Prediction of intercluster separation and Schottky-type heat-capacity contribution in surface-segregated binary and ternary alloy nanocluster systems

Site-specific average atomic concentrations computed for systems of Rh-Cu, Ni-Cu and Rh-Ni-Cu icosahedral and cuboctahedral free nanoclusters of different sizes by the “free-energy concentration expansion method” are used for evaluating pertinent cluster thermodynamic functions. Compared to stable surface segregated “magic-number” structures, at intermediate overall compositions the cluster system is expected to separate into these “phases.” A Schottky-type heat-capacity anomaly is predicted and attributed to atomic exchange (e.g., desegregation) excitation processes. Its measurement can elucidate the cluster segregation energetics.

Figure 1

$F^{\mathit{mix}}$-$c$ curves computed using FCEM output concentrations for Rh-Cu 2-shell 13-atom icosahedron (ICO) (a) and 4-shell 55-atom ICO clusters (b) at different temperatures (K). Convexity between the indicated magic-number compositions (structures) signifies intercluster separation.

Figure 2

Mixing free energy of ternary Rh-Ni-Cu 55-atom ICO cluster plotted with respect to the concentration Gibbs triangle (100 K). A major convexity region lies between circles on the 2D contour plot, marking magic compositions (arrows point at the $F^{\mathit{mix}}$ global minimum computed for the “ternary magic composition”).

Figure 3

$S-$$c$ curves at different temperatures (K) computed for Rh-Cu 55-atom ICO clusters (bottom). Heat-capacity curves corresponding to the two magic compositions (top).

Figure 4

Schottky-type desegregation contribution to the cluster heat capacity: 309-atom ICO vs CO clusters having ${\mathrm{Ni}}_{147}{\mathrm{Cu}}_{162}$ “magic” composition. The lowest level in the energy scheme corresponds to a completely Cu surface-segregated cluster, and desegregation excitations of single Cu atom to the Ni core are indicated by vertical arrows. $T_0$ signifies the onset of the desegregation effect involving the lowest (111) excitation. $T_m$ and $C_m$ refer to the heat-capacity maximum.

Figure 5

The maximum heat capacity computed for 13 to 923-atom ICO and CO Rh-Cu and Ni-Cu clusters with overall magic compositions (Cu surface, Rh or Ni cores). Dashed line: the product of surface and core site fractions, representing the number of surface-core desegregation excitations. Inset: $C_m$ of Ni-Cu ICO and CO clusters plotted as a function of the fraction product.