Melting Is Well-Known, but Is It Also Well-Understood?

Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

Two-Steps Versus One-Step Solidification Pathways of Binary Metallic Nanodroplets

The solidification of AgCo, AgNi, and AgCu nanodroplets is studied by molecular dynamics simulations in the size range of 2-8 nm. All these systems tend to phase separate in the bulk solid with surface segregation of Ag. Despite these similarities, the simulations reveal clear differences in the solidification pathways. AgCo and AgNi already separate in the liquid phase, and they solidify in configurations close to equilibrium. They can show a two-step solidification process in which Co-/Ni-rich parts solidify at higher temperatures than the Ag-rich part. AgCu does not separate in the liquid and solidifies in one step, thereby remaining in a kinetically trapped state down to room temperature. The solidification mechanisms and the size dependence of the solidification temperatures are analyzed, finding qualitatively different behaviors in AgCo/AgNi compared to AgCu. These differences are rationalized by an analytical model.

Molecular dynamics investigation of structure evolution and thermodynamics of Ni-Fe nanoparticles during inert gas condensation

Synthesis of magnetic nanoparticles is relevant to many applications in the fields of catalysis, energy storage, and biomedicine. Understanding the growth mechanisms and morphology of nanoparticles during inert gas condensation is crucial to rationally improve the performance of the final nanoparticles. In this work, molecular dynamics simulations are carried out to study the structural and thermodynamic behavior of Ni-Fe nanoparticles from homogenous vapor phase in Ar atmosphere. It is revealed that the final morphology of the resulting nanoparticles presents a spherical shape by cluster coalescence at high temperatures where the small clusters are liquid droplets prior to their collisions. However, probabilistic nucleation and cluster growth indicate that the occurrence of spherical shape is more controlled by the probability limits for different Fe concentrations. Meanwhile, a larger inert gas density induces a more efficient cooling effect leading to a larger probability control of the cluster formation with non-spherical shape by agglomeration. Furthermore, the solidification of the as-formed Ni-Fe clusters is examined by evaluating the evolution of crystalline and amorphous structure. The linear scaling-down dependence of the solidification temperature on the reciprocal of the nanoparticle size clearly signifies a linear size-depression effect for the liquid-to-solid phase change of Ni-Fe nanoparticles. Our findings thus extend the current understanding of inert gas condensation behavior and mechanisms of Ni-Fe nanoparticles from an atomic/molecular perspective.

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.

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.

Thermodynamics of CuPt nanoalloys

The control of structural and chemical transitions in bimetallic nanoalloys at finite temperatures is one of the challenges for their use in advanced applications. Comparing Nested Sampling and Molecular Dynamics simulations, we investigate the phase changes of CuPt nanoalloys with the aim to elucidate the role of kinetic effects during their solidification and melting processes. We find that the quasi-thermodynamic limit for the nucleation of (CuPt)₃₀₉ is 965 ± 10 K, but its prediction is increasingly underestimated when the system is cooled faster than 10⁹ K/s. The solidified nanoparticles, classified following a novel tool based on Steinhardt parameters and the relative orientation of characteristic atomic environments, are then heated back to their liquid phase. We demonstrate the kinetic origin of the hysteresis in the caloric curve as (i) it closes for rates slower than 10⁸ K/s, with a phase change temperature of 970 K ± 25 K, in very good agreement with its quasi-thermodynamic limit; (ii) the process happens simultaneously in the inner and outer layers; (iii) an onion-shell chemical order - Cu-rich surface, Pt-rich sub-surface, and mixed core - is always preserved.