Diffusion migration enthalpy

An Arrhenius plot of the cation self-diffusivity will then possess two linear regions. In the high-temperature intrinsic regime, the slope will be — Hg/3 + Hm)/k in the low-temperature extrinsic regime, the slope will be simply Hm/k, where Hm is the migration enthalpy of a cation vacancy. 

When moving in a crystal, an atom has to surmount an energy barrier, which is called the migration enthalpy AHm. The mobility of a diffusing species is, therefore, thermally activated and diffusion is described by the... 

For diffusion by a vacancy mechanism, the temperature dependence of dilfusivity will depend on both the migration enthalpy A// and the energy required to form the vacancies if the latter are thermally activated i.e., the concentration of intrinsic defects is much greater than the concentration of extrinsic defects. If, however, A is fixed by doping, it becomes a constant independent of temperature. The activation energy for diffusion in the latter case will only depend on A/f, . 

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,... 

The current majority opinion is that both types of point defects are important. Thermal equilibrium concentrations of point defects at the melting point are orders of magnitude lower in Si than in metals. Therefore, a direct determination of their nature by Simmons-Balluffi-type experiments (26) has not been possible. The accuracy of calculated enthalpies of formation and migration is within 1 eV, and the calculations do not help in distinguishing between the dominance of vacancies or interstitials in diffusion. The interpretation of low-temperature experiments on the migration of irradiation-induced point defects is complicated by the occurrence of radiation-induced migration of self-interstitials (27, 28). 

Values of measured for reversible reactions under conditions permitting absorption equilibration between gas and solid products are often comparable with the reaction enthalpy [1,47]. Under such conditions the identification of the rate expression, g(nr) = kt, on the single criterion that this equation gives the most acceptable correlation coefficient is not a sufficient foimdation to characterize a geometric reaction model. The use of additional information, for example microscopy, can provide confirmatory evidence concerning interface development. Similarly, the value of studies which conclude that kinetic results are satisfactorily described by equations based on diffusion models is increased considerably if the identity of the migrating species is established [53]. 

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]. 

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. 

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