Thermally-induced chemical-order transitions in medium–large alloy nanoparticles predicted using a coarse-grained layer model

Polak, M.; Rubinovich, Leonid

doi:10.1039/c5cp00497g

Cited by 6 publications

(7 citation statements)

References 25 publications

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“…The FCEM was validated by Monte Carlo simulations 61 as well as by a fair agreement with density-functional calculations. 62 In addition to energetics, the FCEM expression for the free energy 31 includes geometric parameters, namely, the number of different atomic sites and the number of NN pair bonds. A numerical minimization procedure via MATLAB provides the temperature-dependent equilibrium site concentrations and corresponding thermodynamic characteristics (free energy, energy, entropy, specific heat, etc.).…”

Section: Methodsmentioning

confidence: 99%

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd–Ir Nanophase Diagrams

Polak

Rubinovich

2022

ACS Nano

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Compared to alloy bulk phase diagrams, the experimental determination of phase diagrams for alloy nanoparticles (NPs), which are useful in various nanotechnological applications, involves significant technical difficulties, making theoretical modeling a feasible alternative. Yet, being quite challenging, modeling of separation nanophase diagrams is scarce in the literature. The task of predicting comprehensive nanophase diagrams for Pd−Ir face-centered cubic-based three cuboctahedra is facilitated in this study by combining the computationally efficient statistical-mechanical Free-energy Concentration Expansion Method, which includes short-range order (SRO) with coordination-dependent bond-energy variations as part of the input and with rotationally symmetric site grouping for extra efficiency. This nanosystem has been chosen mainly because of the very small atomic mismatch that simplifies the modeling, e.g., in the assessment of vibrational entropy contributions based in this work on fitting to the Pd−Ir experimental bulk critical temperature. This entropic effect, together with SRO, leads to significant destabilization of low-T Quasi-Janus (QJ) asymmetric configurations of the NP core, which transform to symmetric partially mixed nanophases. First-order and second-order intracore transitions are predicted for dilute and intermediate-range compositions, respectively. Caloric curves computed for the former case yield the NP-size dependent transition latent heat, and in the latter case critical temperatures exhibit a specific scaling behavior. The computed separation diagrams and intracore solubility diagrams reflect enhanced elemental mixing in smaller QJ nanophases. In addition to these diagrams, the revealed near-surface compositional variations are likely to be pertinent to the utilization of Pd−Ir NPs, e.g., in catalysis.

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Section: Methodsmentioning

confidence: 99%

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd–Ir Nanophase Diagrams

Polak

Rubinovich

2022

ACS Nano

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“…The stability of the various configurations was also studied with the Ising-type model. Polak and Rubinovitch , investigated the chemical order of nanoparticles using coordination-dependent bond-energy variations and the statistical-mechanical free-energy concentration expansion method adapted for handling axially symmetric structures. This model is more efficient than the Bragg–Williams approach because it takes into account local ordering effects, but even if this approach provides a semianalytical modeling, the determination of the competing driving forces that govern phase stability is nontrivial.…”

Section: Introductionmentioning

confidence: 99%

Stability Diagram of Janus and Core–Shell Configurations in Bimetallic Nanowires

2016

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Alloy nanoparticles can exhibit several different structures due to segregation and phase separation. In the case of an alloy with a tendency to phase separate, the core–shell (CS) configuration and the so-called “Janus” one are the most commonly observed configurations. For a given alloy, the relative stability of these configurations depends on the size of the particle, the temperature, and the chemical composition. Using canonical Monte Carlo simulation on a rigid lattice, we study the stability diagram of bimetallic nanowires and its evolution as a function of the length of nanowires. We consider successively alloys with a weak and strong superficial segregation tendency. The simplicity of this 1D system allows us to extract the pertinent energetic parameters that control the relative stabilities. Furthermore, we find that the critical temperature decreases when increasing the size of the system. Phase diagrams and stability diagrams are compared and discussed in terms of the behavior of an assembly in mutual equilibrium with each other or of an assembly of isolated nanoparticles.

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“…8 In view of the very limited and quite simplified theoretical treatments of finite-size effects on separation transitions in nanoalloys, a reasonably accurate and highly efficient new modelling is desirable in order to obtain a more comprehensive and realistic description of the phenomena. Thus, the present study employs the statistical-thermodynamic analytical expression derived in the canonical ensemble by the ''free energy concentration expansion method'' (FCEM), 9 which we developed before for Ising alloys. This mean-field approach can cope with the computationally demanding task that comprises finding separation transition temperatures in progressively larger alloy nanoparticles, as well as thermodynamic functions, in order to elucidate scaling behaviour including the determination of critical exponents.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, all temperature-dependent layer-by-layer average concentrations in large nanoparticles can be obtained by the FCEM together with the course-grained layer model (CGLM). 9 The presently employed (see below) approximate version of the FCEM/CGLM expression for the free-energy of A-B alloy nanoparticles reads…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, this amounts to the number of layers along the separation axis, as introduced in our recent study of chemical order in platinum-iridium TO nanoparticles. It used FCEM adapted for handling axially symmetric structures, 9,14 predicting distinct transitions from intra-particle Pt/Ir sideseparated Janus-like configurations to a solid-solution-like nanophase at increasingly higher critical temperatures for larger TO nanoparticles, still well below the bulk value, T bulk C . In order to come closer to this limit (and so to have access to possible finite-size scaling effects) the present structural and energetic model can handle efficiently even larger NPs consisting of up to B70 000 atoms.…”

Section: Introductionmentioning

confidence: 99%

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Nano-size scaling of alloy intra-particle vs. inter-particle separation transitions: prediction of distinctly interface-affected critical behaviour

Polak

Rubinovich

2016

Phys. Chem. Chem. Phys.

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Phase-separation second-order transitions in binary alloy particles consisting of ∼1000 up to ∼70 000 atoms (∼1-10 nm) are modeled focusing on the unexplored issue of finite-size scaling in such systems, particularly on evaluation of correlation-length critical exponents. Our statistical-thermodynamic approach is based on mean-field analytical expression for the Ising model free energy that facilitates highly efficient computations furnishing comprehensive data for fcc rectangular nanoparticles (NPs). These are summed up in intra- and inter-particle scaling plots as well as in nanophase separation diagrams. Temperature-induced variations in the interface thickness in Janus-type intra-particle configurations and NP size-dependent shifts in the critical temperature of their transition to solid-solution reflect power-law behavior with the same critical exponent, ν = 0.83. It is attributed to dominant interfacial effects that are absent in inter-particle transitions. Variations in ν with nano-size, as revealed by a refined analysis, are linearly extrapolated in order to bridge the gap to larger particles within and well beyond the nanoscale, ultimately yielding ν = 1.0. Besides these findings, the study indicates the key role of the surface-area to volume ratio as an effective linear size, revealing a universal, particle-shape independent, nanoscaling of the critical-temperature shifts.

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Thermally-induced chemical-order transitions in medium–large alloy nanoparticles predicted using a coarse-grained layer model

Cited by 6 publications

References 25 publications

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd–Ir Nanophase Diagrams

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd–Ir Nanophase Diagrams

Stability Diagram of Janus and Core–Shell Configurations in Bimetallic Nanowires

Nano-size scaling of alloy intra-particle vs. inter-particle separation transitions: prediction of distinctly interface-affected critical behaviour

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