Kinetic, mobility and environment
A crucial objective in nanoalloy research is to define experimental protocols for controlling both the distribution of the components inside individual nanoparticles and the spatial distribution of a population of nanoparticles in their medium. Nanoalloys are prepared under non-equilibrium conditions which produce metastable configurations evolving to the equilibrium state on a variety of time scales. From the very initial stage of nucleation to long-time ageing, the kinetic way from metastable structures towards a thermodynamic equilibrium may include several steps, from growth, to coalescence, ripening, oxidation. These phenomena may happen also because the environment is changing with time, for example nanoalloy may be exposed to a change of temperature, or to an oxidizing atmosphere, they may be deposited on a substrate; which induces a change of their equilibrium state. Some of the mentioned phenomena have collective character, since they imply transfer of matter between different particles.
- Growth Kinetics
State of the art
In order to produce the desired final arrangement of atoms in nanoalloys, the different steps of nanoalloys formation must be carefully controlled. Depending on the growth method, several different steps must be taken into account. In some cases, nanoalloys are grown in a homogeneous medium, a solvent (in chemical methods ) or an inert gas vapor (in physical methods), and subsequently deposited at an interface, which is very often a solid substrate . In other cases, single atoms are deposited on a substrate so that aggregation takes place and is governed by a variety of atomic process at the surface. Moreover, nanoalloys have been also recently synthetized from high-temperature reduction of an oxide coating or substrate, in the frame of a strong metal-support interaction . While the concepts developed for single elements also apply for alloys, new phenomena arise, in particular due to the different time and length scales involved in the growth. The control of temperature, flux, sequence of growth and annealing allows one to build different structures: icosahedral structure at large sizes , mixed but not necessarily ordered nanoalloys [5,6], core-shell or Janus that do not necessarily reflect an equilibrium state. It is thus possible to obtain alloyed nanoparticles of non-miscible elements or core-shell structures of miscible ones [7,8].
Perspectives for the next years
The experimental objective in this domain is to control the growth parameters and the growth sequence to obtain equilibrium or non-equilibrium atom arrangements in agreement with the desired properties. For that, it is essential to evaluate, in addition to direct growth mechanisms, the time scales to reach the equilibrium from non-equilibrium initial structures (see section 2.2). These time scales are governed by the energy barriers of the rate-limiting processes.
The nucleation/growth phenomena at the nanoscale are very dependent on the growth medium but also on the growth sequence (co-reduction vs sequential reduction in liquid phase, co-deposition vs sequential deposition on a substrate). A scientific breakthrough in this domain would be achieved by a true combination of theoretical modeling of growth kinetics (by Langevin Dynamics, Molecular Dynamics – MD and Kinetic-Monte Carlo – KMC methods ), with in situ and real time investigation methods, like X-ray scattering (SAXS, WAXS), STEM or AFM-STM techniques under-gas/in-liquid media/UHV. Some steps in this direction have been made for example in Ref. [9,10]. However there are still some difficulties. From the experimental point of view, the difficulty is in controlling the growth media in a characterization set-up (atom flux) with a data collection time compatible with the growth rate. Theoretically, the difficulty is to model the growth processes in their growing environment like in liquid phase or on complex substrates (roughness, defect, chemical heterogeneity).
Understanding the growth parameter effects on a single particle is already a challenging task if we consider only the supply of atoms from the gas or liquid phase. It becomes extremely complex when considering an ensemble of growing nanoalloys on a substrate. In this case, the supply of atoms can come from the others particles and further phenomena appear during or after growth, such as coalescence and ripening, or a simple atom mobility on the substrate. This part is developed in section 2.3.
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- Ageing : from metastable initial state to equilibrium
State of the art
Because as-prepared nanoalloys are typically out-of-equilibrium, detailed studies of their stability over long time scales, including their environment, are necessary to fully characterize their chemico-physical properties. Despite the importance of these stakes, the ageing of nanoalloys has been the subject of quite few studies [1,2]. The question of whether an equilibrium state can actually be reached in realistic conditions and time scales is usually left unanswered. In general, measuring diffusion processes at the nanoscale is a very complicated task. Hence obtaining data on the diffusion mechanisms and on their rates remains a highly complex and challenging issue. To accelerate the diffusion process experimentalists usually proceed to in situ annealing under ultra-high vacuum conditions. This procedure has been used to produce chemically ordered phases whose characterization has been performed in situ either by synchrotron Grazing Incidence Wide Angle X-ray Scattering  or by High Resolution Transmission Electron Microscopy [4, 5]. In perspective, the experimental study of the ageing kinetics of metastable nanoalloys associated to theoretical studies should provide a better understanding of the diffusion mechanisms. However, up to now computational studies have been mostly focused on the thermodynamics rather than the kinetics of chemical ordering.
Perspectives for the next years
Experimental ageing studies are possible on a reasonable time-scale. Exploration of different systems should make it possible to determine the kinetics of the transformation from an initial non-equilibrium configuration to the equilibrium one both in vacuum and in an oxidizing atmosphere. The ageing kinetics of nanoparticles of constant size and composition will be studied, looking at the evolution of the distribution of constituents with the possibility to observe blocking on long-lived metastable chemical configurations. From a theoretical point of view, first principles simulations can be used for small particles  and atomistic molecular dynamics (MD) or accelerated MD methods can be used to follow the structural evolution of nanoalloys during heating process  or at temperatures close to the melting point [8-11] in order to speed up the kinetics. To explore larger nanoparticle and to probe the dynamics on longer time scales, on-lattice methods (kinetic mean-field approach and Kinetic Monte Carlo (KMC) simulations) can be developed . To identify the relevant diffusion mechanisms, the Activation-Relaxation Technique (ART) is particularly powerful for generating events and calculating barriers . This self-learning method can be a very useful tool for the numerical study of ageing kinetics in nanoalloys. Also metadynamics will be a powerful tool to search for transition pathways and rare events in nanoalloys, as shown very recently .
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- Collective effects in assemblies of nanoalloys
State of the art
An ensemble of nanoparticles can evolve in time by different types of coarsening phenomena, such as coalescence and ripening. In spite of the relevance of these phenomena for practical applications of nanoalloys, experimental and simulation studies are at present quite few. The occurrence of coalescence and/or ripening has been demonstrated in a few experiments [1-5], whereas coalescence of nanoalloys has been the subject of some simulation studies [1,6,7].
Coalescence takes place via the collision between preformed clusters and their subsequent rearrangement into a single unit. Coalescence therefore implies the mobility of nanoparticles in their environment. It is likely to take place in the advanced stages of nanoparticle formation by any route.
In the Ostwald ripening process, small nanoparticles dissolve by evaporating atoms to the advantage of larger nanoparticles on which these atoms reattach. In this way, fewer and fewer large aggregates survive in the long-time limit. Ripening is possible when the detachment of monomers from nanoparticles and the transport of atoms between them are sufficiently fast. In nanoalloys, ripening is more complex than in elemental nanoparticles, because the different atomic species may present different detachment and diffusion rates. This can cause changes in the compositions of different nanoparticles in an evolving population, besides changing their average sizes. This has been clearly demonstrated by monitoring the evolution of a population of CoPt nanoalloys .
Perspectives for the next years
Very often growth/synthesis methods are designed to avoid coalescence because the rearrangement after collision may be slow and ineffective, so that quite irregular nanoparticle shapes may result as a final undesired product. Moreover, coalescence phenomena may introduce polydispersity in the sample, which is an undesired feature in most cases. On the other hand, coalescence can be exploited for producing size-selected multicore nanoparticles  and thermal annealing, beyond morphological changes and classical Oswald ripening that leads to coarsening, can also drastically modify the composition distribution of the NPs assembly . The surface nanostructuration can also been used to control the growth  limiting the polydispersity.
Simulation of the coalescence on long time scales and/or of large nanoalloys (containing several thousand atoms) will take advantage of the accelerated MD methods mentioned in section 2.2. On the other hand, the evolution of the large ensembles of nanoalloys involved in the ripening process requires the development of more coarse-grained approaches, which should bridge between atomistic modelling and continuum equations.
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