Atomistic mechanism of interfacial reaction and asymmetric growth kinetics in an immiscible $\mathrm{Cu}\text{−}\mathrm{Ru}$ system at equilibrium

An $n$-body potential is first constructed for the immiscible $\mathrm{Cu}\text{−}\mathrm{Ru}$ system at equilibrium with the aid of ab initio calculations for obtaining some physical properties necessary to fit the $\mathrm{Cu}\text{−}\mathrm{Ru}$ cross-potential. Molecular dynamics simulations are then performed to pursue atomistic modeling of interfacial reaction between the $\mathrm{Cu}\text{−}\mathrm{Ru}$ 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., $10\mathrm{at}.\%$ of Ru and $20\mathrm{at}.\%$ of Cu, thus determining an intrinsic glass-forming range of the system to be within 10–$80\mathrm{at}.\%$ Ru, which matches well with the observations in ion-beam mixing experiments. Using the $\mathrm{Cu}\text{−}\mathrm{Ru}$ 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 $2.91\mathrm{nm}$, 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 $(10\mathrm{at}.\%)$ is smaller than that of Cu in Ru $(20\mathrm{at}.\%)$.

Figure 1

The calculated Gibbs free energy diagram of the $\mathrm{Cu}\text{−}\mathrm{Ru}$ system based on Miedema’s theory and Alonso’s method at the temperature of $T=300\mathrm{K}$.

Figure 2

Correlations of the total energies against the atomic volume of the ${\mathrm{Cu}}_3\mathrm{Ru}$ (a) and ${\mathrm{CuRu}}_3$ (b) alloys of some simple structures obtained by ab initio calculations.

Figure 3

The projections of atomic positions for the (a) ${\mathrm{Cu}}_5{\mathrm{Ru}}_{95}$, (b) ${\mathrm{Cu}}_{20}{\mathrm{Ru}}_{80}$, and (c) ${\mathrm{Cu}}_{50}{\mathrm{Ru}}_{50}$ hcp solid solutions after annealing at $300\mathrm{K}$ for $120000$ MD time steps, respectively. Open circles: Cu. Filled triangles: Ru.

Figure 4

The calculated density profiles ${\rho }_{\alpha }\left(z\right)$ of Cu and Ru atoms along the $z$ direction in (a) ${\mathrm{Cu}}_5{\mathrm{Ru}}_{95}$, (b) ${\mathrm{Cu}}_{20}{\mathrm{Ru}}_{80}$, and (c) ${\mathrm{Cu}}_{50}{\mathrm{Ru}}_{50}$ hcp solid solutions after annealing at $300\mathrm{K}$ for $120000$ MD time steps, respectively. ${\rho }_{\mathrm{Ru}}\left(z\right)$ is represented by the solid line and ${\rho }_{\mathrm{Cu}}\left(z\right)$ by the dotted line. The ordinate is in arbitrary units.

Figure 5

Total pair-correlation functions $g\left(r\right)$ of (a) ${\mathrm{Cu}}_5{\mathrm{Ru}}_{95}$ and (b) ${\mathrm{Cu}}_{20}{\mathrm{Ru}}_{80}$ hcp solid solutions after annealing at $300\mathrm{K}$ for $120000$ MD time steps, respectively.

Figure 6

The schemes of the $\mathrm{Cu}\text{−}\mathrm{Ru}$ multilayers. (a) Configuration of the initial state with preset disordered interlayer between Cu and Ru. (b) The state after solid-state amorphization. The open circle symbols represent Cu and filled triangles represent Ru.

Figure 7

The density profiles ${\rho }_{\alpha }\left(Z\right)$ of Cu (solid line) and Ru (dash line) along the $z$ direction at the initial state (a) and the annealing states at $300\mathrm{K}$ for (b) $25\mathrm{ns}$, respectively.

Figure 8

Selected area diffraction (SAD) patterns for the ${\mathrm{Cu}}_{25}{\mathrm{Ru}}_{75}$ multilayered films of the as-deposited state (a) and amorphous state (b) after irradiation to a dose of $1\times {10}^{15}{\mathrm{Xe}}^{+}∕{\mathrm{cm}}^2$.