Cation diffusion energy

Figure 15.11 Dependence of the deviation of the apparent activation energy from the cation diffusion energy, as predicted by Wakai s model [81]. The three curves correspond to the three values of the surface step energy used for Figure 15.5. See Ref. [49] for further details.

In the very early stages of oxidation the oxide layer is discontinuous both kinetic and electron microscope" studies have shown that oxidation commences by the lateral extension of discrete oxide nuclei. It is only once these interlace that the direction of mass transport becomes of importance. In the majority of cases the metal then diffuses across the oxide layer in the form of cations and electrons (cationic diffusion), or as with the heavy metal oxides, oxygen may diffuse as ions with a flow of electrons in the reverse direction (anionic diffusion). The number of metals oxidising by both cationic and anionic diffusion is believed to be small, since a favourable energy of activation for one ion generally means an unfavourable value for the other... 

Both Tg and the activation energy below Tg Increase with cation size (Table VI). The activation energy values for p-Cl-PHMP compare favorably with the results of 1on conductivity measurements 1n cellulose acetate (16.18). shown 1n Figure 8. This relationship speaks strongly for cation diffusion as being Involved in the rate determining step. 

The subscripts and superscripts 1 and 2 refer to cross-slip and climb, respectively. Dislocation motion must overcome significant structural barriers or must cross-slip or climb past obstructions. At the lower temperatures, dislocation crossslip and climb both occur. At the higher temperatures, dislocation climb becomes a rate-controlling mechanism and classic values of the stress exponent (n = 4.5) are obtained. The creep-activation energy is that of cation diffusion. 

Wagner begins with the assumption that in certain cases the solubilities and mobilities of A ions in BX and of ions in AY are so low, and consequently the product layers are formed so slowly, that another reaction mechanism may predominate once nucleation has occurred. This reaction mechanism is shown in Fig. 6-11 (b). Essentially, a closed circular flow of cations occurs in the product phases such that the cations diffuse only in their own respective compounds, A quantitative approximation to the reaction rate can be made as follows. Since three phases are in simultaneous contact, it is sufficient to specify only one additional variable in addition to P and T in order to uniquely determine the problem. If the partial pressure Px2 is chosen as this variable, then it is a simple matter to calculate the activity gradient of A in AY if the free energies of formation of the individual compounds are known. This is essentially given by the standard free energy A of the reaction AX 4- BY == AY 4- BX. Then, if the diffusional resistances in AY and BX are known, it is possible to calculate the rate of the displacement reaction for this limiting case as well. 

This value for the diffusion coefficient would apply to the case of interstitial diffusion in a metal having its atoms in cubic close-packing. It should also apply to the case of cation diffusion in the NaCl structure if the diffusion is by a vacancy mechanism. However, this calculated cation diffusion coefficient would have to be reduced by the correlation factor. It would probably not be applicable to interstitialcy diffusion, because the sequence of energy barriers to be surmounted for diffusion by that mechanism would probably differ from those proposed here. 

Even under the assumption that the process is properly described by the diffusion model described above, the magnitude of E unfortunately did not provide unambiguous support for the above proposal that molecules (CuCl) rather than cations (Cu+) are the diffusing species, since the activation energies for cation diffusion were found to be of about the same magnitude [294,295]. 

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