Non-linear model of impurity diffusion in nanoporous materials upon   ultrasonic treatment
  Non-linear theory of diffusion of impurities in porous materials upon ultrasonic treatment is described. It is shown that at a defined value of deformation amplitude, an average concentration of vacancies and temperature as a result of the effect of ultrasound possibly leads to the formation of nanoclusters of vacancies and to their periodic educations in porous materials. It is shown that at a temperature smaller than some critical value, a significant growth of a diffusion coefficient is observed in porous materials. 
R.M. Peleshchak, O.V. Kuzyk, O.O. Dan'kiv
cond-mat.mes-hall