Minimal model of a Plateau-Rayleigh instability of a solid binary alloy nanowire: impacts of surface segregation

Minimal model and its linear stability analysis (LSA) for Plateau-Rayleigh (PR) instability of an intermixed, solid binary alloy nanowire is presented. Model accounts only for the surface diffusions of the alloy components without anisotropies of a surface energies, and for a classical thermodynamic surface segregation. Model allows to assess a deviation of a longwave instability cutoff wavelength $λ_c$ from the classical value $2πr_0$ (a wire circumference) as a function of a surface composition deviation from its equilibrium value, a wire radius, and a bulk concentration of a minority component. Results of LSA are presented for AuNi, PtNi, and CoNi nanowires, where an important distinction is that a surface segregation curve for CoNi is qualitatively different from the one for AuNi and PtNi. For each nanowire there is a sizable region of a parameter space where $λ_c<2πr_0$ and correspondingly, a fastest growing perturbation wavelength $λ_{max}$ is also less than a wire circumference. This is in stark contrast to PR instability of a single-component nanowire transporting mass by surface diffusion - in this case $λ_c$ and $λ_{max}$ are larger than a wire circumference. Strong surface segregation is primarily responsible for unusually small $λ_c$ and $λ_{max}$. Results suggest that a large number of small and closely spaced nanoparticles may emerge upon disintegration via annealing of a binary alloy nanowire.