Equilibrium segregation patterns and alloying in Cu/Ni nanoparticles: Experiments versus modeling

We analyze the segregation behavior of bimetallic nanoparticles (NPs) with moderate miscibility gap by applying a combined experimental/simulation approach to Cu/Ni as a model system. Using a hybrid molecular dynamics/Metropolis Monte Carlo algorithm (MD/MMC) based on the embedded atom method (EAM), we derive the equilibrium distribution of atomic species in the clusters for varying concentrations and particle structures. To cross-check the predictive power of our approach, we compare these results with modified EAM (MEAM) and density functional theory based ab initio calculations. This permits to identify possible shortcomings of the EAM when used to describe bimetallic NPs. Additionally, we isolate vibrational entropy contributions to the free energy of the NPs and special focus is put on the possibility of entropic stabilization of segregated versus solid solution NPs. Finally, we complement our simulations by experimental results, which are obtained by studying the behavior of plasma gas condensation synthesized Ni@Cu core-shell (CS) particles upon annealing.

Figure 1

Representative segregation patterns in bimetallic Cu/Ni NPs obtained at $100\mathrm{K}$, thus below the order/disorder transition temperature for varying concentrations (left to right) and structures (top to bottom): (a) spherical fcc crystallite with $\mathrm{N}=532$, (b) decahedron with $\mathrm{N}=484$, and (c) icosahedron with $\mathrm{N}=561$. Cu atoms are depicted in blue, Ni atoms in red.

Figure 2

Excess specific heat calculated for Cu and Ni using the EAM (a) [16] potential. Blue dots denote available literature data [31].

Figure 3

Internal energies and entropies calculated within the present study: (a) relative energy per atom of a cluster with Cu/Ni composition 55/45 and thermal fluctuations as well as free energy (inset). (b) Relative entropy change using concentration weighted elemental cluster entropy values as a reference, and (c) exemplary bimetallic clusters employed in this study (CS: core-shell, ON: onionlike, JA; januslike, RA: random distribution).

Figure 4

Normalized relative relaxation $\mathrm{\Delta }d$ perpendicular to the surface of the slab as a function of the atomic layer for all simulation approaches employed in the present study: (110), (100), and (111) surfaces from left to right and for bulk (a), (b), (c) vs subsurface (d), (e), (f) placement of a single layer of Ni atoms into the Cu slab.

Figure 5

STEM micrographs (left) and EDX maps (right) of annealed CS-NPs, with increasing time and temperature from top to bottom: (a) $3\mathrm{h}\mathrm{at}300{}^{\circ }\mathrm{C}$, (b) $12\mathrm{days}\mathrm{at}300{}^{\circ }\mathrm{C}$, and (c) $3\mathrm{h}\mathrm{at}400{}^{\circ }\mathrm{C}$. The same color coding as in the simulation section has been used: Cu in blue, Ni in red, Fe impurities are shown in green (inset).

Figure 6

High resolution TEM picture of a Ni nanoparticle prior to coating. The pronounced polycrystallinity of the NP structure becomes apparent. Diffraction rings correspond to the (111) and (200) reflexes of a polycrystalline fcc Ni sample.

Figure 7

High-resolution TEM micrograph of a Ni@Cu NP after annealing for 12 days at $300{}^{\circ }\mathrm{C}$. The particle still exhibits a nanocrystalline structure. The theoretical (111) and (200) maxima for a polycrystalline fcc structure of lattice constant $a=3.57\AA$ have been indicated by rings in the FFT. Since the expected fcc lattice constants of Cu ($a=3.62\AA$) and Ni ($a=3.52\AA$) are very close, there is pronounced overlap in the experimental core-shell image. Additional contributions to the FFT stem from the amorphous and semicrystalline oxide surface.

Figure 8

Atomic level pressures with increasing particle size highlighting increased stress release in JA-like particles in comparison to CS structures with growing NP radius.

Figure 9

NP equilibrium configurations after approximately $1.5\times {10}^5$ MMC/MD steps as a function of the twist boundary angle and concentration at $100\mathrm{K}$. Twist boundary planes divide the particles in two halves with equal number of atoms—the cutting plane in the above pictures is perpendicular to the twist boundary plane, which is marked with a dashed line.