SelfDiffusion

Self-diffusion is the diffusion of atoms of a given species within a material, typically the same species as the host lattice. In a pure element or a single-component material, the diffusing species is identical to the lattice atoms, so there is no concentration gradient driving the process. Self-diffusion is often characterized by a tracer diffusion coefficient obtained from isotopic labeling, giving a measure of how quickly atoms move through the solid or liquid.

In solids, self-diffusion occurs mainly through two mechanisms. The vacancy mechanism involves atoms exchanging places with neighboring vacancies, a process that requires defects and becomes slow at low temperatures. The interstitial mechanism, common for small atoms such as hydrogen, carbon, or nitrogen in metals, involves rapid hops between interstitial sites and often dominates diffusion at lower defect concentrations. The relative importance of these mechanisms depends on temperature, crystal structure, and the diffusing species.

The temperature dependence of self-diffusion is typically described by an Arrhenius relation, D = D0 exp(-Q/kT), where D is the diffusion coefficient, Q is the activation energy, and D0 is a pre-exponential factor. For vacancy diffusion, Q is the sum of the vacancy formation energy and the migration energy; for interstitial diffusion, it is the interstitial formation and migration energy. The pre-exponential factor reflects jump frequency and jump distance.

Measurement methods include tracer diffusion experiments with radioactive or stable isotopes, secondary ion mass spectrometry, and NMR techniques in liquids. Self-diffusion data are essential for understanding and modeling processes such as homogenization, sintering, creep, and phase transformations in materials.