General Trends in Core–Shell Preferences for Bimetallic Nanoparticles

Surface segregation phenomena dictate core–shell preference of bimetallic nanoparticles and thus play a crucial role in the nanoparticle synthesis and applications. Although it is generally agreed that surface segregation depends on the constituent materials’ physical properties, a comprehensive picture of the phenomena on the nanoscale is not yet complete. Here we use a combination of molecular dynamics (MD) and Monte Carlo (MC) simulations on 45 bimetallic combinations to determine the general trend on the core–shell preference and the effects of size and composition. From the extensive studies over sizes and compositions, we find that the surface segregation and degree of the core–shell tendency of the bimetallic combinations depend on the sufficiency or scarcity of the surface-preferring material. Principal component analysis (PCA) and linear discriminant analysis (LDA) on the molecular dynamics simulations results reveal that cohesive energy and Wigner–Seitz radius are the two primary factors that have an “additive” effect on the segregation level and core–shell preference in the bimetallic nanoparticles studied. When the element with the higher cohesive energy also has the larger Wigner–Seitz radius, its core preference decreases, and thus this combination forms less segregated structures than what one would expect from the cohesive energy difference alone. Highly segregated structures (highly segregated core–shell or Janus-like) are expected to form when both the relative cohesive energy difference is greater than ∼20%, and the relative Wigner–Seitz radius difference is greater than ∼4%. Practical guides for predicting core–shell preference and degree of segregation level are presented.


0.2(A): 0.8(B) composition
The simulation for Ag(0.2)-Au(0.8) 6 nm in diameter nanoparticle, which is in the low core-shell category, showed that the patchiness is decreased. That is, the Ag surface occupancy ratio improved from 38 % to 47 %. Similarly, in Au (0.2) : Pt (0.8) 6 nm in diameter nanoparticle which is categorized as Janus-like, Au surface occupancy ratio improved from 59 % to 97 %. In AuPt, the surface patchiness has disappeared completely. This confirms that the patchy surface seen in the 3 nm bimetallic nanoparticles with 0.2 (A) : 0.8 (B) composition is related to the number of atoms, not to the particular composition. Nanoparticle size effect on core-shell preference In all types of structures, the patchiness of the surface is observed. Due to a high surface-to-volume ratio for the size of the nanoparticle simulated here, there are relatively few surface-preferring atoms available for forming the surface. Thus, the core purity with the core preferred material is higher in this particle size.

(B) composition
For the larger NPs with diameters of 6 nm and 10 nm, eight bimetallic combinations were simulated due to computational cost. Pt-Au and Ni-Ag (Janus-like), Co-Au and Pd-Ag (high CS), Pd-Au, Cu-Au, and Co-Pd (low CS), and Fe-Au (mixed) were chosen as representatives for each structure group (SI Figure  4). Due to the relatively lower surface-to-volume ratio for the larger particles, the surface occupancy ratios by the surface-preferring materials in these bigger particles are improved compared to the small particles (1 nm) (SI figure 5). Figure S5. Surface occupancy ratio of the surface-preferring material in bimetallic nanoparticles as a function of the particle size. The surface occupancy ratios by the surface-preferring materials in these bigger particles are increased compared to the small particles (1 nm).

Principal component analysis (PCA)
After running the PCA algorithm on our data, we found that the cumulative variance of the eightcomponent analysis revealed that the first two principal components and the first three components reflected 74 % and 93 % of the total variation, respectively. For all eight components, we get PC1: 40.8 %, PC2: 33.4 %, PC3: 18.4 %, PC4: 4.2 %, PC5: 2.7 %, PC6: 0.35 %, PC7: 0.17 %, and PC8: 0.03 %. Therefore, we consider the first three principal components in our further analysis.
In PCA, finding the optimal number of principal components (PCs) is done by selecting a set of minimum PCs having a significantly larger Eigenvalue than the rest of PCs. The scree plot shown in SI Figure 6 suggests that the first three principal components adequately explain the variability of the data. Therefore, we used the first 3 principal components whose eigenvalues are greater than approximately 1.
Relative Wigner-Seitz radius difference vs cohesive energy difference Figure S9. MD/MC results plotted in the two-dimensional space spanned only by the relative Wigner-Seitz radius difference and relative cohesive energy difference A simulation using a BCC Fe interatomic potential Surface atom identification using alpha-shape Using the alpha-shape method, the surface atoms of each system are identified. SI Figure 11 shows an example of the results. Here the CuAu system is analysed using an alpha value of 2.45 (i.e., 0.6 times the lattice constant of Au), which enable the surface atoms to be distinguished from the core atoms. Figure S11. Identified surface atoms of CuAu system. Atoms are color coded: Surface Cu atoms: white, surface Au atoms: black, Cu core atoms: orange, Au core atoms: yellow. Figure S10. The preferred structure for Fe-Cu was obtained using MD simulation with interatomic potential for BCC Fe. (a) full view(left) and cross-sectional view (right) of the bimetallic NP with strongly core-preferring Fe (red) and surfacepreferring Cu(orange). The structure is a highly segregated Janus-like. (b) The crystalline structure of the Janus-like Fe-Cu bimetallic NP.
Effects of cooling rate on the surface segregation Effects of cooling rate on the degree of core-shell tendency were investigated by performing MD simulations at different cooling rates (0.013 K/ps and 1.3 K/ps). The simulations were carried out for AgPd (high core-shell) and CoNi (mixed). The results indicate that the segregation level is consistent throughout the simulations performed at the different cooling rates. Figure S12. Effects of cooling rate on the degree of core-shell tendency for AgPd and CoNi. In AgPd, Ag is the surfacepreferring material with a surface occupancy ratio approximately 95 %. In CoNi, the surface composition is mixed as the occupancy ratio of neither of the elements is above 70 %.

Effects of final temperature
Effects of the final temperature on the degree of core-shell tendency were investigated by performing the simulations with different final temperatures: 150 K, 300 K, and 450 K for AgPd and CoNi. Note that the cooling rate was set to 0.13 K/ps for all simulations. The segregation level is found to be consistent with negligible fluctuations in the surface and core occupancy ratios.