Diffusivity through interactions with vacancies

Surface vacancies were shown to be responsible for the motion of embedded In and Pd atoms in the Cu(00 1) surface. The density of surface vacancies at room temperature is extremely low, but they diffuse through the surface at an extremely high rate leading to significant diffusion rates of Cu(00 1) terrace atoms. In the STM measurements the rapid diffusion of these vacancies leads to long jumps of embedded tracer atoms. Measurements of the jump length distribution show a shape of the distribution that is consistent with the model that we discussed in Section 3. In turn, this shows that the vacancy-mediated diffusion process can be accurately described with the model that is presented in Section 3, provided that the interaction between the tracer atom and the surface vacancy is properly taken into... 

We built an atomistic kinetic model for Al-Zr binary system using ab-initio calculations as well as experimental data. So as to be as realistic as it should be at this atomic scale, this model describes diffusion through vacancy jumps. Thanks to ab-initio calculations we could improve usual thermodynamic descriptions based on pair interactions and incorporate multisite interactions for clusters containing more than two lattice points so as to consider dependence of bonds with their local environment. 

The electrostatic interaction is apparently insufficient to bind both 0 to the cation vacancy While one 0 remains with the vacancy, though locally delocalized (22.), the other becomes unbound (22). An unbound 0 is a mobile charge carrier moving through the host matrix by a succession of electron jumps from 02 to 02". Because the 0 states are positively charged with respect to 02 they have been called "positive holes" (22). 0 states repel each other in the bulk and tend to diffuse towards the surface causing the surface to become positively charged. 

Activated diffusion The process by which a penetrant molecule moves through a membrane from one transient vacancy to another with an energy interaction between the penetrant and the membrane. 

---