Vacancy migration energy

The contribution of A1 to the saddle point energy, ej, is deduced from the experimental value of the vacancy migration energy in pure Al, Ey = 0.61 eV [30], and the attempt frequency from the experimental Al self-diffusion coefficient, Dai- = Da exp —Q/ksT), the self-diffusion activation energy Q being the sum of the vacancy formation and migration energies in pure Al and Do = 1.73 x 10 m. s [33]. 

In alloys presenting an order-disorder transition (case of CuZn see Kuper et at., 1956), the Arrhenius plot of nD versus 1/r shows a change of slope at the transition and a curvature in the LRO state. This has been tentatively explained by (i) an increase of the vacancy migration energy with the LRO parameter S (Girifalco, 1964), (ii) a decrease of the correlation factor in the LRO state (Bakker, 1984), or (iii) different competing mechanisms (Stolwijk et al., 1980). 

In a few cases, vacancy migration energies have been determined by isothermal variations of a physical property measured during the thermal recovery of a quenched or electron-irradiated sample ... 

Theoretical values for vacancy formation in the silicon and carbon sublattices are AITbsi = 4.93 eV and AlVvc = 2.92 eV, respectively energies of antisite defect formation are AlTsic = 3.2 eV and AlVcsi = 2.9 eV. The experimental value of the carbon vacancy migration energy is 1.2 eV for temperatures 1080-1300 K. 

Let us now consider the crystal MO. If the diffusion takes place by migration of cationic vacancies, the number of atoms that undergo the process depends on the vacancy concentration [Vm] and the thermal state of single atoms M (the jump takes place only whenever atom M in the neighborhood of the vacancy has sufficient energy to perform it). The diffusion coefficient associated with the vacancy migration process is given by... 

Vacancy formation and migration energies, such as Hy and Hy, have been... 

Self-Diffusion by the Interstitialcy Mechanism. If their formation energy is not too large, the equilibrium population of self-interstitials may be large enough to contribute to the self-diffusivity. In this case, the self-diffusivity is similar to that for self-diffusion via the vacancy mechanism (Eq. 8.19) with the vacancy formation and migration energies replaced by corresponding self-interstitial quantities. The... 

The extrinsic case applies at low temperatures or large doping levels. The site fraction of cation vacancies is equal to the solute-atom site-fraction and is therefore temperature independent. In the extrinsic regime, no thermal defect formation is necessary for cation self-diffusion and the activation energy consists only of the activation energy for cation vacancy migration. 

In the absence of an electric field the charged vacancy migrates randomly, and its mobility depends on temperature since this determines the ease with which the Na+ surmounts the energy barrier to movement. Because the crystal is highly ionic in character the barrier is electrostatic in origin, and the ion in its normal lattice position is in an electrostatic potential energy well (Fig. 2.17). 

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