The results of comparative atomistic simulation are presented for segregation and thermally induced structural transformations (melting/crystallization) in binary Pt–Pd nanoalloys and ternary Pt–Pd–Ni nanoparticles, where Ni (20 at

The Gibbs method of surface excesses was extended to nanosized objects and exemplified by evaluations of the specific (per unit area) surface excess energies of Ih nanoclusters of fcc metals (Ag, Au, Cu, Ni, Pb, and Pt), the specific (per unit length) line energies of edges of Ih nanoclusters, and excess point energies of their vertices. In particular, for this purpose, an original interpretation of the Gibbs equimolecular surface concept has been employed. To perform all the above-mentioned evaluations, the extended Gibbs method was combined with the nearest neighbor interaction model. The results of our evaluations of the specific surface energy agree with the experimental values of the specific surface energy for corresponding solid bulk fcc metals. Then, we have found that the values of the specific excess line energy of the Ih nanocluster edges are positive and fall in order of magnitude within the range of 10(-10) to 10(-9) J/m, which agrees with the available evaluations for other types of linear boundaries. The vertex point energy was found to be on the order of 10(-20) J and positive as well. A hypothesis is put forward that the positivity of the excess energies of the edges and vertices results in their instability, i.e., in a trend for the formation of a more rounded shape of polyhedral nanoparticles, especially in the vicinity of their melting temperatures. In addition, some molecular dynamics results on Ih metal nanoclusters are discussed. For Au and Pt Ih nanoclusters, the theoretically calculated values of the specific surface energy are compared with those obtained by combining the Gibbs method with our molecular dynamics results on the size dependence of the potential term into the specific (per atom) internal energy of Ih nanoparticles.

10.26456/pcascnn/2024.16.387 Abstract: Employing results of our molecular dynamics experiments performed by using the LAMMPS program and embedded atom method, phase diagrams for binary Ag-Cu and Cu-Ni nanoalloys (binary nanoparticles containing 2000 and 5000 atoms) were constructed and analyzed. The concentration dependence of the melting temperature of nanoparticles was interpreted as the liquidus line. It was found that for the Ag-Cu nanoalloy, the phase diagram corresponds to the simple eutectic, and for the Cu-Ni nanoalloy, it corresponds to the phase diagram of an alloy with unlimited mutual solubility of components. The above results agree with the phase diagrams for the corresponding bulk alloys. It was found that the eutectic temperature decreases with decreasing nanoparticle size; and the value of the mole fraction corresponding to the eutectic point and equal to 0,4 coincides with the value corresponding to the bulk alloy. A hypothesis is put forward about the relationship between the surface segregation of one of the components of the binary alloy/nanoalloy and the eutectic type of the phase diagram. It is concluded that the surface segregation effect is a necessary condition for the eutectic behavior, but is not the sufficient condition.

После краткого обсуждения проблемы стабильности и нестабильности дисперсных систем в коллоидной химии, включая идеи и концепции, восходящие к П. А. Ребиндеру, предложена следующая классификация нестабильностей отдельных (свободных) наночастиц: 1) нестабильность по отношению к спонтанному распаду на отдельные молекулы (атомы) или нанокластеры меньшего размера; 2) нестабильность формы; 3) нестабильность интегральной структуры наночастиц; 4) нестабильность мезоскопической структуры; 5) нестабильность физико-химических характеристик наночастиц; 6) нестабильность по отношению к воздействию внешней среды, в том числе химическая нестабильность, включая нестабильность к окислению. В качестве примеров рассмотрены проблемы стабильности изомеров металлических нанокластеров и стабильности биметаллических наноструктур ядро-оболочка. Теоретические концепции, связанные со стабильностью и нестабильностью наночастиц, проиллюстрированы нашими молекулярно-динамическими результатами для изомеров нанокластеров Au и для взаимно инверсных (альтернативных) биметаллических наноструктур ядро-оболочка Co@Au и Au@Co (первый элемент (перед символом @) отвечает центральной области (ядру) частицы, а второй – ее оболочке).

After briefly discussing the problem of stability/instability of dispersed systems in colloid chemistry, including ideas and concepts dating back to P.A. Rehbinder, the following classification has been proposed for instabilities of individual (free) nanoparticles: (1) instability with respect to the spontaneous disintegration into individual molecules (atoms) or smaller nanoclusters; (2) instability of shape; (3) instability of the integral structure of nanoparticles; (4) instability of the mesoscopic structure; (5) instability of physicochemical characteristics of nanoparticles; and (6) instability with respect to an external environment, including chemical instability, e.g., instability to oxidation. The problems concerning the stability of isomers of metal nanoclusters and of bimetallic core-shell nanostructures are considered as examples. The theoretical concepts of stability and instability have been illustrated by our molecular dynamics data on isomers of Au nanoclusters and mutually inverse (alternative) bimetallic Co@Au and Au@Co core-shell nanostructures, where the first element (before symbol @) corresponds to the central region (core) of a particle, while the second one refers to its shell.

Melting of cuboctahedral nanoclusters of fcc metals (Ag, Au , Cu , Ni , Pd & icy; Pt ) containing 561 atoms and a transition to icosahedral isomers preceding their melting were simulated using the isothermal molecular dynamics. The heating process was simulated in the NVT ensemble using the well-known open LAMMPS program, the Verlet velocity algorithm and the Nos & eacute;-Hoover thermostat. The interatomic interactions in metal nanoparticles were reproduced by employing the embedded atom method. At a relatively low for MD experiments heating rate of 0,15 K/ps, the cuboctahedron -> icosahedron transition was observed in the face-centered cubic nanoparticles of all the above metals, except for Ag nanoparticles. However, an increase in the heating rate to 1,5 K/ps led to the fact that the cuboctahedron -> icosahedron transition began to be observed in Ag nanoclusters as well. Unlike nanoparticles of other metals, the cuboctahedron -> icosahedron transition in Pt nanoclusters occurs at a very low temperature, close to the initial temperature preceding the heating of the particles and equal to 10 K. In contrast, in Ni particles the cuboctahedron -> icosahedron transition was observed at a temperature close to the melting point.

A complex approach based on thermodynamic and atomistic simulations is used to predict segregation in binary metal nanoparticles of Cu–Ni and Ag–Au. The results of thermodynamic simulation within the model of limited source of segregating component agree with those of the atomistic simulation, and both predict the surface segregation of Cu atoms in the Cu–Ni nanoalloys and the segregation of Ag atoms at the surface of the binary Ag–Au nanoparticles.

Taking into account results of our molecular dynamics experiments, we have concluded that of the three commonly considered alternative models of nanoparticle melting (homogeneous melting, liquid shell, nucleation of liquid and growth), the latter is the most adequate. At the same time, a more adequate model corresponds to a combination of continuous melting at the initial stage of the process with its subsequent abrupt completion. In other words, nucleation and growth of a liquid-like surface layer occur until a certain critical radius of the crystalline core of the particle is reached, and then melting is completed very quickly, almost abruptly (in fractions of a nanosecond) at a temperature interpreted as the nanoparticle melting temperature Tm. Then, the role of surface melting in nanoparticle sintering is discussed. According to our results, the sintering of metal nanoparticles at high temperatures cannot be reduced to a single mechanism: a certain role play surface melting, surface and bulk diffusion, deformation in the contact zone, and collective effects associated with the displacements of groups (clusters) of atoms rather than of individual atoms. We also have put forward and substantiated the hypothesis that the previously introduced redetermined Tamman temperature T-T=0,5T(m) corresponds to the switching of the scenario of sintering of metal nanoparticles from formation of a dumbbell-shaped nanocrystal at low temperatures to the scenario corresponding to coalescence of solid nanoparticles resulting in the formation of a defective nanocrystal of a shape close to spherical.

Being the first part of a two-part series, published in this issue of the journal, this paper combines a brief overview of theoretical and experimental studies, as well as the results of atomistic simulations of surface melting in bulk bodies and nanoparticles with presentation of our own molecular dynamics results. We have studied the patterns and mechanisms of surface melting in metal nanoparticles (gold, silver, copper, lead and nickel). The patterns and mechanisms of this phenomenon were studied in most detail on gold and silver nanoparticles. It has been established that the effect of surface premelting is characteristic for nanoparticles of all the above metals, although with decreasing particle size this effect manifests itself to a lesser extent. In addition, our molecular dynamics results do not confirm theoretical predictions of some authors about the existence of a quite definite characteristic (critical) radius of nanoparticles, below which the effect of surface melting is completely absent.

After analyzing the problem of extending the Gibbs surface excess method to nanoscale objects, two different approaches to the application of the Gibbs method for finding the specific surface energy of metal nanoparticles are being considered. The first approach involves the use of the local coordination approximation to estimate the specific surface energy of icosahedral FCC metal nanoparticles (magic nanoclusters). For the first time, we have drawn attention to the fact that for such a nanocluster, it is possible to accurately calculate both the fraction of surface atoms and the values of the first coordination number in the inner region of the nanoparticle and on its surface (faces, edges, and vertices). The second approach implemented by us earlier for spherical Au nanoparticles and here for FCC Pt nanoparticles, involves the complex application of the Gibbs method adapted for nanoparticles and the results of molecular dynamics simulation. Estimates using both approaches agree with the experimental values of the surface energy corresponding to the flat surface of the bulk phases of the corresponding metals. In the final section of the work, the limits of applicability of thermodynamics to nanosystems are discussed.

Employing the isothermal molecular dynamics and the embedded atom method, we simulated melting of metallic nanoparticles (Au, Ag, Cu, Ni, and Pb ones). In more detail, the results for Au and Ag nanoparticles are presented and discussed. At first, we analyzed the behavior of the temperature dependences for the potential (cohesive) term into the specific (per atom) internal energy and for the degree of crystallinity in the course of heating nanoparticles. We have found that the results obtained for nanoparticles of about 4 and 8 nm in size (containing 2093 and 20,113 atoms, respectively) demonstrate the continuous melting. Employing the dependence of the specific potential energy on the distance to the nanoparticle center of mass and the common neighbor analysis, we showed that the continuous melting occurs via the surface pre-melting mechanism. Then, we evaluated the self-diffusion coefficient in the surface disordered layers of Au and Ag nanoparticles and found that our results agree in order of magnitude (10 −9 m 2 /s) with the values of the self-diffusion coefficient for the bulk Au and Ag melts at the corresponding bulk melting temperatures. Finally, combining in our molecular dynamics experiments continuous heating Au nanoparticles with annealing them at some constant selected temperatures, we have shown that the liquid nucleation and growth mechanism should be most adequate to the melting behavior of metallic nanoparticles.

Employing classical isothermal molecular dynamics, we simulated coalescence of mesoscopic Au nanodroplets, containing from several thousands to several hundred thousands of atoms, and sintering of mesoscopic solid Au nanoparticles. For our atomistic simulations, we used the embedded atom method. The employed open access program large-scale atomic/molecular massively parallel simulator makes it possible to realize parallel graphical processing unit calculations. We have made a conclusion that the regularities and mechanisms of the nanodroplet coalescence (temperature is higher than the nanoparticle melting temperature) and of the solid nanoparticle sintering differ from each other. We have also concluded that the nanodroplet coalescence may be interpreted as a hydrodynamic phenomenon at the nanoscale whereas sintering of solid nanoparticles is a much more complex phenomenon related to different mechanisms, including collective rearrangements of atoms, the surface diffusion, and other types of diffusion. At the same time, collective rearrangements of atoms relate not only to the solid nanoparticle sintering but also to the nanodroplet coalescence. In general, our molecular dynamics results on sintering of Au nanoparticles consisting of 10 000-30 000 atoms agree with the Ferrando-Minnai kinetic trapping concept that was earlier confirmed in molecular dynamics experiments on Au nanoclusters consisting of about 100 atoms.

We have accurately recalculated the embedding functions for Pt and Pd in the frames of the basic embedded atom method (EAM) scheme primarily developed by Daw and Baskes. The main motivation behind such a problem is that some later EAM parameterizations inadequately predict for Pd a higher melting temperature than for Pt. So, other results obtained by employing these parameterizations are also called into question. Our numerically calculated EAM functions for Pt and Pd were verified theoretically and in molecular dynamics simulations of bulk Pt and Pd phases as well as of Pt, Pd, and binary Pt–Pd nanoparticles. In particular, bulk densities in the solid and liquid states, temperatures and heats of melting, and bulk moduli of Pt and Pd were evaluated. Besides, the elastic constants $$C_{11} , C_{12}$$ , and $$C_{44}$$ were theoretically recalculated. All the verification results at least satisfactorily agree with the available experimental data. One of the advantages of our embedding functions is that they are suitable for atomistic simulations of Pt- and Pd-based alloys as well. In particular, our embedding functions quite adequately predict segregation of Pd atoms to the surface of binary Pt–Pd nanoparticles.

Coalescence of metal nanodroplets and sintering of solid Au, Pd, and Pt nanoparticles were simulated using isothermal molecular dynamics and the embedded-atom method. It was found that the scheme describing sintering of solid nanoparticles transfers to the coalescence scheme not at the nanoparticle melting point Tm, but at a lower characteristic temperature T0 ≈ 0.9 Tm, which can be interpreted as a critical temperature corresponding to the bifurcation phenomenon. The bifurcation in question indicates that at the same fixed temperature in the range from (T0 − 2 K) to (T0 + 2 K) daughter nanoparticles containing the same number of atoms can be either liquid-like (coalescence) or crystalline (sintering).

According to an earlier hypothesis on the relationship between the spontaneous surface segregation of a component of binary nanoparticles A–B and the stability/instability of nanostructures of the core-shell type (A@B and B@A, where the first component corresponds to the core of a particle and the second to its shell), the stability should be the same as that of the nanostructure whose shell corresponds to the component of binary nanoparticles spontaneously segregating to the surface. This hypothesis is tested, and possible deviations from this pattern are identified through the atomistic modeling of Co@Au, Au@Co, Ni@Cu, and Cu@Ni nanostructures.