Atomistic mechanism of interfacial reaction and asymmetric growth kinetics in an immiscibleCu−Rusystem at equilibrium

Abstract

An $n$-body potential is first constructed for the immiscible $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Ru}$ system at equilibrium with the aid of ab initio calculations for obtaining some physical properties necessary to fit the $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Ru}$ cross-potential. Molecular dynamics simulations are then performed to pursue atomistic modeling of interfacial reaction between the $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Ru}$ metal layers. Using the solid solution model, simulations reveal that the Cu-based and the Ru-based solid solutions collapse at their respective critical solid solubilities, i.e., $10\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ of Ru and $20\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ of Cu, thus determining an intrinsic glass-forming range of the system to be within 10--$80\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ Ru, which matches well with the observations in ion-beam mixing experiments. Using the $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Ru}$ sandwich model, simulations clarify that the interfacial free energy is the major driving force for interfacial reaction, resulting in spontaneous solid-state amorphization and that when the interfacial free energy is completely consumed, the reaction terminates, thus determining a maximum amorphous interlayer to be $2.91\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, which is in good agreement with that predicted from a recently proposed thermodynamic and kinetic model. Kinetically, simulations further reveal that the growth of the amorphous interlayer features an asymmetric behavior, i.e., the growth advances faster toward the Cu lattice than toward the Ru side, because the critical solid solubility of Ru in Cu $(10\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%)$ is smaller than that of Cu in Ru $(20\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%)$.