Compositional structures and thermodynamic properties of Pd-Cu, Rh-Pd, and Rh-Pd-Cu nanoclusters computed by a combined free-energy concentration expansion method and tight-binding approach

Abstract

The statistical-mechanical free-energy concentration expansion method in conjunction with tight-binding elemental bonding energetics are used in atomistic modeling of alloy cluster compositional structures. The study focuses on three systems of 923-atom cuboctahedron clusters, Pd-Cu, Rh-Pd, and Rh-Pd-Cu, each capable of inter-cluster atomic exchange. At low temperatures, cluster core ordering and surface mixed-type ordering are predicted for Pd-Cu compositional "magic-number" clusters, whereas the system of Rh-Pd clusters tends to separate into clusters exhibiting demixed order. In the former case, slight deviations from magicnumber compositions strongly affect segregation levels. At high temperatures, Pd-Cu clusters exhibit surface segregation that affects order-disorder transitions, and at even higher temperatures a surface desegregation process, all of which are reflected in characteristic Schottky-type configurational heat capacity versus T curves. Comparing Pd-Cu with Rh-Pd-Cu reveals distinct ternary alloying effects. The role of surface induced bond energy variations in segregation related order-disorder transitions is demonstrated.

Comparative modelling of chemical ordering in palladium-iridium nanoalloys

“…Details of the expression for the free energy of a bimetallic NP can be found elsewhere. 19,20 For T = 0 K, energetic contributions (no entropic or short-range order terms) are given by…”

“…The free energy concentration expansion method (FCEM) is a statistical mechanical approximation for the prediction of chemical ordering in NAs of up to 1000 atoms, 19,20 and beyond (Rubinovich and Polak, to be published). However, FCEM is limited to the prediction of the lowest energy homotop for a given crystalline structure only.…”

Homogeneous nucleation with magic numbers: Aluminum

“…22 ͒ However, the experiments are always at finite temperature and sometimes at a high temperature, and one needs to consider thermal energy and entropy as well as the energy of the lowestenergy structure. [23][24][25][26][27][28][29][30] Thus the magic numbers determined from the energy of the lowest-energy structure need not agree with the magic numbers determined from free energies or from kinetically controlled experiments. 18 In the present work we use the term "magic numbers" always to refer to local minima of the profile of free energy versus cluster size.…”

Prediction of distinct surface segregation effects due to coordination-dependent bond-energy variations in alloy nanoclusters

“…In particular, the free-energy concentration expansion method ͑FCEM͒, which takes into account short-range order ͑SRO͒ ͑Ref. 3͒ in a system of equilibrated atom-exchanging clusters, has proven to be highly efficient in computation of site-specific concentrations ͑obtainable by F minimization͒ vs overall composition, temperature and cluster size, 4 as compared to Monte Carlo simulations, for example.…”