Fusion Features of Monocomponent Parts in Janus-Like Nanoscale Clusters Under Impacts of Low− and Ultra−Low−Energy Ar13 and Ar Projectiles

doi:10.21203/rs.3.rs-3321263/v1

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Fusion Features of Monocomponent Parts in Janus-Like Nanoscale Clusters Under Impacts of Low− and Ultra−Low−Energy Ar13 and Ar Projectiles

https://doi.org/10.21203/rs.3.rs-3321263/v1

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Molecular dynamics simulation of metastable Janus-like Ni-Al, Cu-Bi and Cu-Au clusters with 195 atoms of each component is performed for 200 ps after impacts of Ar₁₃ and Ar ions with different cases of initial energies from 25 to 300 eV. The boiling state of the components is achieved either at a high negative heat of mixing (Al, Ni-Al) or at a low boiling point of at least one of the components (Bi, Cu-Bi), provided that the Ar₁₃ projectiles have the initial energy from 200 eV. In other cases, the Ni-Al cluster is also in a molten state, while the Cu-Bi cluster, as well as the Cu-Au cluster in all impact cases, may be in a molten state or have an atomic structure of varying degrees of regularity of one/both component(s). The molten clusters form spatial core-shell distributions of the components, while in other cases different degrees and forms of their overlapping and eccentricity are possible during the time of simulation.

Studies of mass transfer processes, changes of morphology and atomic structure in multi-component nanoscale clusters along with their creation and stability taking into account various external conditions holds significance for industry, specific phenomenological calculation schemes and for a detailed clarification of the relevant elementary atomic-discrete relocation mechanisms [1–14]. As for external influences, incident energy atomic particles, interacting with targets of nanostructures, cause various processes of modification in their constituent clusters [15]. The study of collisional effects in spatially limited volumes of nanoclusters and the prediction of the selective changes in them caused by energetic bombarding particles has been a permanent trend of research since the beginning of this century [16–21].

In this regard, Janus-like binary clusters [22–33], namely nanoparticles consisting of two spatially separated types of atoms having an interface, as a variety of multicomponent clusters, demonstrate essential features of mass transfer regularities and structural changes under external bombardment by energetic multi- and mono-atomic projectiles [34]. The strong influence of the multi-atomic nature of the bombarding particle on the intensity of nonlinear collisional processes in a nanocluster at relatively low impact energies of several hundred electron-volts was previously shown using the molecular dynamics (MD) simulation of mono-component surface clusters Cu_n (n = 13–195 atoms) under bombardment by Cu₂ dimers [35]. These results showed that the energetic multi-atomic projectiles, taking into account various factors, can become the basis of the precision techniques for controlled modifications of numerous types of mono- and multicomponent cluster targets. In general, the efficiency of energy transfer to the atoms of the cluster targets from impact projectiles as well as cluster component mutual mixing, cohesive energies, surface binding energies, melting and boiling points of the semi-cluster mono-component parts demonstrate their noticeable influences on the parameters of fusion processes of the components in the Janus-like clusters, namely on the cluster temperature, characteristic times, spatial distributions of components, final morphology, etc. [36].

In our early study [34] the MD simulation was carried out for the free 390 - atom binary clusters at the initial energies above 100 eV of Ar₁₃ and Ar bombarding particles. In many cases, under such conditions, the target clusters very quickly lost their crystal structure and initial shape due to atomic collisions and subsequently induced high temperatures exceeding the melting points, although such temperatures of the final clusters, as noted above, were not only the result of high bombardment energies. In high-energy impact cases, mainly during bombardment with Ar₁₃ projectiles the preferential sputtering of the target binary clusters with the thermal yield contribution is the critically counterproductive effect. The yields of atoms were so intense due to the spatial limitations of atomic collisions with the energy transfer in the free nanoscale clusters that the original concept of the binary clusters ceased to be relevant. For this reason, interest in the ion bombardment regimes with impact energies below 300 eV, in some sense the defining point of very intense sputtering of those Janus-like clusters, consisting of 390 atoms of both components, was indicated in the conclusion of that article.

Despite several determining factors affecting the generation of a high temperature of clusters, in this work using MD model we tried to decrease their temperature by applying ultra-low-energy projectiles, reducing the bombardment energy almost to the sputtering energy threshold, although the upper energy limit of 300 eV was chosen for the comparison. The purpose of this work is to simulate such "easy" regimes of cluster transformation under the action of multi- and mono-atomic bombarding particles, in which the sputtering yields are minimal or there is no sputtering effect at all as well as to highlight the features of their influence on clusters. At such conditions in some cases the regularity of the atomic structures of the clusters or at least one of their components is preserved without any noticeable distortions even until the end of the simulation. Ultimately, we strive to formulate some special rules for choosing of ion bombardment regimes that will make it possible to obtain technologically relevant morphologies of nanoscale multicomponent clusters, namely “core-shell” or “ball-and-cup” types of spatial atomic distributions [8, 10, 12] with minimal loss of atoms and controlled destruction of atomic orders of components using the examples of initial Janus-like binary clusters.

The classic MD model, which was applied for simulation of the Janus-like binary Cu-Au, Ni-Al, and Cu-Bi clusters under impacts of the Ar₁₃ and Ar projectiles, was presented earlier in [34,37,38]. The original metastable Janus-like clusters have two mono-component parts, each consisting of 195 atoms, with a small spatial overlap. Their initial temperatures have been minimized and are very close to zero. The model details of the initial cluster preparation also were presented in [39]. In the present simulation, we used the same set of interatomic potentials as in [34,37–40], with the parameters of many-body Ackland potentials [41–43] for pure Al, Ni, Cu, Au, Bi elements, as well as for their corresponding pairs. The potential maintains the heats of mixing, which correlate with the known experimental values, namely, the selected Ni-Al, Cu-Bi and Cu-Au pairs of bulk metal samples have the heats of mixing equal to -22 kJ/mol, 15 kJ/mol and -9 kJ/mol, respectively, at 50 –50% concentrations of atomic components [44]. Thus, simulated heats of mixing are large negative for Ni-Al, positive for Cu-Bi and slightly negative for Cu-Au element pairs. Also, these potentials showed good results for stable temperature crystals with a flat free surface under ion bombardment and at calculation of the bulk cohesive energies [45,46]. Here the impact energies were 25, 50, 100, 200 and 300 eV. The evolution of the clusters during 200 ps was simulated using authors’ MD code, which is based on the C++ realization of OpenMP and MPI programming technologies of parallel computations with distributed and shared memory. The 200 impacts of the bombarding projectiles, initially randomly directed every time to the center of mass of the initial Janus-like cluster, were performed in every simulated case for accumulation of atomic trajectory statistics.

Detailed information about the destruction of the regular atomic structure of clusters under the influence of external energy multi- and mono-atomic projectiles, as well as under the influence of temperature, was obtained by calculating the AEI (Atomic Equivalence Indexes) parameter with some model time steps and at different temperatures [47,48]:

Table 1. MD simulated melting and boiling points of the free 195-atom clusters as well as the table points and MD simulated cohesive energies of the corresponding bulk materials

where i,j – indexes of atoms, r_i(j)(t) – radius-vector of i(j)-th atom. The evolution of the AEI parameter over time in each case was formed based on a single impact test.

The average component radii (hereinafter just the component radii) and the intercenter distances, earlier introduced in [34], were applied here for analysis of the cluster evolution. Here the component radius is the mean distance from all unsputtered atoms of one type to the center of mass of the corresponding mono-component part of the cluster. The distance between centers of mass of the mono – component parts is the intercenter distance. The boiling and melting points of the mono-component parts of the Janus-like clusters were simulated using model experiments [40] with external changing of the cluster temperature in the frameworks of the Berendsen approach [49].

3.1 Melting and boiling points of the cluster mono-component parts

The melting points of free 195-atom Cu, Au, Ni, Al, Bi clusters are estimated from calculations of the presented in Fig. 1 AEI parameter as a function of temperature. AEI calculations at different temperatures show that the outer regions of clusters lose their regular atomic structure at lower temperatures, and these temperatures may differ for different groups/layers of atoms by 100-300 degrees depending on the cluster. The melting points of the inner regions of clusters are usually higher, that is also seen in Fig. 1. This agrees with the values of binding energies of the surface and bulk atoms and the results [48,50]. The boiling points of the components were also simulated according to [48,51]. The inner melting points (hereinafter, simply melting points, unless otherwise noted) of Ni, Al, Cu, Au, Bi free clusters with correspondent table bulk melting points, which are expected considerably higher [48,52], MD simulated and table boiling points as well as MD simulated bulk cohesive energies are presented in Table 1. Thus, the calculated melting temperatures of the mono-component clusters of a certain size, indicated in the Table 1, are only approximate upper temperature limits for the destruction of the crystal structures of mono-component clusters, which obviously lose their order to a large extent at lower temperatures, especially under the condition of ion bombardment, which initiates the formation of radiation damages in clusters.

3.2 The collision stage of the cluster evolution

One of the conditions of this simulation is the minimization of the sputtering effect caused by ion-induced collisions of cluster atoms by using low impact energy with its decreasing to the ultra-low sputtering near-threshold values. Otherwise, under impact conditions of intense yield of atoms from the cluster, a masking effect takes place for the surface concentrations of components and the cluster ceases to exist in the original sense [40]. In general, the ion-induced collisions of atoms in the limited spaces of the clusters occur in the time intervals of up to 5 ps as the initial stages of cluster evolutions. Sharp temperature spikes of different intensity are seen in the cases of impacts by Ar₁₃ and Ar projectiles with energies of 100-300 eV in Fig. 2 (a - f) in the time intervals of about 1 ps just after the impact. The temperature spikes are noticeably more intense and longer at the Ar₁₃ impacts that well correlate with differences of initial stages of evolution of the cluster potential energy at Ar₁₃ and Ar impacts (see Fig. 3 (a - f)). The main reason is that Ar₁₃ projectiles demonstrate a higher efficiency of energy transfer to cluster atoms compared to Ar ones [53]. The temperature spikes are practically absent at the impacts of Ar₁₃ and Ar projectiles with sputtering near-threshold energies of 25-50 eV due to the transfer of relatively small portions of energy to atomic systems of the Janus-like clusters. Few damped oscillations on the background of slow increase of the component radii during 1-5 ps after Ar impacts look less impressive against the background of a very fast significant increase with some number of damped oscillations of the component radii after Ar₁₃ impacts (see Fig. 4 - 6). Accordingly, the intercenter distances in Fig. 7 (a - f) also demonstrate a rather noticeable excess at the Ar₁₃impacts as compared to the case of the Ar impacts within the time interval up to several picoseconds. All these details confirm the dominant role of the mechanisms of atomic collisions in increasing the component radii and the geometric features of the cluster morphology in the specified initial time interval.

3.3 Cluster states and thermal processes

3.3.1 Boiling/melting state of the clusters

The results of the simulation show that the temperatures reach values close to the calculated boiling points of the Al and Bi components (see Section 3.1, Table 1 and Fig. 2) in the original Janus-like cluster forms only in the Ni-Al and Cu-Bi clusters after impacts of Ar₁₃ projectiles with energies of 300 eV and to some extent 200 eV. These are the only cases in the present work, when the Al and Bi components demonstrate very intense preferential sputtering as a result, including the activation of the long-term thermal yields [54]. The main reasons for the achievement of cluster temperatures of the component boiling points in the initial forms of the Ni-Al and Cu-Bi clusters are different. In the Ni-Al cluster, very high temperature is generated mainly by the large negative heat of mixing, while the positive heat of mixing contributes to lowering the temperature of the forced mixed Cu-Bi cluster. In both cases, the temperature increase is supported by the effective energy transfer at the Janus-like cluster-Ar₁₃ collisional interactions, reduction of the cluster free surface in the process of the fusion of semi-cluster mono-component parts as well as the preferential penetration of the component atoms with smaller surface binding energies (see Table 1, cohesive energies) and larger effective size of atoms to the near-surface range. Only a relatively low boiling point of the Bi component in the initial Cu-Bi Janus-like cluster (see Table 1) makes it possible to achieve the required boiling conditions.

Based on the evolutions of the temperature in Fig. 2 (a), potential energy in Fig. 3 (a), component radii in Fig. 4 (a, b), intercenter distance in Fig. 7 (a), it can be seen that the strongly modified Ni-Al cluster reaches the quasi-stable state in less than 40-50 ps. Manifestations of the long-term yield of Al atoms from the clusters at the Ar₁₃ impacts with energy of 300 eV are also seen in Fig. 2(a), where after 40–50 ps from the beginning of the process, a slight monotonic decrease of the temperature takes place to the end of the simulation. Under such conditions, the potential energy of the Ni-Al cluster demonstrates the opposite trend, namely slight monotonic long-term increase at large times (see Fig. 3 (a)). Simultaneously approximate visible local invariance of the component radii is presented in Fig. 4 (a, b). Analogical slight long-term opposite monotonic trends in the potential energy and temperature of the Ni-Al clusters were visually more obvious for higher impact energies in [40]. In all pointed cases these very slow monotonic changes indicate the loss of the most energetic atoms by the Ni-Al cluster atomic system at high temperature yields.

In the Cu-Bi cluster under 300 eV Ar₁₃ impacts, the same parameters (see above) in Figs. 2 (c), 3 (c), 5 (a, b), 7 (c) demonstrate an onset of the quasi-stable state after 70-150 ps of the evolution. This happens much later than in the Ni-Al cluster. Even though the sputtering yield of the Bi atoms in the Cu-Bi cluster is about four times lower compared to the sputtering yield of the Al atoms in the Ni-Al cluster at 300 eV of impact energy [34,38], similar effects with the temperature and potential energy are seen here. In the Cu-Bi cluster, a small monotonic decrease of the temperature is observed at long times, while the potential energy demonstrates a weak increase. In this case, where component radii do not show any noticeable change at long times the abovementioned effect is also related to the temperature stimulated long-term preferential yield of Bi atoms. It is visually even more noticeable than in the Ni-Al cluster. Also, this effect is more pronounced in the Cu-Bi cluster at higher impact energies [34]. Obviously, it is additionally stimulated by the positive heat of mixing of the Cu and Bi components.

The characteristic time intervals of the processes of destruction of the Ni-Al regular atomic structure are about 1 - 4 ps at the impact energy of 300 eV for Ar₁₃ and Ar projectiles that is clearly seen in the examples of the evolution of the AEI parameter in Fig. 8 (a, c) and (b, d). These characteristic times indicate that at so high impact energy the violation of the metastability is initiated throughout the cluster but in the case of Ar₁₃ projectiles this process is more intense. Further active mutual approach, compression and mixing of the mono-component semi-clusters within 15–25 ps occur already in a disordered form. Subsequent relocations of atoms in the Ni-Al cluster are determined mainly by the properties of the components and the temperature. The temperatures in the cases of Ar₁₃and Ar projectiles, as can be seen in Fig. 2 (a, b), are critically different. As a result, the AEI patterns in the case of Ar₁₃ impacts are located higher. In addition, there is a monotonic weak decrease in the entire pattern of AEI for Al atoms with time in Fig. 8(b), that is associated with intense preferential sputtering, including the long-term thermal contribution after impacts of Ar₁₃ projectiles. At the same impact energy, the Cu-Bi cluster atomic system also very quickly, within a few picoseconds, loses the regular structure, especially if the projectile mostly hits and destroys the more tightly bound Cu semi-cluster first.

Boiling state after impact of a projectile in general can lead to the relative depletion of atoms of the preferentially sputtered cluster components, mainly in the near-surface regions. This applies more to the Ni-Al than to the Cu-Bi clusters, that is clearly seen in the spherical distributions of cluster atoms in [34,40]. This is also illustrated by the smaller Al and Ni component radii at 300 eV as compared to the cases of 200 and 100 eV (and even to the case of 50 eV for the Al component) after 25 ps in Fig. 4 (a, b) as well as some smaller Cu and Bi component radii at 300 eV as compared to the case of 200 eV after 150 and 50 ps, respectively in Fig. 5 (a, b) at Ar₁₃ impacts. Besides, the Al component radius is only insignificantly larger than the Ni component radius while the Bi component radius is noticeably larger than Cu one at 300 eV Ar₁₃ impacts. In these cases, the Ni and Cu-companion components in the Ni-Al and Cu-Bi clusters are in the melting state while at higher impact energies these components were also close to the boiling state [34,40].

The intercenter distances are very close to zero after 20-50 ps for Ni-Al and after 100 - 125 ps for Cu-Bi clusters (see Fig. 7 (a, c)) at 200 and 300 eV Ar₁₃impacts. It is obvious that the relatively noticeable non-unit ratio of the component radii and about zero values of the intercenter distance at the quasi-stable state indicate the trend to formation of the core-shell clusters, in particular from the Ni-Al and Cu-Bi Janus-like clusters. This is in good agreement with the general rules of formation of the core-shell cluster morphology in [9] and the example of the core-shell morphology in the initially Janus-like Cu-Ag cluster when it reaches the melt state upon gradual heating without taking into account evaporation [10]. There are obvious trends in the predominance of Al and Bi atoms in the outer regions, as well as Ni and Cu atoms in the inner regions of the corresponding clusters. Following the results of [40], the output of Al atoms to the Ni-Al cluster surface is masked by its intense preferential sputtering, while in the case of Bi component [34], masking is not effective enough due to a roughly four times lower sputtering yield at the 300 eV Ar₁₃ case. As result the surface of the Cu-Bi cluster at such impact conditions is obviously enriched with Bi atoms. In addition, the above differences in the characteristic relaxation times of intercenter distances for the Ni-Al and Cu-Bi clusters are associated with the dominant mechanisms for the transfer of component atoms in the volume and on the surface of the clusters, respectively, as well as with the different signs of the corresponding heats of mixing.

3.3.2 Melting/solid state of the clusters

Ni-Al. The temperature of the Ni-Al cluster exceeded the melting points of the Ni and Al cluster components in the initial Janus-like forms (see Table 1) even at the ultra-low impact energy of 25 eV for both Ar and Ar₁₃ projectiles due to the large negative heat of mixing (see Fig. 2 (a, b)). This practically predetermines the loss of regularity of the atomic system before the complete end of the active nonstationary stage of the evolution of cluster morphology. For Ar₁₃ projectiles at such a low energy, the temperature rises relatively slowly compared to the Ar ion impacts, and the stage of an active nonstationary process lasts more than 200 ps. At such bombarding conditions and a high negative heat of mixing, the role of the impact projectile is reduced practically to a spatially localized violation of the metastability of the Janus-like cluster and an initiation of the atomic relocation processes with destruction of the regular atomic structure. At 25 eV, Ar₁₃ projectiles due to small velocity very softly primary distort some surface range of the cluster’s atomic structure, and therefore the front of collective atomic displacements starts to develop and spread in the cluster from this impact area. The potential energy in Fig. 3 (a), radii of the components in Fig. 4 (a, b) and the intercenter distance in Fig. 7 (a) at 25 eV Ar₁₃ impacts demonstrate qualitatively similar character of the evolution.

Under such conditions the Ni-Al cluster tends to complete mixing of the components and the formation of their spatial core-shell distribution with the Ni-enriched core and Al-enriched shell. It well agrees with conditions of formation of the core-shell morphology [9] and confirms by the evolution of Janus-like Cu-Ag cluster during its heating and melting [10]. The process of cluster modification develops without loss of atoms for sputtering. This result qualitatively agrees with model results [54] where Ni atoms readily incorporate in the Al cluster. In our case the interval of 200 ps is clearly not enough for this. The patterns of the AEI parameter, which illustrate the structural evolution of the Ni and Al components of the Ni-Al cluster in the Ar₁₃ and Ar projectile cases at the impact energy of 25 eV in Fig. 9 (a, c) and (b, d), are similar in general that indicates the dominance of the component and geometrical properties in this process although the evolution in the case of Ar impacts looks some faster. In both cases the atomic structure order of the inner regions of mono-component parts of the Janus-like Ni-Al cluster is retained for 20–30 ps after which the catastrophic deformation of the semi-clusters and their mixing begins. In more detail, the AEI parameter of the Ni semi-cluster in the Janus-like cluster demonstrates the regularity of the atomic structure longer than that of Al one.

At higher energies of Ar₁₃ projectiles and in the cases of impacts by Ar projectiles regardless of the impact energy, the active nonstationary stage of the mass transfer processes has clear time limits of less than 60 ps since it begins almost at once in the entire body of the cluster. In all cases numerical values of AEI also show that, in an almost stationary state, Al atoms tend to be located preferentially in the outer regions of mixed clusters compared to Ni atoms. The intercenter distances clearly tend to zero in these cases (see Fig. 7 (a, b)) and the Al component radii are larger than the Ni ones (see Fig. 4). All these details demonstrate formation of the spatial core-shell atomic distributions with enrichment of the outer region of the cluster in Al atoms and the inner region in Ni atoms at different time intervals. This is also confirmed by the spherical atomic distributions of the mono-component atomic parts in the Ni-Al cluster after 100 and 500 ps of evolution in the cases of the Ar and Ar₁₃ projectiles with energy of 100 eV [40]. The sputtering yields of components can be practically neglected at impact energies below 200 eV and, accordingly, there is not any masking effect.

Cu-Bi. A critically different order is observed in the Cu-Bi cluster. In the case of the Ar₁₃ projectiles, the change in the impact energy, as can be seen from Fig. 2 (c), makes it possible, in principle, to choose the energy at which the melt state of only the Bi component or both components in the initial cluster forms is reached. In particular, in the conditional boundary case of the 100 eV Ar₁₃the temperature of the cluster reaches the melting point of the Cu component in 100 ps whereas the melting point of the Bi component was reached in about 10 ps. The evolutions of the intercenter distance (see Fig. 7 (c)), the component radii (see Fig. 5 (a, b)) and visual observations confirm formation of the core-shell Cu-Bi cluster with Bi-enriched outer region and some delay in the melting of the Cu-enriched core. Here and below, the coverage of the Cu core by Bi atoms agrees with the general view on the formation of the core-shell and similar distributions in two-component clusters in [9]. In this case, the Bi component relatively quickly loses the regularity of the atomic structure with simultaneous enveloping of the Cu semi-cluster, whereas the complete loss of the regular structure of the Cu component is not observed in many tests during the simulation. Some kind of shallow lateral interpenetrations of atoms of both components is possible. The small amount of introduced energy explains smoother evolution and no stationarity of temperature, potential energy, component radii and intercenter distance in the first 100 - 200 ps as compared to the cases of higher impact energies. A similar, in a certain sense, the case of the melt state of the Ag component and the crystalline state of the Cu component in a Janus-like Cu-Ag cluster with diffusion of Ag atoms predominantly over the surface of the Cu semi-cluster upon heating with forming of the quasi-Janus (or off-center core–shell) structures is described in [10].

The spherical atomic distributions of the mono-component parts in the Cu-Bi cluster after 100 and 500 ps of evolution upon bombardment with Ar₁₃ ions and the energy of 100 eV from the unpublished results of the previous work [34], based on the same MD model, are presented in Fig. 10 (a). The results clearly demonstrate dominant enrichments of the near-surface region with Bi atoms and the cluster core with Cu atoms after 500 ps. The corresponding trends in the redistribution of atoms in the cluster at an early stage are confirmed by the results for 100 ps, although the cluster morphology is far from the core-shell shape, as evidenced by the intercenter distance of about 8 Å in Fig. 7(c). After 100 ps, a significant eccentricity of the cluster morphology is observed. At this stage, the Cu semi-cluster is partially covered by a certain amount of more mobile Bi atoms.

At ultra-low impact energies of 25 and 50 eV of Ar₁₃ projectiles, according to the results of Figs. 2(c), 3(c), 5 (a, b), 7(c) the inter-component mixing is practically absent in the frameworks of applied MD model due to the positive heat of mixing. In more detail, under impact energy of 50 eV, the Cu mono-component part of the cluster retains the regular character of the atomic structures, while the Bi component part gradually envelopes the Cu part and loses the regularity of its atomic structure. In the time intervals of presented MD simulation this process looks like formation of the ball-and-cup spatial distributions of atoms [55]. In this case, the cluster’s atomic system is far from the stationary state.

For comparison, in the case of Ar impacts the temperature of the Cu-Bi cluster does not reach the melting point of the initial Cu Janus-like semi-cluster at any impact energies while the melting point of the Bi semi-cluster was reached at the impact energies of 100 eV or more (see Fig. 2 (d)). Sufficient decreasing of the intercenter distances in Fig. 7 (d), which, however, are still far from zero after 200 ps of the evolution, and some proximity to saturation of the Bi component radius in Fig. 5 (d) at 100 eV or more high energies, support impact energy condition of the melting of the Bi component. In general, the cluster atomic system is still far from a stationary state after 200 ps at 100 eV Ar impacts. In many impact tests only some fragment of the Bi semi-cluster can be in the disordered state for some initial time interval since the direction of the projectile impact on the Janus-like cluster strongly affects the initial stage of kinetics of the melting process of its mono-component parts. Under such conditions, the Cu and Bi components are mixed with predominant tendency of surface enveloping of the Cu-enriched core with a Bi-enriched shell. This has also been illustrated by unpublished earlier results for the impact energy of 100 eV with evolution times of 100 and 500 ps [34] in Fig. 10 (b). After the evolution of 100 ps, such a large eccentricity of the cluster morphology is observed. It is practically still a flattened along its axis Janus-like cluster with a much larger cross section of the inter-component contact. At this stage, the Cu semi-cluster is partially covered by a small number of Bi atoms. At the same time, both semi-clusters demonstrate the regularity of their atomic structures in the most impact tests, although the Bi component gradually loses it. At the impact energies of 25 and 50 eV the initial Cu semi-cluster retains the correct regularity of its structure to a greater extent than the Bi semi-cluster due to stronger interatomic bonds as for other impact cases (see cohesive energies of Cu and Bi bulk materials in Table 1). A large eccentricity presents and insignificant coverage of the Cu semi-cluster by Bi atoms is observed mainly near the contact of the components at such low impact energies.

Cu-Au. The Cu-Au Janus-like cluster is intermediate for the Ni-Al and Cu-Bi ones in respect of the heat of mixing which is slightly negative for the pair of Cu and Au components. Thus, the expected trends in the formation of the special non-uniform spatial distributions of components in the cluster will be relatively weak compared to the Ni-Al and Cu-Bi clusters. The cluster temperature exceeds the melting points of the components in the initial mono-component forms of the Cu-Au cluster at impact energies of 200 and 300 eV in the case of Ar₁₃ projectiles, as seen in Fig. 2 (e). Under such conditions, the atomic structure of the cluster loses its regularity in 1 - 4 ps. An active deformation of the semi-clusters and the mixing of the atoms of the components, which have already lost the order of their locations, continue for approximately 30–40 ps that are shown in Fig. 11 (a, b). In this case the Cu semi-cluster loses the regularity of its atomic structure faster than the Au one. Note, that the calculated cohesive energy of the pure bulk gold is larger than the bulk copper (see Table 1).

At Ar₁₃ impacts the regularity of the atomic structure of the cluster is observed at ultra-low energies of 25 and 50 eV, and to a much lesser extent at 100 eV, that correlates with the evolution of the intercenter distances for the long times in Fig. 7 (e). For comparison, at Ar impacts the Cu-Au Janus-like cluster does not reach the melting points of the cluster’s components at all simulated impact energies (see Fig. 2 (f)). Nevertheless, at energies above 100 eV, the loss of the initial regularity of the atomic structure becomes more evidently with increasing impact energy and in every test depends, to a large extent, on the impact direction and is associated with the generation of radiation damages. Temporal conservation of regular atomic structure of one mono-component part of the Janus-like cluster or some inner regions of mono-component parts is possible as can be seen in Fig. 11 (c, d), sometimes practically up to the end of the simulation time. At the 25 and 50 eV Ar projectile cases the atomic system of the Cu-Au Janus-like cluster as a whole retains its structure, similarly to the Ar₁₃ projectile impacts with the same energies, that also correlates with results in Fig. 7 (f). In these ultra-low energy cases, only insignificant distortions of the cluster atomic structure can occur in some near-surface local region.

The character of the changes of the intercenter distances in Fig. 7 (e, f) supports the conclusion that the total or partial destruction of the regular atomic structure of the Cu-Au cluster has been reached in some impact cases. Indeed, the cases of impacts by Ar₁₃ projectiles with energies of 200 and 300 eV demonstrate that the intercenter distances tend to zero. At all the impact energies of Ar projectiles the intercenter distances are on average far from zero to varying degrees, with significant no stationarity remaining after 200 ps of evolution, excluding impact energies of 25 and 50 eV. In all cases, the radius of the Cu component is smaller than the radius of the Au component, as can be seen in Fig. 6. Thus, the cases of 200 and 300 eV Ar₁₃ impacts demonstrate a clear tendency to form the core-shell spatial distributions of components with an outer region enriched with Au atoms and the core enriched with Cu atoms. Obviously, this is due to the large size of the Au atoms. Surface domination of Au atoms qualitatively agrees with the model results in [54], where the Cu atoms, deposited on the Au cluster, tend to penetrate into the cluster. It was also shown in [56], where in small Cu-Au clusters of 2–4 nm in size, the most stable configuration of atoms is observed when Au atoms segregate on the surface. In other simulated cases of Ar and Ar₁₃ impacts the structures with varying degrees of mutual convergence and significant eccentricity are forming.

Spherical atomic distributions of the mono-component parts of the Cu-Au cluster after 100 and 500 ps at 300 eV Ar and Ar₁₃ impacts are presented in [34]. Figure 12 shows the spherical distributions of Cu and Au atoms of the cluster components after 100 and 500 ps at the bombardment energy of 100 eV from partially unpublished results [34]. The radial profiles of the number of atoms in Fig. 12 for the cases of Ar and Ar₁₃ projectiles only differ a little from each other. In addition, the profiles of the number of Au atoms generally change very little over 500 ps that is quite understandable for the relatively high binding energy and mass of Au atoms. Against this background, Cu atoms look more mobile, although the changes in the radial profiles of the number of Cu atoms over 500 ps are not critical. At 100 eV, the Cu-Au cluster exhibits stability of the Janus-like morphology type, with some differences for the cases of Ar and Ar₁₃ projectiles. In particular, the cluster demonstrates some preservation of the regularity of atomic structures after Ar impacts due to relatively low efficiency of energy transfer between colliding Ar and Au atoms, while in the case of Ar₁₃ impacts the regularity of the structure of one or both components is lost with simultaneous significant overlap of the components. Obviously, the bombardment energy of Ar₁₃ impacts can be chosen such that only the Cu component is in the disordered state during the simulation.

Molecular dynamics simulation of the evolution of the free Ni-Al, Cu-Bi and Cu-Au Janus-like clusters during 200 ps after impacts of Ar and Ar₁₃ projectiles with initial energies no more than 300 eV was performed. The formation of the technologically demanded core-shell and ball-and-cup spatial distributions of atoms of cluster components, as well as the conditions for reaching the boiling and melting states or maintaining the cluster components in the solid state were studied. Of all the variety of simulated combinations and states, the most promising for the formation of relevant spatial distributions of atoms during a few hundred picoseconds are the cases of a melting of two or one of the components of Janus-like clusters without numerous losses of atoms. In this regard, the Ni-Al cluster shows the greatest tendency to the melt state. Other clusters, under certain conditions, can show the predominant melting of the "shell" (Bi, Cu-Bi) or "core" (Cu, Cu-Au) components as well as both components too. The two last cases at some specific impact conditions demonstrate manifestation of different mass transfer mechanisms with predominantly surface and bulk relocations of atoms of a more mobile and disordered to varying degrees components for the formation of relevant spatial distributions with their typical characteristic times and geometric parameters. In the latter case, the tendency of Au atoms to cover the Cu semi-cluster over its surface is also observed, that, however, is a manifestation of the same mechanism. As a result, such features provide additional options for controlling actual elementary mass transfer processes.

Wherein the use of low and ultra-low bombardment energies is not a universal control means of minimizing ion-induced changes in two-component clusters and their reforming without considerable yield of atoms, since mass transfer and lattice destruction processes in clusters are also determined by the properties of the cluster components. But in any case, the use of multi-atomic projectiles with a variable initial energy up to two hundred electron-volts provides more opportunities than single-atom ones for obtaining clusters in the states with predictable spatial distributions of components due to the greater efficiency of impact energy transfer to target atoms and more “easy” collisional interactions with them.

ACKNOWLEDGEMENTS

The work was supported by the Ministry of Education and Science of Ukraine within the framework of the project No. 0122U000776. O.A.G. acknowledges support from Scholarships (2P05, 2023-2026) for Excellent Researchers Threatened by the Military Conflict in Ukraine (Slovakia).

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Competing interests

The authors declare that they have no conflict of interest.

Authors' contributions

G.V.K. and D.V.S. wrote the main manuscript text.

G.V.K. and D.V.S. made computer simulations, data analysis, plots' preparation.

O.A.G and I.S.K made comments on the first and further draft.

O.A.G and I.S.K. did a literature search.

O.A.G and I.S.K. provided ideas for practical applications.

All authors read and approved the final manuscript.

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Fusion Features of Monocomponent Parts in Janus-Like Nanoscale Clusters Under Impacts of Low− and Ultra−Low−Energy Ar13 and Ar Projectiles

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