for Na ion migration and the enthalpy of Schottky defect formation from the data shown in Fig. 7.3. Discuss all assumptions. 

KNs. The d.c. electrical conduction of KN3 in aqueous-solution-grown crystals and pressed pellets was studied by Maycock and Pai Verneker [127]. The room-temperature conductivity was found to be approximately 10" (ohm cm) in the pure material. Numerical values for the enthalpies of migration and defect formation were calculated from ionic measurements to be 0.79 0.05 and 1.43 0.05 eV (76 and 138 kJ/mole), respectively. In a subsequent paper [128], the results were revised slightly and the fractional number of defects, the cation vacancy mobility, and the equilibrium constant for the association reaction were calculated. The incorporation of divalent barium ions in the lattice was found to enhance the conductivity in the low-temperature region. Assuming the effect of the divalent cation was to increase the number of cation vacancies, the authors concluded that the charge-carrying species is the cation, and the diffusion occurs by means of a vacancy mechanism. 

Sharma and Laskar [129] measured the self-diffusion of potassium in melt-grown potassium azide using a radioactive tracer sectioning technique. The diffusion coefficient in the range 85-254°C was found to be (0.19 0.03) exp [(- 0.80 0.06) eV/kT] cm sec. They concluded that the cation is the predominantly mobile species, with diffusion occurring by a vacancy mechanism. The value of 0.80 0.06 eV (77 kJ/mole) for the enthalpy of migration agrees well with the results of Maycock and Pai Verneker [127]. 

The temperature dependence of the kinetics at constant oxygen pressure is often plotted as log kp or log k-p versus 1/T. In addition to the migration enthalpy of the mobile species, the slope of such an Arrhenius plot may reflect an enthalpy for the change in composition of the oxide with temperature. 

Akimov and Kraftmakher (1970), using heat capacity measurements, determined the enthalpy of formation AH (23 kcal/mole) of thermally activated defects in /3-La. This value represents one-half of the experimentally measured activation energy for self-diffusion (Dariel et al., 1969b). Since Q = AH + AHm (with AHm the enthalpy of migration of the defects) and since it is well established that AH = AHm for vacancies as diffusion determining defects in fee metals, the heat capacity results seem to constitute further evidence for a vacancy dominated self-diffusion mechanism in the close-packed structures. 

The activation enthalpy obtained for tracer diffusion could be interpreted as the enthalpy of migration of extrinsic oxygen vacancies induced by impurities with lower valency on niobium sites. 

Alkenes.—Kinetic studies of alkene isomerization, catalysed by transition-metal complexes, are rare. One recent example is isomerization of hex-l-ene, catalysed by Co(N2)(PPh3)3, where the rate is proportional to the square of the catalyst concentration this suggests hydrogen migration in a dinuclear intermediate. The activation enthalpy for this isomerization is 10.1 kcal mol , the activation entropy being - 21 cal deg mol . Isomerization... 

An example of the determination of activation enthalpies is shown in Figs. 11 and 12. A valuable indication for associating the correct minimum with the ionic conductivity is the migration effect of the minimum with the temperature (Fig. 11) and the linear dependence in the cr(T versus 1/T plot (Fig. 12). However, the linearity may be disturbed by phase transitions, crystallization processes, chemical reactions with the electrodes, or the influence of the electronic leads. 

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