Thermodynamics of CuPt nanoalloys

Machine-learnt potential highlights melting and freezing of aluminum nanoparticles

We investigated the complete thermodynamic cycle of aluminum nanoparticles through classical molecular dynamics simulations, spanning a wide size range from 200 atoms to 11 000 atoms. The aluminum-aluminum interactions are modeled using a newly developed Bayesian Force Field (BFF) from the FLARE suite, a cutting-edge tool in our field. We discuss the database requirements to include melted nanodroplets to avoid unphysical behavior at the phase transition. Our study provides a comprehensive understanding of structural stability up to sizes as large as 3 × 105 atoms. The developed Al-BFF predicts an icosahedral stability range up to 2000 atoms, ∼2 nm, followed by a region of stability for decahedra, up to 25 000 atoms. Beyond this size, the expected structure favors face-centered cubic shapes. At a fixed heating/cooling rate of 100 K/ns, we consistently observe a hysteresis loop, where the melting temperatures are higher than those associated with solidification. The annealing of a liquid droplet further stabilizes icosahedral structures, extending their stability range to 5000 atoms. Using a hierarchical k-means clustering, we find no evidence of surface melting but observe some mild indication of surface freezing. In any event, the liquid droplet's surface shows local structural order at all sizes.

A partition function estimator

We propose an estimator that allows us to calculate the value of a simple system's partition function using finite sampling. The core idea is to neglect the contribution from high energy microstates, which are difficult to be sampled properly, and then calculate a volume correction term to compensate for this. As a proof of concept, the estimator is applied to calculate the partition function for several model systems, ranging from a simple harmonic oscillator to a Lennard-Jones fluid with hundreds of particles. Our results agree well with the numerically exact solutions or reference data, demonstrating that efficiently estimating partition functions for the studied example cases is possible and computationally affordable.

Harvesting nucleating structures in nanoparticle crystallization: The example of gold, silver, and iron

The thermodynamics and kinetics of nanoparticle crystallization, as opposed to bulk phases, may be influenced by surface and size effects. We investigate the importance of such factors in the crystallization process of gold, silver, and iron nanodroplets using numerical simulations in the form of molecular dynamics combined with path sampling. This modeling strategy is targeted at obtaining representative ensembles of structures located at the transition state of the crystallization process. A structural analysis of the transition state ensembles reveals that both the average size and location of the critical nucleation cluster are influenced by surface and nanoscale size effects. Furthermore, we also show that transition state structures in smaller nanodroplets exhibit a more ordered liquid phase, and differentiating between a well-ordered critical cluster and its surrounding disordered liquid phase becomes less evident. All in all, these findings demonstrate that crystallization mechanisms in nanoparticles go beyond the assumptions of classical nucleation theory.

Surface phase diagrams from nested sampling

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling.

Analysis of Dynamical Peculiarities in Nanoalloys at Subsystems Level: Dynamical Degrees of Freedom, Temperature Differences, and the Chameleon Effect

A novel analysis of the dynamical behavior of nanoalloy systems, as represented by model Ni/Al 13-atom clusters, over a broad range of energies that cover the stage-wise transition of the systems from their solid-like to liquid-like state is presented. Conceptually, the analysis is rooted in partitioning the systems into judiciously chosen subsystems and characterizing the latter in terms of subsystem-specific dynamical descriptors that include dynamical degrees of freedom, root-mean-square bond-length fluctuation, and element-specific subsystem temperature. The analysis reveals a host of intriguing new peculiarities in the dynamical behavior of the Ni/Al 13-mers, among which are what we call the chameleon effect and the difference in the temperatures of the Ni and Al subsystems at high energies, a difference that strongly depends on the cluster composition and also changes with energy. These do not have an analog in pure Ni13 and Al13 and are explained in terms of the coupled effects of the difference between the masses of the Ni and Al atoms (the mass effect) and of the difference in the anharmonicity of the overall interaction potential as experienced by the Ni and Al subsystems of the clusters (the potential effect).

Structural characterisation of nanoalloys for (photo)catalytic applications with the Sapphire library

A non-trivial interplay rules the relationship between the structure and the chemophysical properties of a nanoparticle. In this context, characterization experiments, molecular dynamics simulations and electronic structure calculations may allow the variables that determine a given property to be pinpointed. Conversely, a rigorous computational characterization of the geometry and chemical ordering of metallic nanoparticles and nanoalloys enables discrimination of which descriptors could be linked with their stability and performance. To this end, we introduce a modular and open-source library, Sapphire, which may classify the structural characteristics of a given nanoparticle through several structural analysis techniques and order parameters. A special focus is geared towards using geometrical descriptors to make predictions on a given nanoparticle's catalytic activity.

Stability of the high-density Jagla liquid in 2D: sensitivity to parameterisation

We computed the pressure-temperature phase diagram of the hard-core two-scale ramp potential in two-dimensions, with the parameterisation originally suggested by Jagla [E. A. Jagla, Phys. Rev. E, 63, 061501 (2001)], as well as with a series of systematically modified variants of the model to reveal the sensitivity of the stability of phases. The nested sampling method was used to explore the potential energy landscape, allowing the identification of thermodynamically relevant phases, such as low- and high-density liquids and various crystalline forms, some of which have not been reported before. We also proposed a smooth version of the potential, which is differentiable beyond the hard-core. This potential reproduces the density anomaly, but forms a dodecahedral quasi-crystal structure at high pressure. Our results allow to hypothesise on the necessary modifications of the original model in order to improve the stability of the metastable high-density liquid phase in 3D.

Nanohardness from First Principles with Active Learning on Atomic Environments

We propose a methodology for the calculation of nanohardness by atomistic simulations of nanoindentation. The methodology is enabled by machine-learning interatomic potentials fitted on the fly to quantum-mechanical calculations of local fragments of the large nanoindentation simulation. We test our methodology by calculating nanohardness, as a function of load and crystallographic orientation of the surface, of diamond, AlN, SiC, BC₂N, and Si and comparing it to the calibrated values of the macro- and microhardness. The observed agreement between the computational and experimental results from the literature provides evidence that our method has sufficient predictive power to open up the possibility of designing materials with exceptional hardness directly from first principles. It will be especially valuable at the nanoscale where the experimental measurements are difficult, while empirical models fitted to macrohardness are, as a rule, inapplicable.

Substitutional-interstitial structural transition in Cu-Pt nano-alloys

Copper-platinum alloys are important binary alloys in catalysis. In this communication, we demonstrate that it is possible to preserve the thermal properties of platinum with a copper-platinum alloy by converting the substitutional alloy into an interstitial one. This conversion occurs when the size of the copper-platinum system is reduced down to the nanoscale. The size-dependent phase diagram of Cu-Pt for a spherical nanoparticle is calculated at various sizes (50, 10 and 5 nm) demonstrating that Cu-Pt alloyed nanoparticles can be formed all over the composition range. Experimentally, the electron microscopy characterization of copper-platinum alloyed nanoparticles synthesized by wet chemistry supports the predicted structural transition.

A universal signature in the melting of metallic nanoparticles

Predicting when phase changes occur in nanoparticles is fundamental for designing the next generation of devices suitable for catalysis, biomedicine, optics, chemical sensing and electronic circuits. The estimate of the temperature at which metallic nanoparticles become liquid is, however, a challenge and a standard definition is still missing. We discover a universal feature in the distribution of the atomic-pair distances that distinguishes the melting transition of monometallic nanoparticles. We analyse the solid-liquid change of several late-transition metals nanoparticles, i.e. Ni, Cu, Pd, Ag, Au and Pt, through classical molecular dynamics. We consider various initial shapes from 146 to 976 atoms, corresponding to the 1.5-4.1 nm size range, placing the nanoparticles in either a vacuum or embedded in a homogeneous environment, simulated by an implicit force-field. Regardless of the material, its initial shape, size and environment, the second peak in the pair-distance distribution function, expected at the bulk lattice distance, disappears when the nanoparticle melts. As the pair-distance distribution is a measurable quantity, the proposed criterion holds for both numerical and experimental investigations. For a more straightforward calculus of the melting temperature, we demonstrate that the cross-entropy between a reference solid pair-distance distribution function and the one of nanoparticles at increasing temperatures present a quasi-first order transition at the phase-change temperature.

Out-of-Equilibrium Polymorph Selection in Nanoparticle Freezing

The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physicochemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via the cooling rate during nanoparticle freezing in the case of Ni₃Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow us to rationalize the complex nucleation process, discovering a switch between two kinetic pathways, yielding the equilibrium structure at room temperature and an alternative metastable one at higher temperature. Our findings address the key challenge in the synthesis of nanoalloys for technological applications, i.e., rationally exploiting the competition between kinetics and thermodynamics by designing a treatment history that forces the system into desirable metastable states.

Correlating Oxygen Reduction Reaction Activity and Structural Rearrangements in MgO-Supported Platinum Nanoparticles

We develop a multi‐scale approach towards the design of metallic nanoparticles with applications as catalysts in electrochemical reactions. The here discussed method exploits the relationship between nanoparticle architecture and electrochemical activity and is applied to study the catalytic properties of MgO(100)‐supported Pt nanosystems undergoing solid‐solid and solid‐liquid transitions. We observe that a major increment in the activity is associated to the reconstruction of the interface layers, supporting the need for a full geometrical characterisation of such structures also when in‐operando.

Structural properties of sub-nanometer metallic clusters

At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.

Intrinsic strain-induced segregation in multiply twinned Cu–Pt icosahedra

We present an atomistic simulation study on the compositional arrangements throughout Cu–Pt icosahedra, with a specific focus on the effects of inherent strain on general segregation trends.