Theoretical explanation of Ag/Cu and Cu/Ni nanoscale multilayers softening

Relationship between metallic multilayers hardness and monolayer thickness has been investigated and explained for electroplated Ag/Cu and Cu/Ni multilayers using a modified Thomas-Fermi-Dirac electron theory. Experiments reveal that the peak hardness of Ag/Cu multilayers occurs at the monolayer thickness of about 25 nm, while the peak hardness of Cu/Ni multilayers occurs at about 50 nm. Critical monolayer thickness corresponding to the peak hardness is approximated by the grain size limit of stable dislocations in Ag crystals for the Ag/Cu multilayers and in Cu crystals for Cu/Ni multilayers. Grains size limits are calculated based on a modified Thomas-Fermi-Dirac electron theory. Developed relationship between the critical monolayer thickness and the grains size limit helps understand nanoscale metallic multilayers softening.