E3 Defects: Dislocations and Vacancies

Topic

The temperature of this metal determines—in accordance with an Arrhenius-type relationship—the equilibrium concentration of vacancies within its crystal lattice: each vacancy (a lattice site that ought to be occupied by an atom but remains empty) entails a specific formation energy, and the higher the metal's temperature, the more vacancies it can sustain in thermal equilibrium despite that energy cost. Consequently, a higher metal temperature results in a higher equilibrium concentration of vacancies, as dictated by this Arrhenius relationship.

Independently of these vacancies, the metal's dislocation density—defined as the total length of dislocation lines per unit volume—stores energy within the elastic strain field surrounding each dislocation; this energy remains trapped in the lattice even after the load that introduced the dislocations is removed. A higher dislocation density leads to greater stored dislocation energy, as there is a greater total length of dislocation lines contributing their respective strain fields to that energy.

This dislocation density does not remain constant: the plastic deformation undergone by the metal progressively increases it—as described by the Kocks-Mecking model—because existing dislocations multiply and generate new ones as they move against each other. As the metal accumulates more plastic deformation, the dislocation density continues to rise according to the Kocks-Mecking model, albeit at a diminishing rate, as the dislocations themselves begin to annihilate one another. Consequently, this model—characterized by the initial concentration of vacancies and dislocation density—establishes that this combined density of point and linear defects governs two distinct aspects of the metal's behavior: on one hand, it feeds into another model within the set—one describing the metal's mechanical strength via the Hall-Petch and Taylor relationships—using this same dislocation density as an input variable; on the other hand, this vacancy concentration, in conjunction with temperature, controls the diffusion kinetics described by a separate model in the set, as these very vacancies enable neighboring atoms to jump from one lattice site to another. Furthermore, the fact that this dislocation density continues to increase with plastic deformation—following the Kocks-Mecking model previously introduced here—allows yet another model in the set to utilize that same Kocks-Mecking framework to describe the metal's strain hardening.

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