A. S. Nowick's Diffusion in Solids. Recent Developments PDF

By A. S. Nowick

ISBN-10: 0125226608

ISBN-13: 9780125226608

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C. LINEAR CHAIN WITH IMPURITY ADJACENT TO A VACANCY Since the complexities of solving the three-dimensional case of an impurity adjacent to a vacancy are imposing, the linear chain case is solved to find the dependence of localized mode frequencies on the defect mass and force constants. The formalism of Montroll and Potts (1955) is utilized here. Consider the simple model shown in Fig. 5 in which y, y', and y" are M L M' M M -0-- "--0--O--<> Fig. 5. Linear chain with a vacancy and an adjacent impurity.

The detailed calculations for realistic three-dimensional models are highly mathematical and are often too complex to solve in a reasonable amount of time with any degree of precision using contemporary techniques. However, calculations have been done on defect systems in which results have been obtained which are directly applicable to diffusion. These include calculations of the defect 1. CLASSICAL AND QUANTUM THEORY OF DIFFUSION 33 modes at vacancies and interstitials in three-dimensional systems.

In this argument, the harmonic force constants increase rapidly as atoms are brought closer together than their equilibrium distance and decrease, but less rapidly, as they are separated (see Fig. 4). Hence, in the 3D crystal, the force constants in a microscopic view are increased under compression and decreased under tension. As a result of this, we expect a tendency toward resonance mode behavior in regions of tension and toward localized mode behavior in regions of compression. An example which represents, qualitatively, the arguments presented here is that of the SPC of vacancy diffusion in the fee structure.

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Diffusion in Solids. Recent Developments by A. S. Nowick

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